1
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Humeniuk A. Approximate Functionals for Multistate Density Functional Theory. J Chem Theory Comput 2024; 20:5497-5509. [PMID: 38905701 DOI: 10.1021/acs.jctc.4c00330] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/23/2024]
Abstract
Recently Lu and Gao [J. Phys. Chem. Lett. 2022, 13 (33), 7762-7769] published a new, rigorous density functional theory for excited states and proved that the projection of the kinetic and electron-repulsion operators into the subspace of the lowest electronic states are a universal functional of the matrix density D(r). This is the first attempt to find an approximation to the multistate universal functional F [ D ( r ) ] . It is shown that F (i) does not explicitly depend on the number of electronic states and (ii) is an analytic matrix functional. The Thomas-Fermi-Dirac-von Weizsäcker model and the correlation energy of the homogeneous electron gas are turned into matrix functionals guided by two principles: that each matrix functional should transform properly under basis set transformations and that the ground state functional should be recovered for a single electronic state. Lieb-Oxford-like bounds on the average kinetic and electron-repulsion energies in the subspace are given. When evaluated on the numerically exact matrix density of LiF, this simple approximation reproduces the matrix elements of the electron-repulsion operator in the basis of the exact eigenstates accurately for all bond lengths. In particular the off-diagonal elements of the effective Hamiltonian that come from the interactions of different electronic states can be calculated with the same or better accuracy than the diagonal elements. Unsurprisingly, the largest error comes from the kinetic energy functional. More exact conditions that constrain the functional form of F are needed to go beyond the local density approximation.
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Affiliation(s)
- Alexander Humeniuk
- Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa-Oiwakecho, Sakyo-Ku, Kyoto 606-8502, Japan
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2
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Lee IS, Filatov M, Min SK. Formulation of transition dipole gradients for non-adiabatic dynamics with polaritonic states. J Chem Phys 2024; 160:154103. [PMID: 38624116 DOI: 10.1063/5.0202095] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2024] [Accepted: 03/31/2024] [Indexed: 04/17/2024] Open
Abstract
A general formulation of the strong coupling between photons confined in a cavity and molecular electronic states is developed for the state-interaction state-average spin-restricted ensemble-referenced Kohn-Sham method. The light-matter interaction is included in the Jaynes-Cummings model, which requires the derivation and implementation of the analytical derivatives of the transition dipole moments between the molecular electronic states. The developed formalism is tested in the simulations of the nonadiabatic dynamics in the polaritonic states resulting from the strong coupling between the cavity photon mode and the ground and excited states of the penta-2,4-dieniminium cation, also known as PSB3. Comparison with the field-free simulations of the excited-state decay dynamics in PSB3 reveals that the light-matter coupling can considerably alter the decay dynamics by increasing the excited state lifetime and hindering photochemically induced torsion about the C=C double bonds of PSB3. The necessity of obtaining analytical transition dipole gradients for the accurate propagation of the dynamics is underlined.
