1
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Park W, Lashkaripour A, Komarov K, Lee S, Huix-Rotllant M, Choi CH. Toward Consistent Predictions of Core/Valence Ionization Potentials and Valence Excitation Energies by MRSF-TDDFT. J Chem Theory Comput 2024; 20:5679-5694. [PMID: 38902891 DOI: 10.1021/acs.jctc.4c00640] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/22/2024]
Abstract
Optimizing exchange-correlation functionals for both core/valence ionization potentials (cIPs/vIPs) and valence excitation energies (VEEs) at the same time in the framework of MRSF-TDDFT is self-contradictory. To overcome the challenge, within the previous "adaptive exact exchange" or double-tuning strategy on Coulomb-attenuating XC functionals (CAM), a new XC functional specifically for cIPs and vIPs was first developed by enhancing exact exchange to both short- and long-range regions. The resulting DTCAM-XI functional achieved remarkably high accuracy in its predictions with errors of less than half eV. An additional concept of "valence attenuation", where the amount of exact exchange for the frontier orbital regions is selectively suppressed, was introduced to consistently predict both VEEs and IPs at the same time. The second functional, DTCAM-XIV, exhibits consistent overall prediction accuracy at ∼0.64 eV. By preferentially optimizing VEEs within the same "valence attenuation" concept, a third functional, DTCAM-VAEE, was obtained, which exhibits improved performance as compared to that of the previous DTCAM-VEE and DTCAM-AEE in the prediction of VEEs, making it an attractive alternative to BH&HLYP. As the combination of "adaptive exchange" and "valence attenuation" is operative, it would be exciting to explore its potential with a more tunable framework in the future.
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Affiliation(s)
- Woojin Park
- Department of Chemistry, Kyungpook National University, Daegu 41566, South Korea
| | - Alireza Lashkaripour
- Department of Chemistry, Kyungpook National University, Daegu 41566, South Korea
| | - Konstantin Komarov
- Center for Quantum Dynamics, Pohang University of Science and Technology, Pohang 37673, South Korea
- Department of Chemistry, University of Zürich, Zürich 8057, Switzerland
| | - Seunghoon Lee
- Department of Chemistry, Seoul National University, Seoul 151-747, South Korea
| | | | - Cheol Ho Choi
- Department of Chemistry, Kyungpook National University, Daegu 41566, South Korea
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2
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Komarov K, Park W, Lee S, Huix-Rotllant M, Choi CH. Doubly Tuned Exchange-Correlation Functionals for Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory. J Chem Theory Comput 2023; 19:7671-7684. [PMID: 37844129 DOI: 10.1021/acs.jctc.3c00884] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2023]
Abstract
It is demonstrated that significant accuracy improvements in MRSF-TDDFT can be achieved by introducing two different exchange-correlation (XC) functionals for the reference Kohn-Sham DFT and the response part of the calculations, respectively. Accordingly, two new XC functionals of doubly tuned Coulomb attenuated method-vertical excitation energy (DTCAM-VEE) and DTCAM-AEE were developed on the basis of the "adaptive exact exchange (AEE)" concept in the framework of the Coulomb-attenuating XC functionals. The values by DTCAM-VEE are in excellent agreement with those of Thiel's set [mean absolute errors (MAEs) and the interquartile range (IQR) values of 0.218 and 0.327 eV, respectively]. On the other hand, DTCAM-AEE faithfully reproduced the qualitative aspects of conical intersections (CIs) of trans-butadiene and thymine and the nonadiabatic molecular dynamics (NAMD) simulations on thymine. The latter functional also remarkably exhibited the exact 1/R asymptotic behavior of the charge-transfer state of an ethylene-tetrafluoroethylene dimer and the accurate potential energy surfaces (PESs) along the two torsional angles of retinal protonated Schiff base model with six double bonds (rPSB6). Overall, DTCAM-AEE generally performs well, as its MAE (0.237) and IQR (0.41 eV) are much improved as compared to BH&HLYP. The current idea can also be applied to other XC functionals as well as other variants of linear response theories, opening a new way of developing XC functionals.
