Computational study of structural, vibrational and electronic properties of the highly symmetric molecules M4S6 (M = P, As, Sb, Bi)

A systematic computational investigation of the structural, electronic and vibrational properties of the group 15 sulfides M4S6 at T-d symmetry was carried out. The performance of DFT and MP2 theoretical methods was assessed compared to the high-level CCSD method. The M-S bond is based on the association between p valence orbitals of M and the 3p of sulfur according to the natural population analysis. Both polarizability and polarizability volume of the cage molecules increase as the size of the atoms increases from P to Bi. A structural 'relaxation' ongoing from phosphorus to bismuth showed an increase of ionic character and it might explain the chemical instability of the heavier cage compounds. For the P4S6 molecule, the functionals wB97XD and CAMB3LYP yielded excellent structural data, while for the heavier molecules As4S6, Sb4S6 and Bi4S6, the M06 and M06L functionals showed high accuracy. We validated eight functionals BP86, M06L, B3LYP, M06, M06-2X, CAMB3LYP, wB97XD, B2PLYP which span from conventional GGA functionals to long-range corrected hybrid ones, and MP2, CCSD ab initio methods. Experimentally, these molecules could be useful in the structural investigation of the isolated gas phase species, besides solving complex structures of liquid, crystalline or amorphous phases.