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Affiliation(s)
- In Seong Lee
- Center for Multidimensional Carbon Materials (CMCM), Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea
| | - Michael Filatov
- Center for Multidimensional Carbon Materials (CMCM), Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea
| | - Seung Kyu Min
- Center for Multidimensional Carbon Materials (CMCM), Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea
- Department of Chemistry, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea
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3
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Lee S, Park W, Nakata H, Filatov M, Choi CH. Recent advances in ensemble density functional theory and linear response theory for strong correlation. B KOREAN CHEM SOC 2021. [DOI: 10.1002/bkcs.12429] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Affiliation(s)
- Seunghoon Lee
- Division of Chemistry and Chemical Engineering California Institute of Technology Pasadena California USA
| | - Woojin Park
- Department of Chemistry Kyungpook National University Daegu South Korea
| | - Hiroya Nakata
- Department of Chemistry Kyungpook National University Daegu South Korea
| | - Michael Filatov
- Department of Chemistry Kyungpook National University Daegu South Korea
| | - Cheol Ho Choi
- Department of Chemistry Kyungpook National University Daegu South Korea
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4
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Park W, Shen J, Lee S, Piecuch P, Filatov M, Choi CH. Internal Conversion between Bright (1 1Bu+) and Dark (2 1Ag-) States in s- trans-Butadiene and s- trans-Hexatriene. J Phys Chem Lett 2021; 12:9720-9729. [PMID: 34590847 DOI: 10.1021/acs.jpclett.1c02707] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Internal conversion (IC) between the two lowest singlet excited states, 11Bu+ and 21Ag-, of s-trans-butadiene and s-trans-hexatriene is investigated using a series of single- and multi- reference wave function and density functional theory (DFT) methodologies. Three independent types of the equation-of-motion coupled-cluster (EOMCC) theory capable of providing an accurate and balanced description of one- as well as two-electron transitions, abbreviated as δ-CR-EOMCC(2,3), DIP-EOMCC(4h2p){No}, and DEA-EOMCC(4p2h){Nu} or DEA-EOMCC(3p1h,4p2h){Nu}, consistently predict that the 11Bu+/21Ag- crossing in both molecules occurs along the bond length alternation coordinate. However, the analogous 11Bu+ and 21Ag- potentials obtained with some multireference approaches, such as CASSCF and MRCIS(D), as well as with the linear-response formulation of time-dependent DFT (TDDFT), do not cross. Hence, caution needs to be exercised when studying the low-lying singlet excited states of polyenes with conventional multiconfigurational methods and TDDFT. The multistate many-body perturbation theory methods, such as XMCQDPT2, do correctly reproduce the curve crossing. Among the simplest and least expensive computational methodologies, the DFT approaches that incorporate the contributions of doubly excited configurations, abbreviated as MRSF (mixed reference spin-flip) TDDFT and SSR(4,4), accurately reproduce our best EOMCC results. This is highly promising for nonadiabatic molecular dynamics simulations in larger systems.
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Affiliation(s)
- Woojin Park
- Department of Chemistry, Kyungpook National University, Daegu 41566, South Korea
| | - Jun Shen
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, United States
| | - Seunghoon Lee
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Piotr Piecuch
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, United States
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, United States
| | - Michael Filatov
- Department of Chemistry, Kyungpook National University, Daegu 41566, South Korea
| | - Cheol Ho Choi
- Department of Chemistry, Kyungpook National University, Daegu 41566, South Korea
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5
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Filatov M, Lee S, Choi CH. Description of Sudden Polarization in the Excited Electronic States with an Ensemble Density Functional Theory Method. J Chem Theory Comput 2021; 17:5123-5139. [PMID: 34319730 DOI: 10.1021/acs.jctc.1c00479] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Sudden polarization (SP) is one of the manifestations of electron transfer in the electronically excited states of molecules. Proposed initially to explain the unusual reactivity of photoexcited olefins, SP often occurs in the excited states of molecules possessing strongly correlated diradical ground state. Theoretical description of SP involves mixing between the singly excited and the doubly excited zwitterionic states, which makes it inaccessible with the use of the popular linear-response time-dependent density functional theory methods. In this work, an extended variant of the state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS, or SSR) method is applied to study SP in a number of organic diradical systems. To this end, the analytical derivative formalism is derived and implemented for the SSR(3,2) method (see the main text for explanation of the acronym), which enables the automatic geometry optimization and obtains the relaxed density matrices as well as the electron binding energies and respective Dyson's orbitals. Application of the new method to SP in the lowest singlet excited state of ethylene agrees with the results obtained previously with the use of multireference methods of wavefunction theory. A number of interesting manifestations of SP are observed, such as the charge transfer in photoexcited tetramethyleneethene (TME) diradical mediated by the vibrational motion and conductivity switching in the excited state of a donor-acceptor dyad placed in an external electric field.
