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Publication# Non-adiabatic coupling vectors within linear response time-dependent density functional theory

Abstract

A method is developed to compute the nonadiabatic coupling vectors (NACVs) between electronic ground and excited states as well as between any possible pair of excited states within the framework of linear response time-dependent density functional theory (TDDFT) in the adiabatic approximation. The development is an extension to our previous work on surface hopping dynamics [E. Tapavicza , Phys. Rev. Lett. 98, 023001 (2007)] for which we improve the description of the TDDFT approximation of the excited state wavefunctions by means of linear response orbitals. The method is first validated on the H+H-2 system that has a region of strong coupling near the conical intersection at the equilateral geometry. These results confirm the quality and the numerical efficiency of the approach, which has an accuracy comparable to the one achieved with wavefunction-based methods. Finally, we apply the method to the calculation of the NACVs of protonated formaldimine (NH2CH2+) along a surface hopping trajectory initiated in the second excited state.

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Ontological neighbourhood

Vibronic coupling

Vibronic coupling (also called nonadiabatic coupling or derivative coupling) in a molecule involves the interaction between electronic and nuclear vibrational motion. The term "vibronic" originates from the combination of the terms "vibrational" and "electronic", denoting the idea that in a molecule, vibrational and electronic interactions are interrelated and influence each other. The magnitude of vibronic coupling reflects the degree of such interrelation.

Conical intersection

In quantum chemistry, a conical intersection of two or more potential energy surfaces is the set of molecular geometry points where the potential energy surfaces are degenerate (intersect) and the non-adiabatic couplings between these states are non-vanishing. In the vicinity of conical intersections, the Born–Oppenheimer approximation breaks down and the coupling between electronic and nuclear motion becomes important, allowing non-adiabatic processes to take place.

Adiabatic theorem

The adiabatic theorem is a concept in quantum mechanics. Its original form, due to Max Born and Vladimir Fock (1928), was stated as follows: A physical system remains in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Hamiltonian's spectrum. In simpler terms, a quantum mechanical system subjected to gradually changing external conditions adapts its functional form, but when subjected to rapidly varying conditions there is insufficient time for the functional form to adapt, so the spatial probability density remains unchanged.

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2020