1
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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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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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Polak E, Englert T, Gander MJ, Wesolowski TA. Symmetrized non-decomposable approximations of the non-additive kinetic energy functional. J Chem Phys 2023; 158:2887765. [PMID: 37129139 DOI: 10.1063/5.0143602] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2023] [Accepted: 04/13/2023] [Indexed: 05/03/2023] Open
Abstract
In subsystem density functional theory (DFT), the bottom-up strategy to approximate the multivariable functional of the non-additive kinetic energy (NAKE) makes it possible to impose exact properties on the corresponding NAKE potential (NAKEP). Such a construction might lead to a non-symmetric and non-homogeneous functional, which excludes the use of such approximations for the evaluation of the total energy. We propose a general formalism to construct a symmetric version based on a perturbation theory approach of the energy expression for the asymmetric part. This strategy is then applied to construct a symmetrized NAKE corresponding to the NAKEP developed recently [Polak et al., J. Chem. Phys. 156, 044103 (2022)], making it possible to evaluate consistently the energy. These functionals were used to evaluate the interaction energy in several model intermolecular complexes using the formal framework of subsystem DFT. The new symmetrized energy expression shows a superior qualitative performance over common decomposable models.
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Affiliation(s)
- Elias Polak
- Department of Physical Chemistry, University of Geneva, Quai Ernest-Ansermet 30, CH-1211 Genève 4, Switzerland
- Section of Mathematics, University of Geneva, Rue du Conseil-Général 7-9, CP 64, CH-1211 Genève 4, Switzerland
| | - Tanguy Englert
- Department of Physical Chemistry, University of Geneva, Quai Ernest-Ansermet 30, CH-1211 Genève 4, Switzerland
| | - Martin J Gander
- Section of Mathematics, University of Geneva, Rue du Conseil-Général 7-9, CP 64, CH-1211 Genève 4, Switzerland
| | - Tomasz A Wesolowski
- Department of Physical Chemistry, University of Geneva, Quai Ernest-Ansermet 30, CH-1211 Genève 4, Switzerland
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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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Niemeyer N, Eschenbach P, Bensberg M, Tölle J, Hellmann L, Lampe L, Massolle A, Rikus A, Schnieders D, Unsleber JP, Neugebauer J. The subsystem quantum chemistry program
Serenity. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1647] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Affiliation(s)
- Niklas Niemeyer
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
| | - Patrick Eschenbach
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
| | - Moritz Bensberg
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
| | - Johannes Tölle
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
| | - Lars Hellmann
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
| | - Lukas Lampe
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
| | - Anja Massolle
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
| | - Anton Rikus
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
| | - David Schnieders
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
| | - Jan P. Unsleber
- Laboratorium für Physikalische Chemie ETH Zürich Zürich Switzerland
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch‐Chemisches Institut and Center for Multiscale Theory and Computation Westfälische Wilhelms‐Universität Münster Münster Germany
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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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De Santis M, Sorbelli D, Vallet V, Gomes AS, Storchi L, Belpassi L. Frozen-Density Embedding for Including Environmental Effects in the Dirac-Kohn-Sham Theory: An Implementation Based on Density Fitting and Prototyping Techniques. J Chem Theory Comput 2022; 18:5992-6009. [PMID: 36172757 PMCID: PMC9558305 DOI: 10.1021/acs.jctc.2c00499] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2022] [Indexed: 11/28/2022]
Abstract
Frozen density embedding (FDE) represents an embedding scheme in which environmental effects are included from first-principles calculations by considering the surrounding system explicitly by means of its electron density. In the present paper, we extend the full four-component relativistic Dirac-Kohn-Sham (DKS) method, as implemented in the BERTHA code, to include environmental and confinement effects with the FDE scheme (DKS-in-DFT FDE). The implementation, based on the auxiliary density fitting techniques, has been enormously facilitated by BERTHA's python API (PyBERTHA), which facilitates the interoperability with other FDE implementations available through the PyADF framework. The accuracy and numerical stability of this new implementation, also using different auxiliary fitting basis sets, has been demonstrated on the simple NH3-H2O system, in comparison with a reference nonrelativistic implementation. The computational performance has been evaluated on a series of gold clusters (Aun, with n = 2, 4, 8) embedded into an increasing number of water molecules (5, 10, 20, 40, and 80 water molecules). We found that the procedure scales approximately linearly both with the size of the frozen surrounding environment (consistent with the underpinnings of the FDE approach) and with the size of the active system (in line with the use of density fitting). Finally, we applied the code to a series of heavy (Rn) and super-heavy elements (Cn, Fl, Og) embedded in a C60 cage to explore the confinement effect induced by C60 on their electronic structure. We compare the results from our simulations, with respect to more-approximate models employed in the atomic physics literature. Our results indicate that the specific interactions described by FDE are able to improve upon the cruder approximations currently employed, and, thus, they provide a basis from which to generate more-realistic radial potentials for confined atoms.