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Affiliation(s)
- Michael Filatov
- Department of Chemistry, Kyungpook National University, Daegu 702-701, South Korea
| | - Seunghoon Lee
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Cheol Ho Choi
- Department of Chemistry, Kyungpook National University, Daegu 702-701, South Korea
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6
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Filatov M, Lee S, Nakata H, Choi CH. Computation of Molecular Electron Affinities Using an Ensemble Density Functional Theory Method. J Phys Chem A 2020; 124:7795-7804. [PMID: 32900199 DOI: 10.1021/acs.jpca.0c06976] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
The computation of electron attachment energies (electron affinities) was implemented in connection with an ensemble density functional theory method, the state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS or SSR) method. With the use of the extended Koopmans' theorem, the electron affinities and the respective Dyson orbitals are obtained directly for the neutral molecule, thus avoiding the necessity to compute the ionized system. Together with the EKT-SSR (extended Koopmans' theorem-SSR) method for ionization potentials, which was developed earlier, EKT-SSR for electron affinities completes the implementation of the EKT-SSR formalism, which can now be used for obtaining electron detachment as well as the electron attachment energies of molecules in the ground and excited electronic states. The extended EKT-SSR method was tested in the calculation of several closed-shell molecules. For the molecules in the ground states, the EKT-SSR energies of Dyson's orbitals are virtually identical to the energies of the unoccupied orbitals in the usual single-reference spin-restricted Kohn-Sham calculations. For the molecules in the excited states, EKT-SSR predicts an increase of the most positive electron affinity by approximately the amount of the vertical excitation energy. The electron affinities of a number of diradicals were calculated with EKT-SSR and compared with the available experimental data. With the use of a standard density functional (BH&HLYP), the EKT-SSR electron affinities deviate on average by ca. 0.2 eV from the experimental data. It is expected that the agreement with the experiment can be improved by designing density functionals parametrized for ionization energies.
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Affiliation(s)
- Michael Filatov
- Department of Chemistry, Kyungpook National University, Daegu 702-701, South Korea
| | - Seunghoon Lee
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Hiroya Nakata
- R&D Center Kagoshima, Kyocera, 1-4 Kokubu Yamashita-cho, Kirishima-shi, Kagoshima 899-4312, Japan
| | - Cheol Ho Choi
- Department of Chemistry, Kyungpook National University, Daegu 702-701, South Korea
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7
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Seritan S, Bannwarth C, Fales BS, Hohenstein EG, Isborn CM, Kokkila‐Schumacher SIL, Li X, Liu F, Luehr N, Snyder JW, Song C, Titov AV, Ufimtsev IS, Wang L, Martínez TJ. TeraChem
: A graphical processing unit
‐accelerated
electronic structure package for
large‐scale
ab initio molecular dynamics. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2020. [DOI: 10.1002/wcms.1494] [Citation(s) in RCA: 53] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Stefan Seritan
- Department of Chemistry and the PULSE Institute Stanford University Stanford California USA
- SLAC National Accelerator Laboratory Menlo Park California USA
| | - Christoph Bannwarth
- Department of Chemistry and the PULSE Institute Stanford University Stanford California USA
- SLAC National Accelerator Laboratory Menlo Park California USA
| | - Bryan S. Fales
- Department of Chemistry and the PULSE Institute Stanford University Stanford California USA
- SLAC National Accelerator Laboratory Menlo Park California USA
| | - Edward G. Hohenstein
- Department of Chemistry and the PULSE Institute Stanford University Stanford California USA
- SLAC National Accelerator Laboratory Menlo Park California USA
| | - Christine M. Isborn
- Department of Chemistry University of California Merced Merced California USA
| | | | - Xin Li
- Division of Theoretical Chemistry and Biology, School of Engineering Sciences in Chemistry, Biotechnology and Health KTH Royal Institute of Technology Stockholm Sweden
| | - Fang Liu
- Department of Chemical Engineering Massachusetts Institute of Technology Cambridge Massachusetts USA
| | | | | | - Chenchen Song
- Department of Physics University of California Berkeley Berkeley California USA
- Molecular Foundry Lawrence Berkeley National Laboratory Berkeley California USA
| | | | - Ivan S. Ufimtsev
- Department of Structural Biology Stanford University School of Medicine Stanford California USA
| | - Lee‐Ping Wang
- Department of Chemistry University of California Davis Davis California USA
| | - Todd J. Martínez
- Department of Chemistry and the PULSE Institute Stanford University Stanford California USA
- SLAC National Accelerator Laboratory Menlo Park California USA
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8
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Fromager E. Individual Correlations in Ensemble Density Functional Theory: State- and Density-Driven Decompositions without Additional Kohn-Sham Systems. PHYSICAL REVIEW LETTERS 2020; 124:243001. [PMID: 32639839 DOI: 10.1103/physrevlett.124.243001] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2020] [Accepted: 06/01/2020] [Indexed: 06/11/2023]
Abstract
Gould and Pittalis [Phys. Rev. Lett. 123, 016401 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.016401 recently revealed a density-driven (DD) correlation energy that is specific to many-electron ensembles and must be accounted for by approximations. We derive in this Letter a general and simpler expression in terms of the ensemble weights, the ensemble Kohn-Sham (KS) orbitals, and their linear response to variations in the ensemble weights. As no additional state-driven KS systems are needed, its evaluation is greatly simplified. We confirm the importance of DD effects and introduce a direct and promising route to approximations.
