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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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2
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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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3
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Sun S, Li X. Relativistic Effects in Magnetic Circular Dichroism: Restricted Magnetic Balance and Temperature Dependence. J Chem Theory Comput 2020; 16:4533-4542. [DOI: 10.1021/acs.jctc.0c00287] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Shichao Sun
- 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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4
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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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5
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Zhao H, Fang C, Gao J, Liu C. Spin-state energies of heme-related models from spin-flip TDDFT calculations. Phys Chem Chem Phys 2016; 18:29486-29494. [DOI: 10.1039/c6cp04826a] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The spin-state energies of heme-related models were calculated by using the spin-flip TDDFT method avoiding spin contamination.
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Affiliation(s)
- Hui Zhao
- Institute of Theoretical Chemistry
- School of Chemistry & Chemical Engineering
- Shandong University
- Jinan
- People's Republic of China
| | - Changfeng Fang
- Department of Physics
- Jining University
- Qufu
- People's Republic of China
| | - Jun Gao
- Institute of Theoretical Chemistry
- School of Chemistry & Chemical Engineering
- Shandong University
- Jinan
- People's Republic of China
| | - Chengbu Liu
- Institute of Theoretical Chemistry
- School of Chemistry & Chemical Engineering
- Shandong University
- Jinan
- People's Republic of China
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6
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Sinha B, Goswami T, Paul S, Misra A. The impact of surface structure and band gap on the optoelectronic properties of Cu2O nanoclusters of varying size and symmetry. RSC Adv 2014. [DOI: 10.1039/c3ra45387a] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
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7
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de Visser SP, Quesne MG, Martin B, Comba P, Ryde U. Computational modelling of oxygenation processes in enzymes and biomimetic model complexes. Chem Commun (Camb) 2014; 50:262-82. [DOI: 10.1039/c3cc47148a] [Citation(s) in RCA: 101] [Impact Index Per Article: 10.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
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8
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9
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Abstract
A theoretical study is made of the Jahn-Teller and other properties of vanadium tetrachloride. Relativistic effective core potentials and corresponding valence spin-orbit operators are used with Gaussian atomic orbitals to compute self-consistent-field and spin-orbit configuration-interaction wave functions. Energy-surface parameters, electronic excitation energies, vibronic energy levels, and g factors are computed. Electron correlation is shown to have a substantial effect on the Jahn-Teller properties. As have others, we find the Jahn-Teller effect in VCl4 to be of the dynamic form.
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Affiliation(s)
- K Zhao
- Department of Chemistry and Biochemistry, The Ohio State University , 100 West 18th Avenue, Columbus, Ohio 43210, United States
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10
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Li Z, Suo B, Zhang Y, Xiao Y, Liu W. Combining spin-adapted open-shell TD-DFT with spin–orbit coupling. Mol Phys 2013. [DOI: 10.1080/00268976.2013.785611] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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11
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Abstract
The classic density-functional theory (DFT) formalism introduced by Hohenberg, Kohn, and Sham in the mid-1960s is based on the idea that the complicated N-electron wave function can be replaced with the mathematically simpler 1-electron charge density in electronic structure calculations of the ground stationary state. As such, ordinary DFT cannot treat time-dependent (TD) problems nor describe excited electronic states. In 1984, Runge and Gross proved a theorem making TD-DFT formally exact. Information about electronic excited states may be obtained from this theory through the linear response (LR) theory formalism. Beginning in the mid-1990s, LR-TD-DFT became increasingly popular for calculating absorption and other spectra of medium- and large-sized molecules. Its ease of use and relatively good accuracy has now brought LR-TD-DFT to the forefront for this type of application. As the number and the diversity of applications of TD-DFT have grown, so too has our understanding of the strengths and weaknesses of the approximate functionals commonly used for TD-DFT. The objective of this article is to continue where a previous review of TD-DFT in Volume 55 of the Annual Review of Physical Chemistry left off and highlight some of the problems and solutions from the point of view of applied physical chemistry. Because doubly-excited states have a particularly important role to play in bond dissociation and formation in both thermal and photochemistry, particular emphasis is placed on the problem of going beyond or around the TD-DFT adiabatic approximation, which limits TD-DFT calculations to nominally singly-excited states.