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Affiliation(s)
- Konstantin Komarov
- Center for Quantum Dynamics, Pohang University of Science and Technology, Pohang 37673, South Korea
| | - Woojin Park
- Department of Chemistry, Kyungpook National University, Daegu 41566, South Korea
| | - Seunghoon Lee
- Department of Chemistry, Seoul National University, Seoul, 151-747, South Korea
| | | | - Cheol Ho Choi
- Department of Chemistry, Kyungpook National University, Daegu 41566, South Korea
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3
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Park W, Komarov K, Lee S, Choi CH. Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory: Multireference Advantages with the Practicality of Linear Response Theory. J Phys Chem Lett 2023; 14:8896-8908. [PMID: 37767969 PMCID: PMC10561896 DOI: 10.1021/acs.jpclett.3c02296] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2023] [Accepted: 09/21/2023] [Indexed: 09/29/2023]
Abstract
The density functional theory (DFT) and linear response (LR) time-dependent (TD)-DFT are of the utmost importance for routine computations. However, the single reference formulation of DFT suffers in the description of open-shell singlet systems such as diradicals and bond-breaking. LR-TDDFT, on the other hand, finds difficulties in the modeling of conical intersections, doubly excited states, and core-level excitations. In this Perspective, we demonstrate that many of these limitations can be overcome by recently developed mixed-reference (MR) spin-flip (SF)-TDDFT, providing an alternative yet accurate route for such challenging situations. Empowered by the practicality of the LR formalism, it is anticipated that MRSF-TDDFT can become one of the major workhorses for general routine tasks.
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Affiliation(s)
- Woojin Park
- Department
of Chemistry, Kyungpook National University, Daegu 41566, South Korea
| | - Konstantin Komarov
- Center
for Quantum Dynamics, Pohang University
of Science and Technology, Pohang 37673, 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 41566, South Korea
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4
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Komarov K, Mironov V, Lee S, Pham BQ, Gordon MS, Choi CH. High-performance strategies for the recent MRSF-TDDFT in GAMESS. J Chem Phys 2023; 158:2890476. [PMID: 37184015 DOI: 10.1063/5.0148005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2023] [Accepted: 05/02/2023] [Indexed: 05/16/2023] Open
Abstract
Multiple ERI (Electron Repulsion Integral) tensor contractions (METC) with several matrices are ubiquitous in quantum chemistry. In response theories, the contraction operation, rather than ERI computations, can be the major bottleneck, as its computational demands are proportional to the multiplicatively combined contributions of the number of excited states and the kernel pre-factors. This paper presents several high-performance strategies for METC. Optimal approaches involve either the data layout reformations of interim density and Fock matrices, the introduction of intermediate ERI quartet buffer, and loop-reordering optimization for a higher cache hit rate. The combined strategies remarkably improve the performance of the MRSF (mixed reference spin flip)-TDDFT (time-dependent density functional theory) by nearly 300%. The results of this study are not limited to the MRSF-TDDFT method and can be applied to other METC scenarios.
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Affiliation(s)
- Konstantin Komarov
- Center for Quantum Dynamics, Pohang University of Science and Technology, Pohang 37673, South Korea
| | - Vladimir Mironov
- Department of Chemistry, Kyungpook National University, Daegu 41566, South Korea
| | - Seunghoon Lee
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Buu Q Pham
- Department of Chemistry and Ames Laboratory, Iowa State University, Ames, Iowa 50011, USA
| | - Mark S Gordon
- Department of Chemistry and Ames Laboratory, Iowa State University, Ames, Iowa 50011, USA
| | - Cheol Ho Choi
- Department of Chemistry, Kyungpook National University, Daegu 41566, South Korea
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5
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Komarov K, Park W, Lee S, Zeng T, Choi CH. Accurate Spin-Orbit Coupling by Relativistic Mixed-Reference Spin-Flip-TDDFT. J Chem Theory Comput 2023; 19:953-964. [PMID: 36655271 DOI: 10.1021/acs.jctc.2c01036] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
Relativistic mixed-reference spin-flip (MRSF)-TDDFT is developed considering the spin-orbit coupling (SOC) within the mean-field approximation. The resulting SOC-MRSF faithfully reproduces the experiments with very high accuracy, which is also consistent with the values by four-component (4c) relativistic CASSCF and 4c-CASPT2 in the spin-orbit-energy splitting calculations of the C, Si, and Ge atoms. Even for the fifth-row element Sn, the SOC-MRSF yielded accurate splittings (∼ 3 % error). In the SOC calculations of the molecular 4-thiothymine with a third-row element, SOC-MRSF values are in excellent agreement with those of the SO-GMC-QDPT2 level, regardless of geometries and exchange-correlation functionals. The same SOC-MRSF predicted the anticipated chance of S1 (nπ*) → T1 (ππ*) intersystem crossing, even in thymine with only second-row elements. With its accuracy and practicality, thus, SOC-MRSF is a promising electronic structure protocol in challenging situations such as nonadiabatic molecular dynamics (NAMD) incorporating both internal conversions and intersystem crossings in large systems.
