1
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Nagy PR. State-of-the-art local correlation methods enable affordable gold standard quantum chemistry for up to hundreds of atoms. Chem Sci 2024:d4sc04755a. [PMID: 39246365 PMCID: PMC11376132 DOI: 10.1039/d4sc04755a] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2024] [Accepted: 07/30/2024] [Indexed: 09/10/2024] Open
Abstract
In this feature, we review the current capabilities of local electron correlation methods up to the coupled cluster model with single, double, and perturbative triple excitations [CCSD(T)], which is a gold standard in quantum chemistry. The main computational aspects of the local method types are assessed from the perspective of applications, but the focus is kept on how to achieve chemical accuracy (i.e., <1 kcal mol-1 uncertainty), as well as on the broad scope of chemical problems made accessible. The performance of state-of-the-art methods is also compared, including the most employed DLPNO and, in particular, our local natural orbital (LNO) CCSD(T) approach. The high accuracy and efficiency of the LNO method makes chemically accurate CCSD(T) computations accessible for molecules of hundreds of atoms with resources affordable to a broad computational community (days on a single CPU and 10-100 GB of memory). Recent developments in LNO-CCSD(T) enable systematic convergence and robust error estimates even for systems of complicated electronic structure or larger size (up to 1000 atoms). The predictive power of current local CCSD(T) methods, usually at about 1-2 order of magnitude higher cost than hybrid density functional theory (DFT), has become outstanding on the palette of computational chemistry applicable for molecules of practical interest. We also review more than 50 LNO-based and other advanced local-CCSD(T) applications for realistic, large systems across molecular interactions as well as main group, transition metal, bio-, and surface chemistry. The examples show that properly executed local-CCSD(T) can contribute to binding, reaction equilibrium, rate constants, etc. which are able to match measurements within the error estimates. These applications demonstrate that modern, open-access, and broadly affordable local methods, such as LNO-CCSD(T), already enable predictive computations and atomistic insight for complicated, real-life molecular processes in realistic environments.
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Affiliation(s)
- Péter R Nagy
- Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics Műegyetem rkp. 3. H-1111 Budapest Hungary
- HUN-REN-BME Quantum Chemistry Research Group Műegyetem rkp. 3. H-1111 Budapest Hungary
- MTA-BME Lendület Quantum Chemistry Research Group Műegyetem rkp. 3. H-1111 Budapest Hungary
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2
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Evangelista FA, Li C, Verma P, Hannon KP, Schriber JB, Zhang T, Cai C, Wang S, He N, Stair NH, Huang M, Huang R, Misiewicz JP, Li S, Marin K, Zhao Z, Burns LA. Forte: A suite of advanced multireference quantum chemistry methods. J Chem Phys 2024; 161:062502. [PMID: 39132791 DOI: 10.1063/5.0216512] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2024] [Accepted: 06/24/2024] [Indexed: 08/13/2024] Open
Abstract
Forte is an open-source library specialized in multireference electronic structure theories for molecular systems and the rapid prototyping of new methods. This paper gives an overview of the capabilities of Forte, its software architecture, and examples of applications enabled by the methods it implements.
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Affiliation(s)
- Francesco A Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Chenyang Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Prakash Verma
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Kevin P Hannon
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Jeffrey B Schriber
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
- Department of Chemistry and Biochemistry, Iona University, New Rochelle, New York 10801, USA
| | - Tianyuan Zhang
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Chenxi Cai
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Shuhe Wang
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Nan He
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Nicholas H Stair
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Meng Huang
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Renke Huang
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Jonathon P Misiewicz
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Shuhang Li
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Kevin Marin
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Zijun Zhao
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Lori A Burns
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA
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3
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Hu G, Liu P, Jensen L. Calculating Molecular Polarizabilities Using Exact Frozen Density Embedding with External Orthogonality. J Chem Theory Comput 2024. [PMID: 39105755 DOI: 10.1021/acs.jctc.4c00692] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/07/2024]
Abstract
Frozen density embedding (FDE) with freeze-thaw cycles is a formally exact embedding scheme. In practice, this method is limited to systems with small density overlaps when approximate nonadditive kinetic energy functionals are used. It has been shown that the use of approximate nonadditive kinetic energy functionals can be avoided when external orthogonality (EO) is enforced, and FDE can then generate exact results even for strongly overlapping subsystems. In this work, we present an implementation of exact FDEc-EO (coupled FDE TDDFT with EO) for the calculation of polarizabilities in the Amsterdam density functional program package. EO is enforced using the level-shift projection operator method, which ensures that orbitals between fragments are orthogonal. For pure functionals, we show that only the symmetric EO contributions to the induced density matrix are needed. This leads to a simplified implementation for the calculation of polarizability that can exactly reproduce the supermolecular TDDFT results. We further discuss the limitation of exact FDEc-EO in interpreting subsystem polarizabilities due to the nonunique partitioning of the total density. We show that this limitation is due to the fact that subsystem polarizability partitioning is dependent on how the subsystems are initially polarized. As supermolecular virtual orbitals are exactly reproduced, this dependence is attributed to the description of the occupied orbitals. In contrast, for excitations of subsystems that are localized within one subsystem, we show that the excitation energies are stable with respect to the order of polarization. This observation shows that impacts from the nonunique nature of exact FDE on subsystem properties can be minimized by better fragmentation of the supermolecular systems if the property is localized. For global properties like polarizability, this is not the case, and nonuniqueness remains independent of the fragmentation used.
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Affiliation(s)
- Gaohe Hu
- Department of Chemistry, The Pennsylvania State University, 104 Benkovic Building, University Park, Pennsylvania 16802, United States
| | - Pengchong Liu
- Department of Chemistry, The Pennsylvania State University, 104 Benkovic Building, University Park, Pennsylvania 16802, United States
| | - Lasse Jensen
- Department of Chemistry, The Pennsylvania State University, 104 Benkovic Building, University Park, Pennsylvania 16802, United States
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4
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Manna A, Jangid B, Pant R, Dutta AK. Efficient State-Specific Natural Orbital Based Equation of Motion Coupled Cluster Method for Core-Ionization Energies: Theory, Implementation, and Benchmark. J Chem Theory Comput 2024. [PMID: 39073757 DOI: 10.1021/acs.jctc.4c00546] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/30/2024]
Abstract
We have implemented a reduced-cost partial triples correction scheme to the equation of motion coupled cluster method for core-ionization energy based on state-specific natural orbitals. The second-order Algebraic Diagrammatic Construction (ADC) method is used to generate the state-specific natural orbital, which provides quicker convergence of the core-IP value with respect to the size of the virtual space than that observed in standard MP2-based natural orbitals. The error due to truncation of the virtual orbital can be reduced by using a perturbative correction. The accuracy of the method can be controlled by a single threshold, and there is a black box to use. The inclusion of the partial triples correction in the natural orbital based EOM-CCSD method greatly improves the agreement of the results with the experiment. The efficiency of the present implementation is demonstrated by calculating the core-ionization energy of a molecule containing 60 atoms and more than 2000 basis functions.
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Affiliation(s)
- Amrita Manna
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Bhavnesh Jangid
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Rakesh Pant
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Achintya Kumar Dutta
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
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5
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Sun Y. Accelerating Density Matrix Embedding with Stochastic Density Fitting Theory: An Application to Hydrogen Bonded Clusters. J Chem Theory Comput 2024. [PMID: 39029091 DOI: 10.1021/acs.jctc.4c00489] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/21/2024]
Abstract
In this work, we demonstrate how using semistochastic density fitting (ss-DF) can accelerate self-consistent density matrix embedding theory (DMET) calculations by reducing the number of auxiliary orbitals in the three-indexed DF integrals. This reduction results in significant time savings when building the Hartree-Fock (HF) Coulomb and Exchange Matrices and in transforming integrals from the atomic orbital (AO) basis to the embedding orbital (EO) basis. We apply ss-DF to a range of hydrogen-bonded clusters to showcase its effectiveness. First, we examine how the amount of deterministic space impacts the quality of the calculation in a (H2O)10 cluster. Next, we test the computational efficiency of ss-DF compared to deterministic DF (d-DF) in water clusters containing 6-30 water molecules using a triple-ζ basis set. Finally, we perform numerical structural optimizations on water and hydrogen fluoride clusters, revealing that DMET can recover weak interactions using a back-transformed energy formula. This work demonstrates the potential of using stochastic resolution of identity in quantum embedding theories and highlights its capability to recover weak interactions effectively.
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Affiliation(s)
- Yi Sun
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, United States
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6
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Sundaram V, Baumeier B. Quantum-Quantum and Quantum-Quantum-Classical Schemes for Near-Gap Excitations with Projection-Based-Embedded GW-Bethe-Salpeter Equation. J Chem Theory Comput 2024; 20:5451-5465. [PMID: 38916411 PMCID: PMC11238541 DOI: 10.1021/acs.jctc.4c00163] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/26/2024]
Abstract
We present quantum-quantum and quantum-quantum-classical schemes based on many-body Green's functions theory in the GW approximation with the Bethe-Salpeter equation (GW-BSE) employing projection-based-embedding (PbE). Such approaches allow defining active and inactive subsystems of larger, complex molecular systems, with only the smaller active subsystem being explicitly treated by GW-BSE offering significant computational advantages. However, as PbE can modify the single-particle states in the Kohn-Sham (KS) ground state calculation and screening effects from the inactive region are not automatically included in GW-BSE, results from such PbE-GW-BSE calculations can deviate from a full-system reference. Here, we scrutinize in detail, e.g., the individual and combined effects of different choices of active regions, the influence of omitting the screening from the inactive region, and strategies for basis set truncation on frontier orbital and near-gap electron-hole excitation energies. As prototypical systems, we consider a diketopyrrolopyrrole bicyclic ring including side-chains, a polarity-sensitive dye (prodan) in aqueous environment, and a π-stacked dimer of benzene and tetracyanoethylene in water, respectively, covering a variety of excitation characters in molecular systems with complex chemical environments and photoinduced processes. Our results suggest that to obtain agreement of approximately 0.1 eV between near-gap excitation energies from embedded and full calculations, the active region should be chosen based on the Mulliken population of the full highest-occupied molecular orbital and that careful benchmarking should be done on the KS level before the actual GW-BSE steps when basis set truncation is used. We find that PbE-GW-BSE offers significant reductions in computation times and, more importantly, memory requirements, making calculations for considerably larger systems tractable.
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Affiliation(s)
- Vivek Sundaram
- Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
- Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
- Department of Applied Physics and Science Education, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
| | - Björn Baumeier
- Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
- Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
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7
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Choudhury A, Santra S, Ghosh D. Understanding the Photoprocesses in Biological Systems: Need for Accurate Multireference Treatment. J Chem Theory Comput 2024; 20:4951-4964. [PMID: 38864715 DOI: 10.1021/acs.jctc.4c00027] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2024]
Abstract
Light-matter interaction is crucial to life itself and revolves around many of the central processes in biology. The need for understanding these photochemical and photophysical processes cannot be overemphasized. Interaction of light with biological systems starts with the absorption of light and subsequent phenomena that occur in the excited states of the system. However, excited states are typically difficult to understand within the mean field approximation of quantum chemical methods. Therefore, suitable multireference methods and methodologies have been developed to understand these phenomena. In this Perspective, we will describe a few methods and methodologies suitable for these descriptions and discuss some persisting difficulties.
