1
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Chibueze CS, Visscher L. Restricted open-shell time-dependent density functional theory with perturbative spin-orbit coupling. J Chem Phys 2024; 161:094112. [PMID: 39234966 DOI: 10.1063/5.0226870] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2024] [Accepted: 08/19/2024] [Indexed: 09/06/2024] Open
Abstract
When using quantum chemical methods to study electronically excited states of open-shell molecules, it is often beneficial to start with wave functions that are spin eigenfunctions. For excited states of molecules containing heavy elements, spin-orbit coupling (SOC) is important and needs to be included as well. An efficient approach is to include SOC perturbatively on top of a restricted open-shell Kohn-Sham (ROKS) time-dependent density functional theory, which can be combined with the Tamm-Dancoff approximation (TDA) to suppress numerical instabilities. We implemented and assessed the potential of such a ROKS-TDA-SOC method, also featuring the possibility of calculating transition dipole moments between states to allow for full spectrum simulation. Our study shows that the ROKS-TDA-SOC formalism yields a clear and easy-to-use method to obtain electronically excited states of open-shell molecules that are of moderate size and contain heavy elements.
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Affiliation(s)
- Chima S Chibueze
- Department of Chemistry and Pharmaceutical Sciences, Vrije Universiteit, De Boelelaan 1108, 1081 HZ Amsterdam, The Netherlands
| | - Lucas Visscher
- Department of Chemistry and Pharmaceutical Sciences, Vrije Universiteit, De Boelelaan 1108, 1081 HZ Amsterdam, The Netherlands
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2
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Arias-Martinez JE, Wu H, Head-Gordon M. Generalization of One-Center Nonorthogonal Configuration Interaction Singles to Open-Shell Singlet Reference States: Theory and Application to Valence-Core Pump-Probe States in Acetylacetone. J Chem Theory Comput 2024; 20:752-766. [PMID: 38164934 DOI: 10.1021/acs.jctc.3c01139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2024]
Abstract
We formulate a one-center nonorthogonal configuration interaction singles (1C-NOCIS) theory for the computation of core excited states of an initial singlet state with two unpaired electrons. This model, which we refer to as 1C-NOCIS two-electron open-shell (2eOS), is appropriate for computing the K-edge near-edge X-ray absorption spectra (NEXAS) of the valence excited states of closed-shell molecules relevant to pump-probe time-resolved (TR) NEXAS experiments. With the inclusion of core-hole relaxation effects and explicit spin adaptation, 1C-NOCIS 2eOS requires mild shifts to match experiment, is free of artifacts due to spin contamination, and can capture the high-energy region of the spectrum beyond the transitions into the singly occupied molecular orbitals (SOMOs). Calculations on water and thymine illustrate the different key features of excited-state NEXAS, namely, the core-to-SOMO transitions as well as shifts and spin-splittings in the transitions analogous to those of the ground state. Simulations of the TR-NEXAS of acetylacetone after excitation to its π → π* singlet excited state at the carbon K-edge, an experiment carried out recently, showcase the ability of 1C-NOCIS 2eOS to efficiently simulate NEXAS based on nonadiabatic molecular dynamics simulations.
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Affiliation(s)
- Juan E Arias-Martinez
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Hamlin Wu
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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3
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Wang X, Wu C, Wang Z, Liu W. When do tripdoublet states fluoresce? A theoretical study of copper(II) porphyrin. Front Chem 2023; 11:1259016. [PMID: 38025061 PMCID: PMC10667454 DOI: 10.3389/fchem.2023.1259016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2023] [Accepted: 10/23/2023] [Indexed: 12/01/2023] Open
Abstract
Open-shell molecules rarely fluoresce, due to their typically faster non-radiative relaxation rates compared to closed-shell ones. Even rarer is the fluorescence from states that have two more unpaired electrons than the open-shell ground state, since they involve excitations from closed-shell orbitals to vacant-shell orbitals, which are typically higher in energy compared to excitations from or out of open-shell orbitals. States that are dominated by the former type of excitations are known as tripdoublet states when they can be described as a triplet excitation antiferromagnetically coupled to a doublet state, and their description by unrestricted single-reference methods (e.g., U-TDDFT) is notoriously inaccurate due to large spin contamination. In this work, we applied our spin-adapted TDDFT method, X-TDDFT, and the efficient and accurate static-dynamic-static second order perturbation theory (SDSPT2), to the study of the excited states as well as their relaxation pathways of copper(II) porphyrin; previous experimental works suggested that the photoluminescence of some substituted copper(II) porphyrins originate from a tripdoublet state, formed by a triplet ligand π → π* excitation antiferromagnetically coupled with the unpaired d electron. Our results demonstrated favorable agreement between the X-TDDFT, SDSPT2 and experimental excitation energies, and revealed noticeable improvements of X-TDDFT compared to U-TDDFT, not only for vertical excitation energies but also for adiabatic energy differences. These suggest that X-TDDFT is a reliable tool for the study of tripdoublet state fluorescence. Intriguingly, we showed that the aforementioned tripdoublet state is only slightly above the lowest doublet excited state and lies only slightly higher than the lowest quartet state, which suggests that the tripdoublet of copper(II) porphyrin is long-lived enough to fluoresce due to a lack of efficient non-radiative relaxation pathways; an explanation for this unusual state ordering is given. Indeed, thermal vibration correlation function (TVCF)-based calculations of internal conversion, intersystem crossing, and radiative transition rates confirm that copper(II) porphyrin emits thermally activated delayed fluorescence (TADF) and a small amount of phosphorescence at low temperature (83 K), in accordance with experiment. The present contribution is concluded by a few possible approaches of designing new molecules that fluoresce from tripdoublet states.
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Affiliation(s)
- Xingwen Wang
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, China
| | - Chenyu Wu
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, China
| | - Zikuan Wang
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, China
- Max-Planck-Institut für Kohlenforschung, Mülheim an der Ruhr, Germany
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, China
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4
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Pokhilko P, Zgid D. Natural orbitals and two-particle correlators as tools for the analysis of effective exchange couplings in solids. Phys Chem Chem Phys 2023; 25:21267-21279. [PMID: 37548912 DOI: 10.1039/d3cp01975f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/08/2023]
Abstract
Using generalizations of spin-averaged natural orbitals and two-particle charge correlators for solids, we investigate the electronic structure of antiferromagnetic transition-metal oxides with a fully self-consistent, imaginary-time GW method. Our findings disagree with the Goodenough-Kanamori (GK) rules that are commonly used for the qualitative interpretation of such solids. First, we found a strong dependence of the natural orbital occupancies on momenta, contradicting GK assumptions. Second, along the momentum path, the character of natural orbitals changes. In particular, the contributions of oxygen 2s orbitals are important, which has not been considered in the GK rules. To analyze the influence of the electronic correlation on the values of effective exchange coupling constants, we use both natural orbitals and two-particle correlators and show that electronic screening modulates the degree of superexchange by stabilizing the charge-transfer contributions, which greatly affects these coupling constants. Finally, we give a set of predictions and recommendations regarding the use of density functional, Green's function, and wave-function methods for evaluating effective magnetic couplings in molecules and solids.
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Affiliation(s)
- Pavel Pokhilko
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA.
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
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5
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Zhang L, Cao Z. Electronic and photophysical properties of selected organic boron‐containing molecules: Insight into effects of heteroatom substitution and aggregation. J CHIN CHEM SOC-TAIP 2022. [DOI: 10.1002/jccs.202200467] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Affiliation(s)
- Lin Zhang
- State Key Laboratory of Physical Chemistry of Solid Surfaces and Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry College of Chemistry and Chemical Engineering, Xiamen University Xiamen China
| | - Zexing Cao
- State Key Laboratory of Physical Chemistry of Solid Surfaces and Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry College of Chemistry and Chemical Engineering, Xiamen University Xiamen China
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6
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Ye L, Wang H, Zhang Y, Liu W. Self-Adaptive Real-Time Time-Dependent Density Functional Theory for X-ray Absorptions. J Chem Phys 2022; 157:074106. [DOI: 10.1063/5.0106250] [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
Real-time time-dependent density functional theory (RT-TDDFT) can in principle access the whole absorption spectrum of a many-electron system exposed to a narrow pulse. However, this requires an accurate and efficient propagator for the numerical integration of the time-dependent Kohn-Sham equation. While a low-order time propagator is already sufficient for the low-lying valence absorption spectra, it is no longer the case for the X-ray absorption spectra (XAS) of systems composed even only of light elements, for which the use of a high-order propagator is indispensable. It is then crucial to choose a largest possible time step and a shortest possible simulation time, so as to minimize the computational cost. To this end, we propose here a robust AutoPST approach to determine automatically (Auto) the propagator (P), step (S), and time (T) for relativistic RT-TDDFT simulations of XAS.