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Affiliation(s)
- Konstantin Komarov
- Center for Quantum Dynamics, Pohang University of Science and Technology, Pohang37673, South Korea
| | - Woojin Park
- Department of Chemistry, Kyungpook National University, Daegu41566, South Korea
| | - Seunghoon Lee
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California91125, USA
| | - Tao Zeng
- Department of Chemistry, York University, Toronto, ONM3J 1P3, Canada
| | - Cheol Ho Choi
- Department of Chemistry, Kyungpook National University, Daegu41566, South Korea
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6
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Shostak S, Park W, Oh J, Kim J, Lee S, Nam H, Filatov M, Kim D, Choi CH. Ultrafast Excited State Aromatization in Dihydroazulene. J Am Chem Soc 2023; 145:1638-1648. [PMID: 36633597 DOI: 10.1021/jacs.2c09800] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
Excited-state aromatization dynamics in the photochemical ring opening of dihydroazulene (DHA) is investigated by nonadiabatic molecular dynamics simulations in connection with the mixed-reference spin-flip (MRSF)-TDDFT method. It is found that, in the main reaction channel, the ring opening occurs in the excited state in a sequence of steps with increasing aromaticity. The first stage lasting ca. 200 fs produces an 8π semiaromatic S1 minimum (S1, min) through an ultrafast damped bond length alternation (BLA) movement synchronized with a partial planarization of the cycloheptatriene ring. An additional ca. 200 fs are required to gain the vibrational energy needed to overcome a ring-opening transition state characterized by an enhanced Baird aromaticity. Unlike other BLA motions of ππ* state, it was shown that their damping is a characteristic feature of aromatic bond-equalization process. In addition, some minor channels of the reaction have also been discovered, where noticeably higher barriers of the S1 non/antiaromatic transition structures must be surmounted. These anti-Baird channels led to reformation of DHA or other closed-ring products. The observed competition between the Baird and anti-Baird channels suggests that the quantum yield of photochemical products can be controllable by tipping their balance. Hence, here we suggest including the concept of anti-Baird, which would expand the applicability of Baird rule to much broader situations.
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Affiliation(s)
- Svetlana Shostak
- Department of Chemistry, Kyungpook National University, Daegu 41566, South Korea
| | - Woojin Park
- Department of Chemistry, Kyungpook National University, Daegu 41566, South Korea
| | - Juwon Oh
- Department of ICT Environmental Health System (Graduate school) and Department of Chemistry, Soonchunhyang University, Asan, Chungnam 31538, Republic of Korea
| | - Jinseok Kim
- Spectroscopy Laboratory for Functional π-Electronic Systems and Department of Chemistry, Yonsei University, Seoul 03722, Korea
| | - Seunghoon Lee
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Hyeongwoo Nam
- Department of Chemistry, Yonsei University, Seoul 03722, Korea
| | - Michael Filatov
- Department of Chemistry, Kyungpook National University, Daegu 41566, South Korea
| | - Dongho Kim
- Spectroscopy Laboratory for Functional π-Electronic Systems and Department of Chemistry, Yonsei University, Seoul 03722, Korea
| | - Cheol Ho Choi
- Department of Chemistry, Kyungpook National University, Daegu 41566, South Korea
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7
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Huix-Rotllant M, Schwinn K, Pomogaev V, Farmani M, Ferré N, Lee S, Choi CH. Photochemistry of Thymine in Solution and DNA Revealed by an Electrostatic Embedding QM/MM Combined with Mixed-Reference Spin-Flip TDDFT. J Chem Theory Comput 2023; 19:147-156. [PMID: 36574493 DOI: 10.1021/acs.jctc.2c01010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
The photochemistry of nucleobases, important for their role as building blocks of DNA, is largely affected by the electrostatic environment in which they are soaked. For example, despite the numerous studies of thymine in solution and DNA, there is still a debate on the photochemical deactivation pathways after UV absorption. Many theoretical models are oversimplified due to the lack of computationally accurate and efficient electronic structure methodologies that capture excited state electron correlation effects when nucleobases are embedded in large electrostatic media. Here, we combine mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) with electrostatic embedding QM/MM using electrostatic potential fittingfitted (ESPF) atomic charges, as a strategy to accurately and efficiently describe the electronic structure of chromophores polarized by an electrostatic medium. In particular, we develop analytic expressions for the energy and gradient of MRSF/MM based on the ESPF coupling using atom-centered grids and total charge conservation. We apply this methodology to the study of solvation effects on thymine photochemistry in water and thymine dimers in DNA. In the former, the combination of trajectory surface hopping (TSH) nonadiabatic molecular dynamics (NAMD) with MRSF/MM remarkably revealed accelerated deactivation decay pathways, which is consistent with the experimental decay time of ∼400 fs. The enhanced hopping rate can be explained by the preferential stabilization of corresponding conical interactions due to their increased dipole moments. Structurally, it is a consequence of characteristic methyl puckered geometries near the conical intersection region. For the thymine dimer in B-DNA, we found new photochemical pathways through conical intersections that could explain the formation of cyclobutadiene dimers and 6-4 photoproducts.
