First-order derivative couplings between excited states from adiabatic TDDFT response theory

We present a complete derivation of derivative couplings between excited states in the framework of adiabatic time-dependent density functional response theory. Explicit working equations are given and the resulting derivative couplings are compared with derivative couplings from a pseudo-wavefuncti...

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Bibliographic Details
Published in:The Journal of chemical physics 2015-02, Vol.142 (6)
Main Authors: Ou, Qi, Subotnik, Joseph E., Bellchambers, Gregory D., Furche, Filipp
Format: Article
Language:English
Subjects:
ADIABATIC APPROXIMATION
COMPARATIVE EVALUATIONS
DENSITY FUNCTIONAL METHOD
EQUATIONS
EXCITATION
EXCITED STATES
INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY
KERNELS
RESPONSE FUNCTIONS
TIME DEPENDENCE
WAVE FUNCTIONS
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Summary:We present a complete derivation of derivative couplings between excited states in the framework of adiabatic time-dependent density functional response theory. Explicit working equations are given and the resulting derivative couplings are compared with derivative couplings from a pseudo-wavefunction ansatz. For degenerate excited states, i.e., close to a conical intersection (CI), the two approaches are identical apart from an antisymmetric overlap term. However, if the difference between two excitation energies equals another excitation energy, the couplings from response theory exhibit an unphysical divergence. This spurious behavior is a result of the adiabatic or static kernel approximation of time-dependent density functional theory leading to an incorrect analytical structure of the quadratic response function. Numerical examples for couplings close to a CI and for well-separated electronic states are given.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.4906941