Orbital relaxation terms

Based on the foregoing discussion, one might suppose that the Fukui function is nothing more than a DFT-inspired restatement of frontier molecular orbital (FMO) theory. This is not quite true. Because DFT is, in principle, exact, the Fukui function includes effects—notably electron correlation and orbital relaxation—that are a priori neglected in an FMO approach. This is most clear when the electron density is expressed in terms of the occupied Kohn-Sham spin-orbitals [16],... 

Now, the most direct interpretation of Eq. (11.5) follows from the observation, suggested by Eqs. (11.1) and (11.2), that/is essentially a relaxation term. In fact, Vk — represents the difference between the electrostatic potential at the h nucleus in the given molecule and the potential that the same nucleus would feel if the atomic orbitals and the equilibrium distances remained the same as in the reference molecule in spite of the change in electron populations. 

In the final step of the EDA, the wave function of the molecule relaxes to its optimal form yielding the orbital interaction term AEoa. This term can be further partitioned into contributions by the orbitals belonging to different irreducible representations of the point group of the interacting system. Thus, it is possible to give energy contributions of the a and tt bonding contributions to a bond that has a mirror plane. More details about the EDA method in the framework of DFT can be found in a recent review article. ... 

From Janak s extension for noninteger occupation numbers,19 the Fukui function can be written as the sum of a frontier orbital density and relaxation terms,... 

Whereas many choices for the zeroth-order Hamiltonian are possible, the Fock operator with the usual one-electron. Coulomb and exchange components has been the usual choice in molecular calculations. In the remaining term, Y, (E), the self-energy operator describes the effects of electron correlation and of orbital relaxation in final states. There are energy-independent and energy-dependent components of the self-energy operator ... 

Table II, which is adapted from a previous description (Nenner 1987 Nenner et al. 1988), presents some of the electronic relaxation processes associated with the decay of a core hole. In these equations, c represents a core orbital, v an occupied valence orbital, u an unoccupied valence or Rydberg orbital, and s represents a shape resonance orbital. The term orbital is used simply to mean a one-electron wavefunction. An electron in a continuum orbital free from the influence of the molecular potential is represented as e .

This theorem is recognized as an approximation as, apart from the inaccuracies inherent in the S.C.F. method (such as neglect of electron correlation and relativistic effects), it assumes that the molecular orbitals are the same for the molecule and the molecular ion. Many ASCF calculations have shown (see for example 14 16)) that if an electron is removed from a metal localized orbital, considerable charge migration towards the metal occurs this is termed relaxation. These relaxation effects give ionization energies smaller values than those expected on the basis of Koopmans theorem. For ionization from ligand based orbitals, relaxation effects are smaller and more constant. 

In related propagator work, it has been conjectured that because of orbital relaxation effects, the 5-block basis operators make important contributions. While adhering to the traditional choice of the P-space, (i.e., and a ), Ohrn and co-workersexplicitly include the 5-block in calculations on Ne and Nj, respectively, via a continued fraction formalism. Their numerical calculations confirm our findings of the importance of these terms. 

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