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Affiliation(s)
| | - Karno Schwinn
- Aix-Marseille Univ, CNRS, ICR, Marseille13013, France
| | - Vladimir Pomogaev
- Department of Chemistry, Kyungpook National University, Daegu41566, South Korea
| | - Maryam Farmani
- Department of Chemistry, Kyungpook National University, Daegu41566, South Korea
| | - Nicolas Ferré
- Aix-Marseille Univ, CNRS, ICR, Marseille13013, France
| | - Seunghoon Lee
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California91125, United States
| | - Cheol Ho Choi
- Department of Chemistry, Kyungpook National University, Daegu41566, South Korea
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8
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Burton HGA. Generalized nonorthogonal matrix elements. II: Extension to arbitrary excitations. J Chem Phys 2022; 157:204109. [DOI: 10.1063/5.0122094] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022] Open
Abstract
Electronic structure methods that exploit nonorthogonal Slater determinants face the challenge of efficiently computing nonorthogonal matrix elements. In a recent publication [H. G. A. Burton, J. Chem. Phys. 154, 144109 (2021)], I introduced a generalized extension to the nonorthogonal Wick’s theorem that allows matrix elements to be derived between excited configurations from a pair of reference determinants with a singular nonorthogonal orbital overlap matrix. However, that work only provided explicit expressions for one- and two-body matrix elements between singly- or doubly-excited configurations. Here, this framework is extended to compute generalized nonorthogonal matrix elements between higher-order excitations. Pre-computing and storing intermediate values allows one- and two-body matrix elements to be evaluated with an [Formula: see text] scaling relative to the system size, and the LIBGNME computational library is introduced to achieve this in practice. These advances make the evaluation of all nonorthogonal matrix elements almost as easy as their orthogonal counterparts, facilitating a new phase of development in nonorthogonal electronic structure theory.
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Affiliation(s)
- Hugh G. A. Burton
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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9
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Park W, Alías-Rodríguez M, Cho D, Lee S, Huix-Rotllant M, Choi CH. Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory for Accurate X-ray Absorption Spectroscopy. J Chem Theory Comput 2022; 18:6240-6250. [PMID: 36166346 DOI: 10.1021/acs.jctc.2c00746] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
It is demonstrated that the challenging core-hole particle (CHP) orbital relaxation for core electron spectra can be readily achieved by the mixed-reference spin-flip (MRSF)-time-dependent density functional theory (TDDFT). With the additional scalar relativistic effects on K-edge excitation energies of 24 second- and 17 third-row molecules, the particular ΔCHP-MRSF(R) exhibited near perfect predictions with RMSE ∼0.5 eV, featuring a median value of 0.3 and an interquartile range of 0.4. Overall, the CHP effect is 2-4 times stronger than relativistic ones, contributing more than 20 eV in the cases of sulfur and chlorine third-row atoms. Such high precision allows to explain the splitting and spectral shapes of O, N, and C atom K-edges in the ground state of thymine with atom as well as orbital specific accuracy. The same protocol with a double hole particle relaxation also produced remarkably accurate K-edge spectra of core to valence hole excitation energies from the first (nO8π*) and second (ππ*) excited states of thymine, confirming the assignment of 1s → n excitation for the experimentally observed 526.4 eV peak. Regarding both accuracy and practicality, therefore, MRSF-TDDFT provides a promising protocol for core electron spectra of both ground and excited electronic states alike.
