Resonance integral coupling factor

To account for this behaviour these authors proposed an extension of the theory, given by Pople and Santry, which predicted that the coupling constant depends upon the energies of the s relative to those of the p, d, etc. electrons of the coupled nuclei and additionally upon the resonance integral between the outer-shell r electrons of the two atoms. It was considered that the first factor remained fairly constant for the P-P bonds and the observed variation was qualitatively explained by the dependence of the second factor upon the electronegativity and the bulkiness of the substituent. 

V is the electronic coupling factor (the resonance integral), v is the velocity of nuclear motion, and Sj and Sf are the slopes of the initial and final terms in the Q,r region. If the exponent of the exponential function is small, then... 

The present section is a brief survey of experimental data on electron transfer rate and its theoretical treatment being focused on (a) the Franc-Condon (FC) factor and (b) electronic coupling (resonance integral) V. Role of the media molecular dynamics on ET is discussed in Sections 3.5.1 and 4.1.7... 

In this equation, the Franck-Condon factors (the squared Franck-Condmi integrals) and the resonance condition [the delta function in Eq. (4)] have been absorbed into the spectral density 2>eet [135]. It can be factored into the line-shape functions for donor emission and acceptor absorption (this is only possible due to the assumption of local vibrational modes). In addition, the dipole approximation can be made for the electronic coupling matrix element ... 

The fundamentals of SSS are based on the theory of impurity centers in a crystal. The optical spectrum of an organic molecule embedded in a matrix is defined by electron-vibrational interaction with intramolecular vibrations (vibronic coupling) and interaction with vibrations of the solvent (electron-phonon coupling). Each vibronic band consists of a narrow zero-phonon line (ZPL) and a relatively broad phonon wing (PW). ZPL corresponds to a molecular transition with no change in the number of phonons in the matrix (an optical analogy of the resonance -line in the Mossbauer effect). PW is determined by a transition which is accompanied by creation or annihilation of matrix phonons. The relative distribution of the integrated intensity of a band between ZPL and PW is characterized by the Debye-Waller factor ... 

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