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Affiliation(s)
| | - Hao Wang
- Shandong University - Qingdao Campus, China
| | | | - Wenjian Liu
- Qingdao Institue for Theoretical and Computational Sciences, Shandong University, China
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7
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Monino E, Boggio-Pasqua M, Scemama A, Jacquemin D, Loos PF. Reference Energies for Cyclobutadiene: Automerization and Excited States. J Phys Chem A 2022; 126:4664-4679. [PMID: 35820169 DOI: 10.1021/acs.jpca.2c02480] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Cyclobutadiene is a well-known playground for theoretical chemists and is particularly suitable to test ground- and excited-state methods. Indeed, due to its high spatial symmetry, especially at the D4h square geometry but also in the D2h rectangular arrangement, the ground and excited states of cyclobutadiene exhibit multiconfigurational characters and single-reference methods, such as standard adiabatic time-dependent density-functional theory (TD-DFT) or standard equation-of-motion coupled cluster (EOM-CC), are notoriously known to struggle in such situations. In this work, using a large panel of methods and basis sets, we provide an extensive computational study of the automerization barrier (defined as the difference between the square and rectangular ground-state energies) and the vertical excitation energies at D2h and D4h equilibrium structures. In particular, selected configuration interaction (SCI), multireference perturbation theory (CASSCF, CASPT2, and NEVPT2), and coupled-cluster (CCSD, CC3, CCSDT, CC4, and CCSDTQ) calculations are performed. The spin-flip formalism, which is known to provide a qualitatively correct description of these diradical states, is also tested within TD-DFT (combined with numerous exchange-correlation functionals) and the algebraic diagrammatic construction [ADC(2)-s, ADC(2)-x, and ADC(3)]. A theoretical best estimate is defined for the automerization barrier and for each vertical transition energy.
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Affiliation(s)
- Enzo Monino
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Martial Boggio-Pasqua
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Denis Jacquemin
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
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8
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Liang W, Pei Z, Mao Y, Shao Y. Evaluation of molecular photophysical and photochemical properties using linear response time-dependent density functional theory with classical embedding: Successes and challenges. J Chem Phys 2022; 156:210901. [PMID: 35676148 PMCID: PMC9162785 DOI: 10.1063/5.0088271] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Accepted: 05/15/2022] [Indexed: 01/04/2023] Open
Abstract
Time-dependent density functional theory (TDDFT) based approaches have been developed in recent years to model the excited-state properties and transition processes of the molecules in the gas-phase and in a condensed medium, such as in a solution and protein microenvironment or near semiconductor and metal surfaces. In the latter case, usually, classical embedding models have been adopted to account for the molecular environmental effects, leading to the multi-scale approaches of TDDFT/polarizable continuum model (PCM) and TDDFT/molecular mechanics (MM), where a molecular system of interest is designated as the quantum mechanical region and treated with TDDFT, while the environment is usually described using either a PCM or (non-polarizable or polarizable) MM force fields. In this Perspective, we briefly review these TDDFT-related multi-scale models with a specific emphasis on the implementation of analytical energy derivatives, such as the energy gradient and Hessian, the nonadiabatic coupling, the spin-orbit coupling, and the transition dipole moment as well as their nuclear derivatives for various radiative and radiativeless transition processes among electronic states. Three variations of the TDDFT method, the Tamm-Dancoff approximation to TDDFT, spin-flip DFT, and spin-adiabatic TDDFT, are discussed. Moreover, using a model system (pyridine-Ag20 complex), we emphasize that caution is needed to properly account for system-environment interactions within the TDDFT/MM models. Specifically, one should appropriately damp the electrostatic embedding potential from MM atoms and carefully tune the van der Waals interaction potential between the system and the environment. We also highlight the lack of proper treatment of charge transfer between the quantum mechanics and MM regions as well as the need for accelerated TDDFT modelings and interpretability, which calls for new method developments.
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Affiliation(s)
- WanZhen Liang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China
| | - Zheng Pei
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China
| | - Yuezhi Mao
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Yihan Shao
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, USA
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9
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Herperger KR, Krumland J, Cocchi C. Laser-Induced Electronic and Vibronic Dynamics in the Pyrene Molecule and Its Cation. J Phys Chem A 2021; 125:9619-9631. [PMID: 34714646 DOI: 10.1021/acs.jpca.1c06538] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
Among polycyclic aromatic hydrocarbons, pyrene is widely used as an optical probe thanks to its peculiar ultraviolet absorption and infrared emission features. Interestingly, this molecule is also an abundant component of the interstellar medium, where it is detected via its unique spectral fingerprints. In this work, we present a comprehensive first-principles study on the electronic and vibrational response of pyrene and its cation to ultrafast, coherent pulses in resonance with their optically active excitations in the ultraviolet region. The analysis of molecular symmetries, electronic structure, and linear optical spectra is used to interpret transient absorption spectra and kinetic energy spectral densities computed for the systems excited by ultrashort laser fields. By disentangling the effects of the electronic and vibrational dynamics via ad hoc simulations with stationary and moving ions, and, in specific cases, with the aid of auxiliary model systems, we rationalize that the nuclear motion is mainly harmonic in the neutral species, while strong anharmonic oscillations emerge in the cation, driven by electronic coherence. Our results provide additional insights into the ultrafast vibronic dynamics of pyrene and related compounds and set the stage for future investigations on more complex carbon-conjugated molecules.
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Affiliation(s)
- Katherine R Herperger
- Department of Physics, University of Ottawa, Ottawa ON K1N 6N5, Canada.,Physics Department and IRIS Adlershof, Humboldt-Universität zu Berlin, 12489 Berlin, Germany
| | - Jannis Krumland
- Physics Department and IRIS Adlershof, Humboldt-Universität zu Berlin, 12489 Berlin, Germany
| | - Caterina Cocchi
- Physics Department and IRIS Adlershof, Humboldt-Universität zu Berlin, 12489 Berlin, Germany.,Institute of Physics, Carl von Ossietzky Universität Oldenburg, 26129 Oldenburg, Germany
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10
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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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11
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Li Z. Structured eigenvalue problems in electronic structure methods from a unified perspective. CHINESE J CHEM PHYS 2021. [DOI: 10.1063/1674-0068/cjcp2107119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Zhendong Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
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12
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Zhang X, Herbert JM. Nonadiabatic dynamics with spin-flip vs linear-response time-dependent density functional theory: A case study for the protonated Schiff base C 5H 6NH 2. J Chem Phys 2021; 155:124111. [PMID: 34598550 DOI: 10.1063/5.0062757] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
Nonadiabatic trajectory surface hopping simulations are reported for trans-C5H6NH2 +, a model of the rhodopsin chromophore, using the augmented fewest-switches algorithm. Electronic structure calculations were performed using time-dependent density functional theory (TDDFT) in both its conventional linear-response (LR) and its spin-flip (SF) formulations. In the SF-TDDFT case, spin contamination in the low-lying singlet states is removed by projecting out the lowest triplet component during iterative solution of the TDDFT eigenvalue problem. The results show that SF-TDDFT qualitatively describes the photoisomerization of trans-C5H6NH2 +, with favorable comparison to previous studies using multireference electronic structure methods. In contrast, conventional LR-TDDFT affords qualitatively different photodynamics due to an incorrect excited-state potential surface near the Franck-Condon region. In addition, the photochemistry (involving pre-twisting of the central double bond) appears to be different for SF- and LR-TDDFT, which may be a consequence of different conical intersection topographies afforded by these two methods. The present results contrast with previous surface-hopping studies suggesting that the LR-TDDFT method's incorrect topology around S1/S0 conical intersections is immaterial to the photodynamics.
