Two-Component Noncollinear Time-Dependent Spin Density Functional Theory for Excited State Calculations

Egidi, Franco; Sun, Shichao; Goings, Joshua J.; Scalmani, Giovanni; Frisch, Michael J.; Li, Xiaosong

doi:10.1021/acs.jctc.7b00104

Cited by 81 publications

(109 citation statements)

References 122 publications

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“…In this contribution, we choose to rely on the latter approach, with the spin‐orbit interaction based on a two‐component Hamiltonian . This Hamiltonian can be used within the framework of DFT provided the functional dependence is adapted to accommodate the fact that two‐component densities can in general be noncollinear; ie, the orientation of the spin magnetization vector may vary with the position in space . Transition densities and properties can be then calculated by performing a two‐component time‐dependent DFT (2c‐TDDFT) calculation starting from the single‐determinant 2c‐DFT reference or, as an alternative, through a real‐time propagation of the two‐component Hamiltonian .…”

Section: Theorymentioning

confidence: 99%

“…Transition densities and properties can be then calculated by performing a two‐component time‐dependent DFT (2c‐TDDFT) calculation starting from the single‐determinant 2c‐DFT reference or, as an alternative, through a real‐time propagation of the two‐component Hamiltonian . Here, we choose the first option, from which we can determine the singlet‐to‐triplet transition densities by solving the response equation through an iterative Davidson algorithm as previously described . Given the computed transition density X in the atomic orbital basis, the transition electric and magnetic dipole moments between the singlet | S ⟩ and the triplet | T ⟩ can be evaluated as

(〈〉, bold-italicS (||, \overset{true\to}{bold-italicμ}) bold-italicT) = bold-italictr bold-italicX \overset{μ}{true}; (〈〉, bold-italicS (||, \overset{true\to}{bold-italicm}) bold-italicT) = bold-italictr bold-italicX \overset{m}{true}

where the electric and magnetic dipole integral matrices are given by

{\overset{true\to}{bold-italicμ}}_{μv} = (〈〉, χ_{μ} (||, \overset{true\to}{bold-italicμ}) χ_{v}); {\overset{true\to}{bold-italicm}}_{μv} = - \frac{e}{bold-italic2 m_{e} bold-italicc} (〈〉, χ_{μ} (||, \overset{r}{true} \times \overset{p}{true}) χ_{v})

where χ denotes the atomic orbital functions, e is the elementary charge, c the speed of light, and m e is the electron mass.…”

Section: Theorymentioning

confidence: 99%

“…[30][31][32][33][34][35][36][37][38][39][40][41] This Hamiltonian can be used within the framework of DFT provided the functional dependence is adapted to accommodate the fact that two-component densities can in general be noncollinear; ie, the orientation of the spin magnetization vector may vary with the position in space. [42][43][44][45][46] Transition densities and properties can be then calculated by performing a twocomponent time-dependent DFT (2c-TDDFT) calculation starting from the single-determinant 2c-DFT reference 40,46 or, as an alternative, through a real-time propagation of the two-component Hamiltonian. 47 Here, we choose the first option, from which we can determine the singletto-triplet transition densities by solving the response equation through an iterative Davidson algorithm as previously described.…”

Section: Spin-orbit Couplingsmentioning

confidence: 99%

“…47 Here, we choose the first option, from which we can determine the singletto-triplet transition densities by solving the response equation through an iterative Davidson algorithm as previously described. 40,46 Given the computed transition density X in the atomic orbital basis, the transition electric and magnetic dipole moments between the singlet | S⟩ and the triplet | T⟩ can be evaluated as where the electric and magnetic dipole integral matrices are given by…”

Section: Spin-orbit Couplingsmentioning

confidence: 99%

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Computational simulation of vibrationally resolved spectra for spin‐forbidden transitions

et al. 2018

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In this computational study, we illustrate a method for computing phosphorescence and circularly polarized phosphorescence spectra of molecular systems, which takes into account vibronic effects including both Franck-Condon and Herzberg-Teller contributions. The singlet and triplet states involved in the phosphorescent emission are described within the harmonic approximation, and the method fully takes mode-mixing effects into account when evaluating Franck-Condon integrals. Spin-orbit couplings, which are responsible for these otherwise forbidden phenomena, are accounted for by means of a relativistic two-component time-dependent density functional theory method. The model is applied to two types of chiral systems: camphorquinone, a rigid organic system that allows for an extensive benchmark, and some members of a class of iridium complexes. The merits and shortcomings of the methods are discussed, and some perspectives for future developments are offered.

