Hartree-Fock calculations numerical illustration

Many computations were made to classify the various types of behavior that no(p) can have in atoms and atomic ions [210,211,225-229], but some confusion persisted because different authors obtained different results in a few problematic cases. Purely numerical Hartree-Fock calculations, free from basis set artifacts, were then used to establish that the ground-state momenmm densities of all the atoms and their ions can be classihed into just three types [230,231] as illustrated in Figure 5.5. 

This inability of Hartree-Fock calculations to model correctly homolytic bond dissociation is commonly illustrated by curves of the change in energy as a bond is stretched, e.g. Fig. 5.19. The phenomenon is discussed in detail in numerous expositions of electron correlation [82]. Suffice it to say here that representing the wavefunction as one determinant (or a few), as is done in Hartree-Fock theory, does not permit correct homolytic dissociation to two radicals because while the reactant (e.g. H2) is a closed-shell species that can (usually) be represented well by one determinant made up of paired electrons in the occupied MOs, the products are two radicals, each with an unpaired electron. Ways of obtaining satisfactory energies,... 

We now turn to the calculation of f and H in quantum chemistry. A straightforward approach is to simply numerically differentiate the energy. Alternatively, it is possible to obtain these derivatives by analytic derivative methods. Let us illustrate some of the essential ideas in the framework of Hartree-Fock calculations. 

The goal of this monograph is to summarize the different quantum-mechanical methods developed in the last 20 years to treat the electronic structure of polymers. Owing to the nature of the problem, these methods consist of a mixture of quantum-chemical and solid-state physical techniques. The theory described in Part I treats, besides the Hartree-Fock problem, the electron correlation, and it has also been developed for disordered polymeric systems. Though for obAdous reasons the book could not include all the existing calculations, each new method described is illustrated by a few applications, with a discussion of the numerical results obtained. For more details see the Introduction to Part I. 

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