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Affiliation(s)
- Xing Zhang
- Department of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - John M Herbert
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
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13
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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: 15] [Impact Index Per Article: 5.0] [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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14
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Epifanovsky E, Gilbert ATB, Feng X, Lee J, Mao Y, Mardirossian N, Pokhilko P, White AF, Coons MP, Dempwolff AL, Gan Z, Hait D, Horn PR, Jacobson LD, Kaliman I, Kussmann J, Lange AW, Lao KU, Levine DS, Liu J, McKenzie SC, Morrison AF, Nanda KD, Plasser F, Rehn DR, Vidal ML, You ZQ, Zhu Y, Alam B, Albrecht BJ, Aldossary A, Alguire E, Andersen JH, Athavale V, Barton D, Begam K, Behn A, Bellonzi N, Bernard YA, Berquist EJ, Burton HGA, Carreras A, Carter-Fenk K, Chakraborty R, Chien AD, Closser KD, Cofer-Shabica V, Dasgupta S, de Wergifosse M, Deng J, Diedenhofen M, Do H, Ehlert S, Fang PT, Fatehi S, Feng Q, Friedhoff T, Gayvert J, Ge Q, Gidofalvi G, Goldey M, Gomes J, González-Espinoza CE, Gulania S, Gunina AO, Hanson-Heine MWD, Harbach PHP, Hauser A, Herbst MF, Hernández Vera M, Hodecker M, Holden ZC, Houck S, Huang X, Hui K, Huynh BC, Ivanov M, Jász Á, Ji H, Jiang H, Kaduk B, Kähler S, Khistyaev K, Kim J, Kis G, Klunzinger P, Koczor-Benda Z, Koh JH, Kosenkov D, Koulias L, Kowalczyk T, Krauter CM, Kue K, Kunitsa A, Kus T, Ladjánszki I, Landau A, Lawler KV, Lefrancois D, Lehtola S, Li RR, Li YP, Liang J, Liebenthal M, Lin HH, Lin YS, Liu F, Liu KY, Loipersberger M, Luenser A, Manjanath A, Manohar P, Mansoor E, Manzer SF, Mao SP, Marenich AV, Markovich T, Mason S, Maurer SA, McLaughlin PF, Menger MFSJ, Mewes JM, Mewes SA, Morgante P, Mullinax JW, Oosterbaan KJ, Paran G, Paul AC, Paul SK, Pavošević F, Pei Z, Prager S, Proynov EI, Rák Á, Ramos-Cordoba E, Rana B, Rask AE, Rettig A, Richard RM, Rob F, Rossomme E, Scheele T, Scheurer M, Schneider M, Sergueev N, Sharada SM, Skomorowski W, Small DW, Stein CJ, Su YC, Sundstrom EJ, Tao Z, Thirman J, Tornai GJ, Tsuchimochi T, Tubman NM, Veccham SP, Vydrov O, Wenzel J, Witte J, Yamada A, Yao K, Yeganeh S, Yost SR, Zech A, Zhang IY, Zhang X, Zhang Y, Zuev D, Aspuru-Guzik A, Bell AT, Besley NA, Bravaya KB, Brooks BR, Casanova D, Chai JD, Coriani S, Cramer CJ, Cserey G, DePrince AE, DiStasio RA, Dreuw A, Dunietz BD, Furlani TR, Goddard WA, Hammes-Schiffer S, Head-Gordon T, Hehre WJ, Hsu CP, Jagau TC, Jung Y, Klamt A, Kong J, Lambrecht DS, Liang W, Mayhall NJ, McCurdy CW, Neaton JB, Ochsenfeld C, Parkhill JA, Peverati R, Rassolov VA, Shao Y, Slipchenko LV, Stauch T, Steele RP, Subotnik JE, Thom AJW, Tkatchenko A, Truhlar DG, Van Voorhis T, Wesolowski TA, Whaley KB, Woodcock HL, Zimmerman PM, Faraji S, Gill PMW, Head-Gordon M, Herbert JM, Krylov AI. Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package. J Chem Phys 2021; 155:084801. [PMID: 34470363 PMCID: PMC9984241 DOI: 10.1063/5.0055522] [Citation(s) in RCA: 480] [Impact Index Per Article: 160.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.
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Affiliation(s)
- Evgeny Epifanovsky
- Q-Chem, Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588, USA
| | | | | | - Joonho Lee
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Yuezhi Mao
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | | | - Pavel Pokhilko
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | - Alec F. White
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Marc P. Coons
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Adrian L. Dempwolff
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Zhengting Gan
- Q-Chem, Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588, USA
| | - Diptarka Hait
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Paul R. Horn
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Leif D. Jacobson
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | | | - Jörg Kussmann
- Department of Chemistry, Ludwig Maximilian University, Butenandtstr. 7, D-81377 München, Germany
| | - Adrian W. Lange
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Ka Un Lao
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Daniel S. Levine
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | | | - Simon C. McKenzie
- Research School of Chemistry, Australian National University, Canberra, Australia
| | | | - Kaushik D. Nanda
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | | | - Dirk R. Rehn
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Marta L. Vidal
- Department of Chemistry, Technical University of Denmark, Kemitorvet Bldg. 207, DK-2800 Kgs Lyngby, Denmark
| | | | - Ying Zhu
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Bushra Alam
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Benjamin J. Albrecht
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | | | - Ethan Alguire
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Josefine H. Andersen
- Department of Chemistry, Technical University of Denmark, Kemitorvet Bldg. 207, DK-2800 Kgs Lyngby, Denmark
| | - Vishikh Athavale
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Dennis Barton
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Khadiza Begam
- Department of Physics, Kent State University, Kent, Ohio 44242, USA
| | - Andrew Behn
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Nicole Bellonzi
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Yves A. Bernard
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | | | - Hugh G. A. Burton
- Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
| | - Abel Carreras
- Donostia International Physics Center, 20080 Donostia, Euskadi, Spain
| | - Kevin Carter-Fenk
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | | | - Alan D. Chien
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | | | - Vale Cofer-Shabica
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Saswata Dasgupta
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Marc de Wergifosse
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | - Jia Deng
- Research School of Chemistry, Australian National University, Canberra, Australia
| | | | - Hainam Do
- School of Chemistry, University of Nottingham, Nottingham, United Kingdom
| | - Sebastian Ehlert
- Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, Beringstr. 4, 53115 Bonn, Germany
| | - Po-Tung Fang
- Department of Physics, National Taiwan University, Taipei 10617, Taiwan
| | | | - Qingguo Feng
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44240, USA
| | - Triet Friedhoff
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - James Gayvert
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA
| | - Qinghui Ge
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Gergely Gidofalvi
- Department of Chemistry and Biochemistry, Gonzaga University, Spokane, Washington 99258, USA
| | - Matthew Goldey
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Joe Gomes
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | | | - Sahil Gulania
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | - Anastasia O. Gunina
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | | | - Phillip H. P. Harbach
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Andreas Hauser
- Institute of Experimental Physics, Graz University of Technology, Graz, Austria
| | | | - Mario Hernández Vera
- Department of Chemistry, Ludwig Maximilian University, Butenandtstr. 7, D-81377 München, Germany
| | - Manuel Hodecker
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Zachary C. Holden
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Shannon Houck
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Xunkun Huang
- Department of Chemistry, Xiamen University, Xiamen 361005, China
| | - Kerwin Hui
- Department of Physics, National Taiwan University, Taipei 10617, Taiwan
| | - Bang C. Huynh
- Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
| | - Maxim Ivanov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | - Ádám Jász
- Stream Novation Ltd., Práter utca 50/a, H-1083 Budapest, Hungary
| | - Hyunjun Ji
- Graduate School of Energy, Environment, Water and Sustainability (EEWS), Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Republic of Korea
| | - Hanjie Jiang
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Benjamin Kaduk
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Sven Kähler
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | - Kirill Khistyaev
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | - Jaehoon Kim
- Graduate School of Energy, Environment, Water and Sustainability (EEWS), Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Republic of Korea
| | - Gergely Kis
- Stream Novation Ltd., Práter utca 50/a, H-1083 Budapest, Hungary
| | | | - Zsuzsanna Koczor-Benda
- Department of Chemistry, Ludwig Maximilian University, Butenandtstr. 7, D-81377 München, Germany
| | - Joong Hoon Koh
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - Dimitri Kosenkov
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA
| | - Laura Koulias
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306, USA
| | | | - Caroline M. Krauter
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Karl Kue
- Institute of Chemistry, Academia Sinica, 128, Academia Road Section 2, Nangang District, Taipei 11529, Taiwan
| | - Alexander Kunitsa
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA
| | - Thomas Kus
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | | | - Arie Landau
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | - Keith V. Lawler
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Daniel Lefrancois
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | | | - Run R. Li
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306, USA
| | - Yi-Pei Li
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Jiashu Liang
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Marcus Liebenthal
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306, USA
| | - Hung-Hsuan Lin
- Institute of Chemistry, Academia Sinica, 128, Academia Road Section 2, Nangang District, Taipei 11529, Taiwan
| | - You-Sheng Lin
- Department of Physics, National Taiwan University, Taipei 10617, Taiwan
| | - Fenglai Liu
- Q-Chem, Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588, USA
| | | | | | - Arne Luenser
- Department of Chemistry, Ludwig Maximilian University, Butenandtstr. 7, D-81377 München, Germany
| | - Aaditya Manjanath
- Institute of Chemistry, Academia Sinica, 128, Academia Road Section 2, Nangang District, Taipei 11529, Taiwan
| | - Prashant Manohar
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | - Erum Mansoor
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Sam F. Manzer
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Shan-Ping Mao
- Department of Physics, National Taiwan University, Taipei 10617, Taiwan
| | | | - Thomas Markovich
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Stephen Mason
