Crude-adiabatic approximation

The term H e is the electron correlation operator, the term H p corresponds to phonon-phonon interaction and H l corresponds to electron-phonon interaction. If we analyze the last term H l we see that when using crude approximation this corresponds to such phonons that force constant in eq. (17) is given as a second derivative of electron-nuclei interaction with respect to normal coordinates. Because we used crude adiabatic approximation in which minimum of the energy is at the point Rg, this is also reflected by basis set used. Therefore this approximation does not properly describes the physical vibrations i.e. if we move the nuclei, electrons are distributed according to the minimum of energy at point Rg and they do not feel correspondingly the R dependence. The perturbation term H) which corresponds to electron-phonon interaction is too large... 

In the so-called "crude adiabatic approximation", the zeroth-order vibronic wave functions may be written as... 

The divergence of nonadiabatic couplings in Eq. 8.7 leads to computational problems in fuU quantum treatments, like those reviewed in this chapter, due to the difficulty to integrate them over the vibrational wavefunctions. Different strategies have been proposed to face these problems. Probably the most traditional solution is to work within the so-called crude-adiabatic approximation, where the electronic wavefunctions at a fixed nuclear configuration go are used in the expansion in Eq. 8.5,... 

Two main assumptions underlie the GF method (1) full separation of electronic and vibrational degrees of freedom (crude adiabatic approximation) and (2) local-... 

In the crude adiabatic approximation with fixed nuclei, the electronic Hamiltonian He does not depend on... 

The electronic wavefunction in the crude adiabatic approximation is defined according to Equation 1.18 at a specific nuclear configuration q and therefore it does not... 

THE CRUDE BORN-OPPENHEIMER ADIABATIC APPROXIMATION OF MOLECULAR POTENTIAL ENERGIES... 

THE CRUDE BORN—OPPENHEIMER ADIABATIC APPROXIMATION 521 Consider the integral... 

THE CRUDE BORN-OPPENHEIMER ADIABATIC APPROXIMATION 555 which is a more general foiin of Eq. (131). The modification is simple ... 

Let us note that sometimes spectra are so well resolved that even some asymmetry of lines is registered [283]. This means that the wings of individual components of a spectral band become observable. Hence, non-adiabatic secularization becomes too crude an approximation. The experiment [283] was interpreted by Kouzov [280] taking into account the co-dependent diagonal part of the relaxational operator. 

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