1
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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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2
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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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3
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Van den Heuvel W, Reinholdt P, Kongsted J. Embedding Beyond Electrostatics: The Extended Polarizable Density Embedding Model. J Phys Chem B 2023; 127:3248-3256. [PMID: 37002869 DOI: 10.1021/acs.jpcb.2c08721] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023]
Abstract
The polarizable density embedding (PDE) model is a focused QM/QM fragment-based embedding model designed to model solvation effects on molecular properties. We extend the PDE model to include exchange and nonadditive exchange-correlation (for DFT) in the embedding potential in addition to the existing electrostatic, polarization, and nonelectrostatic effects already present. The resulting model, termed PDE-X, yields localized electronic excitation energies that accurately capture the range dependence of the solvent interaction and gives close agreement with full quantum mechanical (QM) results, even when using minimal QM regions. We show that the PDE-X embedding description consistently improves the accuracy of excitation energies for a diverse set of organic chromophores. The improved embedding description leads to systematic solvent effects that do not average out when applying configurational sampling.
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Affiliation(s)
- Willem Van den Heuvel
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark
| | - Peter Reinholdt
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark
| | - Jacob Kongsted
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark
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4
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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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5
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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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6
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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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7
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Shao X, Lopez AC, Khan Musa MR, Nouri MR, Pavanello M. Adaptive Subsystem Density Functional Theory. J Chem Theory Comput 2022; 18:6646-6655. [PMID: 36179128 DOI: 10.1021/acs.jctc.2c00698] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Subsystem density functional theory (DFT) is emerging as a powerful electronic structure method for large-scale simulations of molecular condensed phases and interfaces. Key to its computational efficiency is the use of approximate nonadditive noninteracting kinetic energy functionals. Unfortunately, currently available nonadditive functionals lead to inaccurate results when the subsystems interact strongly such as when they engage in chemical reactions. This work disrupts the status quo by devising a workflow that extends subsystem DFT's applicability also to strongly interacting subsystems. This is achieved by implementing a fully automated adaptive definition of subsystems which is realized during geometry optimizations or ab initio molecular dynamics simulations. The new method prescribes subsystem merging and splitting events redistributing the resources (both for work and data) in an efficient way making use of modern parallelization strategies and object-oriented programming. We showcase the method with examples probing from moderate-to-strong inter-subsystem interactions, opening the door to using subsystem DFT for modeling chemical reactions in molecular condensed phases with a black box computational tool.
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Affiliation(s)
- Xuecheng Shao
- Department of Chemistry, Rutgers University, Newark, New Jersey07102, United States
| | | | - Md Rajib Khan Musa
- Department of Chemistry, Rutgers University, Newark, New Jersey07102, United States
| | - Mohammad Reza Nouri
- Department of Chemistry, Rutgers University, Newark, New Jersey07102, United States
| | - Michele Pavanello
- Department of Physics, Rutgers University, Newark, New Jersey07102, United States
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8
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Treß RS, Hättig C, Höfener S. Employing Pseudopotentials to Tackle Excited-State Electron Spill-Out in Frozen Density Embedding Calculations. J Chem Theory Comput 2022; 18:1737-1747. [PMID: 35107998 DOI: 10.1021/acs.jctc.1c00732] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
In frozen density embedding (FDE), the properties of a target molecule are computed in the presence of an effective embedding potential, which accounts for the attractive and repulsive contributions of the environment. The formally exact embedding potential, however, is in practice calculated using explicit kinetic-energy functionals for which the resulting potentials are in many cases not repulsive enough to account fully for Pauli repulsion by the electrons of the environment and to compensate thereby the strong electron-nuclear attraction. For the excited states on the target molecule, this leads to charge spill-out when diffuse basis functions are included, which allow that valence electrons are excited to those regions of the environment where the strong nuclear attraction is not sufficiently compensated by repulsive contributions. To reduce this insufficiency, we propose in the present work the inclusion of atomic all-electron pseudopotentials for all environment atoms on top of the conventional embedding potential. In the current work, the pseudopotentials are applied for computing vertical excitation energies of local excited states in complex systems employing the second-order algebraic diagrammatic construction (ADC(2)) scheme. The proposed approach leads to significantly reduced charge spill-out and an improved agreement of FDE and supermolecular calculations in the frozen solvent approximation. In particular, when diffuse functions are employed, the mean absolute deviation (MAD) is reduced from 0.27 to 0.05 eV for the investigated cases.