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Affiliation(s)
- Matteo De Santis
- Univ.
Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Diego Sorbelli
- Dipartimento
di Chimica, Biologia e Biotecnologie, Università
degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
- Istituto
di Scienze e Tecnologie Chimiche (SCITEC), Consiglio Nazionale delle
Ricerche c/o Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
| | - Valérie Vallet
- Univ.
Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | | | - Loriano Storchi
- Istituto
di Scienze e Tecnologie Chimiche (SCITEC), Consiglio Nazionale delle
Ricerche c/o Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
- Dipartimento
di Farmacia, Università degli Studi
‘G. D’Annunzio’, Via dei Vestini 31, 66100 Chieti, Italy
| | - Leonardo Belpassi
- Istituto
di Scienze e Tecnologie Chimiche (SCITEC), Consiglio Nazionale delle
Ricerche c/o Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
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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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Wesolowski TA. Is the non-additive kinetic potential always equal to the difference of effective potentials from inverting the Kohn-Sham equation? J Chem Phys 2022; 157:081102. [DOI: 10.1063/5.0101791] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The relation used frequently in the literature {according to which the non-additive kinetic potential which is a functional depending on a pair of electron densities is equal (up to a constant) to} the difference of two potentials obtained from inverting two Kohn-Sham equations, is examined. <p>The relation is based on a silent assumption that the two densities can be obtained from two independent Kohn-Sham equations - i.e. are $v_s$-representable.</p> <p>It is shown that this assumption does not hold for pairs of densities: $\rho_{tot}$ - being the Kohn-Sham density in some system and $\rho_B$ obtained from such partitioning of $\rho_{tot}$ that the difference $\rho_{tot}-\rho_B$ vanish on a Lebesgue measurable volume element. The inversion procedure is still applicable for $\rho_{tot}-\rho_B$ but cannot be interpreted as the inversion of Kohn-Sham equation but rather inversion of Kohn-Sham equation with an additional constraint. The obtained effective potential comprises a "contaminant" that might even not be unique. It is shown, that the construction of the non-additive kinetic potential based on the examined relation is not applicable for such pairs.
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Affiliation(s)
- Tomasz A. Wesolowski
- Department of Physical Chemistry, University of Geneva Faculty of Science, Switzerland
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10
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Miranda-Quintana RA, Heidar-Zadeh F, Fias S, Chapman AEA, Liu S, Morell C, Gómez T, Cárdenas C, Ayers PW. Molecular Interactions From the Density Functional Theory for Chemical Reactivity: The Interaction Energy Between Two-Reagents. Front Chem 2022; 10:906674. [PMID: 35769444 PMCID: PMC9234655 DOI: 10.3389/fchem.2022.906674] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2022] [Accepted: 04/19/2022] [Indexed: 12/13/2022] Open
Abstract
Reactivity descriptors indicate where a reagent is most reactive and how it is most likely to react. However, a reaction will only occur when the reagent encounters a suitable reaction partner. Determining whether a pair of reagents is well-matched requires developing reactivity rules that depend on both reagents. This can be achieved using the expression for the minimum-interaction-energy obtained from the density functional reactivity theory. Different terms in this expression will be dominant in different circumstances; depending on which terms control the reactivity, different reactivity indicators will be preferred.
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Affiliation(s)
- Ramón Alain Miranda-Quintana
- Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, FL, United States
- *Correspondence: Ramón Alain Miranda-Quintana, ; Carlos Cárdenas, ; Paul W. Ayers, ; Tatiana Gómez,
| | | | - Stijn Fias
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, ON, Canada
| | - Allison E. A. Chapman
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, ON, Canada
| | - Shubin Liu
- Research Computing Center, University of North Carolina, Chapel Hill, NC, United States
| | - Christophe Morell
- Université de Lyon, Université Claude Bernard Lyon 1, Institut des Sciences Analytiques-UMR CNRS 5280, Villeurbanne, France
| | - Tatiana Gómez
- Theoretical and Computational Chemistry Center, Institute of Applied Chemical Sciences, Faculty of Engineering, Universidad Autonoma de Chile, Santiago, Chile
- *Correspondence: Ramón Alain Miranda-Quintana, ; Carlos Cárdenas, ; Paul W. Ayers, ; Tatiana Gómez,
| | - Carlos Cárdenas
- Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Santiago, Chile
- Centro para el desarrollo de la Nanociencias y Nanotecnologia, CEDENNA, Santiago, Chile
- *Correspondence: Ramón Alain Miranda-Quintana, ; Carlos Cárdenas, ; Paul W. Ayers, ; Tatiana Gómez,
| | - Paul W. Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, ON, Canada
- *Correspondence: Ramón Alain Miranda-Quintana, ; Carlos Cárdenas, ; Paul W. Ayers, ; Tatiana Gómez,
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11
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Erhard J, Trushin E, Görling A. Numerically stable inversion approach to construct Kohn-Sham potentials for given electron densities within a Gaussian basis set framework. J Chem Phys 2022; 156:204124. [PMID: 35649824 DOI: 10.1063/5.0087356] [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
