Hartree-Fock theory dissociation

Hartree-Fock theory is very useful for providing initial, first-level predictions for many systems. It is also reasonably good at computing the structures and vibrational frequencies of stable molecules and some transition states. As such, it is a good base-level theory. However, its neglect of electron correlation makes it unsuitable for some purposes. For example, it is insufficient for accurate modeling of the energetics of reactions and bond dissociation. 

Equilibrium geometries, dissociation energies, and energy separations between electronic states of different spin multiplicities are described substantially better by Mpller-Plesset theory to second or third order than by Hartree-Fock theory. 

The boud dissociatiou euergy of hydrogeu peroxide has been accurately predicted by high-level ab initio theory . It was disclosed very early that Hartree-Fock theory, in the absence of electron-correlation correction, simply cannot be applied to problems involving 0-0 bond dissociation. For example, the predicted 0-0 bond energy in peroxyformic acid is only 1.0 kcalmoD by Hartree-Fock theory, whereas at the... 

Consider bond dissociation in H2. The product (H ) contains oidy a single electron and its energy is given exactly by Hartree-Fock theory. The reactant (Hj) contains two electrons and its energy is too positive. Therefore, the bond dissociation energy is too small. 

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,... 

In this section, then, we first introduce a set of unrestricted spin orbitab to derive the spatial eigenvalue equations of unrestricted Hartree-Fock theory. We then introduce a basis set and generate the unrestricted Pople-Nesbet matrix equations, which are analogous to the restricted Roothaan equations. We then perform some sample calculations to illustrate solutions to the unrestricted equations. Finally, we discuss the dissociation problem and its unrestricted solution. 

To complete our discussion of unrestricted Hartree-Fock theory, we will use our minimal basis H2 model to investigate the description of bond dissociation by unrestricted wave functions. 

The problems are not limited to H2. A classic foible is that of F2 in which a molecule with a weak covalent bond is calculated to be unbound by Hartree-Fock theory. While the difference in the calculated energy of the covalent/ionic combination and that of the molecule at equilibrium has occasionally been taken to be the bond energy, the energy difference between that of the neutral separated products and of the molecule is more formally correct. The calculated energy of the F2 molecule at equilibrium is less stable than that of the separated atoms. Calculated results are usually not that wrong. However, problems with dissociation are not limited to homonuclear bonds or even to covalent bonds. For example, in the gas phase, hence in the absence of solvent, the ionic NaCl homolytically dissociates into Na-l-CI and not Na+ - -Cr the electron affinity of Cl is less than the ionization energy of Na. Furthermore, the problem is not merely at infinite separation - even at the equilibrium distance there is an incorrect contribution of the ionic component to the molecular wavefunction. Any dissociation for which the number of unpaired electrons in the molecule and its components differ is problematic. We note the problem... 

Figure 4. Double bond dissociation of the water molecule using the perfect pairing (PP), imperfect pairing (IP) and restricted pairing (GVB-RCC) local correlation models, compared to full configuration interaction (FCI) and Hartree-Fock theory in a minimal (STO-3G) basis.

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