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Affiliation(s)
- Robert S Treß
- Department of Theoretical Chemistry, Ruhr University Bochum, Bochum 44801, Germany
| | - Christof Hättig
- Department of Theoretical Chemistry, Ruhr University Bochum, Bochum 44801, Germany
| | - Sebastian Höfener
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe 76131, Germany
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9
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Harshan AK, Bronson MJ, Jensen L. Local-Field Effects in Linear Response Properties within a Polarizable Frozen Density Embedding Method. J Chem Theory Comput 2021; 18:380-393. [PMID: 34905917 DOI: 10.1021/acs.jctc.1c00816] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
In this work, we present a polarizable frozen density embedding (FDE) method for calculating polarizabilities of coupled subsystems. The method (FDE-pol) combines a FDE method with an explicit polarization model such that the expensive freeze/thaw cycles can be bypassed, and approximate nonadditive kinetic potentials are avoided by enforcing external orthogonality between the subsystems. To describe the polarization of the frozen environment, we introduce a Hirshfeld partition-based density-dependent method for calculating the atomic polarizabilities of atoms in molecules, which alleviates the need to fit the atomic parameters to a specific system of interest or to a larger general set of molecules. We show that the Hirshfeld partition-based method predicts molecular polarizabilities close to the basis set limit, and thus, a single basis set-dependent scaling parameter can be introduced to improve the agreement against the reference polarizability data. To test the model, we characterized the uncoupled and coupled response of small interacting molecular complexes. Here, the coupled response properties include the perturbation of the frozen system due to the external perturbation which is ignored in the uncoupled response. We show that FDE-pol can accurately reproduce both the exact uncoupled polarizability and the coupled polarizabilities of the supermolecular systems. Using damped response theory, we also demonstrate that the coupled frequency-dependent polarizability can be described by including local field effects. The results emphasize the necessity of including local-field effects for describing the response properties of coupled subsystems, as well as the importance of accurate atomic polarizability models.
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Affiliation(s)
- Aparna K Harshan
- Department of Chemistry, The Pennsylvania State University, 104 Chemistry Building, University Park 16802, United States
| | - Mark J Bronson
- Department of Chemistry, The Pennsylvania State University, 104 Chemistry Building, University Park 16802, United States
| | - Lasse Jensen
- Department of Chemistry, The Pennsylvania State University, 104 Chemistry Building, University Park 16802, United States
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10
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Giannone G, Śmiga S, D'Agostino S, Fabiano E, Della Sala F. Plasmon Couplings from Subsystem Time-Dependent Density Functional Theory. J Phys Chem A 2021; 125:7246-7259. [PMID: 34403247 DOI: 10.1021/acs.jpca.1c05384] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Many applications in plasmonics are related to the coupling between metallic nanoparticles (MNPs) or between an emitter and a MNP. The theoretical analysis of such a coupling is thus of fundamental importance to analyze the plasmonic behavior and to design new systems. While classical methods neglect quantum and spill-out effects, time-dependent density functional theory (TD-DFT) considers all of them and with Kohn-Sham orbitals delocalized over the whole system. Thus, within TD-DFT, no definite separation of the subsystems (the single MNP or the emitter) and their couplings is directly available. This important feature is obtained here using the subsystem formulation of TD-DFT, which has been originally developed in the context of weakly interacting organic molecules. In subsystem TD-DFT, interacting MNPs are treated independently, thus allowing us to compute the plasmon couplings directly from the subsystem TD-DFT transition densities. We show that subsystem TD-DFT, as well as a simplified version of it in which kinetic contributions are neglected, can reproduce the reference TD-DFT calculations for gap distances greater than about 6 Å or even smaller in the case of hybrid plasmonic systems (i.e., molecules interacting with MNPs). We also show that the subsystem TD-DFT can be also used as a tool to analyze the impact of charge-transfer effects.
