Molecular-Orbital Studies of Intermolecular Interaction Energies. II. Approximations Concerned with Coulomb Interactions and Comparison of the Two London Schemes

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Abstract
In the semiempirical calculations of wavefunctions in molecules with π-electron systems, molecular orbitals are constructed from atomic orbitals that are assumed to be orthogonal to each other. Since the Slater orbitals are not orthogonal, the atomic orbitals are usually interpreted to be the Löwdin orbitals. The Löwdin orbitals are delocalized, and therefore a question arises of how to use the computed coefficients of these orbitals for calculating the electronic charge distribution. It is found that the charge distribution may be somewhat different from the distribution where Slater orbitals are used instead of Löwdin orbitals. The magnitude of the difference depends on the kind of approximation used for the product functions of two Slater orbitals centered on different atoms. The difference vanishes for the Mulliken approximation. Numerical analysis for a guanine—cytosine base pair indicates that when the Löwdin approximation, or a similar approximation, is used instead of the Mulliken approximation, the difference in atomic charges amounts to about 20%. The effect of this on the intermolecular Coulomb energy between two guanine—cytosine base pairs in a DNA-like arrangement amounts to about 20%. Of the two well-known London schemes for the calculation of intermolecular Coulomb energies, the second London scheme is much superior to the first one for application to many organic and biological molecules. The numerical analysis reveals a difference of 50% between the two schemes, when applied to the guanine—cytosine dimer.

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