We present a Kohn-Sham (KS) inversion approach to construct KS exchange-correlation potentials corresponding to given electron densities. This method is based on an iterative procedure using linear response to update potentials. All involved quantities, i.e., orbitals, potentials, and response functions, are represented by Gaussian basis functions. In contrast to previous KS inversion methods relying on Gaussian basis sets, the method presented here is numerically stable even for standard basis sets from basis set libraries due to a preprocessing of the auxiliary basis used to represent an exchange-correlation charge density that generates the exchange-correlation potential. The new KS inversion method is applied to reference densities of various atoms and molecules obtained by full configuration interaction or CCSD(T) (coupled cluster singles doubles perturbative triples). The considered examples encompass cases known to be difficult, such as stretched hydrogen or lithium hydride molecules or the beryllium isoelectronic series. For the stretched hydrogen molecule, potentials of benchmark quality are obtained by employing large basis sets. For the carbon monoxide molecule, we show that the correlation potential from the random phase approximation (RPA) is in excellent qualitative and quantitative agreement with the correlation potential from the KS inversion of a CCSD(T) reference density. This indicates that RPA correlation potentials, in contrast to those from semi-local density-functionals, resemble the exact correlation potential. Besides providing exchange-correlation potentials for benchmark purposes, the proposed KS inversion method may be used in density-partition-based quantum embedding and in subsystem density-functional methods because it combines numerical stability with computational efficiency.
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Affiliation(s)
- Jannis Erhard
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
| | - Egor Trushin
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
| | - Andreas Görling
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
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12
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Shi Y, Chávez VH, Wasserman A. n2v
: A density‐to‐potential inversion suite. A sandbox for creating, testing, and benchmarking density functional theory inversion methods. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1617] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Yuming Shi
- Department of Physics and Astronomy Purdue University West Lafayette Indiana USA
| | - Victor H. Chávez
- Department of Chemistry Purdue University West Lafayette Indiana USA
| | - Adam Wasserman
- Department of Physics and Astronomy Purdue University West Lafayette Indiana USA
- Department of Chemistry Purdue University West Lafayette Indiana USA
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13
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De Santis M, Vallet V, Gomes ASP. Environment Effects on X-Ray Absorption Spectra With Quantum Embedded Real-Time Time-Dependent Density Functional Theory Approaches. Front Chem 2022; 10:823246. [PMID: 35295974 PMCID: PMC8919347 DOI: 10.3389/fchem.2022.823246] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2021] [Accepted: 02/04/2022] [Indexed: 11/13/2022] Open
Abstract
In this work we implement the real-time time-dependent block-orthogonalized Manby-Miller embedding (rt-BOMME) approach alongside our previously developed real-time frozen density embedding time-dependent density functional theory (rt-TDDFT-in-DFT FDE) code, and investigate these methods' performance in reproducing X-ray absorption spectra (XAS) obtained with standard rt-TDDFT simulations, for model systems comprised of solvated fluoride and chloride ions ([X@( H 2 O ) 8 - , X = F, Cl). We observe that for ground-state quantities such as core orbital energies, the BOMME approach shows significantly better agreement with supermolecular results than FDE for the strongly interacting fluoride system, while for chloride the two embedding approaches show more similar results. For the excited states, we see that while FDE (constrained not to have the environment densities relaxed in the ground state) is in good agreement with the reference calculations for the region around the K and L1 edges, and is capable of reproducing the splitting of the 1s1 (n + 1)p1 final states (n + 1 being the lowest virtual p orbital of the halides), it by and large fails to properly reproduce the 1s1 (n + 2)p1 states and misses the electronic states arising from excitation to orbitals with important contributions from the solvent. The BOMME results, on the other hand, provide a faithful qualitative representation of the spectra in all energy regions considered, though its intrinsic approximation of employing a lower-accuracy exchange-correlation functional for the environment induces non-negligible shifts in peak positions for the excitations from the halide to the environment. Our results thus confirm that QM/QM embedding approaches are viable alternatives to standard real-time simulations of X-ray absorption spectra of species in complex or confined environments.
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14
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Prentice JCA. Efficiently Computing Excitations of Complex Systems: Linear-Scaling Time-Dependent Embedded Mean-Field Theory in Implicit Solvent. J Chem Theory Comput 2022; 18:1542-1554. [PMID: 35133827 PMCID: PMC9082505 DOI: 10.1021/acs.jctc.1c01133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
Quantum embedding schemes have the
potential to significantly reduce
the computational cost of first-principles calculations while maintaining
accuracy, particularly for calculations of electronic excitations
in complex systems. In this work, I combine time-dependent embedded
mean field theory (TD-EMFT) with linear-scaling density functional
theory and implicit solvation models, extending previous work within
the ONETEP code. This provides a way to perform multilevel calculations
of electronic excitations on very large systems, where long-range
environmental effects, both quantum and classical in nature, are important.
