Electronic matrix elements for

Table 15.4. Comparison of some one- and two-electron matrix elements for pure and SCVB 2pz orbitals. All energies are in hartrees.

In this formula, V is the electron matrix element for electron tunneling transition, l is the distance between the centres of the D and A particles, a is the width of the charge transfer band, and EmSLX is the position of the maximum of this band. Emax = Eu — EA + A, where (ED — EA) is the difference of the redox potentials of the donor and the acceptor and A is the energy spent on the excitation of the vibrational degrees of freedom. 

The single-electron matrix elements for the passive and the active electrons contain different projections of the electron spin. Since neither the photon operator nor the unity operator (in the overlap matrix element) acts on the spin, the quantum numbers M, and ms are fixed by the corresponding spin of the formerly bound ls-electron. This yields... 

In the case where an avoided crossing is being represented by adiabatic curves, a relation between electronic matrix elements for basis functions belonging to adiabatic versus diabatic curves can be derived easily (Bandrauk and Child, 1970 Oppenheimer, 1972), as shown below. 

Table I. Electronic Matrix Elements for Direct and Indirect Mixing °...

Table 1.1. Calculated Electronic Matrix Elements for Self Exchange Reactions "...

Ljj Lj. local 1-electron matrix element for ligand orbitals in contact in the transition state, and N is the number of such contacts. 

Third, as a consequence of the foregoing, the use of IDs is suitable in investigating the dependence of the electronic matrix element for radiationless transition on the nuclear coordinates. This problem can be solved, as has been shown in Chapter 5, by considering the matrix element as one that of an operator that depends upon both electronic and nuclear displacements and by introducing a q-centroid approximation for the electronic factor. The latter is obtained as an average with DSWVO factor. The familiar Condon approximation can be so improved as to write the whole matrix element as a product of a vibrational overlap integral and an electronic factor, the latter being evaluated at some (j-centroid for the nuclear positions. 

Freed, KF. and Lin, S.H. (1975) Nuclear coordinate dependence of electronic matrix elements for radiationless transitions. Chem. Phys., 11, 409. 

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