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Affiliation(s)
- M E Casida
- Laboratoire de Chimie Théorique, Département de Chimie Moléculaire, Institut de Chimie Moléculaire de Grenoble, Université Joseph Fourier, France.
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12
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Li Z, Liu W. Spin-adapted open-shell time-dependent density functional theory. III. An even better and simpler formulation. J Chem Phys 2011; 135:194106. [DOI: 10.1063/1.3660688] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
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13
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Li Z, Liu W, Zhang Y, Suo B. Spin-adapted open-shell time-dependent density functional theory. II. Theory and pilot application. J Chem Phys 2011; 134:134101. [DOI: 10.1063/1.3573374] [Citation(s) in RCA: 63] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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14
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Yi HB, Xia FF, Zhou Q, Zeng D. [CuCl3]− and [CuCl4]2− Hydrates in Concentrated Aqueous Solution: A Density Functional Theory and ab Initio Study. J Phys Chem A 2011; 115:4416-26. [DOI: 10.1021/jp109723v] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Affiliation(s)
- Hai-Bo Yi
- College of Chemistry and Chemical Engineering, Hunan University, Changsha, Hunan, China.
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15
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Kowalczyk T, Yost SR, Voorhis TV. Assessment of the ΔSCF density functional theory approach for electronic excitations in organic dyes. J Chem Phys 2011; 134:054128. [DOI: 10.1063/1.3530801] [Citation(s) in RCA: 133] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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Bhattacharya D, Shil S, Misra A. Photoresponsive magnetization reversal in green fluorescent protein chromophore based diradicals. J Photochem Photobiol A Chem 2011. [DOI: 10.1016/j.jphotochem.2010.11.013] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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17
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Li Z, Liu W. Spin-adapted open-shell random phase approximation and time-dependent density functional theory. I. Theory. J Chem Phys 2010; 133:064106. [PMID: 20707560 DOI: 10.1063/1.3463799] [Citation(s) in RCA: 64] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The spin-adaptation of single-reference quantum chemical methods for excited states of open-shell systems has been nontrivial. The primary reason is that the configuration space, generated by a truncated rank of excitations from only one component of a reference multiplet, is spin-incomplete. Those "missing" configurations are of higher ranks and can, in principle, be recaptured by a particular class of excitation operators. However, the resulting formalisms are then quite involved and there are situations [e.g., time-dependent density functional theory (TD-DFT) under the adiabatic approximation] that prevent one from doing so. To solve this issue, we propose here a tensor-coupling scheme that invokes all the components of a reference multiplet (i.e., a tensor reference) rather than increases the excitation ranks. A minimal spin-adapted n-tuply excited configuration space can readily be constructed by tensor products between the n-tuple tensor excitation operators and the chosen tensor reference. Further combined with the tensor equation-of-motion formalism, very compact expressions for excitation energies can be obtained. As a first application of this general idea, a spin-adapted open-shell random phase approximation is first developed. The so-called "translation rule" is then adopted to formulate a spin-adapted, restricted open-shell Kohn-Sham (ROKS)-based TD-DFT (ROKS-TD-DFT). Here, a particular symmetry structure has to be imposed on the exchange-correlation kernel. While the standard ROKS-TD-DFT can access only excited states due to singlet-coupled single excitations, i.e., only some of the singly excited states of the same spin (S(i)) as the reference, the new scheme can capture all the excited states of spin S(i)-1, S(i), or S(i)+1 due to both singlet- and triplet-coupled single excitations. The actual implementation and computation are very much like the (spin-contaminated) unrestricted Kohn-Sham-based TD-DFT. It is also shown that spin-contaminated spin-flip configuration interaction approaches can easily be spin-adapted via the tensor-coupling scheme.