- School of Chemistry, University of Nottingham, Nottingham, United Kingdom
| | - Simon A. Maurer
- Department of Chemistry, Ludwig Maximilian University, Butenandtstr. 7, D-81377 München, Germany
| | - Peter F. McLaughlin
- Q-Chem, Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588, USA
| | | | - Jan-Michael Mewes
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Stefanie A. Mewes
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Pierpaolo Morgante
- Department of Chemistry, Florida Institute of Technology, Melbourne, Florida 32901, USA
| | - J. Wayne Mullinax
- Department of Chemistry, Florida Institute of Technology, Melbourne, Florida 32901, USA
| | | | | | - Alexander C. Paul
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Suranjan K. Paul
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Fabijan Pavošević
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, USA
| | - Zheng Pei
- School of Electrical and Computer Engineering, University of Oklahoma, Norman, Oklahoma 73019, USA
| | - Stefan Prager
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Emil I. Proynov
- Q-Chem, Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588, USA
| | - Ádám Rák
- Stream Novation Ltd., Práter utca 50/a, H-1083 Budapest, Hungary
| | - Eloy Ramos-Cordoba
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Bhaskar Rana
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Alan E. Rask
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Adam Rettig
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Ryan M. Richard
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Fazle Rob
- Q-Chem, Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588, USA
| | - Elliot Rossomme
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Tarek Scheele
- Institute for Physical and Theoretical Chemistry, University of Bremen, Bremen, Germany
| | - Maximilian Scheurer
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Matthias Schneider
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Nickolai Sergueev
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44240, USA
| | - Shaama M. Sharada
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Wojciech Skomorowski
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | - David W. Small
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Christopher J. Stein
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Yu-Chuan Su
- Department of Physics, National Taiwan University, Taipei 10617, Taiwan
| | - Eric J. Sundstrom
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Zhen Tao
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, USA
| | - Jonathan Thirman
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Gábor J. Tornai
- Stream Novation Ltd., Práter utca 50/a, H-1083 Budapest, Hungary
| | - Takashi Tsuchimochi
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Norm M. Tubman
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | | | - Oleg Vydrov
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Jan Wenzel
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Jon Witte
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Atsushi Yamada
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44240, USA
| | - Kun Yao
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - Sina Yeganeh
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Shane R. Yost
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Alexander Zech
- Department of Physical Chemistry, University of Geneva, 30, Quai Ernest-Ansermet, CH-1211 Geneva 4, Switzerland
| | - Igor Ying Zhang
- Department of Chemistry, Fudan University, Shanghai 200433, China
| | - Xing Zhang
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Yu Zhang
- Q-Chem, Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588, USA
| | - Dmitry Zuev
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | - Alán Aspuru-Guzik
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Alexis T. Bell
- Department of Chemical Engineering, University of California, Berkeley, California 94720, USA
| | - Nicholas A. Besley
- School of Chemistry, University of Nottingham, Nottingham, United Kingdom
| | - Ksenia B. Bravaya
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA
| | - Bernard R. Brooks
- Laboratory of Computational Biophysics, National Institute of Health, Bethesda, Maryland 20892, USA
| | - David Casanova
- Donostia International Physics Center, 20080 Donostia, Euskadi, Spain
| | | | - Sonia Coriani
- Department of Chemistry, Technical University of Denmark, Kemitorvet Bldg. 207, DK-2800 Kgs Lyngby, Denmark
| | | | | | - A. Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306, USA
| | - Robert A. DiStasio
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Barry D. Dunietz
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44240, USA
| | - Thomas R. Furlani
- Department of Chemistry, University at Buffalo, State University of New York, Buffalo, New York 14260, USA
| | - William A. Goddard
- Materials and Process Simulation Center, California Institute of Technology, Pasadena, California 91125, USA
| | | | - Teresa Head-Gordon
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | | | | | | | - Yousung Jung
- Graduate School of Energy, Environment, Water and Sustainability (EEWS), Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Republic of Korea
| | - Andreas Klamt
- COSMOlogic GmbH & Co. KG, Imbacher Weg 46, D-51379 Leverkusen, Germany
| | - Jing Kong
- Q-Chem, Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588, USA
| | - Daniel S. Lambrecht
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | | | | | - C. William McCurdy
- Department of Chemistry, University of California, Davis, California 95616, USA
| | - Jeffrey B. Neaton
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Christian Ochsenfeld
- Department of Chemistry, Ludwig Maximilian University, Butenandtstr. 7, D-81377 München, Germany
| | - John A. Parkhill
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - Roberto Peverati
- Department of Chemistry, Florida Institute of Technology, Melbourne, Florida 32901, USA
| | - Vitaly A. Rassolov
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA
| | | | | | | | - Ryan P. Steele
- Department of Chemistry and Henry Eyring Center for Theoretical Chemistry, University of Utah, Salt Lake City, Utah 84112, USA
| | - Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Alex J. W. Thom
- Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
| | - Alexandre Tkatchenko
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Donald G. Truhlar
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Tomasz A. Wesolowski
- Department of Physical Chemistry, University of Geneva, 30, Quai Ernest-Ansermet, CH-1211 Geneva 4, Switzerland
| | - K. Birgitta Whaley
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - H. Lee Woodcock
- Department of Chemistry, University of South Florida, Tampa, Florida 33620, USA
| | - Paul M. Zimmerman
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Shirin Faraji
- Zernike Institute for Advanced Materials, University of Groningen, 9774AG Groningen, The Netherlands
| | | | - Martin Head-Gordon
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - John M. Herbert
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Anna I. Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA,Author to whom correspondence should be addressed:
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Zhao R, Grofe A, Wang Z, Bao P, Chen X, Liu W, Gao J. Dynamic-then-Static Approach for Core Excitations of Open-Shell Molecules. J Phys Chem Lett 2021; 12:7409-7417. [PMID: 34328742 DOI: 10.1021/acs.jpclett.1c02039] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Delta self-consistent-field methods are widely used in studies of electronically excited states. However, the nonaufbau determinants are generally spin-contaminated. Here, we describe a general approach for spin-coupling interactions of open-shell molecules, making use of multistate density functional theory (MSDFT). In particular, the effective exchange integrals that determine spin coupling are obtained by enforcing the multiplet degeneracy of the S+1 state in the MS = S manifold. Consequently, they are consistent with the energy of the high-spin state that is adequately treated by Kohn-Sham density functional theory (DFT) and, thereby, free of double counting of correlation. The method was applied to core excitations of open-shell molecules and compared with those by spin-adapted time-dependent DFT. An excellent agreement with experiment was found employing the BLYP functional and aug-cc-pCVQZ basis set. Overall, MSDFT provides an effective combination of the strengths of DFT and wave function theory to achieve efficiency and accuracy.
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Affiliation(s)
- Ruoqi Zhao
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, Guangdong, China
- Institute of Theoretical Chemistry, Jilin University Changchun 130023, Jilin, China
| | - Adam Grofe
- Institute of Theoretical Chemistry, Jilin University Changchun 130023, Jilin, China
| | - Zikuan Wang
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao 266237, Shandong, China
| | - Peng Bao
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
| | - Xin Chen
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, Guangdong, China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao 266237, Shandong, China
| | - Jiali Gao
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, Guangdong, China
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis 55455, Minnesota, United States
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16
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Yu L, Shi M, Wang Z, Xing X, Umair Ali M, He Y, Meng H. Tuning the UV/Vis Absorption Spectra of Electrochromic Small Molecular Radicals Through Bridge Modulation. Chemphyschem 2021; 22:1684-1691. [PMID: 34164904 DOI: 10.1002/cphc.202100369] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2021] [Revised: 06/19/2021] [Indexed: 02/02/2023]
Abstract
Studies on the optical properties of donor-bridge-acceptor (DBA) materials in their radical anion state are rare but important. Such investigations can help to extend the application of DBA materials to opto-electrochemical devices and no longer limit them to optical physics research. In this work, a series of new DBA materials, TACzs, for overcoming this limitation are reported. All TACzs show strong intramolecular charge transfer (ICT) in their photoexcited states, leading to noticeable solvatochromism. Besides, the electronic structures of their radical anions show great variability, displaying different absorption spectra and diverse colors. Moreover, the potential application of TACzs as electrochromic and electro-fluorochromic materials are discussed. This work demonstrates that manipulating the π bridge between the donor and acceptor in the DBA system is an effective pathway not only to tailor the ICT properties of materials in their neutral state, but also to tune the absorption characteristics of their radical anion state, which makes them very promising for applications in electroluminescent and electrochemical devices.
