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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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2
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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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3
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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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4
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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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5
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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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6
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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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7
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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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8
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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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9
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Abstract
Quantum embedding schemes are a promising way to extend multireference computations to large molecules with strong correlation effects localized on a small number of atoms. This work introduces a second-order active-space embedding theory [ASET(2)] which improves upon mean-field frozen embedding by treating fragment-environment interactions via an approximate canonical transformation. The canonical transformation employed in ASET(2) is formulated using the driven similarity renormalization group. The ASET(2) scheme is benchmarked on the N═N bond dissociation in pentyldiazene, the S0 to S1 excitation in 1-octene, and the interaction energy of the O2-benzene complex. The ASET(2) explicit treatment of fragment-environment interactions beyond the mean-field level generally improves the accuracy of embedded computations, and it becomes necessary to achieve an accurate description of excitation energies of 1-octene and the singlet-triplet gap of the O2-benzene complex.
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Affiliation(s)
- Nan He
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Chenyang Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Francesco A Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
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10
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Graham DS, Wen X, Chulhai DV, Goodpaster J. Huzinaga Projection Embedding for Efficient and Accurate Energies of Systems with Localized Spin-densities. J Chem Phys 2022; 156:054112. [DOI: 10.1063/5.0076493] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Xuelan Wen
- Department of Chemistry, University of Minnesota Twin Cities, United States of America
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11
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Waldrop JM, Windus TL, Govind N. Projector-Based Quantum Embedding for Molecular Systems: An Investigation of Three Partitioning Approaches. J Phys Chem A 2021; 125:6384-6393. [PMID: 34260852 DOI: 10.1021/acs.jpca.1c03821] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Projector-based embedding is a relatively recent addition to the collection of methods that seek to utilize chemical locality to provide improved computational efficiency. This work considers the interactions between the different proposed procedures for this method and their effects on the accuracy of the results. The interplay between the embedded background, projector type, partitioning scheme, and level of atomic orbital (AO) truncation are investigated on a selection of reactions from the literature. The Huzinaga projection approach proves to be more reliable than the level-shift projection when paired with other procedural options. Active subsystem partitioning from the subsystem projected AO decomposition (SPADE) procedure proves slightly better than the combination of Pipek-Mezey localization and Mulliken population screening (PMM). Along with these two options, a new partitioning criteria is proposed based on subsystem von Neumann entropy and the related subsystem orbital occupancy. This new method overlaps with the previous PMM method, but the screening process is computationally simpler. Finally, AO truncation proves to be a robust option for the tested systems when paired with the Huzinaga projection, with satisfactory results being acquired at even the most severe truncation level.
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Affiliation(s)
| | - Theresa L Windus
- Ames Laboratory, Ames, Iowa 50011, United States.,Department of Chemistry, Iowa State University, Ames, Iowa 50011, United States
| | - Niranjan Govind
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
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12
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Macetti G, Genoni A. Initial Maximum Overlap Method for Large Systems by the Quantum Mechanics/Extremely Localized Molecular Orbital Embedding Technique. J Chem Theory Comput 2021; 17:4169-4182. [PMID: 34196174 DOI: 10.1021/acs.jctc.1c00388] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Quantum chemistry offers a large variety of methods to treat excited states. Many of them are based on a multireference wave function ansatz and are therefore characterized by an intrinsic complexity and high computational costs. To overcome these drawbacks and also some limitations of simpler single-reference approaches (e.g., configuration interaction singles and time-dependent density functional theory), the single-determinant Δself-consistent field-initial maximum overlap method (ΔSCF-IMOM) has been proposed. This strategy substitutes the aufbau principle with a criterion that occupies molecular orbitals at successive SCF iterations on the basis of their maximum overlap with a proper set of guess orbitals for the target excited state. In this way, it prevents the SCF process to collapse to the ground state wave function and provides excited state single Slater determinant solutions to the SCF equations. Here, we propose to extend the applicability of the IMOM to the treatment of localized excited states of large systems. To accomplish this task, we coupled it with the QM/ELMO (quantum mechanics/extremely localized molecular orbitals) strategy, a quantum mechanical embedding method in which the most chemically relevant part of the system is treated with traditional quantum chemical approaches, while the rest is described by extremely localized molecular orbitals transferred from recently constructed libraries or proper model molecules. After presenting the theoretical foundations of the new IMOM/ELMO technique, in this paper, we will show and discuss the results of preliminary test calculations carried out on both model systems (i.e., decanoic acid, decene, decapentaene, and solvated acrolein) and a system of biological interest (flavin mononucleotide in the flavodoxin protein). We observed that, for localized excited states, the new IMOM/ELMO method provides reliable results, and it reproduces the outcomes of fully IMOM calculations within the chemical accuracy threshold (i.e., 0.043 eV) by including only a limited number of atoms in the QM region. Furthermore, the first application of our embedding technique to a larger biological system gave completely plausible results in line with those obtained through more traditional quantum mechanical methods, thus opening the possibility of using the new approach in future investigations of photobiology problems.