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Affiliation(s)
- Zhendong Li
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, 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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18
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Calculation of Magnetic Circular Dichroism Spectra With Time-Dependent Density Functional Theory. ADVANCES IN INORGANIC CHEMISTRY 2010. [DOI: 10.1016/s0898-8838(10)62002-8] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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19
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Huix-Rotllant M, Natarajan B, Ipatov A, Muhavini Wawire C, Deutsch T, Casida ME. Assessment of noncollinear spin-flip Tamm–Dancoff approximation time-dependent density-functional theory for the photochemical ring-opening of oxirane. Phys Chem Chem Phys 2010; 12:12811-25. [DOI: 10.1039/c0cp00273a] [Citation(s) in RCA: 87] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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20
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Hadt RG, Nemykin VN. Exploring the ground and excited state potential energy landscapes of the mixed-valence biferrocenium complex. Inorg Chem 2009; 48:3982-92. [PMID: 19344155 DOI: 10.1021/ic801801m] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Density functional theory (DFT) and time-dependent DFT (TDDFT) have been used to explore the potential energy landscapes in the class II (in Robin and Day classification) mixed-valence biferrocenium mono-cation (BF(+)) in an effort to evaluate factors affecting optical and thermal intramolecular electron transfer rates. Both energy- and spectroscopy-based benchmarks were used to explore the adiabatic potential energy surfaces (PESs) of the mixed-valence BF(+) cation along with the optimization of appropriate ground-, excited-, and transition-state geometries. The calculation of Mossbauer isomer shifts and quadrupole splittings, UV-vis excitation energies, and the electronic coupling matrix element, H(ab), corroborate the PES analyses. The adiabatic electron transfer pathway is also analyzed with respect to several possible vibronic coordinates. The degree of the electronic coupling between iron sites, the value of H(ab), and the nature of the electron transfer pathway correlate with the amount of Hartree-Fock exchange involved in the DFT calculation with hybrid (approximately 20% of Hartree-Fock exchange) methods providing the best agreement between theory and experiment. DFT (B3LYP) predicted values of H(ab) (839, 1085, and 1265 cm(-1)) depend on the computational method and are in good agreement with experimental data.
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Affiliation(s)
- Ryan G Hadt
- Department of Chemistry & Biochemistry, University of Minnesota Duluth, Duluth, Minnesota 55812, USA
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21
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Casanova D, Slipchenko LV, Krylov AI, Head-Gordon M. Double spin-flip approach within equation-of-motion coupled cluster and configuration interaction formalisms: Theory, implementation, and examples. J Chem Phys 2009; 130:044103. [DOI: 10.1063/1.3066652] [Citation(s) in RCA: 82] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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22
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García-Lastra JM, Moreno M, Barriuso MT. Pressure effects on CrCl63− embedded in cubic Cs2NaMCl6 (M=Sc,Y) lattices: Study through periodic and cluster calculations. J Chem Phys 2008; 128:144708. [DOI: 10.1063/1.2894546] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
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23
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Vlček A, Záliš S. Modeling of charge-transfer transitions and excited states in d6 transition metal complexes by DFT techniques. Coord Chem Rev 2007. [DOI: 10.1016/j.ccr.2006.05.021] [Citation(s) in RCA: 384] [Impact Index Per Article: 22.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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24
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Rong C, Lian S, Yin D, Shen B, Zhong A, Bartolotti L, Liu S. Towards understanding performance differences between approximate density functionals for spin states of iron complexes. J Chem Phys 2006; 125:174102. [PMID: 17100424 DOI: 10.1063/1.2378830] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Density functional theory has been widely used to investigate the structural and electronic properties of heme-containing proteins such as cytochrome P450. Nevertheless, recent studies have shown that approximate exchange-correlation energy density functionals can incorrectly predict the stability order of spin states in, for instance, iron-containing pyridine and imidazole systems. This raises questions about the validity of earlier theoretical studies. In this work, we systematically investigate a few typical inorganic and organic iron-containing complexes and try to understand the performance difference of various density functionals. Two oxidation states of iron, Fe(II) and Fe(III), with different spin states and both adiabatic and vertical structures are considered. A different description of the outmost molecular orbital is found to play the crucial role. Local density and generalized gradient based functionals bias the lower spin state and produce a more localized frontier orbital that is higher in energy than the hybrid functionals. Energy component analysis has been performed, together with comparison of numerous structural and electronic properties. Implications of the present work to the theoretical study of heme-containing biological molecules and other spin-related systems are discussed.
