Charge density time independence

Note that in all current implementations of TDDFT the so-called adiabatic approximation is employed. Here, the time-dependent exchange-correlation potential that occurs in the corresponding time-dependent Kohn-Sham equations and which is rigorously defined as the functional derivative of the exchange-correlation action Axc[p] with respect to the time-dependent electron-density is approximated as the functional derivative of the standard, time-independent Exc with respect to the charge density at time t, i. e.,... 

The vibrational structure may be explained as follows For each state of a molecule there is a wave function that depends on time, as well as on the internal space and spin coordinates of all electrons and all nuclei, assuming that the overall translational and rotational motions of the molecule have been separated from internal motion. A set of stationary states exists whose observable properties, such as energy, charge density, etc., do not change in time. These states may be described by the time-independent part of their wave functions alone. Their wave functions are the solutions of the time-independent Schrddinger equation and depend only on the internal coordinates q = 9, Qz,. . . of all electrons and the internal coordinates Q = Q, Qz, of all nuclei. 

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