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Affiliation(s)
- Giovanni Macetti
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
| | - Alessandro Genoni
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
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13
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Carter-Fenk K, Mundy CJ, Herbert JM. Natural Charge-Transfer Analysis: Eliminating Spurious Charge-Transfer States in Time-Dependent Density Functional Theory via Diabatization, with Application to Projection-Based Embedding. J Chem Theory Comput 2021; 17:4195-4210. [PMID: 34189922 DOI: 10.1021/acs.jctc.1c00412] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
For many types of vertical excitation energies, linear-response time-dependent density functional theory (LR-TDDFT) offers a useful degree of accuracy combined with unrivaled computational efficiency, although charge-transfer excitation energies are often systematically and dramatically underestimated, especially for large systems and those that contain explicit solvent. As a result, low-energy electronic spectra of solution-phase chromophores often contain tens to hundreds of spurious charge-transfer states, making LR-TDDFT needlessly expensive in bulk solution. Intensity borrowing by these spurious states can affect intensities of the valence excitations, altering electronic bandshapes. At higher excitation energies, it is difficult to distinguish spurious charge-transfer states from genuine charge-transfer-to-solvent (CTTS) excitations. In this work, we introduce an automated diabatization that enables fast and effective screening of the CTTS acceptor space in bulk solution. Our procedure introduces "natural charge-transfer orbitals" that provide a means to isolate orbitals that are most likely to participate in a CTTS excitation. Projection of these orbitals onto solvent-centered virtual orbitals provides a criterion for defining the most important solvent molecules in a given excitation and be used as an automated subspace selection algorithm for projection-based embedding of a high-level description of the CTTS state in a lower-level description of its environment. We apply this method to an ab initio molecular dynamics trajectory of I-(aq) and report the lowest-energy CTTS band in the absorption spectrum. Our results are in excellent agreement with the experiment, and only one-third of the water molecules in the I-(H2O)96 simulation cell need to be described with LR-TDDFT to obtain excitation energies that are converged to <0.1 eV. The tools introduced herein will improve the accuracy, efficiency, and usability of LR-TDDFT in solution-phase environments.
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Affiliation(s)
- Kevin Carter-Fenk
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Christopher J Mundy
- Physical Science Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States.,Department of Chemical Engineering, University of Washington, Seattle, Washington 98195, United States
| | - John M Herbert
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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14
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Parravicini V, Jagau TC. Embedded equation-of-motion coupled-cluster theory for electronic excitation, ionisation, electron attachment, and electronic resonances. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1943029] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Valentina Parravicini
- Department of Chemistry, KU Leuven, Leuven, BelgiumThis article is dedicated to Professor John Stanton on the occasion of his 60th birthday
| | - Thomas-C. Jagau
- Department of Chemistry, KU Leuven, Leuven, BelgiumThis article is dedicated to Professor John Stanton on the occasion of his 60th birthday
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15
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Martirez JMP, Carter EA. Projector-Free Capped-Fragment Scheme within Density Functional Embedding Theory for Covalent and Ionic Compounds. J Chem Theory Comput 2021; 17:4105-4121. [DOI: 10.1021/acs.jctc.1c00285] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- John Mark P. Martirez
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, United States
| | - Emily A. Carter
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, United States
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16
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Egidi F, Angelico S, Lafiosca P, Giovannini T, Cappelli C. A polarizable three-layer frozen density embedding/molecular mechanics approach. J Chem Phys 2021; 154:164107. [PMID: 33940798 DOI: 10.1063/5.0045574] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
We present a novel multilayer polarizable embedding approach in which the system is divided into three portions, two of which are treated using density functional theory and their interaction is based on frozen density embedding (FDE) theory, and both also mutually interact with a polarizable classical layer described using an atomistic model based on fluctuating charges (FQ). The efficacy of the model is demonstrated by extending the formalism to linear response properties and applying it to the simulation of the excitation energies of organic molecules in aqueous solution, where the solute and the first solvation shell are treated using FDE, while the rest of the solvent is modeled using FQ charges.