I demonstrate the power of this method by performing simulations on
a variety of systems, including a molecular dimer, a chromophore in
solution, and a doped molecular crystal. This work paves the way for
high accuracy calculations to be performed on large-scale systems
that were previously beyond the reach of quantum embedding schemes.
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Affiliation(s)
- Joseph C A Prentice
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
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15
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Tölle J, Neugebauer J. The Seamless Connection of Local and Collective Excited States in Subsystem Time-Dependent Density Functional Theory. J Phys Chem Lett 2022; 13:1003-1018. [PMID: 35061387 DOI: 10.1021/acs.jpclett.1c04023] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
The theoretical understanding of photoinduced processes in multichromophoric systems requires, as an essential ingredient, the possibility of accurately describing their electronically excited states. However, the size of these systems often prohibits the usage of conventional electronic-structure methods, so that often multiscale approaches based on phenomenologically motivated models are employed. In contrast, subsystem time-dependent density functional theory (sTDDFT) allows for a subsystem-based ab initio description of multichromophoric systems and therefore allows for, in principle, an exact description of photoinduced processes. This Perspective aims to outline the theoretical foundations and commonly used practical realizations as well as to illustrate benefits of recent developments and open issues in the field of sTDDFT. Prospective, potential future applications and possible methodological developments are discussed.
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Affiliation(s)
- 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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16
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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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17
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Sen R, González-Espinoza CE, Zech A, Dreuw A, Wesolowski TA. Benchmark of the Extension of Frozen-Density Embedding Theory to Nonvariational Correlated Methods: The Embedded-MP2 Case. J Chem Theory Comput 2021; 17:4049-4062. [PMID: 34137597 DOI: 10.1021/acs.jctc.1c00228] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The extension of the frozen-density embedding theory for nonvariational methods [J. Chem. Theory Comput. 2020, 16, 6880] was utilized to evaluate intermolecular interaction energies for complexes in the Zhao-Truhlar basis set. In the applied method (FDET-MP2-FAT-LDA), the same auxiliary system is used to evaluate the correlation energy by means of the second-order Møller-Plesset perturbation theory (MP2), as in our previous work [J. Chem. Phys. 2019, 150, 121101]. Local density approximation is used for ExcTnad[ρA,ρB] in both cases. Additionally, the contribution to the energy due to the neglected correlation potential was evaluated and analyzed. The domain of applicability of the local density approximation for ExcTnad[ρA,ρB] was determined based on deviations from the interaction energies from the conventional MP2 calculations. The local density approximation for ExcTnad[ρA,ρB] performs well for hydrogen- or dipole-bound complexes. The relative errors in the interaction energy lie within 3-30%. While for charge-transfer complexes, this approximation fails consistently, and for other types of complexes, the performance of this approximation is not systematic. The sources of error are discussed in detail.
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Affiliation(s)
- Reena Sen
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | | | - Alexander Zech
- Department of Physical Chemistry, University of Geneva, 30, Quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Tomasz A Wesolowski
- Department of Physical Chemistry, University of Geneva, 30, Quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
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18
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Shi Y, Wasserman A. Inverse Kohn-Sham Density Functional Theory: Progress and Challenges. J Phys Chem Lett 2021; 12:5308-5318. [PMID: 34061541 DOI: 10.1021/acs.jpclett.1c00752] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Inverse Kohn-Sham (iKS) methods are needed to fully understand the one-to-one mapping between densities and potentials on which density functional theory is based. They can contribute to the construction of empirical exchange-correlation functionals and to the development of techniques for density-based embedding. Unlike the forward Kohn-Sham problems, numerical iKS problems are ill-posed and can be unstable. We discuss some of the fundamental and practical difficulties of iKS problems with constrained-optimization methods on finite basis sets. Various factors that affect the performance are systematically compared and discussed, both analytically and numerically, with a focus on two of the most practical methods: the Wu-Yang method (WY) and the partial differential equation constrained optimization (PDE-CO). Our analysis of the WY and PDE-CO highlights the limitation of finite basis sets. We introduce new ideas to make iKS problems more tractable, provide an overall strategy for performing numerical density-to-potential inversions, and discuss challenges and future directions.