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Affiliation(s)
- Woojin Park
- Department of Chemistry, Kyungpook National University, Daegu 41566, South Korea
| | - Marc Alías-Rodríguez
- Aix-Marseille Univ, CNRS, Institut de Chimie Radicalaire, Marseille 13284, France
| | - Daeheum Cho
- Department of Chemistry, Kyungpook National University, Daegu 41566, South Korea
| | - Seunghoon Lee
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Miquel Huix-Rotllant
- Aix-Marseille Univ, CNRS, Institut de Chimie Radicalaire, Marseille 13284, France
| | - Cheol Ho Choi
- Department of Chemistry, Kyungpook National University, Daegu 41566, South Korea
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10
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Park W, Filatov (Gulak) M, Sadiq S, Gerasimov I, Lee S, Joo T, Choi CH. A Plausible Mechanism of Uracil Photohydration Involves an Unusual Intermediate. J Phys Chem Lett 2022; 13:7072-7080. [PMID: 35900137 PMCID: PMC9358713 DOI: 10.1021/acs.jpclett.2c01694] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2022] [Accepted: 07/11/2022] [Indexed: 05/28/2023]
Abstract
It is well-known that photolysis of pyrimidine nucleobases, such as uracil, in an aqueous environment results in the formation of hydrate as one of the main products. Although several hypotheses regarding photohydration have been proposed in the past, e.g., the zwitterionic and "hot" ground-state mechanisms, its detailed mechanism remains elusive. Here, theoretical nonadiabatic simulations of the uracil photodynamics reveal the formation of a highly energetic but kinetically stable intermediate that features a half-chair puckered pyrimidine ring and a strongly twisted intracyclic double bond. The existence and the kinetic stability of the intermediate are confirmed by a variety of computational chemistry methods. According to the simulations, the unusual intermediate is mainly formed almost immediately (∼50-200 fs) upon photoabsorption and survives long enough to engage in a hydration reaction with a neighboring water. A plausible mechanism of uracil photohydration is proposed on the basis of the modeling of nucleophilic insertion of water into the twisted double bond of the intermediate.
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Affiliation(s)
- Woojin Park
- Department
of Chemistry, Kyungpook National University, Daegu 41566, South Korea
| | | | - Saima Sadiq
- Department
of Chemistry, Kyungpook National University, Daegu 41566, South Korea
| | - Igor Gerasimov
- Department
of Chemistry, Kyungpook National University, Daegu 41566, South Korea
| | - Seunghoon Lee
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Taiha Joo
- Department
of Chemistry, Pohang University of Science
and Technology (POSTECH), Pohang 37673, South Korea
| | - Cheol Ho Choi
- Department
of Chemistry, Kyungpook National University, Daegu 41566, South Korea
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11
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Yalouz S, Koridon E, Senjean B, Lasorne B, Buda F, Visscher L. Analytical Nonadiabatic Couplings and Gradients within the State-Averaged Orbital-Optimized Variational Quantum Eigensolver. J Chem Theory Comput 2022; 18:776-794. [PMID: 35029988 DOI: 10.1021/acs.jctc.1c00995] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
We introduce several technical and analytical extensions to our recent state-averaged orbital-optimized variational quantum eigensolver (SA-OO-VQE) algorithm (see Yalouz et al. Quantum Sci. Technol. 2021, 6, 024004). Motivated by the limitations of current quantum computers, the first extension consists of an efficient state-resolution procedure to find the SA-OO-VQE eigenstates, and not just the subspace spanned by them, while remaining in the equi-ensemble framework. This approach avoids expensive intermediate resolutions of the eigenstates by postponing this problem to the very end of the full algorithm. The second extension allows for the estimation of analytical gradients and nonadiabatic couplings, which are crucial in many practical situations ranging from the search of conical intersections to the simulation of quantum dynamics, in, for example, photoisomerization reactions. The accuracy of our new implementations is demonstrated on the formaldimine molecule CH2NH (a minimal Schiff base model relevant for the study of photoisomerization in larger biomolecules), for which we also perform a geometry optimization to locate a conical intersection between the ground and first-excited electronic states of the molecule.