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Affiliation(s)
- Franco Egidi
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Sara Angelico
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Piero Lafiosca
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Tommaso Giovannini
- 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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17
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Senjean B, Sen S, Repisky M, Knizia G, Visscher L. Generalization of Intrinsic Orbitals to Kramers-Paired Quaternion Spinors, Molecular Fragments, and Valence Virtual Spinors. J Chem Theory Comput 2021; 17:1337-1354. [PMID: 33555866 DOI: 10.1021/acs.jctc.0c00964] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Abstract
Localization of molecular orbitals finds its importance in the representation of chemical bonding (and antibonding) and in the local correlation treatments beyond mean-field approximation. In this paper, we generalize the intrinsic atomic and bonding orbitals [G. Knizia, J. Chem. Theory Comput. 2013, 9, 11, 4834-4843] to relativistic applications using complex and quaternion spinors, as well as to molecular fragments instead of atomic fragments only. By performing a singular value decomposition, we show how localized valence virtual orbitals can be expressed on this intrinsic minimal basis. We demonstrate our method on systems of increasing complexity, starting from simple cases such as benzene, acrylic acid, and ferrocene molecules, and then demonstrate the use of molecular fragments and inclusion of relativistic effects for complexes containing heavy elements such as tellurium, iridium, and astatine. The aforementioned scheme is implemented into a standalone program interfaced with several different quantum chemistry packages.
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Affiliation(s)
- Bruno Senjean
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
| | - Souloke Sen
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, The Netherlands
| | - Michal Repisky
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Gerald Knizia
- Department of Chemistry, The Pennsylvania State University, University Park, State College, Pennsylvania 16802, United States
| | - Lucas Visscher
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, The Netherlands
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18
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Macetti G, Wieduwilt EK, Genoni A. QM/ELMO: A Multi-Purpose Fully Quantum Mechanical Embedding Scheme Based on Extremely Localized Molecular Orbitals. J Phys Chem A 2021; 125:2709-2726. [DOI: 10.1021/acs.jpca.0c11450] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Affiliation(s)
- Giovanni Macetti
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
| | - Erna K. Wieduwilt
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
| | - Alessandro Genoni
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
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19
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Marrazzini G, Giovannini T, Scavino M, Egidi F, Cappelli C, Koch H. Multilevel Density Functional Theory. J Chem Theory Comput 2021; 17:791-803. [PMID: 33449681 PMCID: PMC7880574 DOI: 10.1021/acs.jctc.0c00940] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
![]()
Following recent
developments in multilevel embedding methods,
we introduce a novel density matrix-based multilevel approach within
the framework of density functional theory (DFT). In this multilevel
DFT, the system is partitioned in an active and an inactive fragment,
and all interactions are retained between the two parts. The decomposition
of the total system is performed upon the density matrix. The orthogonality
between the two parts is maintained by solving the Kohn–Sham
equations in the MO basis for the active part only, while keeping
the inactive density matrix frozen. This results in the reduction
of computational cost. We outline the theory and implementation and
discuss the differences and similarities with state-of-the-art DFT
embedding methods. We present applications to aqueous solutions of
methyloxirane and glycidol.