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Affiliation(s)
- Yuming Shi
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, United States
| | - Adam Wasserman
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, United States
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, United States
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19
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Shao X, Mi W, Pavanello M. GGA-Level Subsystem DFT Achieves Sub-kcal/mol Accuracy Intermolecular Interactions by Mimicking Nonlocal Functionals. J Chem Theory Comput 2021; 17:3455-3461. [PMID: 33983729 DOI: 10.1021/acs.jctc.1c00283] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
The key feature of nonlocal kinetic energy functionals is their ability to reduce to the Thomas-Fermi functional in the regions of high density and to the von Weizsäcker functional in the region of low-density/high reduced density gradient. This behavior is crucial when these functionals are employed in subsystem DFT simulations to approximate the nonadditive kinetic energy. We propose a GGA nonadditive kinetic energy functional which mimics the good behavior of nonlocal functionals, retaining the computational complexity of typical semilocal functionals. Crucially, this functional depends on the inter-subsystem density overlap. The new functional reproduces Kohn-Sham DFT and benchmark CCSD(T) interaction energies of weakly interacting dimers in the S22-5 and S66 test sets with a mean absolute deviation well below 1 kcal/mol.
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Affiliation(s)
- Xuecheng Shao
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, United States
| | - Wenhui Mi
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, United States
| | - Michele Pavanello
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, United States.,Department of Physics, Rutgers University, Newark, New Jersey 07102, United States
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20
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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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21
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Chi YC, Shaban Tameh M, Huang C. Efficient Embedded Cluster Density Approximation Calculations with an Orbital-Free Treatment of Environments. J Chem Theory Comput 2021; 17:2737-2751. [PMID: 33856795 DOI: 10.1021/acs.jctc.0c01133] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The computational cost of the Kohn-Sham density functional theory (KS-DFT), employing advanced orbital-based exchange-correlation (XC) functionals, increases quickly for large systems. To tackle this problem, we recently developed a local correlation method in the framework of KS-DFT: the embedded cluster density approximation (ECDA). The aim of ECDA is to obtain accurate electronic structures in an entire system. With ECDA, for each atom in a system, we define a cluster to enclose that atom, with the rest atoms treated as the environment. The system's electron density is then partitioned among the cluster and the environment. The cluster's XC energy density is then calculated based on its electron density using an advanced orbital-based XC functional. The system's XC energy is obtained by patching all clusters' XC energy densities in an atom-by-atom manner. In our previous formulation of ECDA, environments were treated by KS-DFT, which makes the following two tasks computationally expensive for large systems. The first task is to partition the system's electron density among a cluster and its environment. The second task is to solve the environments' Sternheimer equations for calculating the system's XC potential. In this work, we remove these two computational bottlenecks by treating the environments with the orbital-free (OF) DFT. The new method is called ECDA-envOF. The performance of ECDA-envOF is examined in two systems: ester and Cl-tetracene, for which the exact exchange (EXX) is used as the advanced XC functional. We show that ECDA-envOF gives results that are very close to the previous formulation in which the environments were treated by KS-DFT. Therefore, ECDA-envOF can be used for future large-scale simulations. Another focus of this work is to examine ECDA-envOF's performance on systems having different bond types. With ECDA-envOF, we calculate the energy curves for stretching/compressing some covalent, metallic, and ionic systems. ECDA-envOF's predictions agree well with the benchmarks by using reasonably large clusters. These examples demonstrate that ECDA-envOF is nearly a black-box local correlation method for investigating heterogeneous materials in which different bond types exist.
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Affiliation(s)
- Yu-Chieh Chi
- Department of Scientific Computing, Florida State University, Tallahassee, Florida 32306, United States
| | - Maliheh Shaban Tameh
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Chen Huang
- Department of Scientific Computing, Materials Science and Engineering Program, National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32306, United States
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22
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Nam S, McCarty RJ, Park H, Sim E. KS-pies: Kohn–Sham inversion toolkit. J Chem Phys 2021; 154:124122. [DOI: 10.1063/5.0040941] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Seungsoo Nam
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, South Korea
| | - Ryan J. McCarty
- Department of Chemistry, University of California Irvine, Irvine, California 92697, USA
| | - Hansol Park
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, South Korea
| | - Eunji Sim
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, South Korea
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23
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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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24
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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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25
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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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26
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Quantum mechanics/extremely localized molecular orbital embedding technique: Theoretical foundations and further validation. ADVANCES IN QUANTUM CHEMISTRY 2021. [DOI: 10.1016/bs.aiq.2021.05.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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27
