Why is methylene a ground state triplet while silylene is a ground state singlet?

The singlet-triplet energy difference in CH2 and SiH2 was calculated at the CASSCF level of theory using large Gaussian basis sets that included f-type functions. The total energy was separated into nuclear repulsion and electronic energy, and the latter was further decomposed into the contributions coming from the two electrons highest in energy (the frontier electrons, denoted by f) and from all the other electrons (denoted by c for core). The contribution of the frontier electrons was further decomposed into the following terms: E-(f) which is the sum of the kinetic energy and the attraction energy to the nucleus of the two frontier electrons and their repulsion energy from all other electrons, and E-ee((f)), the repulsion energy between the two frontier electrons. The results are used to explain why CH2 is a ground state triplet (lying ca. 10 kcal/mol lower in energy than the singlet) while SiH2 is a ground state singlet (with the triplet lying ca. 20 kcal/mol higher in energy). The major conclusions are as follows: (1) In addition to the frontier electrons, the core electrons and the nuclear repulsion energy also affect the singlet-triplet gap. (2) About 60% of the singlet-triplet energy difference between CH2 and SiH2 of 29 kcal/mol may be attributed to the E-ee((f)) term. (3) The remaining 40% of the energy difference can be interpreted as resulting from a balance between E-(f), the energy of the core electrons (E-(c)), and the nuclear repulsion energy (E-nuc); these terms may be related to the HOMO-LUMO energy difference, which is often used in qualitative discussions of singlet-triplet energy gaps. A detailed discussion of the results is presented.