Vibrational center-ligand couplings in transition metal complexes.

The mode-tracking principle [J. Chem. Phys. 2003, 118, 1634] for the direct quantum chemical calculation of preselected, characteristic molecular vibrations makes vibrational analyses of very large molecules feasible. This is demonstrated here for the (Ph(3)PAu)(6)C complex, in which 18 phenyl groups in the ligand sphere are explicitly taken into account. We are aiming at the motion of the endohedral carbon atom, which is in an extraordinary bonding situation because it is surrounded by an octahedral core of gold atoms in this cluster. Secondary effects of the full ligand sphere on the vibrations of the [Au(6)C] core embedded in (R(3)PAu)(6)C clusters are investigated. For this purpose, local vibrations of the octahedral core are generated, and their long-range couplings with the phosphine ligand sphere become visible in the mode-tracking iterations. The exact normal modes of these characteristic vibrations of the cluster are then obtained after convergence of the mode-tracking refinement. This protocol allows us to assess the coupling of the outer ligand sphere with the inner core of the cluster in terms of changes of the vibrational frequencies and of the collective motions of the atomic nuclei. The vibrational frequencies of the octahedral [Au(6)C] core split due to symmetry breaking in the C(1)-symmetric (Ph(3)PAu)(6)C cluster. Our study demonstrates how effects of the periphery of a large molecule on local vibrations can be quantified. Furthermore, we predict the first set of characteristic vibrational frequencies obtained with first-principles methods for this gold cluster, whose vibrational spectra have not yet been recorded experimentally.