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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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28
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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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29
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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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30
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De Santis M, Belpassi L, Jacob CR, Severo Pereira Gomes A, Tarantelli F, Visscher L, Storchi L. Environmental Effects with Frozen-Density Embedding in Real-Time Time-Dependent Density Functional Theory Using Localized Basis Functions. J Chem Theory Comput 2020; 16:5695-5711. [PMID: 32786918 PMCID: PMC8009524 DOI: 10.1021/acs.jctc.0c00603] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2020] [Indexed: 12/14/2022]
Abstract
Frozen-density embedding (FDE) represents a versatile embedding scheme to describe the environmental effect on electron dynamics in molecular systems. The extension of the general theory of FDE to the real-time time-dependent Kohn-Sham method has previously been presented and implemented in plane waves and periodic boundary conditions [Pavanello, M.; J. Chem. Phys. 2015, 142, 154116]. In the current paper, we extend our recent formulation of the real-time time-dependent Kohn-Sham method based on localized basis set functions and developed within the Psi4NumPy framework to the FDE scheme. The latter has been implemented in its "uncoupled" flavor (in which the time evolution is only carried out for the active subsystem, while the environment subsystems remain at their ground state), using and adapting the FDE implementation already available in the PyEmbed module of the scripting framework PyADF. The implementation was facilitated by the fact that both Psi4NumPy and PyADF, being native Python API, provided an ideal framework of development using the Python advantages in terms of code readability and reusability. We employed this new implementation to investigate the stability of the time-propagation procedure, which is based on an efficient predictor/corrector second-order midpoint Magnus propagator employing an exact diagonalization, in combination with the FDE scheme. We demonstrate that the inclusion of the FDE potential does not introduce any numerical instability in time propagation of the density matrix of the active subsystem, and in the limit of the weak external field, the numerical results for low-lying transition energies are consistent with those obtained using the reference FDE calculations based on the linear-response TDDFT. The method is found to give stable numerical results also in the presence of a strong external field inducing nonlinear effects. Preliminary results are reported for high harmonic generation (HHG) of a water molecule embedded in a small water cluster. The effect of the embedding potential is evident in the HHG spectrum reducing the number of the well-resolved high harmonics at high energy with respect to the free water. This is consistent with a shift toward lower ionization energy passing from an isolated water molecule to a small water cluster. The computational burden for the propagation step increases approximately linearly with the size of the surrounding frozen environment. Furthermore, we have also shown that the updating frequency of the embedding potential may be significantly reduced, much less than one per time step, without jeopardizing the accuracy of the transition energies.
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Affiliation(s)
- Matteo De Santis
- Dipartimento di
Chimica, Biologia e Biotecnologie, Università
degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
- Istituto di Scienze
e Tecnologie Chimiche (SCITEC), Consiglio Nazionale delle Ricerche
c/o Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
| | - Leonardo Belpassi
- Istituto di Scienze
e Tecnologie Chimiche (SCITEC), Consiglio Nazionale delle Ricerche
c/o Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
| | - Christoph R. Jacob
- Institute of Physical and Theoretical Chemistry, Technische Universität Braunschweig, Gaußstr. 17, 38106 Braunschweig, Germany
| | | | - Francesco Tarantelli
- Dipartimento di
Chimica, Biologia e Biotecnologie, Università
degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
| | - Lucas Visscher
- Theoretical Chemistry, Faculty of Science, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Loriano Storchi
- Istituto di Scienze
e Tecnologie Chimiche (SCITEC), Consiglio Nazionale delle Ricerche
c/o Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
- Dipartimento di Farmacia, Università
degli Studi ‘G. D’Annunzio’, Via dei Vestini 31, 66100 Chieti, Italy
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31
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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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32
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Ricardi N, Ernst M, Macchi P, Wesolowski TA. Embedding-theory-based simulations using experimental electron densities for the environment. Acta Crystallogr A Found Adv 2020; 76:571-579. [PMID: 32869754 PMCID: PMC7459768 DOI: 10.1107/s2053273320008062] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2020] [Accepted: 06/16/2020] [Indexed: 11/26/2022] Open
Abstract
The basic idea of frozen-density embedding theory (FDET) is the constrained minimization of the Hohenberg-Kohn density functional EHK[ρ] performed using the auxiliary functional E_{v_{AB}}^{\rm FDET}[\Psi _A, \rho _B], where ΨA is the embedded NA-electron wavefunction and ρB(r) is a non-negative function in real space integrating to a given number of electrons NB. This choice of independent variables in the total energy functional E_{v_{AB}}^{\rm FDET}[\Psi _A, \rho _B] makes it possible to treat the corresponding two components of the total density using different methods in multi-level simulations. The application of FDET using ρB(r) reconstructed from X-ray diffraction data for a molecular crystal is demonstrated for the first time. For eight hydrogen-bonded clusters involving a chromophore (represented as ΨA) and the glycylglycine molecule [represented as ρB(r)], FDET is used to derive excitation energies. It is shown that experimental densities are suitable for use as ρB(r) in FDET-based simulations.