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Affiliation(s)
- Arpan Choudhury
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Supriyo Santra
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Debashree Ghosh
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
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8
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Alessio M, Paran GP, Utku C, Grüneis A, Jagau TC. Coupled-cluster treatment of complex open-shell systems: the case of single-molecule magnets. Phys Chem Chem Phys 2024; 26:17028-17041. [PMID: 38836327 PMCID: PMC11186456 DOI: 10.1039/d4cp01129e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2024] [Accepted: 05/22/2024] [Indexed: 06/06/2024]
Abstract
We investigate the reliability of two cost-effective coupled-cluster methods for computing spin-state energetics and spin-related properties of a set of open-shell transition-metal complexes. Specifically, we employ the second-order approximate coupled-cluster singles and doubles (CC2) method and projection-based embedding that combines equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) with density functional theory (DFT). The performance of CC2 and EOM-CCSD-in-DFT is assessed against EOM-CCSD. The chosen test set includes two hexaaqua transition-metal complexes containing Fe(II) and Fe(III), and a large Co(II)-based single-molecule magnet with a non-aufbau ground state. We find that CC2 describes the excited states more accurately, reproducing EOM-CCSD excitation energies within 0.05 eV. However, EOM-CCSD-in-DFT excels in describing transition orbital angular momenta and spin-orbit couplings. Moreover, for the Co(II) molecular magnet, using EOM-CCSD-in-DFT eigenstates and spin-orbit couplings, we compute spin-reversal energy barriers, as well as temperature-dependent and field-dependent magnetizations and magnetic susceptibilities that closely match experimental values within spectroscopic accuracy. These results underscore the efficiency of CC2 in computing state energies of multi-configurational, open-shell systems and highlight the utility of the more cost-efficient EOM-CCSD-in-DFT for computing spin-orbit couplings and magnetic properties of complex and large molecular magnets.
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Affiliation(s)
- Maristella Alessio
- Department of Chemistry, KU Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium.
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria
| | | | - Cansu Utku
- Department of Chemistry, KU Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium.
| | - Andreas Grüneis
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria
| | - Thomas-C Jagau
- Department of Chemistry, KU Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium.
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9
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Capone M, Romanelli M, Castaldo D, Parolin G, Bello A, Gil G, Vanzan M. A Vision for the Future of Multiscale Modeling. ACS PHYSICAL CHEMISTRY AU 2024; 4:202-225. [PMID: 38800726 PMCID: PMC11117712 DOI: 10.1021/acsphyschemau.3c00080] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/30/2023] [Revised: 01/31/2024] [Accepted: 02/01/2024] [Indexed: 05/29/2024]
Abstract
The rise of modern computer science enabled physical chemistry to make enormous progresses in understanding and harnessing natural and artificial phenomena. Nevertheless, despite the advances achieved over past decades, computational resources are still insufficient to thoroughly simulate extended systems from first principles. Indeed, countless biological, catalytic and photophysical processes require ab initio treatments to be properly described, but the breadth of length and time scales involved makes it practically unfeasible. A way to address these issues is to couple theories and algorithms working at different scales by dividing the system into domains treated at different levels of approximation, ranging from quantum mechanics to classical molecular dynamics, even including continuum electrodynamics. This approach is known as multiscale modeling and its use over the past 60 years has led to remarkable results. Considering the rapid advances in theory, algorithm design, and computing power, we believe multiscale modeling will massively grow into a dominant research methodology in the forthcoming years. Hereby we describe the main approaches developed within its realm, highlighting their achievements and current drawbacks, eventually proposing a plausible direction for future developments considering also the emergence of new computational techniques such as machine learning and quantum computing. We then discuss how advanced multiscale modeling methods could be exploited to address critical scientific challenges, focusing on the simulation of complex light-harvesting processes, such as natural photosynthesis. While doing so, we suggest a cutting-edge computational paradigm consisting in performing simultaneous multiscale calculations on a system allowing the various domains, treated with appropriate accuracy, to move and extend while they properly interact with each other. Although this vision is very ambitious, we believe the quick development of computer science will lead to both massive improvements and widespread use of these techniques, resulting in enormous progresses in physical chemistry and, eventually, in our society.
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Affiliation(s)
- Matteo Capone
- Department
of Physical and Chemical Sciences, University
of L’Aquila, L’Aquila 67010, Italy
| | - Marco Romanelli
- Department
of Chemical Sciences, University of Padova, Padova 35131, Italy
| | - Davide Castaldo
- Department
of Chemical Sciences, University of Padova, Padova 35131, Italy
| | - Giovanni Parolin
- Department
of Chemical Sciences, University of Padova, Padova 35131, Italy
| | - Alessandro Bello
- Department
of Chemical Sciences, University of Padova, Padova 35131, Italy
- Department
of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, Modena 41125, Italy
| | - Gabriel Gil
- Department
of Chemical Sciences, University of Padova, Padova 35131, Italy
- Instituto
de Cibernética, Matemática y Física (ICIMAF), La Habana 10400, Cuba
| | - Mirko Vanzan
- Department
of Chemical Sciences, University of Padova, Padova 35131, Italy
- Department
of Physics, University of Milano, Milano 20133, Italy
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10
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Giovannini T, Scavino M, Koch H. Time-Dependent Multilevel Density Functional Theory. J Chem Theory Comput 2024; 20:3601-3612. [PMID: 38648031 DOI: 10.1021/acs.jctc.4c00041] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
We present a novel three-layer approach based on multilevel density functional theory (MLDFT) and polarizable molecular mechanics to simulate the electronic excitations of chemical systems embedded in an external environment within the time-dependent DFT formalism. In our method, the electronic structure of a target system, the chromophore, is determined in the field of an embedded inactive layer, which is treated as frozen. Long-range interactions are described by employing the polarizable fluctuating charge (FQ) force field. The resulting MLDFT/FQ thus accurately describes both electrostatics (and polarization) and non-electrostatic target-environment interactions. The robustness and reliability of the approach are demonstrated by comparing our results with experimental data reported for various organic molecules in solution.
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Affiliation(s)
| | - Marco Scavino
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Henrik Koch
- Department of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway
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11
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Szirmai ÁB, Hégely B, Tajti A, Kállay M, Szalay PG. Projected Atomic Orbitals As Optimal Virtual Space for Excited State Projection-Based Embedding Calculations. J Chem Theory Comput 2024; 20:3420-3425. [PMID: 38626416 DOI: 10.1021/acs.jctc.4c00104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/18/2024]
Abstract
The projected atomic orbital (PAO) technique is presented for the construction of virtual orbital spaces in projection-based embedding (PbE) applications. The proposed straightforward procedure produces a set of virtual orbitals that are used in the final, high-level calculation of the embedded active subsystem. The PAO scheme is demonstrated on intermolecular potentials of bimolecular complexes in ground and excited states, including Rydberg excitations. The results show the outstanding performance of the PbE method when used with PAO virtual orbitals compared with those produced using common orbital localization techniques. The good agreement of the resulting PbE potential curves with those from high-level ab initio dimer calculations, also in diffuse basis sets, confirms that the PAO technique can be suggested for future applications using top-down embedding methods.
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Affiliation(s)
- Ádám B Szirmai
- Laboratory of Theoretical Chemistry, Institute of Chemistry, ELTE Eötvös Loránd University, P.O. Box 32, H-1518 Budapest, Hungary
- György Hevesy Doctoral School, ELTE Eötvös Loŕnd University, Institute of Chemistry, H-1117 Budapest, Hungary
| | - Bence Hégely
- Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- HUN-REN-BME Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- MTA-BME Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
| | - Attila Tajti
- Laboratory of Theoretical Chemistry, Institute of Chemistry, ELTE Eötvös Loránd University, P.O. Box 32, H-1518 Budapest, Hungary
| | - Mihály Kállay
- Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- HUN-REN-BME Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- MTA-BME Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
| | - Péter G Szalay
- Laboratory of Theoretical Chemistry, Institute of Chemistry, ELTE Eötvös Loránd University, P.O. Box 32, H-1518 Budapest, Hungary
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12
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Türkmen I, Dolg M. Linear Scaling Incremental Scheme for Correlation Energies with Embedding Generated Virtuals. J Chem Theory Comput 2024; 20:3154-3168. [PMID: 38588492 DOI: 10.1021/acs.jctc.3c01377] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/10/2024]
Abstract
A novel incremental scheme is presented including an incremental expansion of the virtual space for the calculation of electron correlation energies, which is compatible with any size-extensive correlation method and scales asymptotically linear for large molecules. The performance is studied for organic molecules, water clusters, and a La(III)-water complex, where the compatibility with pseudopotentials is also examined. The computational requirements are already reduced tremendously for medium-sized water clusters and hydrocarbons with respect to the canonical CCSD as well as the ordinary incremental scheme references. Correlation energies within chemical accuracy have been observed for all studied systems. The novelty of the method is that relatively small virtual spaces are used in combination with tuples of localized occupied spaces. The corresponding orthonormal occupied and virtual orbitals are obtained from QM/QM embedding calculations and can thus be used with standard quantum chemistry codes for correlation calculations. It is presented how relevant virtual spaces are selected and the correlation energies are linked in the new virtual space expansion.
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Affiliation(s)
- Ilyas Türkmen
- Institute for Theoretical Chemistry, University of Cologne, Greinstr. 4, D-50939 Cologne, Germany
| | - Michael Dolg
- Institute for Theoretical Chemistry, University of Cologne, Greinstr. 4, D-50939 Cologne, Germany
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13
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Csóka J, Hégely B, Nagy PR, Kállay M. Development of analytic gradients for the Huzinaga quantum embedding method and its applications to large-scale hybrid and double hybrid DFT forces. J Chem Phys 2024; 160:124113. [PMID: 38530010 DOI: 10.1063/5.0194463] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2023] [Accepted: 03/06/2024] [Indexed: 03/27/2024] Open
Abstract
The theory of analytic gradients is presented for the projector-based density functional theory (DFT) embedding approach utilizing the Huzinaga-equation. The advantages of the Huzinaga-equation-based formulation are demonstrated. In particular, it is shown that the projector employed does not appear in the Lagrangian, and the potential risk of numerical problems is avoided at the evaluation of the gradients. The efficient implementation of the analytic gradient theory is presented for approaches where hybrid DFT, second-order Møller-Plesset perturbation theory, or double hybrid DFT are embedded in lower-level DFT environments. To demonstrate the applicability of the method and to gain insight into its accuracy, it is applied to equilibrium geometry optimizations, transition state searches, and potential energy surface scans. Our results show that bond lengths and angles converge rapidly with the size of the embedded system. While providing structural parameters close to high-level quality for the embedded atoms, the embedding approach has the potential to relax the coordinates of the environment as well. Our demonstrations on a 171-atom zeolite and a 570-atom protein system show that the Huzinaga-equation-based embedding can accelerate (double) hybrid gradient computations by an order of magnitude with sufficient active regions and enables affordable force evaluations or geometry optimizations for molecules of hundreds of atoms.
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Affiliation(s)
- József Csóka
- Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- HUN-REN-BME Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- MTA-BME Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
| | - Bence Hégely
- Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- HUN-REN-BME Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- MTA-BME Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
| | - Péter R Nagy
- Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- HUN-REN-BME Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- MTA-BME Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
| | - Mihály Kállay
- Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- HUN-REN-BME Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- MTA-BME Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
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14
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Käfer S, Niemeyer N, Tölle J, Neugebauer J. Triplet Excitation-Energy Transfer Couplings from Subsystem Time-Dependent Density-Functional Theory. J Chem Theory Comput 2024; 20:2475-2490. [PMID: 38450637 DOI: 10.1021/acs.jctc.3c01365] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/08/2024]
Abstract
We present an implementation of triplet excitation-energy transfer (TEET) couplings based on subsystem-based time-dependent density-functional theory (sTDDFT). TEET couplings are systematically investigated by comparing "exact" and approximate variants of sTDDFT. We demonstrate that, while sTDDFT utilizing explicit approximate non-additive kinetic energy (NAKE) density functionals is well-suited for describing singlet EET processes, it is inadequate for characterizing TEET. However, we show that projection-based embedding (PbE)-based sTDDFT addresses the challenges faced by NAKE-sTDDFT and emerges as a promising method for accurately describing electronic couplings in TEET processes. We also introduce the mixed PbE-/NAKE-embedding procedure to investigate the TEET effects in solvated pairs of chromophores. This approach offers a good balance between accuracy and efficiency, enabling comprehensive studies of TEET processes in complex environments.
