Electron correlation methods dissociation

This inability of HF 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 [62]. Suffice it to say here that representing the waveflmction 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, with and without the use of electron correlation methods, for processes involving homolytic cleavage, are discussed further in section 5.5.2. 

The HF wave funetion eontains equal amounts of ionie and eovalent eontributions (Section 4.3), For covalently bonded systems, like H2O, the HF wave funetion is too ionie, and the effect of electron correlation is to increase the covalent contribution. Since the ionic dissociation limit is higher in energy than the covalent, the effect is that the equiUbrium bond length increases when correlation methods are used. For dative bonds, such as metal-ligand compounds, the situation is reversed. In this case the HF wave function dissociates correctly, and bond lengths are normally too long. Inclusion of... 

Figure 4.8 Relativistic increase ApDe in dissociation energy for Au2 calculated in the years from 1989 to 2001 using a variety of different quantum chemical methods. Electron correlation effects AcDg = De(corr.)—De(HF) at the relativistic level are shown on the right hand side of each bar if available. For details see Figure 4.7.

C-H and N-H bond dissociation energies (BDEs) of various five- and six-membered ring aromatic compounds (including 1,2,5-oxadiazole) were calculated using composite ab initio CBS-Q, G3, and G3B3 methods. It was found that all these composite ab initio methods provided very similar BDEs, despite the fact that different geometries and different procedures in the extrapolation to complete incorporation of electron correlation and complete basis set limit were used. A good quantitive structure-activity relationship (QSAR) model for the C-H BDEs of aromatic compounds... 

P. C. Hiberty, S. Humbel, P. Archirel, J. Phys. Chem. 98, 11697 (1994). Nature of the Differential Electron Correlation in Three-Electron Bond Dissociation. Efficiency of a Simple Two-Configuration Valence Bond Method with Breathing Orbitals. 

One of the inherent problems with ab initio calculations is that they do not take full account of electron correlation, which arises from electrons keeping away from the vicinity of other electrons. This can make a significant contribution to the energy and is especially significant for accurate calculations of reaction energies and bond dissociation. One early method used for adding the effects of electron correlation to the Hartree-Fock method incorporated Moller-Plesset perturbation theory and led to methods labeled MP2, MP3, MP4, etc. 

The electronic structure methods are based primarily on two basic approximations (1) Born-Oppenheimer approximation that separates the nuclear motion from the electronic motion, and (2) Independent Particle approximation that allows one to describe the total electronic wavefunction in the form of one electron wavefunc-tions i.e. a Slater determinant [26], Together with electron spin, this is known as the Hartree-Fock (HF) approximation. The HF method can be of three types restricted Hartree-Fock (RHF), unrestricted Hartree-Fock (UHF) and restricted open Hartree-Fock (ROHF). In the RHF method, which is used for the singlet spin system, the same orbital spatial function is used for both electronic spins (a and (3). In the UHF method, electrons with a and (3 spins have different orbital spatial functions. However, this kind of wavefunction treatment yields an error known as spin contamination. In the case of ROHF method, for an open shell system paired electron spins have the same orbital spatial function. One of the shortcomings of the HF method is neglect of explicit electron correlation. Electron correlation is mainly caused by the instantaneous interaction between electrons which is not treated in an explicit way in the HF method. Therefore, several physical phenomena can not be explained using the HF method, for example, the dissociation of molecules. The deficiency of the HF method (RHF) at the dissociation limit of molecules can be partly overcome in the UHF method. However, for a satisfactory result, a method with electron correlation is necessary. 

There are two types of electron correlation static and dynamic. The static correlation is related to the behavior of HF method at the dissociation limit of the molecule and deals with the long range behavior of this approach. On the other hand dynamic electron correlation is related to the electron repulsion term and is the reciprocal function of a distance between two electrons and thus represents short range phenomena. However, it should be noted that the electron correlation in the HF method is included in the indirect manner by the consideration of an electronic motion in an effective potential field due to the nuclei and the rest of the electrons and due to the inclusion of electron spin. Therefore, despite the known shortcomings, HF method has been extensively used in chemical calculations and has been quite successful for systems which are not extensive for electron correlation. 

The future of this field clearly will rely on extending these, or some other, methods to study two-electron systems and simple molecular systems. There is evidence that electron-electron correlation continues to play a role in excitation dynamics even in very intense fields. The interaction can be small, but it has been observed to yield orders of magnitude enhancements in the production of doubly charged ions for intensities below that at which sequential ionization becomes efficient. In molecules, the transfer of absorbed energy from the electrons to the nuclei which controls the competition between ionization and dissociation is another important and developing field of research. 

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