Electronic structure representation Hartree-Fock approximation

Since rigorous theoretical treatments of molecular structure have become more and more common in recent years, there exists a definite need for simple connections between such treatments and traditional chemical concepts. One approach to this problem which has proved useful is the method of localized orbitals. It yields a clear picture of a molecule in terms of bonds and lone pairs and is particularly well suited for comparing the electronic structures of different molecules. So far, it has been applied mainly within the closed-shell Hartree-Fock approximation, but it is our feeling that, in the future, localized representations will find more and more widespread use, including applications to wavefunctions other than the closed-shell Hartree-Fock functions. 

In a first approximation, we can consider the electron structure as frozen under the photoelectron emission process and identify Eb with the Hartree-Fock energy eigenvalues of the orbitals (Koopman s theorem). A schematic representation of an expected photoelectron spectrum could then be the one in Figure 9. 

Analogically to the representation of the wave-function in structural terms, there is a way to separate (hyper)polarizabilities into the individual contributions from individual atoms. A method for such separation was developed by Bredas [15, 16] and is called the real-space finite-field method. The approach can be easily implemented for a post-Hartree-Fock method in the r-electron approximation due to the simplicity of e calculation of the one-electron reduced density matrix (RDMl) elements. In our calculations we are using a simple munerical-derivative two-points formula for RDMl matrix elements (Z ) [88] (see also [48]) ... 

Unfortunately, measured vibrational frequencies have some anharmonic component, and the vibrational frequencies computed in the manner above are harmonic. Thus, even the most accurate representation of the molecular structure and force constant will result in the calculated value having a positive deviation from experiment (Pople et al. 1981). Other systematic errors may be included in calculations of vibrational frequencies as well. For instance, Hartree-Fock calculations overestimate the dissociation energy of two atoms due to the fact that no electron correlation is included within the Hartree-Fock method (Hehre et al. 1986 Foresman and Frisch 1996). Basis sets used for frequency calculations are also typically limited (Curtiss et al. 1991) due to the requirements of performing a full energy minimization. Thus, errors due to the harmonic approximation, neglect of electron correlation and the size of the basis set selected can all contribute to discrepancies between experimental and calculated vibrational frequencies. 

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