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Affiliation(s)
- Chunying Rong
- College of Chemistry and Chemical Engineering, Hunan Normal University, Changsha, Hunan 410081, People's Republic of China
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Moreno M, Barriuso MT, Aramburu JA, García-Fernández P, García-Lastra JM. Microscopic insight into properties and electronic instabilities of impurities in cubic and lower symmetry insulators: the influence of pressure. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2006; 18:R315-R360. [PMID: 21690765 DOI: 10.1088/0953-8984/18/17/r01] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
This article reviews the microscopic origin of properties due to transition-metal (TM) impurities, M, in insulator materials. Particular attention is paid to the influence of pressure upon impurity properties. Basic concepts such as the electronic localization in an MX(N) complex, the electrostatic potential, V(R), arising from the rest of the lattice ions or the elastic coupling of the complex to the host lattice are initially exposed. The dependence of optical and magnetic parameters on the impurity-ligand distance, R, in cubic lattices is discussed in a first step. Emphasis is put on the actual origin of the R dependence of 10Dq. Examples revealing that laws for strict cubic symmetry cannot in general be transferred to lower symmetries are later given. This relevant fact is shown to come from allowed hybridizations like nd-(n+1)s as well as the influence of V(R). As a salient feature the different colour in ruby and emerald is stressed to arise from distinct V(R) potentials in Al(2)O(3) and Be(3)Si(6)Al(2)O(18). The last part of this review deals with electronic instabilities. The phenomena associated with the Jahn-Teller (JT) effect in cubic lattices, the origin of the energy barrier among equivalent minima and the existence of coherent tunnelling in systems like MgO:Cu(2+) are discussed. An increase of elastic coupling is pointed out to favour a transition from an elongated to a compressed equilibrium conformation. Interestingly the equilibrium geometry of JT ions in non-cubic lattices is shown to be controlled by mechanisms different to those in cubic systems, V(R) playing again a key role. The relevance of first principles calculations for clarifying the subtle mechanisms behind off-centre instabilities is also pointed out. Examples concern monovalent and divalent TM impurities in lattices with the CaF(2) structure. The instability due to the transition from the ground to an excited state is finally considered. For complexes with significant elastic coupling vibrational frequencies and the Stokes shift are expected to undergo bigger changes through a chemical rather than a hydrostatic pressure. The reduction of Huang-Rhys factors upon increasing the pressure is discussed as well.
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Affiliation(s)
- M Moreno
- Departamento de Ciencias de la Tierra y Física de la Materia Condensada, Universidad de Cantabria, 39005 Santander, Spain
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Seth M, Ziegler T. Calculation of excitation energies of open-shell molecules with spatially degenerate ground states. II. Transformed reference via intermediate configuration Kohn-Sham time dependent density functional theory oscillator strengths and magnetic circular dichroism C terms. J Chem Phys 2006; 124:144105. [PMID: 16626178 DOI: 10.1063/1.2187004] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An extension of the transformed reference via an intermediate configuration Kohn-Sham time dependent density functional theory (TRICKS-TDDFT) method for calculating the transition energies of molecules with spatially degenerate ground states is proposed that enables oscillator strengths to also be evaluated. The oscillator strengths are calculated starting from a description of the degenerate ground state and the excited states of interest in terms of linear combinations of Slater determinants based upon the F-vectors obtained in the TRICKS-TDDFT calculation. This approach for calculating oscillator strengths can also be applied to several other properties that involve excited states. An example of such a property, the C term of magnetic circular dichroism (MCD), is presented. The new method is illustrated through example calculations of the absorbance and MCD spectra of several octahedral and C(4v) d(5) transition metal complexes. The calculated transition energies and oscillator strengths are somewhat too low and too high, respectively, but these errors are within the range that would normally be expected for TDDFT calculations of this type. The calculations help to resolve some previously unexplained problems with the MCD spectra of the C(4v) complexes.
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Affiliation(s)
- Michael Seth
- Department of Chemistry, University of Calgary, University Drive 2500, Calgary, Alberta T2N-1N4, Canada
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