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Section: Theorymentioning

confidence: 99%

(〈〉, bold-italicS (||, \overset{true\to}{bold-italicμ}) bold-italicT) = bold-italictr bold-italicX \overset{μ}{true}; (〈〉, bold-italicS (||, \overset{true\to}{bold-italicm}) bold-italicT) = bold-italictr bold-italicX \overset{m}{true}

where the electric and magnetic dipole integral matrices are given by

{\overset{true\to}{bold-italicμ}}_{μv} = (〈〉, χ_{μ} (||, \overset{true\to}{bold-italicμ}) χ_{v}); {\overset{true\to}{bold-italicm}}_{μv} = - \frac{e}{bold-italic2 m_{e} bold-italicc} (〈〉, χ_{μ} (||, \overset{r}{true} \times \overset{p}{true}) χ_{v})

where χ denotes the atomic orbital functions, e is the elementary charge, c the speed of light, and m e is the electron mass.…”

Section: Theorymentioning

confidence: 99%

Section: Spin-orbit Couplingsmentioning

confidence: 99%

Section: Spin-orbit Couplingsmentioning

confidence: 99%

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Computational simulation of vibrationally resolved spectra for spin‐forbidden transitions

et al. 2018

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“…One proposed solution is to modify the definition of the functional only for the regions of numerical instability, where the magnetization is almost zero. Recently, this method has been successfully extended to the linear response relativistic two‐component time‐dependent DFT (2c‐TDDFT) framework for excited states …”

Section: Noncollinear Dftmentioning

confidence: 99%

Current development of noncollinear electronic structure theory

Goings

Egidi

2017

Int J of Quantum Chemistry

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In this Perspective, we review recent developments in noncollinear electronic structure theory.After a brief historical overview of studies into broken symmetry wave functions, we show that noncollinear wave functions are necessary for studying spin and magnetic phenomena on account of spin-symmetry breaking terms in the Hamiltonian. Recent developments applying noncollinear electronic structure theory to magnetization dynamics, spin dynamics, and spin-orbit coupling in excited state properties are showcased. We also discuss some recent developments in noncollinear density functional theory. Finally, we comment on the future of noncollinear electronic structure theory.noncollinear spin, relativistic electronic structure theory, symmetry breaking, time-dependent electronic structure theory, two-component method 1 | I N TR ODU C TI ON Mean-field, and self-consistent field (SCF), methods are the backbone of modern electronic structure theory. Since the introduction of the singledeterminant ansatz by Hartree and Fock, there has been a great deal of work on understanding the nature of the Hartree-Fock (HF) solutions as well as how to improve their utility in the description of atoms and molecules. It was recognized early on that the solution of the HF equations required a balance between two (sometimes competing) goals. [1][2][3][4][5] The first was that the HF equations would be at a variational minimum: the best SCF solution would be the lowest energy single-determinant approximation to the full configuration interaction (FCI) equations (for a given basis).Solutions of the HF equations would always seek to find the lowest possible energy solution, so as to satisfy the variational principle. Conversely, it was known that the underlying electronic Hamiltonian is invariant to several unitary transformations, most notably spin rotations. This invariance expresses itself as a conservation law, and the conserved quantity is total spin angular momentum S 2 as well as the spin projection along an arbitrary axis, S z . Surely a physically meaningful solution of the HF approximation would also have good quantum numbers, so invariance to rotations in the spin manifold was built-in to the HF equations as a constraint in the single determinantal expression. For example, the restricted Hartree-Fock (RHF) equations contain only paired electrons in orbitals, yielding solutions with good spin quantum numbers.Unfortunately, it was quickly found that there are many cases where insisting that the HF solution be a spin eigenstate yields energies that are higher than they would otherwise be if spin symmetry constraints were relaxed. For example, in the classic example of the dissociation of H 2 one finds that when the bond is stretched to a certain distance (the Coulson-Fischer point) an RHF to UHF instability forms and qualitatively correct dissociation curve are obtained only in the spin symmetry broken state. The spin symmetry breaking arises when the solutions approach a (near) degeneracy. Hartree-Fock solutions are unstable...

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Natural transition orbitals for complex two‐component excited state calculations

Kasper

2020

J Comput Chem

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While the natural transition orbital (NTO) method has allowed electronic excitations from time-dependent Hartree-Fock and density functional theory to be viewed in a traditional orbital picture, the extension to multicomponent molecular orbitals such as those used in relativistic two-component methods or generalized Hartree-Fock (GHF) or generalized Kohn-Sham (GKS) is less straightforward due to mixing of spincomponents and the inherent inclusion of spin-flip transitions in time-dependent GHF/GKS. An extension of single-component NTOs to the two-component framework is presented, in addition to a brief discussion of the practical aspects of visualizing two-component complex orbitals. Unlike the single-component analog, the method explicitly describes the spin and frequently obtains solutions with several significant orbital pairs. The method is presented using calculations on a mercury atom and a CrO 2 Cl 2 complex. K E Y W O R D S generalized Hartree-Fock, generalized Kohn-Sham, natural transition orbitals, relativistic methods, TDDFT, two-component electronic structure method

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Two-Component Noncollinear Time-Dependent Spin Density Functional Theory for Excited State Calculations

Cited by 81 publications

References 122 publications

Computational simulation of vibrationally resolved spectra for spin‐forbidden transitions

Computational simulation of vibrationally resolved spectra for spin‐forbidden transitions

Current development of noncollinear electronic structure theory

Natural transition orbitals for complex two‐component excited state calculations

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