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Affiliation(s)
- Gioia Marrazzini
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Tommaso Giovannini
- Department of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway
| | - Marco Scavino
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Franco Egidi
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Chiara Cappelli
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Henrik Koch
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
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20
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Giovannini T, Koch H. Energy-Based Molecular Orbital Localization in a Specific Spatial Region. J Chem Theory Comput 2021; 17:139-150. [PMID: 33337150 DOI: 10.1021/acs.jctc.0c00737] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
We present a novel energy-based localization procedure able to localize molecular orbitals into predefined spatial regions. The method is defined in a multiscale framework based on the multilevel Hartree-Fock approach. In particular, the system is partitioned into active and inactive fragments. The localized molecular orbitals are obtained maximizing the repulsion between the two fragments. The method is applied to several cases including both conjugated and non-conjugated systems. Our multiscale approach is compared with reference values for both ground-state properties, such as dipole moments, and local excitation energies. The proposed approach is useful to extend the application range of high-level electron correlation methods. In fact, the reduced number of molecular orbitals can lead to a large reduction in the computational cost of correlated calculations.
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Affiliation(s)
- Tommaso Giovannini
- Department of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway
| | - Henrik Koch
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
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21
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Goletto L, Giovannini T, Folkestad SD, Koch H. Combining multilevel Hartree–Fock and multilevel coupled cluster approaches with molecular mechanics: a study of electronic excitations in solutions. Phys Chem Chem Phys 2021; 23:4413-4425. [DOI: 10.1039/d0cp06359b] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present the coupling of different quantum-embedding approaches with a third molecular-mechanics layer, which can be either polarizable or non-polarizable.
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Affiliation(s)
- Linda Goletto
- Department of Chemistry
- Norwegian University of Science and Technology (NTNU)
- 7491 Trondheim
- Norway
| | - Tommaso Giovannini
- Department of Chemistry
- Norwegian University of Science and Technology (NTNU)
- 7491 Trondheim
- Norway
| | - Sarai D. Folkestad
- Department of Chemistry
- Norwegian University of Science and Technology (NTNU)
- 7491 Trondheim
- Norway
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22
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Massolle A, Neugebauer J. Subsystem density-functional theory for interacting open-shell systems: spin densities and magnetic exchange couplings. Faraday Discuss 2020; 224:201-226. [PMID: 33000819 DOI: 10.1039/d0fd00063a] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
We investigate the possibility of describing interacting open-shell systems in high-spin and broken-symmetry (BS) states with subsystem density-functional theory (sDFT). This subsystem method typically starts from the electronic-structure results obtained for individual systems, for which the spin states can be individually defined. Through the confining effect of the embedding potential and/or the use of monomer basis sets, these individual spin states can be preserved in sDFT calculations. This offers the possibility of easy convergence to broken-symmetry states with arbitrary local spin patterns. We show that the resulting spin densities are in very good agreement with successfully converged broken-symmetry Kohn-Sham density-functional theory (KS-DFT) calculations. Yet sDFT can even cure those BS cases where KS-DFT suffers from convergence problems or convergence to undesired spin states. In contrast to KS-DFT, the sDFT-results only show a mild exchange-correlation functional dependence. We also show that magnetic coupling constants from sDFT are not satisfactory with standard approximations for the non-additive kinetic energy. When this component is evaluated "exactly", i.e. based on potential reconstruction, however, the magnetic coupling constants derived from spin-state energy differences are greatly improved. Hence, the interacting radicals studied here represent cases where even (semi-)local approximations for the non-additive kinetic-energy potential work well, while the parent energy functionals do not yield satisfactory results for spin-state energy differences.
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Affiliation(s)
- Anja Massolle
- Theoretische Organische Chemie, Organisch-Chemisches Institut, Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 36, 48149 Münster, Germany.
