Molecular orbitals, open-shell molecules

Berthier, G., Self-Consistent Field Methods for Open-Shell Molecules, in Molecular Orbitals in Chemistry, Physics, and Biology, P. O. Lbwdin and B. Pullman, Eds., Academic Press, New York, 1964, pp. 57-82. 

Finally we describe several methods that combine molecule-dependent empirical parameters with a moderate level ab initio molecular orbital method. The BAC-MP4 method of Melius and coworkers115-118 combines a computationally inexpensive molecular orbital method with a bond additivity correction. This procedure uses a set of accurate experimental data to obtain a correction for bonds of different types that is then used to adjust calculated thermochemical data such as enthalpies of formation. Quite accurate results can be obtained if suitable reference molecules are available and if the errors in the calculation are systematic. The computational methodology is based on an MP4/6-31G(d,p)//HF/6-/31G(d) calculation. A pairwise additive empirical bond correction is derived for different bonds from fitting to experimental enthalpies of formation or in some cases to high quality ab initio computations. In addition, for open-shell molecules an additional correction is needed to compensate for spin contamination of the wavefunction from higher spin states in the unrestricted Hartree-Fock (UHF) method. 

The symmetric and antisymmetric squares have special prominence in molecular spectroscopy as they give information about some of the simplest open-shell electronic states. A closed-shell configuration has a totally symmetric space function, arising from multiplication of all occupied orbital symmetries, one per electron. The required antisymmetry of the space/spin wavefunction as a whole is satisfied by the exchange-antisymmetric spin function, which returns Fq as the term symbol. In open-shell molecules belonging to a group without... 

Thus far, the spin-independent forms of the various calculation methods have been described without clear notification, despite these forms being available only in the electronic state calculations for closed-shell molecules, in which electrons occupy molecular orbitals two by two. To take open-shell molecules containing unpaired electrons into consideration, spin orbitals should be explicitly considered. As a simple method for calculating the electronic states of open-shell molecules, Pople and Nesbet developed the unrestricted Hartree-Fock (UHF) method (Pople and Nesbet 1954), which independently deals with the spatial orbitals for a and P spins, in 1954. 

It is also possible to apply the same idea of using radiation to control the electron charge distribution in open-shell molecules. For example, the lithium dimer (Li2) has a closed-shell electronic structure in its X E+ ground state in which both valence electrons are spin paired in tire same a molecular orbital. Witii visible radiation, Li2 is readily excited to its A H state in which one electron... 

The fact is that the molecular orbitals describing the resulting cation may well be quite different from those of the parent molecule. We speak of electron relaxation, and so we need to examine the problem of calculating accurate HF wavefunctions for open-shell systems. 

For OH and SH, the NOF EAs are larger than the experimental values. This trend is due to the expected underestimation of the correlation energy for open-shell states with our approach. In fact, we fix the unpaired electron in the corresponding HF higher-occupied molecular orbital (HOMO) of the neutral molecule, and then this level does not participate in the correlation. Note that for these molecules the total spin of the neutral molecule is greater than the total spin of the anion (S > Sa)- The underestimation of the total energy is for neutral molecules larger than for anions and therefore the NOF vertical EAs are overestimated. 

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