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Affiliation(s)
- Sabine Käfer
- Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, University of Münster, Corrensstraße 36, Münster 48149, Germany
| | - Niklas Niemeyer
- Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, University of Münster, Corrensstraße 36, Münster 48149, Germany
| | - Johannes Tölle
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Johannes Neugebauer
- Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, University of Münster, Corrensstraße 36, Münster 48149, Germany
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15
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Gimbal-Zofka Y, González-Espinoza CE, Rumble CA, Wesolowski TA. Assessment of Approximations to the Embedding Potential in Frozen-Density Embedding Theory for the Calculation of Electric Field Gradients. J Chem Theory Comput 2024; 20:348-356. [PMID: 38116618 DOI: 10.1021/acs.jctc.3c00773] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2023]
Abstract
The approximations to the embedding potential in frozen-density embedding theory (FDET) have been assessed for the first time for the calculation of the electric field gradient (EFG) at a nucleus. FDET-based methods using a hierarchy of approximations are applied to evaluate the EFG at the nuclei of an HCl molecule in several noncovalently bound clusters chosen to represent potential liquid or molecular crystal systems. A detailed assessment of such approximations is made for the Hartree-Fock treatment of electron-electron correlation (both in FDET and in the reference calculations for the whole cluster). The emerging choice of the optimal set of approximations is reconfirmed in calculations in which electron-electron calculations are treated at the MP2 level. Our optimized protocol produces average errors in the complexation-induced EFG shift on the order of 25% relative to conventional quantum mechanical calculations for the whole cluster. This protocol is shown to be numerically robust and leads to enormous computational savings compared to a complete quantum mechanical treatment of the embedded species and its environment. For a cluster comprising a Na+ cation and up to 24 water molecules, the computation time is reduced by a factor of 30,000 at the expense of introducing an error in the environment-induced EFG shift of 22%.
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Affiliation(s)
- Yann Gimbal-Zofka
- Départment de Chimie Physique, Université de Genève, 30, quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
| | | | - Christopher A Rumble
- Department of Chemistry, Altoona College, The Pennsylvania State University, 3000 Ivyside Park, Altoona, 16601 Pennsylvania, United States
| | - Tomasz A Wesolowski
- Départment de Chimie Physique, Université de Genève, 30, quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
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16
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Lafiosca P, Rossi F, Egidi F, Giovannini T, Cappelli C. Multiscale Frozen Density Embedding/Molecular Mechanics Approach for Simulating Magnetic Response Properties of Solvated Systems. J Chem Theory Comput 2024; 20:266-279. [PMID: 38109486 PMCID: PMC10782454 DOI: 10.1021/acs.jctc.3c00850] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Revised: 11/06/2023] [Accepted: 11/10/2023] [Indexed: 12/20/2023]
Abstract
We present a three-layer hybrid quantum mechanical/quantum embedding/molecular mechanics approach for calculating nuclear magnetic resonance (NMR) shieldings and J-couplings of molecular systems in solution. The model is based on the frozen density embedding (FDE) and polarizable fluctuating charges (FQ) and fluctuating dipoles (FQFμ) force fields and permits the accurate ab initio description of short-range nonelectrostatic interactions by means of the FDE shell and cost-effective treatment of long-range electrostatic interactions through the polarizable force field FQ(Fμ). Our approach's accuracy and potential are demonstrated by studying NMR spectra of Brooker's merocyanine in aqueous and nonaqueous solutions.
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Affiliation(s)
- Piero Lafiosca
- Scuola
Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Federico Rossi
- Scuola
Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Franco Egidi
- Software
for Chemistry and Materials BV, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | | | - Chiara Cappelli
- Scuola
Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
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17
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Ditte M, Barborini M, Medrano Sandonas L, Tkatchenko A. Molecules in Environments: Toward Systematic Quantum Embedding of Electrons and Drude Oscillators. PHYSICAL REVIEW LETTERS 2023; 131:228001. [PMID: 38101380 DOI: 10.1103/physrevlett.131.228001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2023] [Revised: 07/26/2023] [Accepted: 10/20/2023] [Indexed: 12/17/2023]
Abstract
We develop a quantum embedding method that enables accurate and efficient treatment of interactions between molecules and an environment, while explicitly including many-body correlations. The molecule is composed of classical nuclei and quantum electrons, whereas the environment is modeled via charged quantum harmonic oscillators. We construct a general Hamiltonian and introduce a variational Ansatz for the correlated ground state of the fully interacting molecule-environment system. This wave function is optimized via the variational Monte Carlo method and the ground state energy is subsequently estimated through the diffusion Monte Carlo method. The proposed scheme allows an explicit many-body treatment of electrostatic, polarization, and dispersion interactions between the molecule and the environment. We study solvation energies and excitation energies of benzene derivatives, obtaining excellent agreement with explicit ab initio calculations and experiments.
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Affiliation(s)
- Matej Ditte
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Matteo Barborini
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Leonardo Medrano Sandonas
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Alexandre Tkatchenko
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
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18
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Shi B, Zen A, Kapil V, Nagy PR, Grüneis A, Michaelides A. Many-Body Methods for Surface Chemistry Come of Age: Achieving Consensus with Experiments. J Am Chem Soc 2023; 145:25372-25381. [PMID: 37948071 PMCID: PMC10683001 DOI: 10.1021/jacs.3c09616] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2023] [Revised: 10/15/2023] [Accepted: 10/17/2023] [Indexed: 11/12/2023]
Abstract
The adsorption energy of a molecule onto the surface of a material underpins a wide array of applications, spanning heterogeneous catalysis, gas storage, and many more. It is the key quantity where experimental measurements and theoretical calculations meet, with agreement being necessary for reliable predictions of chemical reaction rates and mechanisms. The prototypical molecule-surface system is CO adsorbed on MgO, but despite intense scrutiny from theory and experiment, there is still no consensus on its adsorption energy. In particular, the large cost of accurate many-body methods makes reaching converged theoretical estimates difficult, generating a wide range of values. In this work, we address this challenge, leveraging the latest advances in diffusion Monte Carlo (DMC) and coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] to obtain accurate predictions for CO on MgO. These reliable theoretical estimates allow us to evaluate the inconsistencies in published temperature-programed desorption experiments, revealing that they arise from variations in employed pre-exponential factors. Utilizing this insight, we derive new experimental estimates of the (electronic) adsorption energy with a (more) precise pre-exponential factor. As a culmination of all of this effort, we are able to reach a consensus between multiple theoretical calculations and multiple experiments for the first time. In addition, we show that our recently developed cluster-based CCSD(T) approach provides a low-cost route toward achieving accurate adsorption energies. This sets the stage for affordable and reliable theoretical predictions of chemical reactions on surfaces to guide the realization of new catalysts and gas storage materials.
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Affiliation(s)
- Benjamin
X. Shi
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield Road, CB2 1EW Cambridge, U.K.
| | - Andrea Zen
- Dipartimento
di Fisica Ettore Pancini, Università
di Napoli Federico II, Monte S. Angelo, I-80126 Napoli, Italy
- Department
of Earth Sciences, University College London, Gower Street, WC1E 6BT London, U.K.
| | - Venkat Kapil
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield Road, CB2 1EW Cambridge, U.K.
| | - Péter R. Nagy
- Department
of Physical Chemistry and Materials Science, Faculty of Chemical Technology
and Biotechnology, Budapest University of
Technology and Economics, Müegyetem rkp. 3, H-1111 Budapest, Hungary
- HUN-REN-BME
Quantum Chemistry Research Group, Müegyetem rkp. 3, H-1111 Budapest, Hungary
- MTA-BME
Lendület Quantum Chemistry Research Group, Müegyetem rkp. 3, H-1111 Budapest, Hungary
| | - Andreas Grüneis
- Institute
for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria
| | - Angelos Michaelides
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield Road, CB2 1EW Cambridge, U.K.
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19
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Mysovsky AS, Bogdanov AI. Seamless Multilayer─A Novel Total Energy Partition Scheme for Embedded and Hybrid Calculations. J Chem Theory Comput 2023. [PMID: 37973151 DOI: 10.1021/acs.jctc.3c00666] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2023]
Abstract
In this paper, we provide general formulation of a multilayer approach, covering both additive and subtractive quantum mechanics/molecular mechanics (QM/MM) as special cases. After that, we suggest a novel definition of QM/MM total energy based on the consideration of a system divided into three layers. In a simplified form, it is E = E Q M ( 1 + 2 ) - E Q M ( 2 ) + E M M ( 2 + 3 ) , where layers 1, 2, and 3 represent inner QM, outer QM, and classical MM regions, respectively. The novel formulation is also not limited by only QM/MM combination of methods─in fact, any computational methods can be combined in a hybrid calculation. In this paper, we call the new approach seamless multilayer. Test calculations performed for silica and boric oxide show that the new approach requires no QM/MM interface parameterization as well as no or very simple correction terms for boundary atoms. This can greatly facilitate QM/MM studies of covalent inorganic solids. However, test calculations of α-Al2O3 show that for ionic compounds, the new method requires some additional development.
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Affiliation(s)
- Andrey S Mysovsky
- A.P. Vinogradov Institute of Geochemistry SB RAS, 1a Favorsky Street, 664033 Irkutsk, Russia
- Institute of Quantum Physics, Irkutsk National Research Technical University, 83 Lermontov Street, 664074 Irkutsk, Russia
| | - Alexander I Bogdanov
- A.P. Vinogradov Institute of Geochemistry SB RAS, 1a Favorsky Street, 664033 Irkutsk, Russia
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20
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Franzke Y, Holzer C, Andersen JH, Begušić T, Bruder F, Coriani S, Della Sala F, Fabiano E, Fedotov DA, Fürst S, Gillhuber S, Grotjahn R, Kaupp M, Kehry M, Krstić M, Mack F, Majumdar S, Nguyen BD, Parker SM, Pauly F, Pausch A, Perlt E, Phun GS, Rajabi A, Rappoport D, Samal B, Schrader T, Sharma M, Tapavicza E, Treß RS, Voora V, Wodyński A, Yu JM, Zerulla B, Furche F, Hättig C, Sierka M, Tew DP, Weigend F. TURBOMOLE: Today and Tomorrow. J Chem Theory Comput 2023; 19:6859-6890. [PMID: 37382508 PMCID: PMC10601488 DOI: 10.1021/acs.jctc.3c00347] [Citation(s) in RCA: 50] [Impact Index Per Article: 50.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Indexed: 06/30/2023]
Abstract
TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.