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23
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Macetti G, Genoni A. Quantum Mechanics/Extremely Localized Molecular Orbital Embedding Strategy for Excited States: Coupling to Time-Dependent Density Functional Theory and Equation-of-Motion Coupled Cluster. J Chem Theory Comput 2020; 16:7490-7506. [PMID: 33241930 DOI: 10.1021/acs.jctc.0c00956] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The QM/ELMO (quantum mechanics/extremely localized molecular orbital) method is a recently developed embedding technique in which the most important region of the system under examination is treated at fully quantum mechanical level, while the rest is described by means of transferred and frozen extremely localized molecular orbitals. In this paper, we propose the first application of the QM/ELMO approach to the investigation of excited states, and, in particular, we present the coupling of the QM/ELMO philosophy with Time-Dependent Density Functional Theory (TDDFT) and Equation-of-Motion Coupled Cluster with single and double substitutions (EOM-CCSD). The proposed TDDFT/ELMO and EOM-CCSD/ELMO strategies underwent a series of preliminary tests that were already considered for the validation of other embedding methods for excited states. The obtained results showed that the novel techniques allow the accurate description of localized excitations in large systems by only including a relatively small number of atoms in the region treated at fully quantum chemical level. Furthermore, for TDDFT/ELMO, it was also observed that (i) the method enables to avoid the presence of artificial low-lying charge-transfer states that may affect traditional TDDFT calculations, even using functionals that do not take into account long-range corrections, and (ii) the novel approach can be also successfully exploited to investigate local electronic transitions in quite large systems (e.g., reduced model of the Green Fluorescent Protein), and the accuracy of the results can be improved by including a sufficient number of chemically crucial fragments/residues in the quantum mechanical region. Finally, concerning EOM-CCSD/ELMO, it was also seen that, despite the quite crude approximation of an embedding potential given by frozen extremely localized molecular orbitals, the new strategy is able to satisfactorily account for the effects of the environment. This work paves the way to further extensions of the QM/ELMO philosophy for the study of local excitations in extended systems, suggesting the coupling of the QM/ELMO approach with other quantum chemical strategies for excited states, from the simplest ΔSCF techniques to the most advanced and computationally expensive multireferences methods.
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Affiliation(s)
- Giovanni Macetti
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
| | - Alessandro Genoni
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
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24
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Lin HH, Maschio L, Kats D, Usvyat D, Heine T. Fragment-Based Restricted Active Space Configuration Interaction with Second-Order Corrections Embedded in Periodic Hartree–Fock Wave Function. J Chem Theory Comput 2020; 16:7100-7108. [DOI: 10.1021/acs.jctc.0c00576] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- Hung-Hsuan Lin
- Theoretische Chemie, Technische Universität Dresden, Dresden, Germany
| | - Lorenzo Maschio
- Dipartimento di Chimica, Università di Torino, Torino, Italy
| | - Daniel Kats
- Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany
| | - Denis Usvyat
- Institut für Chemie, Humboldt-Universität zu Berlin, Berlin, Germany
| | - Thomas Heine
- Theoretische Chemie, Technische Universität Dresden, Dresden, Germany
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25
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Hoyer CE, Li X. Relativistic two-component projection-based quantum embedding for open-shell systems. J Chem Phys 2020; 153:094113. [DOI: 10.1063/5.0012433] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Chad E. Hoyer
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
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26
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Sun Q, Zhang X, Banerjee S, Bao P, Barbry M, Blunt NS, Bogdanov NA, Booth GH, Chen J, Cui ZH, Eriksen JJ, Gao Y, Guo S, Hermann J, Hermes MR, Koh K, Koval P, Lehtola S, Li Z, Liu J, Mardirossian N, McClain JD, Motta M, Mussard B, Pham HQ, Pulkin A, Purwanto W, Robinson PJ, Ronca E, Sayfutyarova ER, Scheurer M, Schurkus HF, Smith JET, Sun C, Sun SN, Upadhyay S, Wagner LK, Wang X, White A, Whitfield JD, Williamson MJ, Wouters S, Yang J, Yu JM, Zhu T, Berkelbach TC, Sharma S, Sokolov AY, Chan GKL. Recent developments in the PySCF program package. J Chem Phys 2020; 153:024109. [DOI: 10.1063/5.0006074] [Citation(s) in RCA: 151] [Impact Index Per Article: 37.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Affiliation(s)
- Qiming Sun
- AxiomQuant Investment Management LLC, Shanghai 200120, China
| | - Xing Zhang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Samragni Banerjee
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Peng Bao
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
| | - Marc Barbry
- Simbeyond B.V., P.O. Box 513, NL-5600 MB, Eindhoven, The Netherlands
| | - Nick S. Blunt
- Department of Chemistry, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Nikolay A. Bogdanov
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - George H. Booth
- Department of Physics, King’s College London, Strand, London WC2R 2LS, United Kingdom
| | - Jia Chen
- Department of Physics, University of Florida, Gainesville, Florida 32611, USA
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Zhi-Hao Cui