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Affiliation(s)
- Emmanuel Fromager
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS, Université de Strasbourg, 4 rue Blaise Pascal, 67000 Strasbourg, France
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9
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Filatov M, Lee S, Choi CH. Computation of Molecular Ionization Energies Using an Ensemble Density Functional Theory Method. J Chem Theory Comput 2020; 16:4489-4504. [PMID: 32421323 DOI: 10.1021/acs.jctc.0c00218] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
Computation of the ionization energies and of the respective Dyson orbitals based on the use of the extended Koopmans theorem (EKT) is implemented in connection with an ensemble density functional theory (eDFT) method, the state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS or SSR) method. The new methodology enables fast computation of the ionization energies and evaluation of the respective Dyson orbitals, the square norms of which are related with the ionization probabilities, in the ground and excited electronic states of molecules. As the application of EKT recycles the intermediate quantities from the SSR analytical energy gradient, evaluation of the ionization energies and probabilities can be carried out on-the-fly during the nonadiabatic molecular dynamics simulations. This opens up a perspective for fast theoretical simulation of the time-resolved photoelectron spectroscopy observations. In the present work, the new methodology is tested in the computation of the ionization energies and Dyson orbitals of several molecules in the ground and excited electronic states, including strongly correlated species, such as the ozone molecule, dissociating chemical bonds, and conical intersections.
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Affiliation(s)
- Michael Filatov
- Department of Chemistry, Kyungpook National University, Daegu 702-701, South Korea
| | - Seunghoon Lee
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Cheol Ho Choi
- Department of Chemistry, Kyungpook National University, Daegu 702-701, South Korea
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10
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First-Principles Characterization of the Elusive I Fluorescent State and the Structural Evolution of Retinal Protonated Schiff Base in Bacteriorhodopsin. J Am Chem Soc 2019; 141:18193-18203. [DOI: 10.1021/jacs.9b08941] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
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11
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Liang R, Liu F, Martínez TJ. Nonadiabatic Photodynamics of Retinal Protonated Schiff Base in Channelrhodopsin 2. J Phys Chem Lett 2019; 10:2862-2868. [PMID: 31083920 DOI: 10.1021/acs.jpclett.9b00701] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Channelrhodopsin 2 (ChR2) is a light-gated ion channel and an important tool in optogenetics. Photoisomerization of retinal protonated Schiff base (RPSB) in ChR2 triggers channel activation. Despite the importance of ChR2 in optogenetics, the detailed mechanism for photoisomerization and channel activation is still not fully understood. Here, we report on computer simulations to investigate the photoisomerization mechanism and its effect on the activation of ChR2. Nonadiabatic dynamics simulation of ChR2 was carried out using the ab initio multiple spawning (AIMS) method and quantum mechanics/molecular mechanics (QM/MM) with a restricted ensemble Kohn-Sham (REKS) treatment of the QM region. Our results agree well with spectroscopic measurements and reveal that the RPSB isomerization is highly specific around the C13=C14 bond and follows the "aborted bicycle-pedal" mechanism. In addition, RPSB photoisomerization facilitates its deprotonation and partially increases the hydration level in the channel, which could trigger subsequent channel opening and ion conduction.