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Affiliation(s)
- Saad Yalouz
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, 4 rue Blaise Pascal, Strasbourg, 67000, France
| | - Emiel Koridon
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, Amsterdam, NL-1081 HV, The Netherlands.,Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, Leiden, 2300 RA, The Netherlands
| | - Bruno Senjean
- CGM, Univ Montpellier, CNRS, ENSCM, Montpellier, 34070, France
| | | | - Francesco Buda
- Leiden Institute of Chemistry, Leiden University, Einsteinweg 55, P.O. Box 9502, Leiden, 2300 RA, The Netherlands
| | - Lucas Visscher
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, Amsterdam, NL-1081 HV, The Netherlands
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12
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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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13
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Pomogaev V, Lee S, Shaik S, Filatov M, Choi CH. Exploring Dyson's Orbitals and Their Electron Binding Energies for Conceptualizing Excited States from Response Methodology. J Phys Chem Lett 2021; 12:9963-9972. [PMID: 34617764 DOI: 10.1021/acs.jpclett.1c02494] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
The molecular orbital (MO) concept is a useful tool, which relates the molecular ground-state energy with the energies (and occupations) of the individual orbitals. However, analysis of the excited states from linear response computations is performed in terms of the initial state MOs or some other forms of orbitals, e.g., natural or natural transition orbitals. Because these orbitals lack the respective energies, they do not allow developing a consistent orbital picture of the excited states. Herein, we argue that Dyson's orbitals enable description of the response states compatible with the concepts of molecular orbital theory. The Dyson orbitals and their energies obtained by mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) for the response ground state are remarkably similar to the canonical MOs obtained by the usual DFT calculation. For excited states, the Dyson orbitals provide a chemically sensible picture of the electronic transitions, thus bridging the chasm between orbital theory and response computations.
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Affiliation(s)
- Vladimir Pomogaev
- 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
| | - Sason Shaik
- The Lise Meitner-Minerva Center for Computational Quantum Chemistry, Institute of Chemistry, The Hebrew University of Jerusalem, Givat Ram Campus, Jerusalem 91904, Israel
| | - Michael Filatov
- Department of Chemistry, Kyungpook National University, Daegu 702-701, South Korea
| | - Cheol Ho Choi
- Department of Chemistry, Kyungpook National University, Daegu 702-701, South Korea
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14
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Wang Z, Wu C, Liu W. NAC-TDDFT: Time-Dependent Density Functional Theory for Nonadiabatic Couplings. Acc Chem Res 2021; 54:3288-3297. [PMID: 34448566 DOI: 10.1021/acs.accounts.1c00312] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
First-order nonadiabatic coupling (NAC) matrix elements (fo-NACMEs) are the basic quantities in theoretical descriptions of electronically nonadiabatic processes that are ubiquitous in molecular physics and chemistry. Given the large size of systems of chemical interests, time-dependent density functional theory (TDDFT) is usually the first choice of methods. However, the lack of many-electron wave functions in TDDFT renders the formulation of NAC-TDDFT for fo-NACMEs conceptually difficult. Because of this, various variants of NAC-TDDFT have been proposed in the literature from different standing points, including the Hellmann-Feynman-like expression and auxiliary/pseudo-wave function (AWF)-, equation-of-motion (EOM)-, and time-dependent perturbation theory (TDPT)-based formulations. Based on critical analyses, the following conclusions are made here: (1) The Hellmann-Feynman-like expression, which is rooted in exact wave function theory, is hardly useful due to huge demand on basis sets. (2) Although most popular, the AWF variants of NAC-TDDFT are not theoretically founded and become ambiguous particularly for the fo-NACMEs between two excited states, although they do agree with the EOM and TDPT variants under the Tamm-Dancoff approximation. (3) The TDPT variant of NAC-TDDFT is theoretically most rigorous but suffers from numerical instabilities on the one hand and does not differ to a significant extent from the EOM variant on the other hand. (4) As such, the EOM variant of NAC-TDDFT for the fo-NACMEs between the ground and excited states and between two excited states is solely the right choice in practice. These formal analyses are fully supported by numerical experimentations, taking azulene as a showcase. The proper implementation of the EOM variant of NAC-TDDFT is also highlighted, showing that the fo-NACMEs between the ground and excited states and between two excited states are computationally very much the same as the analytic energy gradients of DFT and TDDFT, respectively. Possible future developments of the EOM variant of NAC-TDDFT are also highlighted. Its extensions to spin-adapted open-shell TDDFT and proper treatment of spin-orbit couplings (which are another source of force for electronically nonadiabatic processes) are particularly warranted in the near future.
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Affiliation(s)
- Zikuan Wang
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China
| | - Chenyu Wu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China
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