Ab initio interpretation of Hund's rule for the methylene molecule: Variational optimization of its molecular geometries and energy component analysis

Hund's spin-multiplicity rule for the ground state of the methylene molecule CH₂ is interpreted by Hartree-Fock (HF) and multi-reference configuration interaction (MRCI) methods. The stabilization of the triplet ground state (X̃³B₁) relative to the second singlet excited state (b̃¹B₁) is ascribed to the greater electron-nucleus attraction energy that is gained at the cost of increasing the electron-electron repulsion energy and with the aid of a reduction in the nucleus-nucleus repulsion energy. The highest spin-multiplicity in the ground state of CH₂ is accompanied by a set of three characteristic features, i.e., elongation of the internuclear distances, reduction in the bond angle, and contraction of the valence electron density distribution around the nuclei involving expansion of the core electron density distribution. The present calculations fulfill the virial theorem to an accuracy of -V/T = 2.000 for both HF and MRCI. Accordingly, the molecular geometries are optimized for each of the two states. The inclusion of correlation by MRCI method reduces the energy splitting between the two states by about 14%. The energy splitting is analyzed by the correlational virial theorem 2T^c + V^c = 0 to make a clear interpretation of the correlation effect.