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Affiliation(s)
- Yannick
J. Franzke
- Fachbereich
Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
| | - Christof Holzer
- Institute
of Theoretical Solid State Physics, Karlsruhe
Institute of Technology (KIT), Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany
| | - Josefine H. Andersen
- DTU
Chemistry, Department of Chemistry, Technical
University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
| | - Tomislav Begušić
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Florian Bruder
- Fachbereich
Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
| | - Sonia Coriani
- DTU
Chemistry, Department of Chemistry, Technical
University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
| | - Fabio Della Sala
- Institute
for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center for
Biomolecular Nanotechnologies @UNILE, Istituto
Italiano di Tecnologia, Via Barsanti, 73010 Arnesano, Italy
| | - Eduardo Fabiano
- Institute
for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center for
Biomolecular Nanotechnologies @UNILE, Istituto
Italiano di Tecnologia, Via Barsanti, 73010 Arnesano, Italy
| | - Daniil A. Fedotov
- DTU
Chemistry, Department of Chemistry, Technical
University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
- Institute
of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Susanne Fürst
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17 Juni 135, 10623, Berlin, Germany
| | - Sebastian Gillhuber
- Institute
of Inorganic Chemistry, Karlsruhe Institute
of Technology (KIT), Engesserstr. 15, 76131 Karlsruhe, Germany
| | - Robin Grotjahn
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Martin Kaupp
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17 Juni 135, 10623, Berlin, Germany
| | - Max Kehry
- Institute
of Physical Chemistry, Karlsruhe Institute
of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Marjan Krstić
- Institute
of Theoretical Solid State Physics, Karlsruhe
Institute of Technology (KIT), Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany
| | - Fabian Mack
- Institute
of Physical Chemistry, Karlsruhe Institute
of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Sourav Majumdar
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Brian D. Nguyen
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Shane M. Parker
- Department
of Chemistry, Case Western Reserve University, 10900 Euclid Ave, Cleveland, Ohio 44106 United States
| | - Fabian Pauly
- Institute
of Physics, University of Augsburg, Universitätsstr. 1, 86159 Augsburg, Germany
| | - Ansgar Pausch
- Institute
of Physical Chemistry, Karlsruhe Institute
of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Eva Perlt
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - Gabriel S. Phun
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Ahmadreza Rajabi
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Dmitrij Rappoport
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Bibek Samal
- Department
of Chemical Sciences, Tata Institute of
Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Tim Schrader
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - Manas Sharma
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - Enrico Tapavicza
- Department
of Chemistry and Biochemistry, California
State University, Long Beach, 1250 Bellflower Boulevard, Long
Beach, California 90840-9507, United States
| | - Robert S. Treß
- Lehrstuhl
für Theoretische Chemie, Ruhr-Universität
Bochum, 44801 Bochum, Germany
| | - Vamsee Voora
- Department
of Chemical Sciences, Tata Institute of
Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Artur Wodyński
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17 Juni 135, 10623, Berlin, Germany
| | - Jason M. Yu
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Benedikt Zerulla
- Institute
of Nanotechnology, Karlsruhe Institute of
Technology (KIT), Hermann-von-Helmholtz-Platz
1, 76344 Eggenstein-Leopoldshafen Germany
| | - Filipp Furche
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Christof Hättig
- Lehrstuhl
für Theoretische Chemie, Ruhr-Universität
Bochum, 44801 Bochum, Germany
| | - Marek Sierka
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - David P. Tew
- Physical
and Theoretical Chemistry Laboratory, University
of Oxford, South Parks
Road, Oxford OX1 3QZ, United Kingdom
| | - Florian Weigend
- Fachbereich
Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
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21
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Di Felice R, Mayes ML, Richard RM, Williams-Young DB, Chan GKL, de Jong WA, Govind N, Head-Gordon M, Hermes MR, Kowalski K, Li X, Lischka H, Mueller KT, Mutlu E, Niklasson AMN, Pederson MR, Peng B, Shepard R, Valeev EF, van Schilfgaarde M, Vlaisavljevich B, Windus TL, Xantheas SS, Zhang X, Zimmerman PM. A Perspective on Sustainable Computational Chemistry Software Development and Integration. J Chem Theory Comput 2023; 19:7056-7076. [PMID: 37769271 PMCID: PMC10601486 DOI: 10.1021/acs.jctc.3c00419] [Citation(s) in RCA: 11] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2023] [Indexed: 09/30/2023]
Abstract
The power of quantum chemistry to predict the ground and excited state properties of complex chemical systems has driven the development of computational quantum chemistry software, integrating advances in theory, applied mathematics, and computer science. The emergence of new computational paradigms associated with exascale technologies also poses significant challenges that require a flexible forward strategy to take full advantage of existing and forthcoming computational resources. In this context, the sustainability and interoperability of computational chemistry software development are among the most pressing issues. In this perspective, we discuss software infrastructure needs and investments with an eye to fully utilize exascale resources and provide unique computational tools for next-generation science problems and scientific discoveries.
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Affiliation(s)
- Rosa Di Felice
- Departments
of Physics and Astronomy and Quantitative and Computational Biology, University of Southern California, Los Angeles, California 90089, United States
- CNR-NANO
Modena, Modena 41125, Italy
| | - Maricris L. Mayes
- Department
of Chemistry and Biochemistry, University
of Massachusetts Dartmouth, North Dartmouth, Massachusetts 02747, United States
| | | | | | - Garnet Kin-Lic Chan
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Wibe A. de Jong
- Lawrence
Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Niranjan Govind
- Physical
Sciences Division, Pacific Northwest National
Laboratory, Richland, Washington 99354, United States
| | - Martin Head-Gordon
- Pitzer Center
for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Matthew R. Hermes
- Department
of Chemistry, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Karol Kowalski
- Physical
Sciences Division, Pacific Northwest National
Laboratory, Richland, Washington 99354, United States
| | - Xiaosong Li
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Hans Lischka
- Department
of Chemistry and Biochemistry, Texas Tech
University, Lubbock, Texas 79409, United States
| | - Karl T. Mueller
- Physical
and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Erdal Mutlu
- Advanced
Computing, Mathematics, and Data Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Anders M. N. Niklasson
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Mark R. Pederson
- Department
of Physics, The University of Texas at El
Paso, El Paso, Texas 79968, United States
| | - Bo Peng
- Physical
Sciences Division, Pacific Northwest National
Laboratory, Richland, Washington 99354, United States
| | - Ron Shepard
- Chemical
Sciences and Engineering Division, Argonne
National Laboratory, Lemont, Illinois 60439, United States
| | - Edward F. Valeev
- Department
of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | | | - Bess Vlaisavljevich
- Department
of Chemistry, University of South Dakota, Vermillion, South Dakota 57069, United States
| | - Theresa L. Windus
- Department
of Chemistry, Iowa State University and
Ames Laboratory, Ames, Iowa 50011, United States
| | - Sotiris S. Xantheas
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
- Advanced
Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Xing Zhang
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Paul M. Zimmerman
- Department
of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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22
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Kolodzeiski E, Stein CJ. Automated, Consistent, and Even-Handed Selection of Active Orbital Spaces for Quantum Embedding. J Chem Theory Comput 2023; 19:6643-6655. [PMID: 37775093 PMCID: PMC10569175 DOI: 10.1021/acs.jctc.3c00653] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Indexed: 10/01/2023]
Abstract
A widely used strategy to reduce the computational cost of quantum-chemical calculations is to partition the system into an active subsystem, which is the focus of the computational efforts, and an environment that is treated at a lower computational level. The system partitioning is mostly based on localized molecular orbitals. When reaction paths or energy differences are to be calculated, it is crucial to keep the orbital space consistent for all structures. Inconsistencies in orbital space can lead to unpredictable errors on the potential energy surface. While successful strategies to ensure this consistency have been established for organic and even metal-organic systems, these methods often fail for metal clusters or nanoparticles with a high density of near-degenerate and delocalized molecular orbitals. However, such systems are highly relevant for catalysis. Accurate yet feasible quantum-mechanical ab initio calculations are therefore highly desired. In this work, we present an approach based on the subsystem projected atomic orbital decomposition algorithm that allows us to ensure automated and consistent partitioning even for systems with delocalized and near-degenerate molecular orbitals and demonstrate the validity of this method for the binding energies of small molecules on transition-metal clusters.
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Affiliation(s)
- Elena Kolodzeiski
- Technical University of Munich, TUM
School of Natural Sciences, Department of Chemistry, Lichtenbergstr. 4, Garching D-85748, Germany
| | - Christopher J. Stein
- Technical University of Munich, TUM
School of Natural Sciences, Department of Chemistry, Lichtenbergstr. 4, Garching D-85748, Germany
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23
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Chakraborty R, Boguslawski K, Tecmer P. Static embedding with pair coupled cluster doubles based methods. Phys Chem Chem Phys 2023; 25:25377-25388. [PMID: 37705409 DOI: 10.1039/d3cp02502k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/15/2023]
Abstract
Quantum embedding methods have recently been significantly developed to model large molecular structures. This work proposes a novel wave function theory in a density functional theory (WTF-in-DFT) embedding scheme based on pair-coupled cluster doubles (pCCD)-type methods. While pCCD can reliably describe strongly-correlated systems with mean-field-like computational cost, the large extent of the dynamic correlation can be accounted for by (linearized) coupled-cluster corrections on top of the pCCD wave function. Here we focus on the linearized coupled-cluster singles and doubles (LCCSD) ansatz for electronic ground states and its extension to excited states within the equation of motion (EOM) formalism. We test our EOM-pCCD-LCCSD-in-DFT approach for the vertical excitation energies of the hydrogen-bonded water-ammonia complex, micro-solvated thymine, and uranyl tetrahalides (UO2X42-, X = F, Cl, Br). Furthermore, we assess the quality of the embedding potential using an orbital entanglement and correlation analysis. The approximate embedding models successfully capture changes in the excitation energies going from bare fragments to supramolecular structures and represent a promising computational method for excited states in large molecular systems.
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Affiliation(s)
- Rahul Chakraborty
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
| | - Paweł Tecmer
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
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24
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Wang B, Wu Y, Liu D, Vasenko AS, Casanova D, Prezhdo OV. Efficient Modeling of Quantum Dynamics of Charge Carriers in Materials Using Short Nonequilibrium Molecular Dynamics. J Phys Chem Lett 2023; 14:8289-8295. [PMID: 37681642 PMCID: PMC10518862 DOI: 10.1021/acs.jpclett.3c02187] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2023] [Accepted: 09/05/2023] [Indexed: 09/09/2023]
Abstract
Nonadiabatic molecular dynamics provides essential insights into excited-state processes, but it is computationally intense and simplifications are needed. The classical path approximation provides critical savings. Still, long heating and equilibration steps are required. We demonstrate that practical results can be obtained with short, partially equilibrated ab initio trajectories. Once the system's structure is adequate and essential fluctuations are sampled, the nonadiabatic Hamiltonian can be constructed. Local structures require only 1-2 ps trajectories, as demonstrated with point defects in metal halide perovskites. Short trajectories represent anharmonic motions common in defective structures, an essential improvement over the harmonic approximation around the optimized geometry. Glassy systems, such as grain boundaries, require different simulation protocols, e.g., involving machine learning force fields. 10-fold shorter trajectories generate 10-20% time scale errors, which are acceptable, given experimental uncertainties and other approximations. The practical NAMD protocol enables fast screening of excited-state dynamics for rapid exploration of new materials.
