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J Chem Phys. 2009 Sep 21;131(11):114101. doi: 10.1063/1.3226344.

All-electron calculation of nonadiabatic couplings from time-dependent density functional theory: Probing with the Hartree-Fock exact exchange.

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WPI International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Ibaraki, Japan.


We present the all-electron scheme of calculating nonadiabatic couplings (NACs) from time-dependent density functional theory (TDDFT) using atomic orbital basis. The formal expression for calculating NAC from linear response TDDFT [Hu et al., J. Chem. Phys. 127, 064103 (2007)] can be straightforwardly adapted to the all-electron TDDFT scheme. However, in contrast to the planewave basis, the nuclear coordinate dependence of atomic orbital basis needs to be considered when constructing the matrix elements of the nuclear derivative of Hamiltonian. Practical calculations show that the contribution of atomic orbital basis ("Pulay term") is significant and comparable to that of the Hellmann-Feynman term. In particular, we probe the all-electron formalism of NAC with the Hartree-Fock exact exchange, which serves as the prerequisite for hybrid functionals. It is validated that in the present framework the sum rule of NAC is rigorously satisfied, which has not been the case in the pseudopotential planewave calculations. Reasonably good results can be obtained in the vicinity of various Renner-Teller (and also Jahn-Teller) intersections when the intersection point is not too closely approached, while further tests show that correlation effects should be taken into account in general cases.

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