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Affiliation(s)
- Lirong Yu
- School of Advanced Materials, Peking University Shenzhen Graduate School, Shenzhen, 518055, China
| | - Ming Shi
- School of Advanced Materials, Peking University Shenzhen Graduate School, Shenzhen, 518055, China
| | - Zikuan Wang
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, Mülheim an der Ruhr, 45470, Germany
| | - Xing Xing
- Research & Development Institute of Northwestern Polytechnical University (Shenzhen), Northwestern Polytechnical University, Shenzhen, 518057, China
| | - Muhammad Umair Ali
- Tsinghua-Berkeley Shenzhen Institute (TBSI), Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen, 518055, China
| | - Yaowu He
- School of Advanced Materials, Peking University Shenzhen Graduate School, Shenzhen, 518055, China
| | - Hong Meng
- School of Advanced Materials, Peking University Shenzhen Graduate School, Shenzhen, 518055, China
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17
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Monino E, Loos PF. Spin-Conserved and Spin-Flip Optical Excitations from the Bethe-Salpeter Equation Formalism. J Chem Theory Comput 2021; 17:2852-2867. [PMID: 33724811 PMCID: PMC8154368 DOI: 10.1021/acs.jctc.1c00074] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
![]()
Like adiabatic time-dependent
density-functional theory (TD-DFT),
the Bethe–Salpeter equation (BSE) formalism of many-body perturbation
theory, in its static approximation, is “blind” to double
(and higher) excitations, which are ubiquitous, for example, in conjugated
molecules like polyenes. Here, we apply the spin-flip ansatz (which considers the lowest triplet state as the reference configuration
instead of the singlet ground state) to the BSE formalism in order
to access, in particular, double excitations. The present scheme is
based on a spin-unrestricted version of the GW approximation
employed to compute the charged excitations and screened Coulomb potential
required for the BSE calculations. Dynamical corrections to the static
BSE optical excitations are taken into account via an unrestricted
generalization of our recently developed (renormalized) perturbative
treatment. The performance of the present spin-flip BSE formalism
is illustrated by computing excited-state energies of the beryllium
atom, the hydrogen molecule at various bond lengths, and cyclobutadiene
in its rectangular and square-planar geometries.
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Affiliation(s)
- Enzo Monino
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Route de Narbonne, 31062 Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Route de Narbonne, 31062 Toulouse, France
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18
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Baek YS, Lee S, Filatov M, Choi CH. Optimization of Three State Conical Intersections by Adaptive Penalty Function Algorithm in Connection with the Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory Method (MRSF-TDDFT). J Phys Chem A 2021; 125:1994-2006. [PMID: 33651623 DOI: 10.1021/acs.jpca.0c11294] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A new adaptive algorithm for penalty function optimization for minimum-energy three-states conical intersections (ME3CI) is suggested. The new algorithm differs from the original penalty function algorithm by (a) removing the redundancy in the target function, (b) using an adaptive increment for the penalty function weighting factor, and (c) using tighter convergence criteria for the energy gap. The latter was introduced to guarantee convergence to a true conical intersection rather than to a narrowly avoided crossing geometry. The new algorithm was tested in the optimization of the ME3CI geometries in butadiene and malonaldehyde, where all of the previously found true ME3CI geometries were recovered. The previously found butadiene's CI3/2/1 turned out to be a narrowly avoided crossing. For butadiene, seven new ME3CI geometries have been located. Because of the removal of the redundancy and the use of the adaptive weighting factor, the convergence rate of the new algorithm is noticeably improved as compared to that of the previously proposed penalty function algorithm. The application to malonaldehyde and butadiene demonstrates that the three-state conical intersections may be more abundant and hence more involved in the photochemistry than previously thought. The recently developed mixed-reference spin flip (MRSF)-TDDFT method yields ME3CI geometries and relative energies quantitatively consistent with the previously reported calculations at a much reduced computational cost.
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Affiliation(s)
- Yong Su Baek
- 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
| | - 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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19
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Horbatenko Y, Sadiq S, Lee S, Filatov M, Choi CH. Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory (MRSF-TDDFT) as a Simple yet Accurate Method for Diradicals and Diradicaloids. J Chem Theory Comput 2021; 17:848-859. [PMID: 33401894 DOI: 10.1021/acs.jctc.0c01074] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
Due to their multiconfigurational nature featuring strong electron correlation, accurate description of diradicals and diradicaloids is a challenge for quantum chemical methods. The recently developed mixed-reference spin-flip (MRSF)-TDDFT method is capable of describing the multiconfigurational electronic states of these systems while avoiding the spin-contamination pitfalls of SF-TDDFT. Here, we apply MRSF-TDDFT to study the adiabatic singlet-triplet (ST) gaps in a series of well-known diradicals and diradicaloids. On average, MRSF displays a very high prediction accuracy of the adiabatic ST gaps with the mean absolute error (MAE) amounting to 0.14 eV. In addition, MRSF is capable of accurately describing the effect of the Jahn-Teller distortion occurring in the trimethylenemethane diradical, the violation of the Hund rule in a series of the didehydrotoluene diradicals, and the potential energy surfaces of the didehydrobenzene (benzyne) diradicals. A convenient criterion for distinguishing diradicals and diradicaloids is suggested on the basis of the easily obtainable quantities. In all of these cases, which are difficult for the conventional methods of density functional theory (DFT), MRSF shows results consistent with the experiment and the high-level ab initio computations. Hence, the present study documents the reliability and accuracy of MRSF and lays out the guidelines for its application to strongly correlated molecular systems.
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Affiliation(s)
- Yevhen Horbatenko
- Department of Chemistry, Kyungpook National University, Daegu 702-701, South Korea
| | - Saima Sadiq
- 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
| | - 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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20
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Curtis K, Panthi D, Odoh SO. Time-Dependent Density Functional Theory Study of Copper(II) Oxo Active Sites for Methane-to-Methanol Conversion in Zeolites. Inorg Chem 2021; 60:1149-1159. [PMID: 33399001 DOI: 10.1021/acs.inorgchem.0c03279] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Abstract
Copper-exchanged zeolites are useful materials for step-wise methane-to-methanol conversion (MMC). However, methanol yields on copper-exchanged zeolites are often modest, spurring interest in the development of active-site species that are activated at moderate temperatures, afford greater yields, and provide excellent methanol selectivities. Ultraviolet-visible (UV-vis) spectroscopy is a major tool for characterizing the active-sites and their evolution during the step-wise MMC process. However, computation of the UV-vis spectra of the copper-oxo active sites using Tamm-Dancoff time-dependent density functional theory (TDA-DFT) can be quite problematic. This has led to utilization of expensive methods based on multireference approaches, Green functions, and the Bethe-Salpeter equation. In this work, we examined the optical spectra of [CuO]+, [Cu2O]2+, [Cu2O2]2+, and [Cu3O3]2+ species implicated in MMC in zeolites. For the larger species, we examined how agreement with experimental data is improved with increasingly larger cluster models. For [CuO]+, we compared TDA-DFT against restricted active space 2nd-order perturbation theory, RASPT2. We found that signature peaks for [CuO]+ have multireference behavior. The excited states have many configuration state functions with a double excitation character. These effects are likely responsible for the poor utility of conventional TDA-DFT methods. Indeed, we obtain good agreement with experimental data and RASPT2 after accounting for 2h/2p excitations within TDA-DFT with a previously described configuration interaction singles and doubles, CIS(D)-style scheme. This was the case for [CuO]+, [Cu2O]2+, as well as a [Cu2O2]2+ species. Using a long-range corrected double-hybrid, ωB2PLYP, we provide for the first time computational evidence for the experimental UV-vis spectrum of the [Cu3O3]2+ active site motif.