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Affiliation(s)
- Bipeng Wang
- Department
of Chemical Engineering, University of Southern
California, Los Angeles, California 90089, United States
| | - Yifan Wu
- Department
of Chemistry, University of Southern California, Los Angeles, California 90089, United States
| | | | - Andrey S. Vasenko
- HSE
University, 101000 Moscow, Russia
- Donostia
International Physics Center (DIPC), 20018 San Sebastián-Donostia, Euskadi, Spain
| | - David Casanova
- Donostia
International Physics Center (DIPC), 20018 San Sebastián-Donostia, Euskadi, Spain
- IKERBASQUE, Basque Foundation for Science, 48009 Bilbao, Euskadi, Spain
| | - Oleg V. Prezhdo
- Department
of Chemical Engineering, University of Southern
California, Los Angeles, California 90089, United States
- Department
of Chemistry, University of Southern California, Los Angeles, California 90089, United States
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25
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Chen MS, Mao Y, Snider A, Gupta P, Montoya-Castillo A, Zuehlsdorff TJ, Isborn CM, Markland TE. Elucidating the Role of Hydrogen Bonding in the Optical Spectroscopy of the Solvated Green Fluorescent Protein Chromophore: Using Machine Learning to Establish the Importance of High-Level Electronic Structure. J Phys Chem Lett 2023; 14:6610-6619. [PMID: 37459252 DOI: 10.1021/acs.jpclett.3c01444] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/28/2023]
Abstract
Hydrogen bonding interactions with chromophores in chemical and biological environments play a key role in determining their electronic absorption and relaxation processes, which are manifested in their linear and multidimensional optical spectra. For chromophores in the condensed phase, the large number of atoms needed to simulate the environment has traditionally prohibited the use of high-level excited-state electronic structure methods. By leveraging transfer learning, we show how to construct machine-learned models to accurately predict the high-level excitation energies of a chromophore in solution from only 400 high-level calculations. We show that when the electronic excitations of the green fluorescent protein chromophore in water are treated using EOM-CCSD embedded in a DFT description of the solvent the optical spectrum is correctly captured and that this improvement arises from correctly treating the coupling of the electronic transition to electric fields, which leads to a larger response upon hydrogen bonding between the chromophore and water.
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Affiliation(s)
- Michael S Chen
- Department of Chemistry, Stanford University, Stanford, California 94305, United States
| | - Yuezhi Mao
- Department of Chemistry, Stanford University, Stanford, California 94305, United States
| | - Andrew Snider
- Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
| | - Prachi Gupta
- Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
| | - Andrés Montoya-Castillo
- Department of Chemistry, University of Colorado, Boulder, Boulder, Colorado 80309, United States
| | - Tim J Zuehlsdorff
- Department of Chemistry, Oregon State University, Corvallis, Oregon 97331, United States
| | - Christine M Isborn
- Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
| | - Thomas E Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, United States
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26
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Jansen M, Reinholdt P, Hedegård ED, König C. Theoretical and Numerical Comparison of Quantum- and Classical Embedding Models for Optical Spectra. J Phys Chem A 2023. [PMID: 37399130 DOI: 10.1021/acs.jpca.3c02540] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/05/2023]
Abstract
Quantum-mechanical (QM) and classical embedding models approximate a supermolecular quantum-chemical calculation. This is particularly useful when the supermolecular calculation has a size that is out of reach for present QM models. Although QM and classical embedding methods share the same goal, they approach this goal from different starting points. In this study, we compare the polarizable embedding (PE) and frozen-density embedding (FDE) models. The former is a classical embedding model, whereas the latter is a density-based QM embedding model. Our comparison focuses on solvent effects on optical spectra of solutes. This is a typical scenario where super-system calculations including the solvent environment become prohibitively large. We formulate a common theoretical framework for PE and FDE models and systematically investigate how PE and FDE approximate solvent effects. Generally, differences are found to be small, except in cases where electron spill-out becomes problematic in the classical frameworks. In these cases, however, atomic pseudopotentials can reduce the electron-spill-out issue.
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Affiliation(s)
- Marina Jansen
- Institute of Physical Chemistry and Electrochemistry, Leibniz University Hannover, Callinstr. 3A, 30167 Hannover, Germany
| | - Peter Reinholdt
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense, Denmark
| | - Erik D Hedegård
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense, Denmark
| | - Carolin König
- Institute of Physical Chemistry and Electrochemistry, Leibniz University Hannover, Callinstr. 3A, 30167 Hannover, Germany
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27
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Barcza B, Szirmai Á, Tajti A, Stanton JF, Szalay PG. Benchmarking Aspects of Ab Initio Fragment Models for Accurate Excimer Potential Energy Surfaces. J Chem Theory Comput 2023; 19:3580-3600. [PMID: 37236166 PMCID: PMC10694823 DOI: 10.1021/acs.jctc.3c00104] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2023] [Indexed: 05/28/2023]
Abstract
While Coupled-Cluster methods have been proven to provide an accurate description of excited electronic states, the scaling of the computational costs with the system size limits the degree for which these methods can be applied. In this work different aspects of fragment-based approaches are studied on noncovalently bound molecular complexes with interacting chromophores of the fragments, such as π-stacked nucleobases. The interaction of the fragments is considered at two distinct steps. First, the states localized on the fragments are described in the presence of the other fragment(s); for this we test two approaches. One method is founded on QM/MM principles, only including the electrostatic interaction between the fragments in the electronic structure calculation with Pauli repulsion and dispersion effects added separately. The other model, a Projection-based Embedding (PbE) using the Huzinaga equation, includes both electrostatic and Pauli repulsion and only needs to be augmented by dispersion interactions. In both schemes the extended Effective Fragment Potential (EFP2) method of Gordon et al. was found to provide an adequate correction for the missing terms. In the second step, the interaction of the localized chromophores is modeled for a proper description of the excitonic coupling. Here the inclusion of purely electrostatic contributions appears to be sufficient: it is found that the Coulomb part of the coupling provides accurate splitting of the energies of interacting chromophores that are separated by more than 4 Å.
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Affiliation(s)
- Bónis Barcza
- Laboratory
of Theoretical Chemistry, Institute of Chemistry, ELTE Eötvös Loránd University, P.O. Box 32, H-1117 Budapest, Hungary
- György
Hevesy Doctoral School, Institute of Chemistry, ELTE Eötvös Loránd University, H-1117 Budapest, Hungary
| | - Ádám
B. Szirmai
- Laboratory
of Theoretical Chemistry, Institute of Chemistry, ELTE Eötvös Loránd University, P.O. Box 32, H-1117 Budapest, Hungary
- György
Hevesy Doctoral School, Institute of Chemistry, ELTE Eötvös Loránd University, H-1117 Budapest, Hungary
| | - Attila Tajti
- Laboratory
of Theoretical Chemistry, Institute of Chemistry, ELTE Eötvös Loránd University, P.O. Box 32, H-1117 Budapest, Hungary
| | - John F. Stanton
- Quantum
Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32611, United States
| | - Péter G. Szalay
- Laboratory
of Theoretical Chemistry, Institute of Chemistry, ELTE Eötvös Loránd University, P.O. Box 32, H-1117 Budapest, Hungary
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28
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Rossmannek M, Pavošević F, Rubio A, Tavernelli I. Quantum Embedding Method for the Simulation of Strongly Correlated Systems on Quantum Computers. J Phys Chem Lett 2023; 14:3491-3497. [PMID: 37011400 DOI: 10.1021/acs.jpclett.3c00330] [Citation(s) in RCA: 11] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/19/2023]
Abstract
Quantum computing has emerged as a promising platform for simulating strongly correlated systems in chemistry, for which the standard quantum chemistry methods are either qualitatively inaccurate or too expensive. However, due to the hardware limitations of the available noisy near-term quantum devices, their application is currently limited only to small chemical systems. One way for extending the range of applicability can be achieved within the quantum embedding approach. Herein, we employ the projection-based embedding method for combining the variational quantum eigensolver (VQE) algorithm, although not limited to, with density functional theory (DFT). The developed VQE-in-DFT method is then implemented efficiently on a real quantum device and employed for simulating the triple bond breaking process in butyronitrile. The results presented herein show that the developed method is a promising approach for simulating systems with a strongly correlated fragment on a quantum computer.
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Affiliation(s)
- Max Rossmannek
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
- IBM Quantum, IBM Research - Zürich, 8803 Rüschlikon, Switzerland
| | - Fabijan Pavošević
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, 10010 New York, United States
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science & Department of Physics, Luruper Chaussee 149, 22761 Hamburg, Germany
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Universidad del País Vasco (UPV/EHU), Av. Tolosa 72, 20018 San Sebastian, Spain
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, 10010 New York, United States
| | - Ivano Tavernelli
- IBM Quantum, IBM Research - Zürich, 8803 Rüschlikon, Switzerland
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29
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Giovannini T, Marrazzini G, Scavino M, Koch H, Cappelli C. Integrated Multiscale Multilevel Approach to Open Shell Molecular Systems. J Chem Theory Comput 2023; 19:1446-1456. [PMID: 36780359 PMCID: PMC10018740 DOI: 10.1021/acs.jctc.2c00805] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/14/2023]
Abstract
We present a novel multiscale approach to study the electronic structure of open shell molecular systems embedded in an external environment. The method is based on the coupling of multilevel Hartree-Fock (MLHF) and Density Functional Theory (MLDFT), suitably extended to the unrestricted formalism, to Molecular Mechanics (MM) force fields (FF). Within the ML region, the system is divided into active and inactive parts, thus describing the most relevant interactions (electrostatic, polarization, and Pauli repulsion) at the quantum level. The surrounding MM part, which is formulated in terms of nonpolarizable or polarizable FFs, permits a physically consistent treatment of long-range electrostatics and polarization effects. The approach is extended to the calculation of hyperfine coupling constants and applied to selected nitroxyl radicals in an aqueous solution.
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Affiliation(s)
| | - Gioia Marrazzini
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Marco Scavino
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Henrik Koch
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy.,Department of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway
| | - Chiara Cappelli
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
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30
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Bensberg M, Reiher M. Corresponding Active Orbital Spaces along Chemical Reaction Paths. J Phys Chem Lett 2023; 14:2112-2118. [PMID: 36802629 PMCID: PMC9986954 DOI: 10.1021/acs.jpclett.2c03905] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/25/2022] [Accepted: 02/10/2023] [Indexed: 06/18/2023]
Abstract
The accuracy of reaction energy profiles calculated with multiconfigurational electronic structure methods and corrected by multireference perturbation theory depends crucially on consistent active orbital spaces selected along the reaction path. However, it has been challenging to choose molecular orbitals that can be considered corresponding in different molecular structures. Here, we demonstrate how active orbital spaces can be selected consistently along reaction coordinates in a fully automatized way. The approach requires no structure interpolation between reactants and products. Instead, it emerges from a synergy of the Direct Orbital Selection orbital mapping ansatz combined with our fully automated active space selection algorithm autoCAS. We demonstrate our algorithm for the potential energy profile of the homolytic carbon-carbon bond dissociation and rotation around the double bond of 1-pentene in the electronic ground state. However, our algorithm also applies to electronically excited Born-Oppenheimer surfaces.
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31
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Amanollahi Z, Lampe L, Bensberg M, Neugebauer J, Feldt M. On the accuracy of orbital based multi-level approaches for closed-shell transition metal chemistry. Phys Chem Chem Phys 2023; 25:4635-4648. [PMID: 36662158 DOI: 10.1039/d2cp05056k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
In this work, we investigate the accuracy of the local molecular orbital molecular orbital (LMOMO) scheme and projection-based wave function-in-density functional theory (WF-in-DFT) embedding for the prediction of reaction energies and barriers of typical reactions involving transition metals. To analyze the dependence of the accuracy on the system partitioning, we apply a manual orbital selection for LMOMO as well as the so-called direct orbital selection (DOS) for both approaches. We benchmark these methods on 30 closed shell reactions involving 16 different transition metals. This allows us to devise guidelines for the manual selection as well as settings for the DOS that provide accurate results within an error of 2 kcal mol-1 compared to local coupled cluster. To reach this accuracy, on average 55% of the occupied orbitals have to be correlated with coupled cluster for the current test set. Furthermore, we find that LMOMO gives more reliable relative energies for small embedded regions than WF-in-DFT embedding.
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Affiliation(s)
- Zohreh Amanollahi
- Leibniz Institute for Catalysis (LIKAT), Albert-Einstein-Str. 29A, 18059 Rostock, Germany.
| | - Lukas Lampe
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 36, 48149 Münster, Germany
| | - Moritz Bensberg
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 36, 48149 Münster, Germany
| | - Milica Feldt
- Leibniz Institute for Catalysis (LIKAT), Albert-Einstein-Str. 29A, 18059 Rostock, Germany.