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Affiliation(s)
- Ruibin Liang
- Department of Chemistry and The PULSE Institute , Stanford University , Stanford , California 94305 , United States
- SLAC National Accelerator Laboratory , 2575 Sand Hill Road , Menlo Park , California 94025 , United States
| | - Fang Liu
- Department of Chemistry and The PULSE Institute , Stanford University , Stanford , California 94305 , United States
- SLAC National Accelerator Laboratory , 2575 Sand Hill Road , Menlo Park , California 94025 , United States
| | - Todd J Martínez
- Department of Chemistry and The PULSE Institute , Stanford University , Stanford , California 94305 , United States
- SLAC National Accelerator Laboratory , 2575 Sand Hill Road , Menlo Park , California 94025 , United States
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12
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Deur K, Fromager E. Ground and excited energy levels can be extracted exactly from a single ensemble density-functional theory calculation. J Chem Phys 2019; 150:094106. [DOI: 10.1063/1.5084312] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Killian Deur
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, 4 Rue Blaise Pascal, 67000 Strasbourg, France
| | - Emmanuel Fromager
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, 4 Rue Blaise Pascal, 67000 Strasbourg, France
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13
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Pradhan E, Sato K, Akimov AV. Non-adiabatic molecular dynamics with ΔSCF excited states. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:484002. [PMID: 30407924 DOI: 10.1088/1361-648x/aae864] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Accurate modelling of nonadiabatic transitions and electron-phonon interactions in extended systems is essential for understanding the charge and energy transfer in photovoltaic and photocatalytic materials. The extensive computational costs of the advanced excited state methods have stimulated the development of many approximations to study the nonadiabatic molecular dynamics (NA-MD) in solid-state and molecular materials. In this work, we present a novel ▵SCF-NA-MD methodology that aims to account for electron-hole interactions and electron-phonon back-reaction critical in modelling photoinduced nuclear dynamics. The excited states dynamics is described using the delta self-consistent field (▵SCF) technique within the density functional formalism and the trajectory surface hopping. The technique is implemented in the open-source Libra-X package freely available on the Internet (https://github.com/Quantum-Dynamics-Hub/Libra-X). This work illustrates the general utility of the developed ▵SCF-NA-MD methodology by characterizing the excited state energies and lifetimes, reorganization energies, photoisomerization quantum yields, and by providing the mechanistic details of reactive processes in a number of organic molecules.
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Affiliation(s)
- Ekadashi Pradhan
- Department of Chemistry, University at Buffalo, The State University of New York, Buffalo, NY 14260-3000, United States of America
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14
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Lischka H, Nachtigallová D, Aquino AJA, Szalay PG, Plasser F, Machado FBC, Barbatti M. Multireference Approaches for Excited States of Molecules. Chem Rev 2018; 118:7293-7361. [DOI: 10.1021/acs.chemrev.8b00244] [Citation(s) in RCA: 197] [Impact Index Per Article: 32.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Hans Lischka
- School of Pharmaceutical Sciences and Technology, Tianjin University, Tianjin 300072, P.R. China
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, United States
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria
| | - Dana Nachtigallová
- Institute of Organic Chemistry and Biochemistry v.v.i., The Czech Academy of Sciences, Flemingovo nám. 2, 16610 Prague 6, Czech Republic
- Regional Centre of Advanced Technologies and Materials, Palacký University, 78371 Olomouc, Czech Republic
| | - Adélia J. A. Aquino
- School of Pharmaceutical Sciences and Technology, Tianjin University, Tianjin 300072, P.R. China
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, United States
- Institute for Soil Research, University of Natural Resources and Life Sciences Vienna, Peter-Jordan-Strasse 82, A-1190 Vienna, Austria
| | - Péter G. Szalay
- ELTE Eötvös Loránd University, Laboratory of Theoretical Chemistry, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
| | - Felix Plasser
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria
- Department of Chemistry, Loughborough University, Leicestershire LE11 3TU, United Kingdom
| | - Francisco B. C. Machado
- Departamento de Química, Instituto Tecnológico de Aeronáutica, São José dos Campos 12228-900, São Paulo, Brazil
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15