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Affiliation(s)
- Kevin Curtis
- Department of Chemistry, University of Nevada Reno, 1664 N. Virginia Street, Reno, Nevada 89557-0216, United States
| | - Dipak Panthi
- Department of Chemistry, University of Nevada Reno, 1664 N. Virginia Street, Reno, Nevada 89557-0216, United States
| | - Samuel O Odoh
- Department of Chemistry, University of Nevada Reno, 1664 N. Virginia Street, Reno, Nevada 89557-0216, United States
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21
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Horbatenko Y, Lee S, Filatov M, Choi CH. How Beneficial Is the Explicit Account of Doubly-Excited Configurations in Linear Response Theory? J Chem Theory Comput 2021; 17:975-984. [DOI: 10.1021/acs.jctc.0c01214] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Affiliation(s)
- Yevhen Horbatenko
- 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
| | - 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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22
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Wang Z, Li Z, Zhang Y, Liu W. Analytic energy gradients of spin-adapted open-shell time-dependent density functional theory. J Chem Phys 2020; 153:164109. [DOI: 10.1063/5.0025428] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Affiliation(s)
- Zikuan Wang
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, People’s Republic of China
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, Shandong 266237, People’s Republic of China
| | - Zhendong Li
- Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, People’s Republic of China
| | - Yong Zhang
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, Shandong 266237, People’s Republic of China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, Shandong 266237, People’s Republic of China
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23
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Affiliation(s)
- Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, Shandong 266237, People’s Republic of China
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24
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Photoinduced Double Proton Transfer in the Glyoxal-Methanol Complex Revisited: The Role of the Excited States. J Chem Theory Comput 2020; 16:3273-3286. [PMID: 32275423 DOI: 10.1021/acs.jctc.0c00007] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Under irradiation in the visible range, the glyoxal-methanol complex in a cryogenic argon matrix undergoes a double proton transfer (DPT) reaction through which the glyoxal molecule isomerizes into hydroxyketene. In this work, we employ electronic structure simulations in order to shed more light on the underlying mechanism. Rewardingly, we find that the lowest singlet excited state (S1) of the complex acts as a gateway to two previously unknown isomerization pathways, of which one takes place entirely in the singlet manifold and the other also involves the lowest triplet state (T1). Both of these pathways are fully compatible with the available experimental data, implying that either or both are operative under experimental conditions. In either pathway, the methanol molecule acts as a proton shuttle between the proton-donating and proton-accepting sites of glyoxal, resulting in a dramatic lowering of the potential energy barrier to isomerization with respect to the case of isolated glyoxal. The occurrence of DPT in the singlet manifold is demonstrated directly with the use of nonadiabatic molecular dynamics simulations at the spin-flip time-dependent density functional theory level.
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25
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Zhang Y, Suo B, Wang Z, Zhang N, Li Z, Lei Y, Zou W, Gao J, Peng D, Pu Z, Xiao Y, Sun Q, Wang F, Ma Y, Wang X, Guo Y, Liu W. BDF: A relativistic electronic structure program package. J Chem Phys 2020; 152:064113. [DOI: 10.1063/1.5143173] [Citation(s) in RCA: 33] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yong Zhang
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, Shandong 266237, People’s Republic of China
| | - Bingbing Suo
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Institute of Modern Physics, Northwest University, Xi’an, Shaanxi 710127, People’s Republic of China
| | - Zikuan Wang
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Beijing 100871, People’s Republic of China
| | - Ning Zhang
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Beijing 100871, People’s Republic of China
| | - Zhendong Li
- Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, People’s Republic of China
| | - Yibo Lei
- Key Laboratory of Synthetic and Natural Functional Molecule Chemistry of Ministry of Education, Shaanxi Key Laboratory of Physico-Inorganic Chemistry, College of Chemistry and Materials Science, Northwest University, Xi’an, Shaanxi 710127, People’s Republic of China
| | - Wenli Zou
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Institute of Modern Physics, Northwest University, Xi’an, Shaanxi 710127, People’s Republic of China
| | - Jun Gao
- Hubei Key Laboratory of Agricultural Bioinformatics, College of Informatics, Huazhong Agricultural University, Wuhan, Hubei 430070, People’s Republic of China
| | - Daoling Peng
- College of Chemistry, South China Normal University, Guangzhou, Guangdong 510006, People’s Republic of China
| | - Zhichen Pu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Beijing 100871, People’s Republic of China
| | - Yunlong Xiao
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Beijing 100871, People’s Republic of China
| | - Qiming Sun
- Tencent America LLC, Palo Alto, California 94306, USA
| | - Fan Wang
- Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Institute of Atomic and Molecular Physics, Sichuan University, Chengdu, Sichuan 610065, People’s Republic of China
| | - Yongtao Ma
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, Shandong 266237, People’s Republic of China
| | - Xiaopeng Wang
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, Shandong 266237, People’s Republic of China
| | - Yang Guo
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, Shandong 266237, People’s Republic of China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, Shandong 266237, People’s Republic of China
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26
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Abstract
This Perspective discusses salient features of the spin-flip approach to strong correlation and describes different methods that sprung from this idea. The spin-flip treatment exploits the different physics of low-spin and high-spin states and is based on the observation that correlation is small for same-spin electrons. By using a well-behaved high-spin state as a reference, one can access problematic low-spin states by deploying the same formal tools as in the excited-state treatments (i.e., linear response, propagator, or equation-of-motion theories). The Perspective reviews applications of this strategy within wave function and density functional theory frameworks as well as the extensions for molecular properties and spectroscopy. The utility of spin-flip methods is illustrated by examples. Limitations and proposed future directions are also discussed.
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Affiliation(s)
- David Casanova
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain. and IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Euskadi, Spain
| | - Anna I Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
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27
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Mato J, Gordon MS. Analytic non-adiabatic couplings for the spin-flip ORMAS method. Phys Chem Chem Phys 2020; 22:1475-1484. [DOI: 10.1039/c9cp05849d] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Analytic non-adiabatic coupling matrix elements (NACME) are derived and implemented for the spin-flip occupation restricted multiple active space configuration interaction (SF-ORMAS-CI) method.
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Affiliation(s)
- Joani Mato
- Department of Chemistry and Ames Laboratory
- Iowa State University
- Ames
- USA
| | - Mark S. Gordon
- Department of Chemistry and Ames Laboratory
- Iowa State University
- Ames
- USA
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28
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Horbatenko Y, Lee S, Filatov M, Choi CH. Performance Analysis and Optimization of Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory (MRSF-TDDFT) for Vertical Excitation Energies and Singlet–Triplet Energy Gaps. J Phys Chem A 2019; 123:7991-8000. [DOI: 10.1021/acs.jpca.9b07556] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Yevhen Horbatenko
- Department of Chemistry, Kyungpook National University, Daegu 41566, Republic of Korea
| | - Seunghoon Lee
- Department of Chemistry, Seoul National University, Seoul 151747, Republic of Korea
| | - Michael Filatov
- Department of Chemistry, Kyungpook National University, Daegu 41566, Republic of Korea
| | - Cheol Ho Choi
- Department of Chemistry, Kyungpook National University, Daegu 41566, Republic of Korea
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29
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Lee S, Kim EE, Nakata H, Lee S, Choi CH. Efficient implementations of analytic energy gradient for mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT). J Chem Phys 2019; 150:184111. [DOI: 10.1063/1.5086895] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- Seunghoon Lee
- Department of Chemistry, Seoul National University, Seoul 151-747, South Korea
| | - Emma Eunji Kim
- Department of Chemistry, Seoul National University, Seoul 151-747, South Korea
| | - Hiroya Nakata
- R & D Center Kagoshima, Kyocera, 1-4 Kokubu Yamashita-cho, Kirishima-shi, Kagoshima 899-4312, Japan
| | - Sangyoub Lee
- Department of Chemistry, Seoul National University, Seoul 151-747, South Korea
| | - Cheol Ho Choi
- Department of Chemistry, Kyungpook National University, Daegu 702-701, South Korea
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30
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He C, Li Z, Lei Y, Zou W, Suo B. Unraveling the Emission Mechanism of Radical-Based Organic Light-Emitting Diodes. J Phys Chem Lett 2019; 10:574-580. [PMID: 30669831 DOI: 10.1021/acs.jpclett.8b03864] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Stable doublet radical molecules have recently emerged as a promising new type of emitters in organic light-emitting diodes (OLEDs), approaching 100% internal quantum efficiency. However, the detailed emission mechanism of these open-shell emitters remains elusive. Through theoretical model analysis and first-principles calculations, we unraveled the emission mechanism of a typical emitter, (4-N-carbazolyl-2,6-dichlorophenyl)bis(2,4,6-trichlorophenyl)methyl (TTM-1Cz). Our study showed that the electroluminescence arises from the first doublet excited state generated by injecting one electron into the singly occupied molecule orbital (SOMO) and one hole into the highest doubly occupied molecule orbital (HDMO). Because of the distinct charge-transfer rates in charge-injection processes, the puzzle of 100% formation ratio of the emissive doublet exciton in experiments is revealed. On the basis of this understanding, we propose simple molecular designs via substitutions that can tune the HDMO-SOMO gap and hence shift the emission wavelength to the region of yellow and green light.