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32
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Sen S, Senjean B, Visscher L. Characterization of excited states in time-dependent density functional theory using localized molecular orbitals. J Chem Phys 2023; 158:054115. [PMID: 36754801 DOI: 10.1063/5.0137729] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Abstract
Localized molecular orbitals are often used for the analysis of chemical bonds, but they can also serve to efficiently and comprehensibly compute linear response properties. While conventional canonical molecular orbitals provide an adequate basis for the treatment of excited states, a chemically meaningful identification of the different excited-state processes is difficult within such a delocalized orbital basis. In this work, starting from an initial set of supermolecular canonical molecular orbitals, we provide a simple one-step top-down embedding procedure for generating a set of orbitals, which are localized in terms of the supermolecule but delocalized over each subsystem composing the supermolecule. Using an orbital partitioning scheme based on such sets of localized orbitals, we further present a procedure for the construction of local excitations and charge-transfer states within the linear response framework of time-dependent density functional theory (TDDFT). This procedure provides direct access to approximate diabatic excitation energies and, under the Tamm-Dancoff approximation, also their corresponding electronic couplings-quantities that are of primary importance in modeling energy transfer processes in complex biological systems. Our approach is compared with a recently developed diabatization procedure based on subsystem TDDFT using projection operators, which leads to a similar set of working equations. Although both of these methods differ in the general localization strategies adopted and the type of basis functions (Slaters vs Gaussians) employed, an overall decent agreement is obtained.
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Affiliation(s)
- Souloke Sen
- Division of Theoretical Chemistry, Faculty of Sciences, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Bruno Senjean
- ICGM, Université de Montpellier, CNRS, ENSCM, Montpellier, France
| | - Lucas Visscher
- Division of Theoretical Chemistry, Faculty of Sciences, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
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33
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Mutual information prediction for strongly correlated systems. Chem Phys Lett 2023. [DOI: 10.1016/j.cplett.2023.140297] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
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34
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Izsák R, Riplinger C, Blunt NS, de Souza B, Holzmann N, Crawford O, Camps J, Neese F, Schopf P. Quantum computing in pharma: A multilayer embedding approach for near future applications. J Comput Chem 2023; 44:406-421. [PMID: 35789492 DOI: 10.1002/jcc.26958] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2022] [Revised: 06/09/2022] [Accepted: 06/10/2022] [Indexed: 01/03/2023]
Abstract
Quantum computers are special purpose machines that are expected to be particularly useful in simulating strongly correlated chemical systems. The quantum computer excels at treating a moderate number of orbitals within an active space in a fully quantum mechanical manner. We present a quantum phase estimation calculation on F2 in a (2,2) active space on Rigetti's Aspen-11 QPU. While this is a promising start, it also underlines the need for carefully selecting the orbital spaces treated by the quantum computer. In this work, a scheme for selecting such an active space automatically is described and simulated results obtained using both the quantum phase estimation (QPE) and variational quantum eigensolver (VQE) algorithms are presented and combined with a subtractive method to enable accurate description of the environment. The active occupied space is selected from orbitals localized on the chemically relevant fragment of the molecule, while the corresponding virtual space is chosen based on the magnitude of interactions with the occupied space calculated from perturbation theory. This protocol is then applied to two chemical systems of pharmaceutical relevance: the enzyme [Fe] hydrogenase and the photosenzitizer temoporfin. While the sizes of the active spaces currently amenable to a quantum computational treatment are not enough to demonstrate quantum advantage, the procedure outlined here is applicable to any active space size, including those that are outside the reach of classical computation.
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Affiliation(s)
| | | | | | | | - Nicole Holzmann
- Riverlane Research Ltd, Cambridge, UK.,Astex Pharmaceuticals, Cambridge, UK
| | | | | | - Frank Neese
- Max-Planck Institut für Kohlenforschung, Mülheim an der Ruhr, Germany
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35
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Beran P, Pernal K, Pavošević F, Veis L. Projection-Based Density Matrix Renormalization Group in Density Functional Theory Embedding. J Phys Chem Lett 2023; 14:716-722. [PMID: 36648273 PMCID: PMC10017021 DOI: 10.1021/acs.jpclett.2c03298] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2022] [Accepted: 01/11/2023] [Indexed: 06/17/2023]
Abstract
The density matrix renormalization group (DMRG) method has already proved itself as a very efficient and accurate computational method, which can treat large active spaces and capture the major part of strong correlation. Its application on larger molecules is, however, limited by its own computational scaling as well as demands of methods for treatment of the missing dynamical electron correlation. In this work, we present the first step in the direction of combining DMRG with density functional theory (DFT), one of the most employed quantum chemical methods with favorable scaling, by means of the projection-based wave function (WF)-in-DFT embedding. On two proof-of-concept but important molecular examples, we demonstrate that the developed DMRG-in-DFT approach provides a very accurate description of molecules with a strongly correlated fragment.
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Affiliation(s)
- Pavel Beran
- J.
Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223Prague 8, Czech Republic
- Faculty
of Mathematics and Physics, Charles University, 121 16Prague, Czech Republic
| | - Katarzyna Pernal
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 217/221, 93-005Lodz, Poland
| | - Fabijan Pavošević
- Center
for Computational Quantum Physics, Flatiron
Institute, 162 Fifth Avenue, New York, 10010New York, United
States
| | - Libor Veis
- J.
Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223Prague 8, Czech Republic
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36
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Initial Maximum Overlap Method Embedded with Extremely Localized Molecular Orbitals for Core-Ionized States of Large Systems. MOLECULES (BASEL, SWITZERLAND) 2022; 28:molecules28010136. [PMID: 36615331 PMCID: PMC9822432 DOI: 10.3390/molecules28010136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Revised: 12/21/2022] [Accepted: 12/22/2022] [Indexed: 12/28/2022]
Abstract
Despite great advances in X-ray absorption spectroscopy for the investigation of small molecule electronic structure, the application to biosystems of experimental techniques developed within this research field remains a challenge. To partially circumvent the problem, users resort to theoretical methods to interpret or predict the X-ray absorption spectra of large molecules. To accomplish this task, only low-cost computational strategies can be exploited. For this reason, some of them are single Slater determinant wavefunction approaches coupled with multiscale embedding techniques designed to treat large systems of biological interest. Therefore, in this work, we propose to apply the recently developed IMOM/ELMO embedding method to the determination of core-ionized states. The IMOM/ELMO technique resulted from the combination of the single Slater determinant Δself-consistent-field-initial maximum overlap approach (ΔSCF-IMOM) with the QM/ELMO (quantum mechanics/extremely localized molecular orbital) embedding strategy, a method where only the chemically relevant region of the examined system is treated at fully quantum chemical level, while the rest is described through transferred and frozen extremely localized molecular orbitals (ELMOs). The IMOM/ELMO technique was initially validated by computing core-ionization energies for small molecules, and it was afterwards exploited to study larger biosystems. The obtained results are in line with those reported in previous studies that applied alternative ΔSCF approaches. This makes us envisage a possible future application of the proposed method to the interpretation of X-ray absorption spectra of large molecules.
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37
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Niemeyer N, Eschenbach P, Bensberg M, Tölle J, Hellmann L, Lampe L, Massolle A, Rikus A, Schnieders D, Unsleber JP, Neugebauer J. The subsystem quantum chemistry program
Serenity. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1647] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Affiliation(s)
- Niklas Niemeyer
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
| | - Patrick Eschenbach
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
| | - Moritz Bensberg
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
| | - Johannes Tölle
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
| | - Lars Hellmann
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
| | - Lukas Lampe
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
| | - Anja Massolle
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
| | - Anton Rikus
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
| | - David Schnieders
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
| | - Jan P. Unsleber
- Laboratorium für Physikalische Chemie ETH Zürich Zürich Switzerland
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
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38
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Sharma M, Sierka M. Efficient Implementation of Density Functional Theory Based Embedding for Molecular and Periodic Systems Using Gaussian Basis Functions. J Chem Theory Comput 2022; 18:6892-6904. [PMID: 36223886 DOI: 10.1021/acs.jctc.2c00380] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A practical and effective implementation of density functional theory based embedding is reported, which allows us to treat both periodic and aperiodic systems on an equal footing. Its essence is the expansion of orbitals and electron density of the periodic system using Gaussian basis functions, rather than plane-waves, which provides a unique all-electron direct-space representation, thus avoiding the need for pseudopotentials. This makes the construction of embedding potential for a molecular active subsystem due to a periodic environment quite convenient, as transformation between representations is far from trivial. The three flavors of embedding, molecule-in-molecule, molecule-in-periodic, and periodic-in-periodic embedding, are implemented using embedding potentials based on non-additive kinetic energy density functionals (approximate) and level-shift projection operator (exact). The embedding scheme is coupled with a variety of correlated wave function theory (WFT) methods, thereby providing an efficient way to study the ground and excited state properties of low-dimensional systems using high-level methods for the region of interest. Finally, an implementation of real time-time-dependent density functional embedding theory (RT-TDDFET) is presented that uses a projection operator-based embedding potential and provides accurate results compared to full RT-TDDFT for systems with uncoupled excitations. The embedding potential is calculated efficiently using a combination of density fitting and continuous fast multipole method for the Coulomb term. The applicability of (i) WFT-in-DFT embedding, in predicting the adsorption and excitation energies, and (ii) RT-TDDFET, in predicting the absorption spectra, is explored for various test systems.
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Affiliation(s)
- Manas Sharma
- Otto Schott Institute of Materials Research, Friedrich Schiller University Jena, Löbdergraben 32, 07743Jena, Germany
| | - Marek Sierka
- Otto Schott Institute of Materials Research, Friedrich Schiller University Jena, Löbdergraben 32, 07743Jena, Germany
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39
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De Santis M, Sorbelli D, Vallet V, Gomes AS, Storchi L, Belpassi L. Frozen-Density Embedding for Including Environmental Effects in the Dirac-Kohn-Sham Theory: An Implementation Based on Density Fitting and Prototyping Techniques. J Chem Theory Comput 2022; 18:5992-6009. [PMID: 36172757 PMCID: PMC9558305 DOI: 10.1021/acs.jctc.2c00499] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2022] [Indexed: 11/28/2022]
Abstract
Frozen density embedding (FDE) represents an embedding scheme in which environmental effects are included from first-principles calculations by considering the surrounding system explicitly by means of its electron density. In the present paper, we extend the full four-component relativistic Dirac-Kohn-Sham (DKS) method, as implemented in the BERTHA code, to include environmental and confinement effects with the FDE scheme (DKS-in-DFT FDE). The implementation, based on the auxiliary density fitting techniques, has been enormously facilitated by BERTHA's python API (PyBERTHA), which facilitates the interoperability with other FDE implementations available through the PyADF framework. The accuracy and numerical stability of this new implementation, also using different auxiliary fitting basis sets, has been demonstrated on the simple NH3-H2O system, in comparison with a reference nonrelativistic implementation. The computational performance has been evaluated on a series of gold clusters (Aun, with n = 2, 4, 8) embedded into an increasing number of water molecules (5, 10, 20, 40, and 80 water molecules). We found that the procedure scales approximately linearly both with the size of the frozen surrounding environment (consistent with the underpinnings of the FDE approach) and with the size of the active system (in line with the use of density fitting). Finally, we applied the code to a series of heavy (Rn) and super-heavy elements (Cn, Fl, Og) embedded in a C60 cage to explore the confinement effect induced by C60 on their electronic structure. We compare the results from our simulations, with respect to more-approximate models employed in the atomic physics literature. Our results indicate that the specific interactions described by FDE are able to improve upon the cruder approximations currently employed, and, thus, they provide a basis from which to generate more-realistic radial potentials for confined atoms.
