Hartree-Fock theory qualitative theories

The second chapter introduces the student to orbitals proper and offers a simplified rationalization for why orbital interaction theory may be expected to work. It does so by means of a qualitative discussion of Hartree-Fock theory. A detailed derivation of Hartree-Fock theory making only the simplifying concession that all wave functions are real is provided in Appendix A. Some connection is made to the results of ab initio quantum chemical calculations. Postgraduate students can benefit from carrying out a project based on such calculations on a system related to their own research interests. A few exercises are provided to direct the student. For the purpose of undergraduate instruction, this chapter and Appendix A may be skipped, and the essential arguments and conclusions are provided to the students in a single lecture as the introduction to Chapter 3. 

One-electron picture of molecular electronic structure provides electronic wavefunction, electronic levels, and ionization potentials. The one-electron model gives a concept of chemical bonding and stimulates experimental tests and predictions. In this picture, orbital energies are equal to ionization potentials and electron affinities. The most systematic approach to calculate these quantities is based on the Hartree-Fock molecular orbital theory that includes many of necessary criteria but very often fails in qualitative and quantitative descriptions of experimental observations. 

Most chemists picture the electronic structure of atoms or molecules by invoking orbitals. The orbital concept has its basis in Hartree-Fock theory, which determines the best wavefunction I ) under the approximation that each electron experiences only the average field of the other electrons. This is also called the one-electron, or independent particle model. While the Hartree-Fock method gives very useful results in many situations, it is not always quantitatively or even qualitatively correct. When this approximation fails, it becomes necessary to include the effects of electron correlation one must model the instantaneous electron-electron repulsions present in the molecular Hamiltonian. 

The UF6 molecule has also been studied extensively using a more elaborate method, namely configuration interaction, to assign the experimental photoelectron spectrum (de Jong and Nieuwpoort 1998). The qualitative analysis of chemical bonding exhibits that the U-F bond is more ionic in the relativistic framework (de Jong and Nieuwpoort 1998). The 6s orbital of uranium remains atom-like in the molecule due to relativistic contraction and does not contribute to chemical bonding, while it contributed in nonrelativistic Hartree-Fock theory. 

Another approach to electron correlation is Moller-Plesset perturbation theory. Qualitatively, Moller-Plesset perturbation theory adds higher excitations to Hartree-Fock theory as a non-iterative correction, drawing upon techniques from the area of mathematical physics known as many body perturbation theory. 

It is important to realize that whenever qualitative or frontier molecular orbital theory is invoked, the description is within the orbital (Hartree-Fock or Density Functional) model for the electronic wave function. In other words, rationalizing a trend in computational results by qualitative MO theory is only valid if the effect is present at the HF or DFT level. If the majority of the variation is due to electron correlation, an explanation in terms of interacting orbitals is not appropriate. 

In the physics and chemistry of many-particle systems comprising atoms, molecules, solid state, and nuclei, quantum mechanics has given very important contributions to the theory of both a qualitative and quantitative nature. The Hartree-Fock scheme has usually been considered as a rather sophisticated approach, but, if one seriously studies the typical errors listed in Tables I and II and Eqs. 11.83 and 11.84 it becomes clear that the qualitative aspects... 

Hartree-Fock (HF), molecular orbital theory satisfies most of the criteria, but qualitative failures and quantitative discrepancies with experiment often render it useless. Methods that systematically account for electron correlation, employed in pursuit of more accurate predictions, often lack a consistent, interpretive apparatus. Among these methods, electron propagator theory [1] is distinguished by its retention of many conceptual advantages that facilitate interpretation of molecular structure and spectra [2, 3, 4, 5, 6, 7, 8, 9]. 

This survey of theoretical methods for a qualitative description of homogeneous catalysis would not be complete without a mention to the Hartree-Fock-Slater, or Xot, method [36]. This approach, which can be formulated as a variation of the LDA DFT, was well known before the formal development of density functional theory, and was used as the more accurate alternative to extended Hiickel in the early days of computational transition metal chemistry. 

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