Energy interaction, contributions

In the present non-Bornian theory it should be noted again that the long-range electrostatic interactions of an ion with solvents in the second and further solvation shells are ignored. However, the electrostatic energies should contribute to a considerable extent to the solvation energies of ions in each phase. Nevertheless, the proposed equations for... 

In addition, separation of the free energy into contributions depends on the path taken to transform the reference system into the target one. In other words, in contrast to AA, the contributions from the interactions of type a, type b and their coupling change if the transformation is performed along a different pathway. This is due to the fact that free energy is a state function of the system, but its contributions are not. 

An additional comment with regard to Eqs (33) and (34) is worth making. These equations are not exact because in addition to the neglect of the interaction contribution of the neutral X system with the polarizable environment, there are the variational errors 8a and Sx associated with the expectation values EA and Ex, respectively. Since we are interested in the energy difference AE = Ea - Ex and because the error 8a and 8x are... 

Another kind of analysis due to Clementi 8 ) allows the partition of the interaction energies into contributions from the individual atoms or groups of atoms in a given complex. 

We can make further approximations to simplify the NRF of the Hamiltonian presented in equation (75) for non-dynamical properties. For such properties, we can freeze the nuclear movements and study only the electronic problem. This is commonly known as the clamped nuclei approximation, and it usually is quite good because of the fact that the nuclei of a molecule are about 1836 times more massive than the electrons, so we can usually think of the nuclei moving slowly in the average field of the electrons, which are able to adapt almost instantaneously to the nuclear motion. Invocation of the clamped nuclei approximation to equation (75) causes all the nuclear contributions which involve the nuclear momentum operator to vanish and the others to become constants (nuclear repulsion, etc.). These constant terms will only shift the total energy of the system. The remaining terms in the Hamiltonian are electronic terms and nuclear-electronic interaction contributions which do not involve the nuclear momentum operator. 

For agglomerated structures, the dipolar interaction between two neighboring crystals contributes to the anisotropy energy. This contribution increases when the inter-crystal distance decreases. 

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