Pseudo Jahn-Teller effect and natural bond orbital analysis of structural properties of tetrahydridodimetallenes M2H4, (M = Si, Ge, and Sn).

The structural properties of ethene (1) and tetrahydridodimetallenes M(2)H(4) [M = Si (2), Ge (3), and Sn (4)] have been examined by means of CCSD(T)/Def2-TZVPP, MP4(SDTQ)/Def2-TZVPP, and B3LYP/Def2-TZVPP levels of theory and natural bond orbital analysis (NBO) interpretations. The results obtained showed the expected planar ground state structure for compound 1 (D(2h) symmetry) but trans-bent ground state structures for compounds 2-4 (C(2h) symmetry). The distortions of the high-symmetry configurations of compounds 2-4 are due to the pseudo Jahn-Teller effect (PJTE), which is the only source of instability of high-symmetry configurations in nondegenerate states. The distortions are due to the mixing of the ground A(g) and excited B(2g) states [i.e., HOMO(B(3u)) → LUMO + 3(B(1u)) for compound 1, HOMO(B(3u)) → LUMO + 2(B(1u)) for compound 2, and HOMO(B(3u)) → LUMO + 1(B(1u)) for compounds 3 and 4]. Importantly, the higher-lying B(1g), B(2u), and B(2g) states are not involved in the PJT interactions. The energy gaps between reference states (Δ) in the undistorted configurations decrease from compound 1 to compound 4, and the PJT stabilization energies increase. Therefore, the primary force constant of the ground state in the Q((b2g)) direction (K(0)) decreases from compound 1 to compound 4. This fact can be justified by the valence isoelectronic systems of these compounds (having similar vibronic coupling constants, F). For the purpose of more chemical transparency, the NBO results were analyzed, and their relation to the PJT interactions has been revealed. The NBO analysis showed that stabilization energy associated with π(M-H) (b(u)) → σ*(M═M) (b(u)) electron delocalization (i.e., the mixing of the distorted b(u) molecular orbitals along the b(2g) bending distortions) increases from compound 1 to compound 4. Also, by using the hybridized orbitals obtained, an n parameter is defined. The NBO results revealed that the n values in the mean hybrid orbitals (sp(n)) increase from compound 1 to 4. The correlations between the PJT stabilization energies, bond orders, n values, π(M-M) → σ*(M═M) electron delocalizations, and structural parameters of compounds 1-4 have been investigated.