The electronic relaxation energy

In the second intermediate state, the density on each fragment is allowed to relax to the extent that the number of elertrons on each fragment is constrained to be the same as in the frozen density (IV and Alg, respectively) that is, no charge transfer. The energy difference between the two intermediate states I and II leads to the polarization component (A poi). 

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The principal stumbling block in the use of chemical shifts to study the nature of chemical bonding is the fact that the electronic relaxation energy is a variable. 

The electronic relaxation energy associated with the core ionization of a molecule can be divided into two parts54) ... 

The symmetry-breaking of the HF function occurs when the resonance between the two localized VB form A+...A and A...A+ is weaker than the electronic relaxation which one obtains by optimizing the core function in a strong static field instead of keeping it in a weak symmetrical field. If one considers for instance binding MOs between A and A they do not feel any field in the SA case and a strong one in the SB solution. The orbitals around A concentrate, those around A become more diffuse than the compromise orbitals of A+ 2 and these optimisations lower the energy of the A. A form. As a... 

In general, fluctuations in any electron Hamiltonian terms, due to Brownian motions, can induce relaxation. Fluctuations of anisotropic g, ZFS, or anisotropic A tensors may provide relaxation mechanisms. The g tensor is in fact introduced to describe the interaction energy between the magnetic field and the electron spin, in the presence of spin orbit coupling, which also causes static ZFS in S > 1/2 systems. The A tensor describes the hyperfine coupling of the unpaired electron(s) with the metal nuclear-spin. Stochastic fluctuations can arise from molecular reorientation (with correlation time Tji) and/or from molecular distortions, e.g., due to collisions (with correlation time t ) (18), the latter mechanism being usually dominant. The electron relaxation time is obtained (15) as a function of the squared anisotropies of the tensors and of the correlation time, with a field dependence due to the term x /(l + x ). 

An electron spin can relax by coupling with a neighboring electron spin. Therefore, when a paramagnetic metal ion interacts with a second paramagnetic metal ion, the electron relaxation rates of the two metal ions may be dramatically affected. If Si and S2 are the two spins coupled by a scalar interaction, new spin levels will be established due to the interaction, with total S varying in unitary steps from Si — S2I to Si + S2. The energies of these spin levels are given by )... 

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