Electron localization function , local nuclear motion

A second simplihcation results from introducing the Born-Oppenheimer separation of electronic and nuclear motions for convenience, the latter is most often considered to be classical. Each excited electronic state of the molecule can then be considered as a distinct molecular species, and the laser-excited system can be viewed as a mixture of them. The local structure of such a system is generally described in terms of atom-atom distribution functions t) [22, 24, 25]. These functions are proportional to the probability of Ending the nuclei p and v at the distance r at time t. Building this information into Eq. (4) and considering the isotropy of a liquid system simplifies the theory considerably. 

Dependent Electron Localization Functions for Coupled Nuclear-Electronic Motion. 

Note that here and later on r denotes the single-particle coordinate whereas R is still used as abbreviation for all nuclear positions as in Eq. (1). The potential (5) consists, on one hand, of an external potential V(r,R), which in our case is time-dependent owing to the atomic motion R( ). On the other hand, there are electron-electron interaction terms, namely the Hartree and the exchange-correlation term, which depend both via the density p on the functions tpj. The exchange-correlation potential VIC is defined within the so-called adiabatic local density approximation [25] which is the natural extension of the lda from stationary dpt. It is assumed to give reliable results for problems where the time scale of the external potential (in our case typical collision times) is larger than the electronic time scale. 

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