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Affiliation(s)
- Matteo De Santis
- Univ.
Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Diego Sorbelli
- Dipartimento
di Chimica, Biologia e Biotecnologie, Università
degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
- Istituto
di Scienze e Tecnologie Chimiche (SCITEC), Consiglio Nazionale delle
Ricerche c/o Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
| | - Valérie Vallet
- Univ.
Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | | | - Loriano Storchi
- Istituto
di Scienze e Tecnologie Chimiche (SCITEC), Consiglio Nazionale delle
Ricerche c/o Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
- Dipartimento
di Farmacia, Università degli Studi
‘G. D’Annunzio’, Via dei Vestini 31, 66100 Chieti, Italy
| | - Leonardo Belpassi
- Istituto
di Scienze e Tecnologie Chimiche (SCITEC), Consiglio Nazionale delle
Ricerche c/o Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
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40
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Eschenbach P, Neugebauer J. Subsystem density-functional theory: A reliable tool for spin-density based properties. J Chem Phys 2022; 157:130902. [PMID: 36209003 DOI: 10.1063/5.0103091] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Subsystem density-functional theory compiles a set of features that allow for efficiently calculating properties of very large open-shell radical systems such as organic radical crystals, proteins, or deoxyribonucleic acid stacks. It is computationally less costly than correlated ab initio wave function approaches and can pragmatically avoid the overdelocalization problem of Kohn-Sham density-functional theory without employing hard constraints on the electron-density. Additionally, subsystem density-functional theory calculations commonly start from isolated fragment electron densities, pragmatically preserving a priori specified subsystem spin-patterns throughout the calculation. Methods based on subsystem density-functional theory have seen a rapid development over the past years and have become important tools for describing open-shell properties. In this Perspective, we address open questions and possible developments toward challenging future applications in connection with subsystem density-functional theory for spin-dependent properties.
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Affiliation(s)
- Patrick Eschenbach
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Simulation, Westfälische Wilhelms-Universität Münster, Corrensstraße 36, 48149 Münster, Germany
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Simulation, Westfälische Wilhelms-Universität Münster, Corrensstraße 36, 48149 Münster, Germany
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41
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Förster A, Visscher L. Quasiparticle Self-Consistent GW-Bethe-Salpeter Equation Calculations for Large Chromophoric Systems. J Chem Theory Comput 2022; 18:6779-6793. [PMID: 36201788 PMCID: PMC9648197 DOI: 10.1021/acs.jctc.2c00531] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
The GW-Bethe–Salpeter equation
(BSE) method
is promising for calculating the low-lying excitonic states of molecular
systems. However, so far it has only been applied to rather small
molecules and in the commonly implemented diagonal approximations
to the electronic self-energy, it depends on a mean-field starting
point. We describe here an implementation of the self-consistent and
starting-point-independent quasiparticle self-consistent (qsGW)-BSE approach, which is suitable for calculations on
large molecules. We herein show that eigenvalue-only self-consistency
can lead to an unfaithful description of some excitonic states for
chlorophyll dimers while the qsGW-BSE vertical excitation
energies (VEEs) are in excellent agreement with spectroscopic experiments
for chlorophyll monomers and dimers measured in the gas phase. Furthermore,
VEEs from time-dependent density functional theory calculations tend
to disagree with experimental values and using different range-separated
hybrid (RSH) kernels does change the VEEs by up to 0.5 eV. We use
the new qsGW-BSE implementation to calculate the
lowest excitation energies of the six chromophores of the photosystem
II (PSII) reaction center (RC) with nearly 2000 correlated electrons.
Using more than 11,000 (6000) basis functions, the calculation could
be completed in less than 5 (2) days on a single modern compute node.
In agreement with previous TD-DFT calculations using RSH kernels on
models that also do not include environmental effects, our qsGW-BSE calculations only yield states with local characters
in the low-energy spectrum of the hexameric complex. Earlier works
with RSH kernels have demonstrated that the protein environment facilitates
the experimentally observed interchromophoric charge transfer. Therefore,
future research will need to combine correlation effects beyond TD-DFT
with an explicit treatment of environmental electrostatics.
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Affiliation(s)
- Arno Förster
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HVAmsterdam, The Netherlands
| | - Lucas Visscher
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HVAmsterdam, The Netherlands
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42
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Hégely B, Szirmai Á, Mester D, Tajti A, Szalay PG, Kállay M. Performance of Multilevel Methods for Excited States. J Phys Chem A 2022; 126:6548-6557. [PMID: 36095318 PMCID: PMC9511572 DOI: 10.1021/acs.jpca.2c05013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2022] [Revised: 08/30/2022] [Indexed: 11/29/2022]
Abstract
The performance of multilevel quantum chemical approaches, which utilize an atom-based system partitioning scheme to model various electronic excited states, is studied. The considered techniques include the mechanical-embedding (ME) of "our own N-layered integrated molecular orbital and molecular mechanics" (ONIOM) method, the point charge embedding (PCE), the electronic-embedding (EE) of ONIOM, the frozen density-embedding (FDE), the projector-based embedding (PbE), and our local domain-based correlation method. For the investigated multilevel approaches, the second-order algebraic-diagrammatic construction [ADC(2)] approach was utilized as the high-level method, which was embedded in either Hartree-Fock or a density functional environment. The XH-27 test set of Zech et al. [ J. Chem. Theory Comput., 2018, 14, 4028] was used for the assessment, where organic dyes interact with several solvent molecules. With the selection of the chromophores as active subsystems, we conclude that the most reliable approach is local domain-based ADC(2) [L-ADC(2)], and the least robust schemes are ONIOM-ME and ONIOM-EE. The PbE, FDE, and PCE techniques often approach the accuracy of the L-ADC(2) scheme, but their precision is far behind. The results suggest that a more conservative subsystem selection algorithm or the inclusion of subsystem charge-transfers is required for the atom-based cost-efficient methods to produce high-accuracy excitation energies.
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Affiliation(s)
- Bence Hégely
- Department
of Physical Chemistry and Materials Science, Faculty of Chemical Technology
and Biotechnology, Budapest University of
Technology and Economics, Műegyetem rkp. 3, H-1111 Budapest, Hungary
- ELKH-BME
Quantum Chemistry Research Group, Műegyetem rkp. 3, H-1111 Budapest, Hungary
| | - Ádám
B. Szirmai
- Laboratory
of Theoretical Chemistry, Institute of Chemistry, ELTE Eötvös Loránd University, P.O. Box 32, H-1518 Budapest 112, Hungary
| | - Dávid Mester
- Department
of Physical Chemistry and Materials Science, Faculty of Chemical Technology
and Biotechnology, Budapest University of
Technology and Economics, Műegyetem rkp. 3, H-1111 Budapest, Hungary
- ELKH-BME
Quantum Chemistry Research Group, Műegyetem rkp. 3, H-1111 Budapest, Hungary
| | - Attila Tajti
- Laboratory
of Theoretical Chemistry, Institute of Chemistry, ELTE Eötvös Loránd University, P.O. Box 32, H-1518 Budapest 112, Hungary
| | - Péter G. Szalay
- Laboratory
of Theoretical Chemistry, Institute of Chemistry, ELTE Eötvös Loránd University, P.O. Box 32, H-1518 Budapest 112, Hungary
| | - Mihály Kállay
- Department
of Physical Chemistry and Materials Science, Faculty of Chemical Technology
and Biotechnology, Budapest University of
Technology and Economics, Műegyetem rkp. 3, H-1111 Budapest, Hungary
- ELKH-BME
Quantum Chemistry Research Group, Műegyetem rkp. 3, H-1111 Budapest, Hungary
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43
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Pavosevic F, Rubio A. Wavefunction embedding for molecular polaritons. J Chem Phys 2022; 157:094101. [DOI: 10.1063/5.0095552] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Polaritonic chemistry relies on the strong light-matter interaction phenomena for altering the chemical reaction rates inside optical cavities. To explain and to understand these processes, the development of reliable theoretical models is essential. While computationally efficient quantum electrodynamics self-consistent field (QED-SCF) methods, such as quantum electrodynamics density functional theory (QEDFT) needs accurate functionals, quantum electrodynamics coupled cluster (QED-CC) methods provide a systematic increase in accuracy but at much greater cost. To overcome this computational bottleneck, herein we introduce and develop the QED-CC-in-QED-SCF projection-based embedding method that inherits all the favorable properties from the two worlds, computational efficiency and accuracy. The performance of the embedding method is assessed by studying some prototypical but relevant reactions, such as methyl transfer reaction, proton transfer reaction, as well as protonation reaction in a complex environment. The results obtained with the new embedding method are in excellent agreement with more expensive QED-CC results. The analysis performed on these reactions indicate that the electron-photon correlation effects are local in nature and that only a small region should be treated at the QED-CC level for capturing important effects due to cavity. This work sets the stage for future developments of polaritonic quantum chemistry methods and it will serve as a guideline for development of other polaritonic embedding models.
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Affiliation(s)
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter, Germany
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44
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Bensberg M, Neugebauer J. Orbital Pair Selection for Relative Energies in the Domain-Based Local Pair Natural Orbital Coupled-Cluster Method. J Chem Phys 2022; 157:064102. [DOI: 10.1063/5.0100010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
For the accurate computation of relative energies, domain-based local pair natural orbital coupled-cluster [DLPNO-CCSD(T0)] has become increasingly popular. Even though DLPNO-CCSD(T0) shows a formally linear scaling of the computational effort with the system size, accurate predictions of relative energies remain costly. Therefore, multi-level approaches are attractive that focus the available computational resources on a minor part of the molecular system, e.g., a reaction center, where changes in the correlation energy are expected to be the largest. We present a pair-selected multi-level DLPNO-CCSD(T0) ansatz that automatically partitions the orbital pairs according to their contribution to the overall correlation energy change in a chemical reaction. To this end, the localized orbitals are mapped between structures in the reaction; all pair energies are approximated through computationally efficient semi-canonical second-order Møller--Plesser perturbation theory, and the orbital pairs for which the pair energies change significantly are identified. This multi-level approach is significantly more robust than our previously suggested, orbital selection-based multi-level DLPNO-CCSD(T0) ansatz [ J. Chem. Phys. 2021, 155, 224102] for reactions showing only small changes in the occupied orbitals. At the same time, it is even more efficient without added input complexity or accuracy loss compared to the full DLPNO-CCSD(T0) calculation. We demonstrate the accuracy of the multi-level approach for a total of 128 chemical reactions and potential energy curves of weakly interacting complexes from the S66x8 benchmark set.
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Affiliation(s)
- Moritz Bensberg
- Westfälische Wilhelms-Universität Münster Fachbereich 12 Chemie und Pharmazie, Germany
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch-Chemisches Institut, Westfälische Wilhelms-Universität Münster Fachbereich 12 Chemie und Pharmazie, Germany
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45
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Barcza B, Szirmai ÁB, Szántó KJ, Tajti A, Szalay PG. Comparison of approximate intermolecular potentials for ab initio fragment calculations on medium sized N-heterocycles. J Comput Chem 2022; 43:1079-1093. [PMID: 35478353 PMCID: PMC9321956 DOI: 10.1002/jcc.26866] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Revised: 03/26/2022] [Accepted: 03/29/2022] [Indexed: 01/15/2023]
Abstract
The ground state intermolecular potential of bimolecular complexes of N-heterocycles is analyzed for the impact of individual terms in the interaction energy as provided by various, conceptually different theories. Novel combinations with several formulations of the electrostatic, Pauli repulsion, and dispersion contributions are tested at both short- and long-distance sides of the potential energy surface, for various alignments of the pyrrole dimer as well as the cytosine-uracil complex. The integration of a DFT/CCSD density embedding scheme, with dispersion terms from the effective fragment potential (EFP) method is found to provide good agreement with a reference CCSD(T) potential overall; simultaneously, a quantum mechanics/molecular mechanics approach using CHELPG atomic point charges for the electrostatic interaction, augmented by EFP dispersion and Pauli repulsion, comes also close to the reference result. Both schemes have the advantage of not relying on predefined force fields; rather, the interaction parameters can be determined for the system under study, thus being excellent candidates for ab initio modeling.