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Janus J. Eriksen
- School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, United Kingdom
| | - Yang Gao
- Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA
| | - Sheng Guo
- Google Inc., Mountain View, California 94043, USA
| | - Jan Hermann
- FU Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany
- TU Berlin, Machine Learning Group, Marchstr. 23, 10587 Berlin, Germany
| | - Matthew R. Hermes
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455, USA
| | - Kevin Koh
- Department of Chemistry and Biochemistry, The University of Notre Dame du Lac, 251 Nieuwland Science Hall, Notre Dame, Indiana 46556, USA
| | - Peter Koval
- Simune Atomistics S.L., Avenida Tolosa 76, Donostia-San Sebastian, Spain
| | - Susi Lehtola
- Department of Chemistry, University of Helsinki, P.O. Box 55 (A. I. Virtasen aukio 1), FI-00014 Helsinki, Finland
| | - Zhendong Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Narbe Mardirossian
- AMGEN Research, One Amgen Center Drive, Thousand Oaks, California 91320, USA
| | | | - Mario Motta
- IBM Almaden Research Center, San Jose, California 95120, USA
| | - Bastien Mussard
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, USA
| | - Hung Q. Pham
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455, USA
| | - Artem Pulkin
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, The Netherlands
| | - Wirawan Purwanto
- Information Technology Services, Old Dominion University, Norfolk, Virginia 23529, USA
| | - Paul J. Robinson
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Enrico Ronca
- Istituto per i Processi Chimico Fisici del CNR (IPCF-CNR), Via G. Moruzzi, 1, 56124 Pisa, Italy
| | - Elvira R. Sayfutyarova
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
| | - Maximilian Scheurer
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University of Heidelberg, 205 Im Neuenheimer Feld, 69120 Heidelberg, Germany
| | - Henry F. Schurkus
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - James E. T. Smith
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, USA
| | - Chong Sun
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Shi-Ning Sun
- Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA
| | - Shiv Upadhyay
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Lucas K. Wagner
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Illinois 61801, USA
| | - Xiao Wang
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
| | - Alec White
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - James Daniel Whitfield
- Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA
| | - Mark J. Williamson
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | | | - Jun Yang
- Department of Chemistry, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Jason M. Yu
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Tianyu Zhu
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Timothy C. Berkelbach
- Department of Chemistry, Columbia University, New York, New York 10027, USA
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
| | - Sandeep Sharma
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, USA
| | - Alexander Yu. Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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27
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Bensberg M, Neugebauer J. Orbital Alignment for Accurate Projection-Based Embedding Calculations along Reaction Paths. J Chem Theory Comput 2020; 16:3607-3619. [DOI: 10.1021/acs.jctc.0c00104] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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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28
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Macetti G, Wieduwilt EK, Assfeld X, Genoni A. Localized Molecular Orbital-Based Embedding Scheme for Correlated Methods. J Chem Theory Comput 2020; 16:3578-3596. [PMID: 32369363 DOI: 10.1021/acs.jctc.0c00084] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
Embedding strategies currently provide the best compromise between accuracy and computational cost in modeling chemical properties and processes of large and complex systems. In this framework, different methods have been proposed all over the years, from the very popular QM/MM approaches to the more recent and very promising density matrix and density functional embedding techniques. Here, we present a further development of the quantum mechanics/extremely localized molecular orbital technique (QM/ELMO) method, a recently proposed multiscale embedding strategy in which the chemically active region of the investigated system is treated at a fully quantum mechanical level, while the rest is described by frozen extremely localized molecular orbitals previously transferred from proper libraries or tailor-made model molecules. In particular, in this work we discuss and assess in detail the extension of the QM/ELMO approach to density functional theory and post-Hartree-Fock techniques by evaluating its performances when it is used to describe chemical reactions, bond dissociations, and intermolecular interactions. The preliminary test calculations have shown that, in the investigated cases, the new embedding strategy enables the results of the corresponding fully quantum mechanical computations to be reproduced within chemical accuracy in almost all the cases but with a significantly reduced computational cost, especially when correlated post-Hartree-Fock strategies are used to describe the quantum mechanical subsystem. In light of the obtained results, we already envisage the future application of the new correlated QM/ELMO techniques to the investigation of more challenging problems, such as the modeling of enzyme catalysis, the study of excited states of biomolecules, and the refinement of macromolecular X-ray crystal structures.