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Affiliation(s)
- Chuhuan He
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Institute of Modern Physics , Northwest University , Xi'an , Shaanxi 710027 , China
| | - Zhendong Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry , Beijing Normal University , Beijing 100875 , China
| | - Yibo Lei
- Key Laboratory of Synthetic and Natural Functional Molecule Chemistry of Ministry of Education, College of Chemistry and Materials Science, Shaanxi Key Laboratory of Physico-Inorganic Chemistry , Northwest University , Xi'an , Shaanxi 710027 , China
| | - Wenli Zou
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Institute of Modern Physics , Northwest University , Xi'an , Shaanxi 710027 , China
| | - Bingbing Suo
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Institute of Modern Physics , Northwest University , Xi'an , Shaanxi 710027 , China
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31
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Huang C, Liu W. iVI‐TD‐DFT: An iterative vector interaction method for exterior/interior roots of TD‐DFT. J Comput Chem 2018; 40:1023-1037. [DOI: 10.1002/jcc.25569] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2018] [Revised: 08/07/2018] [Accepted: 08/07/2018] [Indexed: 01/28/2023]
Affiliation(s)
- Chao Huang
- Beijing National Center for Molecular SciencesInstitute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University Beijing, 100871 People's Republic of China
| | - Wenjian Liu
- Beijing National Center for Molecular SciencesInstitute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University Beijing, 100871 People's Republic of China
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32
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Xu L, Xu Y, Cheung NH, Wong KY. Practical approach for beryllium atomic clusters: TD-DFT potential energy surfaces from equilibrium to dissociation for excited states of 2s → 2p. Theor Chem Acc 2018. [DOI: 10.1007/s00214-018-2324-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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33
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Lee S, Filatov M, Lee S, Choi CH. Eliminating spin-contamination of spin-flip time dependent density functional theory within linear response formalism by the use of zeroth-order mixed-reference (MR) reduced density matrix. J Chem Phys 2018; 149:104101. [DOI: 10.1063/1.5044202] [Citation(s) in RCA: 43] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Seunghoon Lee
- Department of Chemistry, Seoul National University, Seoul 151-747, South Korea
| | - Michael Filatov
- Department of Chemistry, School of Natural Sciences, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, South Korea
| | - Sangyoub Lee
- Department of Chemistry, Seoul National University, Seoul 151-747, South Korea
| | - Cheol Ho Choi
- Department of Chemistry, Kyungpook National University, Daegu 702-701, South Korea
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34
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Suo B, Lian Y, Zou W, Lei Y. Electronic Structure of OsSi Calculated by MS-NEVPT2 with Inclusion of the Relativistic Effects. J Phys Chem A 2018; 122:5333-5341. [DOI: 10.1021/acs.jpca.8b00825] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Bingbing Suo
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Institute of Modern Physics, Northwest University, Xi’an, Shaanxi 710127, China
| | - Yongqin Lian
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Institute of Modern Physics, Northwest University, Xi’an, Shaanxi 710127, China
| | - Wenli Zou
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Institute of Modern Physics, Northwest University, Xi’an, Shaanxi 710127, China
| | - Yibo Lei
- Key Laboratory of Synthetic and Natural Functional Molecule Chemistry of Ministry of Education, The College of Chemistry and Materials Science, Northwest University, Xi’an, Shaanxi 710127, China
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35
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Abstract
The foundations, formalisms, technicalities, and practicalities of relativistic time-dependent density functional theories (R-TD-DFT) for spinor excited states of molecular systems containing heavy elements are critically reviewed.
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Affiliation(s)
- Wenjian Liu
- Beijing National Center for Molecular Sciences
- Institute of Theoretical and Computational Chemistry
- College of Chemistry and Molecular Engineering
- Peking University
- Beijing 100871
| | - Yunlong Xiao
- Beijing National Center for Molecular Sciences
- Institute of Theoretical and Computational Chemistry
- College of Chemistry and Molecular Engineering
- Peking University
- Beijing 100871
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36
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Grofe A, Chen X, Liu W, Gao J. Spin-Multiplet Components and Energy Splittings by Multistate Density Functional Theory. J Phys Chem Lett 2017; 8:4838-4845. [PMID: 28914545 PMCID: PMC5792056 DOI: 10.1021/acs.jpclett.7b02202] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Kohn-Sham density functional theory has been tremendously successful in chemistry and physics. Yet, it is unable to describe the energy degeneracy of spin-multiplet components with any approximate functional. This work features two contributions. (1) We present a multistate density functional theory (MSDFT) to represent spin-multiplet components and to determine multiplet energies. MSDFT is a hybrid approach, taking advantage of both wave function theory and density functional theory. Thus, the wave functions, electron densities and energy density-functionals for ground and excited states and for different components are treated on the same footing. The method is illustrated on valence excitations of atoms and molecules. (2) Importantly, a key result is that for cases in which the high-spin components can be determined separately by Kohn-Sham density functional theory, the transition density functional in MSDFT (which describes electronic coupling) can be defined rigorously. The numerical results may be explored to design and optimize transition density functionals for configuration coupling in multiconfigurational DFT.
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Affiliation(s)
- Adam Grofe
- Theoretical Chemistry Institute, Jilin University , Changchun, Jilin Province 130023, People's Republic of China
- Department of Chemistry, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Xin Chen
- Theoretical Chemistry Institute, Jilin University , Changchun, Jilin Province 130023, People's Republic of China
- Department of Chemistry, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Wenjian Liu
- Beijing National Laboratory for Molecular Sciences and College of Chemistry and Molecular Engineering , Beijing 100871, People's Republic of China
| | - Jiali Gao
- Theoretical Chemistry Institute, Jilin University , Changchun, Jilin Province 130023, People's Republic of China
- Department of Chemistry, University of Minnesota , Minneapolis, Minnesota 55455, United States
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37
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Nanda KD, Krylov AI. Effect of the diradical character on static polarizabilities and two-photon absorption cross sections: A closer look with spin-flip equation-of-motion coupled-cluster singles and doubles method. J Chem Phys 2017; 146:224103. [DOI: 10.1063/1.4984822] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Affiliation(s)
- Kaushik D. Nanda
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, USA
| | - Anna I. Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, USA
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38
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Suo B, Shen K, Li Z, Liu W. Performance of TD-DFT for Excited States of Open-Shell Transition Metal Compounds. J Phys Chem A 2017; 121:3929-3942. [DOI: 10.1021/acs.jpca.7b00752] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Bingbing Suo
- Shaanxi
Key Laboratory for Theoretical Physics Frontiers, Institute of Modern
Physics, Northwest University, Xi’an 710069, Shaanxi, People’s Republic of China
| | - Kaiyuan Shen
- Shaanxi
Key Laboratory for Theoretical Physics Frontiers, Institute of Modern
Physics, Northwest University, Xi’an 710069, Shaanxi, People’s Republic of China
| | - Zhendong Li
- Beijing
National Laboratory for Molecular Sciences, Institute of Theoretical
and Computational Chemistry, State Key Laboratory of Rare Earth Materials
Chemistry and Applications, College of Chemistry and Molecular Engineering,
and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
| | - Wenjian Liu
- Beijing
National Laboratory for Molecular Sciences, Institute of Theoretical
and Computational Chemistry, State Key Laboratory of Rare Earth Materials
Chemistry and Applications, College of Chemistry and Molecular Engineering,
and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
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39
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Li H, Liu W, Suo B. Localization of open-shell molecular orbitals via least change from fragments to molecule. J Chem Phys 2017; 146:104104. [DOI: 10.1063/1.4977929] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Hongyang Li
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
| | - Wenjian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
| | - Bingbing Suo
- Institute of Modern Physics, Northwest University, Xi’an 710069, People’s Republic of China
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40
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Cao Z, Li Z, Wang F, Liu W. Combining the spin-separated exact two-component relativistic Hamiltonian with the equation-of-motion coupled-cluster method for the treatment of spin–orbit splittings of light and heavy elements. Phys Chem Chem Phys 2017; 19:3713-3721. [DOI: 10.1039/c6cp07588f] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
An accurate and efficient treatment of spin–orbit splittings has been achieved by combining the sf-X2C+soc-DKH1 Hamiltonian with the equation-of-motion coupled-cluster method.