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Affiliation(s)
- Niccolò Ricardi
- Department of Physical Chemistry, University of Geneva, 30, Quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
| | - Michelle Ernst
- University of Bern, Freiestraße 3, 3012 Bern, Switzerland
| | - Piero Macchi
- Department of Chemistry, Materials and Chemical Engineering, Polytechnic of Milan, via Mancinelli 7, Milano 20131, Italy
| | - Tomasz Adam Wesolowski
- Department of Physical Chemistry, University of Geneva, 30, Quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
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33
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Subsystems of many-electron system and reduced density matrices. COMPUT THEOR CHEM 2020. [DOI: 10.1016/j.comptc.2020.112875] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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34
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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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35
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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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36
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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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37
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Abstract
By invoking a divide-and-conquer strategy, subsystem DFT dramatically reduces the computational cost of large-scale, ab initio electronic structure simulations of molecules and materials. The central ingredient setting subsystem DFT apart from Kohn-Sham DFT is the nonadditive kinetic energy functional (NAKE). Currently employed NAKEs are at most semilocal (i.e., they only depend on the electron density and its gradient), and as a result of this approximation, so far large-scale simulations only included systems composed of weakly interacting subsystems. In this work, we advance the state-of-the-art by introducing fully nonlocal NAKEs in subsystem DFT simulations for the first time. A benchmark analysis based on the S22-5 test set shows that nonlocal NAKEs considerably improve the computed interaction energies and electron densities compared to commonly employed GGA NAKEs, especially when increasing intersubsystem electron density overlap is considered. Most importantly, we resolve the long-standing problem of too attractive interaction energy curves typically resulting from the use of GGA NAKEs.
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Affiliation(s)
- Wenhui Mi
- Department of Chemistry , Rutgers University , Newark , New Jersey 07102 , United States
- Department of Physics , Rutgers University , Newark , New Jersey 07102 , United States
| | - Michele Pavanello
- Department of Chemistry , Rutgers University , Newark , New Jersey 07102 , United States
- Department of Physics , Rutgers University , Newark , New Jersey 07102 , United States
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38
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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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39
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Cui ZH, Zhu T, Chan GKL. Efficient Implementation of Ab Initio Quantum Embedding in Periodic Systems: Density Matrix Embedding Theory. J Chem Theory Comput 2019; 16:119-129. [DOI: 10.1021/acs.jctc.9b00933] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Affiliation(s)
- Zhi-Hao Cui
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Tianyu Zhu
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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40
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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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41
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Prentice JCA, Charlton RJ, Mostofi AA, Haynes PD. Combining Embedded Mean-Field Theory with Linear-Scaling Density-Functional Theory. J Chem Theory Comput 2019; 16:354-365. [DOI: 10.1021/acs.jctc.9b00956] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Joseph C. A. Prentice
- Department of Materials, Department of Physics, and the Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, London SW7 2AZ, United Kingdom
| | - Robert J. Charlton
- Department of Materials, Department of Physics, and the Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, London SW7 2AZ, United Kingdom
| | - Arash A. Mostofi
- Department of Materials, Department of Physics, and the Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, London SW7 2AZ, United Kingdom
| | - Peter D. Haynes
- Department of Materials, Department of Physics, and the Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, London SW7 2AZ, United Kingdom
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42
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Li W, Chen M, Rabani E, Baer R, Neuhauser D. Stochastic embedding DFT: Theory and application to p-nitroaniline in water. J Chem Phys 2019; 151:174115. [PMID: 31703523 DOI: 10.1063/1.5110226] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Over this past decade, we combined the idea of stochastic resolution of identity with a variety of electronic structure methods. In our stochastic Kohn-Sham density functional theory (DFT) method, the density is an average over multiple stochastic samples, with stochastic errors that decrease as the inverse square root of the number of sampling orbitals. Here, we develop a stochastic embedding density functional theory method (se-DFT) that selectively reduces the stochastic error (specifically on the forces) for a selected subsystem(s). The motivation, similar to that of other quantum embedding methods, is that for many systems of practical interest, the properties are often determined by only a small subsystem. In stochastic embedding DFT, two sets of orbitals are used: a deterministic one associated with the embedded subspace and the rest, which is described by a stochastic set. The method agrees exactly with deterministic calculations in the limit of a large number of stochastic samples. We apply se-DFT to study a p-nitroaniline molecule in water, where the statistical errors in the forces on the system (the p-nitroaniline molecule) are reduced by an order of magnitude compared with nonembedding stochastic DFT.
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Affiliation(s)
- Wenfei Li
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA
| | - Ming Chen
- Department of Chemistry, University of California and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Eran Rabani
- Department of Chemistry, University of California and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA
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43
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Schulz A, Jacob CR. Description of intermolecular charge transfer with subsystem density-functional theory. J Chem Phys 2019; 151:131103. [PMID: 31594348 DOI: 10.1063/1.5125218] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Efficient quantum-chemical methods that are able to describe intermolecular charge transfer are crucial for modeling organic semiconductors. However, the correct description of intermolecular charge transfer with density-functional theory (DFT) is hampered by the fractional charge error of approximate exchange-correlation (xc) functionals. Here, we investigate the charge transfer induced by an external electric field in a tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) complex as a test case. For this seemingly simple model system, a supermolecular DFT treatment fails with most conventional xc functionals. Here, we present an extension of subsystem DFT to subsystems with a fractional number of electrons. We show that within such a framework, it becomes possible to overcome the fractional charge error by enforcing the correct dependence of each subsystem's total energy on the subsystem's fractional charge. Such a subsystem DFT approach allows for a correct description of the intermolecular charge transfer in the TTF-TCNQ model complex. The approach presented here can be generalized to larger molecular aggregates and will thus allow for modeling organic semiconductor materials accurately and efficiently.