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Affiliation(s)
- Giovanni Macetti
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
| | - Erna K Wieduwilt
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
| | - Xavier Assfeld
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, Boulevard des Aiguilletes, BP 70239, F-54506 Vandoeuvre-lès-Nancy, France
| | - Alessandro Genoni
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
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29
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Niemeyer N, Tölle J, Neugebauer J. Approximate versus Exact Embedding for Chiroptical Properties: Reconsidering Failures in Potential and Response. J Chem Theory Comput 2020; 16:3104-3120. [PMID: 32301613 DOI: 10.1021/acs.jctc.0c00125] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We investigate the suitability of subsystem time-dependent density-functional theory (sTDDFT) for describing chiroptical properties with a focus on optical rotation parameters. Our starting point is a new implementation of the recently proposed projection-based, coupled frozen-density embedding (FDEc) framework. We adapt the generalized, non-Hermitian formulation of TDDFT and derive corresponding expressions for regular and damped response properties from subsystem TDDFT. We verify that our implementation of this "exact" formulation allows to reproduce supermolecular results of electronic circular dichroism (ECD) spectra, of optical rotatory dispersion, and of polarizabilities. We present a systematic test of the main approximations typically introduced in practical frozen-density embedding (FDE) calculations of response properties: (i) the use of approximate nonadditive kinetic-energy (NAKE) functionals, which can be avoided through projection techniques, (ii) the use of monomer (subsystem) basis sets rather than supersystem basis sets, and (iii) the neglect of intersubsystem response coupling within the so-called uncoupled FDE (or FDEu) approximation. While approximation (i) is known to generally lead to large errors for covalently bound subsystems, we present cases in which either the basis set or the coupling step are similarly or even (much) more important. In particular, we explicitly demonstrate by comparison to a fully coupled calculation that missing intersubsystem response couplings are responsible for the failure of FDE reported in a previous study [ J. Chem. Theory Comput. 2015, 11, 5305-5315]. We show that good agreement with reference results can be obtained in this case even with standard NAKE approximations for the FDE potentials and efficient monomer basis sets, making calculations for larger systems well accessible.
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Affiliation(s)
- Niklas Niemeyer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster Corrensstraße 40, 48149 Münster, Germany
| | - Johannes Tölle
- 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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30
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He N, Evangelista FA. A zeroth-order active-space frozen-orbital embedding scheme for multireference calculations. J Chem Phys 2020; 152:094107. [PMID: 33480706 DOI: 10.1063/1.5142481] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Multireference computations of large-scale chemical systems are typically limited by the computational cost of quantum chemistry methods. In this work, we develop a zeroth-order active space embedding theory [ASET(0)], a simple and automatic approach for embedding any multireference dynamical correlation method based on a frozen-orbital treatment of the environment. ASET(0) is combined with the second-order multireference driven similarity renormalization group and tested on several benchmark problems, including the excitation energy of 1-octene and bond-breaking in ethane and pentyldiazene. Finally, we apply ASET(0) to study the singlet-triplet gap of p-benzyne and 9,10-anthracyne diradicals adsorbed on a NaCl surface. Our results show that despite its simplicity, ASET(0) is a powerful and sufficiently accurate embedding scheme applicable when the coupling between the fragment and the environment is in the weak to medium regime.
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Affiliation(s)
- Nan He
- Department of Chemistry, Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Francesco A Evangelista
- Department of Chemistry, Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
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31
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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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32
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Bensberg M, Neugebauer J. Density functional theory based embedding approaches for transition-metal complexes. Phys Chem Chem Phys 2020; 22:26093-26103. [PMID: 33201953 DOI: 10.1039/d0cp05188h] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
Transition metal species are commonly discussed by considering the metal atom embedded in a ligand environment. This apparently makes them interesting targets for modern embedding strategies based on Kohn-Sham density functional theory (DFT), which aim at modelling accurate predictions for large systems by combining different quantum chemical methods. In this perspective, we will focus on subsystem density functional theory and projection-based embedding. We review the developments in the field for transition metal species, demonstrate benefits, drawbacks and analyse error sources of the different strategies using the example of chromium hexacarbonyle, before giving a perspective where the field is currently heading.