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Affiliation(s)
- Giulia Giannone
- Center for Biomolecular Nanotechnologies, Istituto Italiano di Tecnologia, Via Barsanti 14, Arnesano (LE) 73010, Italy.,Department of Mathematics and Physics "E. De Giorgi", University of Salento, Via Arnesano, Lecce 73100, Italy
| | - Szymon Śmiga
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudzia̧dzka 5, Toruń 87-100, Poland
| | - Stefania D'Agostino
- Center for Biomolecular Nanotechnologies, Istituto Italiano di Tecnologia, Via Barsanti 14, Arnesano (LE) 73010, Italy.,Department of Mathematics and Physics "E. De Giorgi", University of Salento, Via Arnesano, Lecce 73100, Italy.,Institute of Nanotechnology, National Research Council (CNR-NANOTEC), c/o Campus Ecotekne, via Monteroni, Lecce 73100, Italy
| | - Eduardo Fabiano
- Center for Biomolecular Nanotechnologies, Istituto Italiano di Tecnologia, Via Barsanti 14, Arnesano (LE) 73010, Italy.,Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, Lecce 73100, Italy
| | - Fabio Della Sala
- Center for Biomolecular Nanotechnologies, Istituto Italiano di Tecnologia, Via Barsanti 14, Arnesano (LE) 73010, Italy.,Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, Lecce 73100, Italy
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11
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Wang Z, Liu W. iOI: An Iterative Orbital Interaction Approach for Solving the Self-Consistent Field Problem. J Chem Theory Comput 2021; 17:4831-4845. [PMID: 34240856 DOI: 10.1021/acs.jctc.1c00445] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
An iterative orbital interaction (iOI) approach is proposed to solve, in a bottom-up fashion, the self-consistent field problem in quantum chemistry. While it belongs grossly to the family of fragment-based quantum chemical methods, iOI is distinctive in that (1) it divides and conquers not only the energy but also the wave function and that (2) the subsystem sizes are automatically determined by successively merging neighboring small subsystems until they are just enough for converging the wave function to a given accuracy. Orthonormal occupied and virtual localized molecular orbitals are obtained in a natural manner, which can be used for all post-SCF purposes.
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Affiliation(s)
- Zikuan Wang
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, P. R. China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, P. R. China
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12
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Graham DS, Wen X, Chulhai DV, Goodpaster JD. Robust, Accurate, and Efficient: Quantum Embedding Using the Huzinaga Level-Shift Projection Operator for Complex Systems. J Chem Theory Comput 2020; 16:2284-2295. [DOI: 10.1021/acs.jctc.9b01185] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Daniel S. Graham
- Department of Chemistry, University of Minnesota, 207 Pleasant St. SE, Minneapolis, Minnesota 55455, United States
| | - Xuelan Wen
- Department of Chemistry, University of Minnesota, 207 Pleasant St. SE, Minneapolis, Minnesota 55455, United States
| | - Dhabih V. Chulhai
- Department of Chemistry, University of Minnesota, 207 Pleasant St. SE, Minneapolis, Minnesota 55455, United States
| | - Jason D. Goodpaster
- Department of Chemistry, University of Minnesota, 207 Pleasant St. SE, Minneapolis, Minnesota 55455, United States
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13
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Jones LO, Mosquera MA, Schatz GC, Ratner MA. Embedding Methods for Quantum Chemistry: Applications from Materials to Life Sciences. J Am Chem Soc 2020; 142:3281-3295. [PMID: 31986877 DOI: 10.1021/jacs.9b10780] [Citation(s) in RCA: 58] [Impact Index Per Article: 14.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
Quantum mechanical embedding methods hold the promise to transform not just the way calculations are performed, but to significantly reduce computational costs and improve scaling for macro-molecular systems containing hundreds if not thousands of atoms. The field of embedding has grown increasingly broad with many approaches of different intersecting flavors. In this perspective, we lay out the methods into two streams: QM:MM and QM:QM, showcasing the advantages and disadvantages of both. We provide a review of the literature, the underpinning theories including our contributions, and we highlight current applications with select examples spanning both materials and life sciences. We conclude with prospects and future outlook on embedding, and our view on the use of universal test case scenarios for cross-comparisons of the many available (and future) embedding theories.
