Three Methods to Look at Walsh-type Diagrams Including Nuclear Repulsions

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Abstract
Energy correlation diagrams for molecules of type AH2 are examined by three different methods: (1) the quantum-mechanical virial theorem, (2) the method of median partition, (3) the integral Hellmann-Feynman theorem. Nuclear-nuclear repulsions are included. The formula for the first method takes the form W=−Σti, where ti is an orbital kinetic energy. The theory is applied to H2O, CH2, and BeH2. Negative-kinetic-energies-versus-angle diagrams for these molecules are presented. The pattern of the diagrams is quite different from the usual Walsh diagram. With this resolution non-bonding electrons play a significant role in determining bond angles. In the second method the resolution of the total energy takes the form W=Σi[ei+Vn(i)], where ei is a median electronic energy and Vn(i) is a resolved nuclear repulsion energy calculated from an expression derived from ideas of population analysis. The energies-versus-angle diagram thus obtained for H2O is similar to the one obtained by the first method. For the third method, the integral Hellmann-Feynman formula for the electronic energy change on bending is written in terms of corresponding orbital contributions, ΔEl=ΣiΔEl(i), and nuclear-nuclear repulsion is added in a resolved form. For H2O the ΔEl resemble Walsh diagrams closely, both with and without the nuclear-nuclear repulsion increments. Wave functions used throughout are LCAO-SCF functions built from medium-size Gaussian basis sets.

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