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Affiliation(s)
- Moritz Bensberg
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster Corrensstraße 36, 48149 Münster, Germany.
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33
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Patel P, Wilson AK. Domain-based local pair natural orbital methods within the correlation consistent composite approach. J Comput Chem 2019; 41:800-813. [PMID: 31891196 DOI: 10.1002/jcc.26129] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2019] [Revised: 10/29/2019] [Accepted: 12/01/2019] [Indexed: 01/15/2023]
Abstract
Ab initio composite approaches have been utilized to model and predict main group thermochemistry within 1 kcal mol-1 , on average, from well-established reliable experiments, primarily for molecules with less than 30 atoms. For molecules of increasing size and complexity, such as biomolecular complexes, composite methodologies have been limited in their application. Therefore, the domain-based local pair natural orbital (DLPNO) methods have been implemented within the correlation consistent composite approach (ccCA) framework, namely DLPNO-ccCA, to reduce the computational cost (disk space, CPU (central processing unit) time, memory) and predict energetic properties such as enthalpies of formation, noncovalent interactions, and conformation energies for organic biomolecular complexes including one of the largest molecules examined via composite strategies, within 1 kcal mol-1 , after calibration with 119 molecules and a set of linear alkanes. © 2019 Wiley Periodicals, Inc.
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Affiliation(s)
- Prajay Patel
- Department of Chemistry, Michigan State University, East Lansing, Michigan, 48824
| | - Angela K Wilson
- Department of Chemistry, Michigan State University, East Lansing, Michigan, 48824
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34
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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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35
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Claudino D, Mayhall NJ. Simple and Efficient Truncation of Virtual Spaces in Embedded Wave Functions via Concentric Localization. J Chem Theory Comput 2019; 15:6085-6096. [DOI: 10.1021/acs.jctc.9b00682] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Daniel Claudino
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, United States
| | - Nicholas J. Mayhall
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, United States
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36
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Petras HR, Graham DS, Ramadugu SK, Goodpaster JD, Shepherd JJ. Fully Quantum Embedding with Density Functional Theory for Full Configuration Interaction Quantum Monte Carlo. J Chem Theory Comput 2019; 15:5332-5342. [DOI: 10.1021/acs.jctc.9b00571] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Hayley R. Petras
- Department of Chemistry, University of Iowa, Iowa City, Iowa 52242, United States
- University of Iowa Informatics Initiative, University of Iowa, Iowa City, Iowa 52242, United States
| | - Daniel S. Graham
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Sai Kumar Ramadugu
- Department of Chemistry, University of Iowa, Iowa City, Iowa 52242, United States
- University of Iowa Informatics Initiative, University of Iowa, Iowa City, Iowa 52242, United States
| | - Jason D. Goodpaster
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - James J. Shepherd
- Department of Chemistry, University of Iowa, Iowa City, Iowa 52242, United States
- University of Iowa Informatics Initiative, University of Iowa, Iowa City, Iowa 52242, United States
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37
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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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38
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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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39
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Hégely B, Nagy PR, Kállay M. Dual Basis Set Approach for Density Functional and Wave Function Embedding Schemes. J Chem Theory Comput 2018; 14:4600-4615. [DOI: 10.1021/acs.jctc.8b00350] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Affiliation(s)
- Bence Hégely
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Péter R. Nagy
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Mihály Kállay
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
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40
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Ghosh S, Verma P, Cramer CJ, Gagliardi L, Truhlar DG. Combining Wave Function Methods with Density Functional Theory for Excited States. Chem Rev 2018; 118:7249-7292. [PMID: 30044618 DOI: 10.1021/acs.chemrev.8b00193] [Citation(s) in RCA: 128] [Impact Index Per Article: 21.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
We review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn-Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe-Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.
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Affiliation(s)
- Soumen Ghosh
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Pragya Verma
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Christopher J Cramer
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Laura Gagliardi
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
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41
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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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42
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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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