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Affiliation(s)
- Leighton O Jones
- Department of Chemistry , Northwestern University , Evanston , Illinois 60208 , United States
| | - Martín A Mosquera
- Department of Chemistry , Northwestern University , Evanston , Illinois 60208 , United States
| | - George C Schatz
- Department of Chemistry , Northwestern University , Evanston , Illinois 60208 , United States
| | - Mark A Ratner
- Department of Chemistry , Northwestern University , Evanston , Illinois 60208 , United States
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14
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Wen X, Graham DS, Chulhai DV, Goodpaster JD. Absolutely Localized Projection-Based Embedding for Excited States. J Chem Theory Comput 2019; 16:385-398. [DOI: 10.1021/acs.jctc.9b00959] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Xuelan Wen
- Department of Chemistry, University of Minnesota, 207 Pleasant Street Southeast, Minneapolis, Minnesota 55455, United States
| | - Daniel S. Graham
- Department of Chemistry, University of Minnesota, 207 Pleasant Street Southeast, Minneapolis, Minnesota 55455, United States
| | - Dhabih V. Chulhai
- Department of Chemistry, University of Minnesota, 207 Pleasant Street Southeast, Minneapolis, Minnesota 55455, United States
| | - Jason D. Goodpaster
- Department of Chemistry, University of Minnesota, 207 Pleasant Street Southeast, Minneapolis, Minnesota 55455, United States
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15
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Pal PP, Liu P, Jensen L. Polarizable Frozen Density Embedding with External Orthogonalization. J Chem Theory Comput 2019; 15:6588-6596. [DOI: 10.1021/acs.jctc.9b00472] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Partha Pratim Pal
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Pengchong Liu
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Lasse Jensen
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
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16
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Bensberg M, Neugebauer J. Direct orbital selection for projection-based embedding. J Chem Phys 2019; 150:214106. [DOI: 10.1063/1.5099007] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Affiliation(s)
- Moritz Bensberg
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 40, 48149 Münster, Germany
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 40, 48149 Münster, Germany
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17
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Bensberg M, Neugebauer J. Automatic basis-set adaptation in projection-based embedding. J Chem Phys 2019; 150:184104. [DOI: 10.1063/1.5084550] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Moritz Bensberg
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 40, 48149 Münster, Germany
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 40, 48149 Münster, Germany
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18
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Schnieders D, Neugebauer J. Accurate embedding through potential reconstruction: A comparison of different strategies. J Chem Phys 2018; 149:054103. [DOI: 10.1063/1.5037638] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- David Schnieders
- Organisch-Chemisches Institut, Westfälische Wilhelms-Universität Münster and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 40, 48149 Münster, Germany
| | - Johannes Neugebauer
- Organisch-Chemisches Institut, Westfälische Wilhelms-Universität Münster and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 40, 48149 Münster, Germany
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19
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Zech A, Ricardi N, Prager S, Dreuw A, Wesolowski TA. Benchmark of Excitation Energy Shifts from Frozen-Density Embedding Theory: Introduction of a Density-Overlap-Based Applicability Threshold. J Chem Theory Comput 2018; 14:4028-4040. [DOI: 10.1021/acs.jctc.8b00201] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Alexander Zech
- Department of Physical Chemistry, University of Geneva, Geneva, Switzerland
| | - Niccolò Ricardi
- Department of Physical Chemistry, University of Geneva, Geneva, Switzerland
| | - Stefan Prager
- Interdisciplinary Center for Scientific Computing, University of Heidelberg, Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, University of Heidelberg, Heidelberg, Germany
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20
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Chulhai DV, Goodpaster JD. Projection-Based Correlated Wave Function in Density Functional Theory Embedding for Periodic Systems. J Chem Theory Comput 2018; 14:1928-1942. [DOI: 10.1021/acs.jctc.7b01154] [Citation(s) in RCA: 55] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Affiliation(s)
- Dhabih V. Chulhai
- Department of Chemistry, University of Minnesota, 207 Pleasant St. SE, Minneapolis, Minnesota 55455, United States
| | - Jason D. Goodpaster
- Department of Chemistry, University of Minnesota, 207 Pleasant St. SE, Minneapolis, Minnesota 55455, United States
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21
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Unsleber JP, Dresselhaus T, Klahr K, Schnieders D, Böckers M, Barton D, Neugebauer J. Serenity: A subsystem quantum chemistry program. J Comput Chem 2018; 39:788-798. [DOI: 10.1002/jcc.25162] [Citation(s) in RCA: 44] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2017] [Revised: 11/08/2017] [Accepted: 12/15/2017] [Indexed: 12/24/2022]
