Comparison of the quality of DFT versus MP2 and MP3 total energies and an unexpected size effect in the conformational equilibria of vinylhalogermanes

The structures of CH₂=CH-GeKL₂ (K=F or CI, L=H for the monohalo and K=H, L=F or CI for the dihalo derivative of our vinylhalogermanes) were investigated by DFT-B3LYP/6-311++G** and ab initio MP2/6-311++G** calculations. The potential functions for the internal rotation of the GeKL₂ rotors were calculated and it was found that they are very similar for the molecules. In both halogen derivatives, both molecules exhibit a conformational equilibrium between the two stable cis and gauche forms, where in all cases the trans conformation is one of the two transition stales. In the case of the vinylmonohalogermanes the gauche forms are slightly lower than the cis ones, while in the case of vinyldihalogermanes the two forms are nearly degenerate. The equilibrium constants of the four equilibria were calculated and are presented. The vibrational frequencies of the two molecules in their stable conformations were computed. The potential energy distributions, PED, among the symmetry coordinates of the normal modes of the vinylchlorogermanes were calculated from normal coordinate calculations and a complete assignment of all spectral modes is provided. Further the infrared and vibrational Raman spectra of the conformational equilibria were plotted and shown in this work. Due to previous experience with comparisons between calculated and experimental spectra, we expect them to be rather reliable predictions of the corresponding experimental ones, especially because instead of relative energies we use now equilibrium constants calculated from Gibbs free energies to determine the populations of the molecules in the equilibria. It is pointed out, that in previous findings in systems with lower electron densities (carbon instead of germanium) usually MP2 yields better total, and thus also better relative energies than DFT. Since for higher electron densities, MP2 which includes only double excitations could deteriorate in comparison to DFT because of the higher importance of triple and quadruple excitations, we decided to study halogermanes of increasing electron densities to study this possibility. Indeed, in the present cases DFT total energies seem to be of similar reliability as MP2 ones in case of the fluoro derivatives and much better than MP2 ones for the chloro derivatives, the latter having the higher electron densities. Thus it seems that besides the principle theoretical deficiency of size inconsistency from which all trunctated CI expansions suffer, but not MP in any order, there appears to be another size problem: with increasing electron density the probability and thus importance of higher order excitations (MP2 includes only doubles and these not completely) increases. It seems, as shown here on the example of vinylhalogermanes. that such effects are implicitely included in the B3LYP functional of DFT. Our MP3 calculations on the chlorogermanes showed, that the effects are small, because MP3 still includes only double excitations, but they are shifting the MP results slightly towards the DFT ones.