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Affiliation(s)
- Anika Schulz
- Technische Universität Braunschweig, Institute of Physical and Theoretical Chemistry, Gaußstr. 17, 38106 Braunschweig, Germany
| | - Christoph R Jacob
- Technische Universität Braunschweig, Institute of Physical and Theoretical Chemistry, Gaußstr. 17, 38106 Braunschweig, Germany
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44
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Huang C. Analytical energy gradient for the embedded cluster density approximation. J Chem Phys 2019; 151:134101. [DOI: 10.1063/1.5112789] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Chen Huang
- Department of Scientific Computing, Materials Science and Engineering Program, and National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32306, USA
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45
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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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46
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Lee SJR, Ding F, Manby FR, Miller TF. Analytical gradients for projection-based wavefunction-in-DFT embedding. J Chem Phys 2019. [DOI: 10.1063/1.5109882] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Affiliation(s)
- Sebastian J. R. Lee
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Feizhi Ding
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Frederick R. Manby
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
| | - Thomas F. Miller
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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47
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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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48
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Abstract
Complex chemical systems present challenges to electronic structure theory stemming from large system sizes, subtle interactions, coupled dynamical time scales, and electronically nonadiabatic effects. New methods are needed to perform reliable, rigorous, and affordable electronic structure calculations for simulating the properties and dynamics of such systems. This Account reviews projection-based quantum embedding for electronic structure, which provides a formally exact method for density functional theory (DFT) embedding. The method also provides a rigorous and accurate approach for describing a small part of a chemical system at the level of a correlated wavefunction (WF) method while the remainder of the system is described at the level of DFT. A key advantage of projection-based embedding is that it can be formulated in terms of an extremely simple level-shift projection operator, which eliminates the need for any optimized effective potential calculation or kinetic energy functional approximation while simultaneously ensuring that no extra programming is needed to perform WF-in-DFT embedding with an arbitrary WF method. The current work presents the theoretical underpinnings of projection-based embedding, describes use of the method for combining wavefunction and density functional theories, and discusses technical refinements that have improved the applicability and robustness of the method. Applications of projection-based WF-in-DFT embedding are also reviewed, with particular focus on recent work on transition-metal catalysis, enzyme reactivity, and battery electrolyte decomposition. In particular, we review the application of projection-based embedding for the prediction of electrochemical potentials and reaction pathways in a Co-centered hydrogen evolution catalyst. Projection-based WF-in-DFT calculations are shown to provide quantitative accuracy while greatly reducing the computational cost compared with a reference coupled cluster calculation on the full system. Additionally, projection-based WF-in-DFT embedding is used to study the mechanism of citrate synthase; it is shown that projection-based WF-in-DFT largely eliminates the sensitivity of the potential energy landscape to the employed DFT exchange-correlation functional. Finally, we demonstrate the use of projection-based WF-in-DFT to study electron transfer reactions associated with battery electrolyte decomposition. Projection-based WF-in-DFT embedding is used to calculate the oxidation potentials of neat ethylene carbonate (EC), neat dimethyl carbonate (DMC), and 1:1 mixtures of EC and DMC in order to overcome qualitative inaccuracies in the electron densities and ionization energies obtained from conventional DFT methods. By further embedding the WF-in-DFT description in a molecular mechanics point-charge environment, this work enables an explicit description of the solvent and ensemble averaging of the solvent configurations. Looking forward, we anticipate continued refinement of the projection-based embedding methodology as well as its increasingly widespread application in diverse areas of chemistry, biology, and materials science.
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Affiliation(s)
- Sebastian J. R. Lee
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Matthew Welborn
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Frederick R. Manby
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
| | - Thomas F. Miller
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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49
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Hoyer CE, Williams-Young DB, Huang C, Li X. Embedding non-collinear two-component electronic structure in a collinear quantum environment. J Chem Phys 2019; 150:174114. [DOI: 10.1063/1.5092628] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Affiliation(s)
- Chad E. Hoyer
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | | | - Chen Huang
- Department of Scientific Computing, Materials Science and Engineering Program, and National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32306, USA
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
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50
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Zhang X, Carter EA. Subspace Density Matrix Functional Embedding Theory: Theory, Implementation, and Applications to Molecular Systems. J Chem Theory Comput 2018; 15:949-960. [DOI: 10.1021/acs.jctc.8b00990] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xing Zhang
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544-5263, United States
| | - Emily A. Carter
- School of Engineering and Applied Science, Princeton University, Princeton, New Jersey 08544-5263, United States
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