Electron-vibrational excited states in molecular crystals

9 Electron vibrational excited states in molecular crystals 

The inaccuracy of the approximation (3.165) is related to the fact that the frequencies of intramolecular vibrations depend strongly on the state of the electronic subsystem (which means that the frequencies z/ depend on the state / in particular, by electronic excitation of molecules of the aromatic series the frequencies change by a quantity of order 50 cm-1). In addition, in (3.165) anhar-monicity is neglected, being important for high values of the numbers n, m,. 

Due to the large differences in the masses of electrons and nuclei it is convenient to use the adiabatic approximation by analysis of molecular spectra. In particular, this approximation enables one to explain specific properties of the relation (3.165). It also allows one to examine the intensity distribution of the above 

Here Vf(R) is the eigenvalue of the operator V r,R) and Ef n is the total energy of the molecule in the vibronic state (/, n). As follows from (3.168), Vf(R) acts as the potential energy for the nuclei motion. So we obtain that the nuclei equilibrium positions depend on the state / of the electronic subsystem. It can be shown that the adiabatic approximation gives reasonable results when for given values R the distance between surfaces Vf(R) (for simplicity, the state / is considered as non-degenerate) and Vf R),f f is much larger than the frequencies of intramolecular vibrations. Only in this case can we assume that excitation of small intramolecular vibrations does not induce the transition / —  

The intensity of a dipole transition from the ground state (/ = 0, n = 0) to an arbitrary vibronic state is given by the square of the dipole matrix element of the molecular dipole moment p. The dipole moment p consists of two contributions, 

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