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Affiliation(s)
- Bónis Barcza
- Institute of Chemistry, Laboratory of Theoretical ChemistryELTE Eötvös Loránd UniversityBudapestHungary
| | - Ádám B. Szirmai
- Institute of Chemistry, Laboratory of Theoretical ChemistryELTE Eötvös Loránd UniversityBudapestHungary
| | - Katalin J. Szántó
- Institute of Chemistry, Laboratory of Theoretical ChemistryELTE Eötvös Loránd UniversityBudapestHungary
| | - Attila Tajti
- Institute of Chemistry, Laboratory of Theoretical ChemistryELTE Eötvös Loránd UniversityBudapestHungary
| | - Péter G. Szalay
- Institute of Chemistry, Laboratory of Theoretical ChemistryELTE Eötvös Loránd UniversityBudapestHungary
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46
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Liang W, Pei Z, Mao Y, Shao Y. Evaluation of molecular photophysical and photochemical properties using linear response time-dependent density functional theory with classical embedding: Successes and challenges. J Chem Phys 2022; 156:210901. [PMID: 35676148 PMCID: PMC9162785 DOI: 10.1063/5.0088271] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Accepted: 05/15/2022] [Indexed: 01/04/2023] Open
Abstract
Time-dependent density functional theory (TDDFT) based approaches have been developed in recent years to model the excited-state properties and transition processes of the molecules in the gas-phase and in a condensed medium, such as in a solution and protein microenvironment or near semiconductor and metal surfaces. In the latter case, usually, classical embedding models have been adopted to account for the molecular environmental effects, leading to the multi-scale approaches of TDDFT/polarizable continuum model (PCM) and TDDFT/molecular mechanics (MM), where a molecular system of interest is designated as the quantum mechanical region and treated with TDDFT, while the environment is usually described using either a PCM or (non-polarizable or polarizable) MM force fields. In this Perspective, we briefly review these TDDFT-related multi-scale models with a specific emphasis on the implementation of analytical energy derivatives, such as the energy gradient and Hessian, the nonadiabatic coupling, the spin-orbit coupling, and the transition dipole moment as well as their nuclear derivatives for various radiative and radiativeless transition processes among electronic states. Three variations of the TDDFT method, the Tamm-Dancoff approximation to TDDFT, spin-flip DFT, and spin-adiabatic TDDFT, are discussed. Moreover, using a model system (pyridine-Ag20 complex), we emphasize that caution is needed to properly account for system-environment interactions within the TDDFT/MM models. Specifically, one should appropriately damp the electrostatic embedding potential from MM atoms and carefully tune the van der Waals interaction potential between the system and the environment. We also highlight the lack of proper treatment of charge transfer between the quantum mechanics and MM regions as well as the need for accelerated TDDFT modelings and interpretability, which calls for new method developments.
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Affiliation(s)
- WanZhen Liang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China
| | - Zheng Pei
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China
| | - Yuezhi Mao
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Yihan Shao
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, USA
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47
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Sirianni DA, Zhu X, Sitkoff DF, Cheney DL, Sherrill CD. The influence of a solvent environment on direct non-covalent interactions between two molecules: A symmetry-adapted perturbation theory study of polarization tuning of π-π interactions by water. J Chem Phys 2022; 156:194306. [PMID: 35597646 DOI: 10.1063/5.0087302] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
High-level quantum chemical computations have provided significant insight into the fundamental physical nature of non-covalent interactions. These studies have focused primarily on gas-phase computations of small van der Waals dimers; however, these interactions frequently take place in complex chemical environments, such as proteins, solutions, or solids. To better understand how the chemical environment affects non-covalent interactions, we have undertaken a quantum chemical study of π-π interactions in an aqueous solution, as exemplified by T-shaped benzene dimers surrounded by 28 or 50 explicit water molecules. We report interaction energies (IEs) using second-order Møller-Plesset perturbation theory, and we apply the intramolecular and functional-group partitioning extensions of symmetry-adapted perturbation theory (ISAPT and F-SAPT, respectively) to analyze how the solvent molecules tune the π-π interactions of the solute. For complexes containing neutral monomers, even 50 explicit waters (constituting a first and partial second solvation shell) change total SAPT IEs between the two solute molecules by only tenths of a kcal mol-1, while significant changes of up to 3 kcal mol-1 of the electrostatic component are seen for the cationic pyridinium-benzene dimer. This difference between charged and neutral solutes is attributed to large non-additive three-body interactions within solvated ion-containing complexes. Overall, except for charged solutes, our quantum computations indicate that nearby solvent molecules cause very little "tuning" of the direct solute-solute interactions. This indicates that differences in binding energies between the gas phase and solution phase are primarily indirect effects of the competition between solute-solute and solute-solvent interactions.
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Affiliation(s)
- Dominic A Sirianni
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA
| | - Xiao Zhu
- Molecular Structure and Design, Bristol Myers Squibb Company, P.O. Box 5400, Princeton, New Jersey 08543, USA
| | - Doree F Sitkoff
- Molecular Structure and Design, Bristol Myers Squibb Company, P.O. Box 5400, Princeton, New Jersey 08543, USA
| | - Daniel L Cheney
- Molecular Structure and Design, Bristol Myers Squibb Company, P.O. Box 5400, Princeton, New Jersey 08543, USA
| | - C David Sherrill
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA
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48
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Xu J, Zhou R, Tao Z, Malbon C, Blum V, Hammes-Schiffer S, Kanai Y. Nuclear-Electronic Orbital Approach to Quantization of Protons in Periodic Electronic Structure Calculations. J Chem Phys 2022; 156:224111. [DOI: 10.1063/5.0088427] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The nuclear-electronic orbital (NEO) method is a well-established approach for treating nuclei quantum mechanically in molecular systems beyond the usual Born-Oppenheimer approximation. In this work, we present a strategy to implement the NEO method for periodic electronic structure calculations, particularly focused on multicomponent density functional theory (DFT). The NEO-DFT method is implemented in an all-electron electronic structure code, FHI-aims, using a combination of analytical and numerical integration techniques as well as a resolution of the identity scheme to enhance computational efficiency. After validating this implementation, proof-of-concept applications are presented to illustrate the effects of quantized protons on the physical properties of extended systems such as two-dimensional materials and liquid-semiconductor interfaces. Specifically, periodic NEO-DFT calculations are performed for a trans-polyacetylene chain, a hydrogen boride sheet, and a titanium oxide-water interface. The zero-point energy effects of the protons, as well as electron-proton correlation, are shown to noticeably impact the density of states and band structures for these systems. These developments provide a foundation for the application of multicomponent DFT to a wide range of other extended condensed matter systems.
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Affiliation(s)
- Jianhang Xu
- Chemistry, The University of North Carolina at Chapel Hill, United States of America
| | | | - Zhen Tao
- Yale University, United States of America
| | | | - Volker Blum
- Duke University Department of Mechanical Engineering and Materials Science, United States of America
| | | | - Yosuke Kanai
- Department of Chemistry, University of North Carolina at Chapel Hill, United States of America
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49
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Jagau TC. Theory of electronic resonances: fundamental aspects and recent advances. Chem Commun (Camb) 2022; 58:5205-5224. [PMID: 35395664 DOI: 10.1039/d1cc07090h] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Abstract
Electronic resonances are states that are unstable towards loss of electrons. They play critical roles in high-energy environments across chemistry, physics, and biology but are also relevant to processes under ambient conditions that involve unbound electrons. This feature article focuses on complex-variable techniques such as complex scaling and complex absorbing potentials that afford a treatment of electronic resonances in terms of discrete square-integrable eigenstates of non-Hermitian Hamiltonians with complex energy. Fundamental aspects of these techniques as well as their integration into molecular electronic-structure theory are discussed and an overview of some recent developments is given: analytic gradient theory for electronic resonances, the application of rank-reduction techniques and quantum embedding to them, as well as approaches for evaluating partial decay widths.
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Affiliation(s)
- Thomas-C Jagau
- Department of Chemistry, KU Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium.
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Samanta B, Morales-García Á, Illas F, Goga N, Anta JA, Calero S, Bieberle-Hütter A, Libisch F, Muñoz-García AB, Pavone M, Caspary Toroker M. Challenges of modeling nanostructured materials for photocatalytic water splitting. Chem Soc Rev 2022; 51:3794-3818. [PMID: 35439803 DOI: 10.1039/d1cs00648g] [Citation(s) in RCA: 26] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
Understanding the water splitting mechanism in photocatalysis is a rewarding goal as it will allow producing clean fuel for a sustainable life in the future. However, identifying the photocatalytic mechanisms by modeling photoactive nanoparticles requires sophisticated computational techniques based on multiscale modeling. In this review, we will survey the strengths and drawbacks of currently available theoretical methods at different length and accuracy scales. Understanding the surface-active site through Density Functional Theory (DFT) using new, more accurate exchange-correlation functionals plays a key role for surface engineering. Larger scale dynamics of the catalyst/electrolyte interface can be treated with Molecular Dynamics albeit there is a need for more generalizations of force fields. Monte Carlo and Continuum Modeling techniques are so far not the prominent path for modeling water splitting but interest is growing due to the lower computational cost and the feasibility to compare the modeling outcome directly to experimental data. The future challenges in modeling complex nano-photocatalysts involve combining different methods in a hierarchical way so that resources are spent wisely at each length scale, as well as accounting for excited states chemistry that is important for photocatalysis, a path that will bring devices closer to the theoretical limit of photocatalytic efficiency.
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Affiliation(s)
- Bipasa Samanta
- Department of Materials Science and Engineering, Technion - Israel Institute of Technology, Haifa 3600003, Israel
| | - Ángel Morales-García
- Departament de Ciència de Materials i Química Física & Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona, c/Martí i Franquès 1-11, 08028 Barcelona, Spain.
| | - Francesc Illas
- Departament de Ciència de Materials i Química Física & Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona, c/Martí i Franquès 1-11, 08028 Barcelona, Spain.
| | - Nicolae Goga
- Faculty of Engineering in Foreign Languages, Universitatea Politehnica din Bucuresti, Bucuresti, Romania.
| | - Juan Antonio Anta
- Department of Physical, Chemical and Natural Systems, Universidad Pablo de Olavide, Crta. De Utrera km. 1, 41089 Sevilla, Spain.
| | - Sofia Calero
- Materials Simulation & Modeling, Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
| | - Anja Bieberle-Hütter
- Electrochemical Materials and Interfaces, Dutch Institute for Fundamental Energy Research (DIFFER), 5600 HH Eindhoven, The Netherlands.
| | - Florian Libisch
- Institute for Theoretical Physics, TU Wien, 1040 Vienna, Austria.
| | - Ana B Muñoz-García
- Dipartimento di Fisica "Ettore Pancini", Università di Napoli Federico II, Via Cintia 21, Napoli 80126, Italy.
| | - Michele Pavone
- Dipartimento di Scienze Chimiche, Università di Napoli Federico II, Via Cintia 21, Napoli 80126, Italy.
| | - Maytal Caspary Toroker
- Department of Materials Science and Engineering, Technion - Israel Institute of Technology, Haifa 3600003, Israel.,The Nancy and Stephen Grand Technion Energy Program, Technion - Israel Institute of Technology, Haifa 3600003, Israel.
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