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Affiliation(s)
- Zhanli Cao
- Institute of Atomic and Molecular Physics
- Key Laboratory of High Energy Density Physics and Technology
- Ministry of Education
- Sichuan University
- Chengdu
| | - Zhendong Li
- Beijing National Laboratory for Molecular Sciences
- Institute of Theoretical and Computational Chemistry
- State Key Laboratory of Rare Earth Materials Chemistry and Applications
- College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering
- Peking University
| | - Fan Wang
- Institute of Atomic and Molecular Physics
- Key Laboratory of High Energy Density Physics and Technology
- Ministry of Education
- Sichuan University
- Chengdu
| | - Wenjian Liu
- Beijing National Laboratory for Molecular Sciences
- Institute of Theoretical and Computational Chemistry
- State Key Laboratory of Rare Earth Materials Chemistry and Applications
- College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering
- Peking University
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41
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Williams-Young D, Egidi F, Li X. Relativistic Two-Component Particle–Particle Tamm–Dancoff Approximation. J Chem Theory Comput 2016; 12:5379-5384. [DOI: 10.1021/acs.jctc.6b00833] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- David Williams-Young
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Franco Egidi
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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42
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Li Z, Liu W. Critical Assessment of Time-Dependent Density Functional Theory for Excited States of Open-Shell Systems: II. Doublet-Quartet Transitions. J Chem Theory Comput 2016; 12:2517-27. [PMID: 27159167 DOI: 10.1021/acs.jctc.5b01219] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Compared with closed-shell systems, open-shell systems place three additional challenges to time-dependent density functional theory (TD-DFT) for electronically excited states: (a) the spin-contamination problem is a serious issue; (b) the exchange-correlation (XC) kernel may be numerically instable; and (c) the single-determinant description of open-shell ground states readily becomes energetically instable. Confined to flip-up single excitations, the spin-contamination problem can largely be avoided by using the spin-flip TD-DFT (SF-TD-DFT) formalism, provided that a noncollinear XC kernel is employed. As for the numerical instabilities associated with such a kernel, only an ad hoc scheme has been proposed so far, viz., the ALDA0 kernel, which amounts to setting the divergent components (arising from density gradients and kinetic energy density) simply to zero. The ground-state instability problem can effectively be avoided by introducing the Tamm-Dancoff approximation (TDA) to TD-DFT. Therefore, on a general basis, the SF-TDA/ALDA0 Ansatz is so far the only promising means within the TD-DFT framework for flip-up single excitations of open-shell systems. To assess systematically the performance of SF-TDA/ALDA0, in total 61 low-lying quartet excited states of the benchmark set of 11 small radicals [J. Chem. Theory Comput. 2016, 12, 238] are investigated with various XC functionals. Taking the MRCISD+Q (multireference configuration interaction with singles and doubles plus the Davidson correction) results as benchmark, it is found that the mean absolute errors of SF-TDA/ALDA0 with the SAOP (statistical averaging of model orbital potentials), global hybrid, and range-separated hybrid functionals are in the range of 0.2-0.4 eV. This is in line not only with the typical accuracy of TD-DFT for singlet and triplet excited states of closed-shell systems but also with the gross accuracy of spin-adapted TD-DFT for spin-conserving excited states of open-shell systems.
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Affiliation(s)
- Zhendong Li
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University , Beijing 100871, People's Republic of China
| | - Wenjian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University , Beijing 100871, People's Republic of China
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43
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Tsuneda T, Singh RK, Nakata A. Relationship between orbital energy gaps and excitation energies for long-chain systems. J Comput Chem 2016; 37:1451-62. [DOI: 10.1002/jcc.24357] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2015] [Revised: 02/12/2016] [Accepted: 02/15/2016] [Indexed: 01/13/2023]
Affiliation(s)
- Takao Tsuneda
- Fuel Cell Nanomaterials Center; University of Yamanashi; Kofu 400-0021 Japan
| | - Raman K. Singh
- Fuel Cell Nanomaterials Center; University of Yamanashi; Kofu 400-0021 Japan
| | - Ayako Nakata
- National Institute for Materials Science (NIMS); Tsukuba 305-0044 Japan
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44
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Li Z, Liu W. Critical Assessment of TD-DFT for Excited States of Open-Shell Systems: I. Doublet–Doublet Transitions. J Chem Theory Comput 2015; 12:238-60. [DOI: 10.1021/acs.jctc.5b01158] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Zhendong Li
- Beijing National Laboratory
for Molecular Sciences, Institute of Theoretical and Computational
Chemistry, State Key Laboratory of Rare Earth Materials Chemistry
and Applications, College of Chemistry and Molecular Engineering,
and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
| | - Wenjian Liu
- Beijing National Laboratory
for Molecular Sciences, Institute of Theoretical and Computational
Chemistry, State Key Laboratory of Rare Earth Materials Chemistry
and Applications, College of Chemistry and Molecular Engineering,
and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
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45
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Zhang X, Herbert JM. Spin-flip, tensor equation-of-motion configuration interaction with a density-functional correction: A spin-complete method for exploring excited-state potential energy surfaces. J Chem Phys 2015; 143:234107. [DOI: 10.1063/1.4937571] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Xing Zhang
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - John M. Herbert
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
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46
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Abstract
Abstract
Any quantum mechanical calculation on electronic structure ought to choose first an appropriate Hamiltonian H and then an Ansatz for parameterizing the wave function Ψ, from which the desired energy/property E(λ) can finally be calculated. Therefore, the very first question is: what is the most accurate many-electron Hamiltonian H? It is shown that such a Hamiltonian i.e. effective quantum electrodynamics (eQED) Hamiltonian, can be obtained naturally by incorporating properly the charge conjugation symmetry when normal ordering the second quantized fermion operators. Taking this eQED Hamiltonian as the basis, various approximate relativistic many-electron Hamiltonians can be obtained based entirely on physical arguments. All these Hamiltonians together form a complete and continuous ‘Hamiltonian ladder’, from which one can pick up the right one according to the target physics and accuracy. As for the many-electron wave function Ψ, the most intriguing questions are as follows. (i) How to do relativistic explicit correlation? (ii) How to handle strong correlation? Both general principles and practical strategies are outlined here to handle these issues. Among the electronic properties E(λ) that sample the electronic wave function nearby the nuclear region, nuclear magnetic resonance (NMR) shielding and nuclear spin-rotation (NSR) coupling constant are especially challenging: they require body-fixed molecular Hamiltonians that treat both the electrons and nuclei as relativistic quantum particles. Nevertheless, they have been formulated rigorously. In particular, a very robust ‘relativistic mapping’ between the two properties has been established, which can translate experimentally measured NSR coupling constants to very accurate absolute NMR shielding scales that otherwise cannot be obtained experimentally. Since the most general and fundamental issues pertinent to all the three components of the quantum mechanical equation HΨ = EΨ (i.e. Hamiltonian H, wave function Ψ, and energy/property E(λ)) have fully been understood, the big picture of relativistic molecular quantum mechanics can now be regarded as established.
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Affiliation(s)
- Wenjian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871, China
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47
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Yang Y, Peng D, Davidson ER, Yang W. Singlet–Triplet Energy Gaps for Diradicals from Particle–Particle Random Phase Approximation. J Phys Chem A 2015; 119:4923-32. [DOI: 10.1021/jp512727a] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Affiliation(s)
| | | | - Ernest R. Davidson
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Weitao Yang
- Key
Laboratory of Theoretical Chemistry of Environment, Ministry of Education,
School of Chemistry and Environment, South China Normal University, Guangzhou 510006, China
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48
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Li Z, Suo B, Liu W. First order nonadiabatic coupling matrix elements between excited states: Implementation and application at the TD-DFT and pp-TDA levels. J Chem Phys 2014; 141:244105. [DOI: 10.1063/1.4903986] [Citation(s) in RCA: 59] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Zhendong Li
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistryand Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
| | - Bingbing Suo
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistryand Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
| | - Wenjian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistryand Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
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49
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Zhang X, Herbert JM. Analytic derivative couplings for spin-flip configuration interaction singles and spin-flip time-dependent density functional theory. J Chem Phys 2014; 141:064104. [DOI: 10.1063/1.4891984] [Citation(s) in RCA: 72] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Affiliation(s)
- Xing Zhang
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - John M. Herbert
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
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50
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Li Z, Liu W. First-order nonadiabatic coupling matrix elements between excited states: A Lagrangian formulation at the CIS, RPA, TD-HF, and TD-DFT levels. J Chem Phys 2014; 141:014110. [DOI: 10.1063/1.4885817] [Citation(s) in RCA: 62] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Zhendong Li
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871, People's Republic of China
| | - Wenjian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871, People's Republic of China
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