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Filatov M, Liu F, Martínez TJ. Analytical derivatives of the individual state energies in ensemble density functional theory method. I. General formalism. J Chem Phys 2018; 147:034113. [PMID: 28734302 DOI: 10.1063/1.4994542] [Citation(s) in RCA: 46] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The state-averaged (SA) spin restricted ensemble referenced Kohn-Sham (REKS) method and its state interaction (SI) extension, SI-SA-REKS, enable one to describe correctly the shape of the ground and excited potential energy surfaces of molecules undergoing bond breaking/bond formation reactions including features such as conical intersections crucial for theoretical modeling of non-adiabatic reactions. Until recently, application of the SA-REKS and SI-SA-REKS methods to modeling the dynamics of such reactions was obstructed due to the lack of the analytical energy derivatives. In this work, the analytical derivatives of the individual SA-REKS and SI-SA-REKS energies are derived. The final analytic gradient expressions are formulated entirely in terms of traces of matrix products and are presented in the form convenient for implementation in the traditional quantum chemical codes employing basis set expansions of the molecular orbitals. The implementation and benchmarking of the derived formalism will be described in a subsequent article of this series.
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Affiliation(s)
- Michael Filatov
- Department of Chemistry, School of Natural Sciences, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798, South Korea
| | - Fang Liu
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA and SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Todd J Martínez
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA and SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
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16
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Filatov M, Martínez TJ, Kim KS. Description of ground and excited electronic states by ensemble density functional method with extended active space. J Chem Phys 2018; 147:064104. [PMID: 28810777 DOI: 10.1063/1.4996873] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An extended variant of the spin-restricted ensemble-referenced Kohn-Sham (REKS) method, the REKS(4,4) method, designed to describe the ground electronic states of strongly multireference systems is modified to enable calculation of excited states within the time-independent variational formalism. The new method, the state-interaction state-averaged REKS(4,4), i.e., SI-SA-REKS(4,4), is capable of describing several excited states of a molecule involving double bond cleavage, polyradical character, or multiple chromophoric units. We demonstrate that the new method correctly describes the ground and the lowest singlet excited states of a molecule (ethylene) undergoing double bond cleavage. The applicability of the new method for excitonic states is illustrated with π stacked ethylene and tetracene dimers. We conclude that the new method can describe a wide range of multireference phenomena.
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Affiliation(s)
- Michael Filatov
- Department of Chemistry, School of Natural Sciences, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, South Korea
| | - Todd J Martínez
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA and SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Kwang S Kim
- Department of Chemistry, School of Natural Sciences, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, South Korea
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17
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Crespo-Otero R, Barbatti M. Recent Advances and Perspectives on Nonadiabatic Mixed Quantum–Classical Dynamics. Chem Rev 2018; 118:7026-7068. [DOI: 10.1021/acs.chemrev.7b00577] [Citation(s) in RCA: 301] [Impact Index Per Article: 50.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Rachel Crespo-Otero
- School of Biological and Chemical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
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18
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Laqua H, Kussmann J, Ochsenfeld C. Communication: Density functional theory model for multi-reference systems based on the exact-exchange hole normalization. J Chem Phys 2018; 148:121101. [DOI: 10.1063/1.5025334] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Henryk Laqua
- Department of Chemistry and Center for Integrated Protein Science (CIPSM), University of Munich (LMU), D-81377 München, Germany
| | - Jörg Kussmann
- Department of Chemistry and Center for Integrated Protein Science (CIPSM), University of Munich (LMU), D-81377 München, Germany
| | - Christian Ochsenfeld
- Department of Chemistry and Center for Integrated Protein Science (CIPSM), University of Munich (LMU), D-81377 München, Germany
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