Affiliation(s)
- Jan P. Unsleber
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster Corrensstraße 40; Münster 48149 Germany
| | - Thomas Dresselhaus
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster Corrensstraße 40; Münster 48149 Germany
| | - Kevin Klahr
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster Corrensstraße 40; Münster 48149 Germany
| | - David Schnieders
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster Corrensstraße 40; Münster 48149 Germany
| | - Michael Böckers
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster Corrensstraße 40; Münster 48149 Germany
| | - Dennis Barton
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster Corrensstraße 40; Münster 48149 Germany
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster Corrensstraße 40; Münster 48149 Germany
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22
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Reinholdt P, Kongsted J, Olsen JMH. Polarizable Density Embedding: A Solution to the Electron Spill-Out Problem in Multiscale Modeling. J Phys Chem Lett 2017; 8:5949-5958. [PMID: 29178794 DOI: 10.1021/acs.jpclett.7b02788] [Citation(s) in RCA: 42] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We analyze the performance of the polarizable density embedding (PDE) model-a new multiscale computational approach designed for prediction and rationalization of general molecular properties of large and complex systems. We showcase how the PDE model very effectively handles the use of large and diffuse basis sets that are otherwise questionable-due to electron spill-out effects-in standard embedding models. Based on our analysis, we find the PDE model to be robust and much more systematic than less sophisticated focused embedding models, and thus outline the PDE model as a very efficient and accurate approach to describe the electronic structure of ground and excited states as well as molecular properties of complex, heterogeneous systems.
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Affiliation(s)
- Peter Reinholdt
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark , Campusvej 55, DK-5230 Odense M, Denmark
| | - Jacob Kongsted
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark , Campusvej 55, DK-5230 Odense M, Denmark
| | - Jógvan Magnus Haugaard Olsen
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark , Campusvej 55, DK-5230 Odense M, Denmark
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23
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Libisch F, Marsman M, Burgdörfer J, Kresse G. Embedding for bulk systems using localized atomic orbitals. J Chem Phys 2017; 147:034110. [DOI: 10.1063/1.4993795] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- F. Libisch
- Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria, EU
| | - M. Marsman
- Faculty of Physics and Center for Computational Materials Science, University of Vienna, Sensengasse 8/12, A-1090 Vienna, Austria, EU
| | - J. Burgdörfer
- Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria, EU
| | - G. Kresse
- Faculty of Physics and Center for Computational Materials Science, University of Vienna, Sensengasse 8/12, A-1090 Vienna, Austria, EU
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24
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Chulhai DV, Goodpaster JD. Improved Accuracy and Efficiency in Quantum Embedding through Absolute Localization. J Chem Theory Comput 2017; 13:1503-1508. [DOI: 10.1021/acs.jctc.7b00034] [Citation(s) in RCA: 39] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Dhabih V. Chulhai
- Department of Chemistry, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455, United States
| | - Jason D. Goodpaster
- Department of Chemistry, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455, United States
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25
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Unsleber JP, Neugebauer J, Jacob CR. No need for external orthogonality in subsystem density-functional theory. Phys Chem Chem Phys 2016; 18:21001-9. [DOI: 10.1039/c6cp00332j] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Contrary to previous claims, there is no formal need for enforcing external orthogonality in subsystem density-functional theory.
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Affiliation(s)
- Jan P. Unsleber
- Theoretische Organische Chemie
- Organisch-Chemisches Institut and Center for Multiscale Theory and Computation
- Westfälische Wilhelms-Universität Münster
- 48149 Münster
- Germany
| | - Johannes Neugebauer
- Theoretische Organische Chemie
- Organisch-Chemisches Institut and Center for Multiscale Theory and Computation
- Westfälische Wilhelms-Universität Münster
- 48149 Münster
- Germany
| | - Christoph R. Jacob
- Institute of Physical and Theoretical Chemistry
- TU Braunschweig
- 38106 Braunschweig
- Germany
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26
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Chulhai DV, Jensen L. External orthogonality in subsystem time-dependent density functional theory. Phys Chem Chem Phys 2016; 18:21032-9. [DOI: 10.1039/c6cp00310a] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present a subsystem TDDFT method which maintains inter-subsystem orbital orthogonality.
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Affiliation(s)
- Dhabih V. Chulhai
- Department of Chemistry
- The Pennsylvania State University
- University Park
- USA
| | - Lasse Jensen
- Department of Chemistry
- The Pennsylvania State University
- University Park
- USA
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