Analytic second derivatives in closed-shell coupled-cluster theory with spin-orbit coupling

The theory for geometrical second derivatives of the energy is outlined for the recently suggested two-component coupled-cluster approach using relativistic effective core potentials with spin-orbit coupling included in the post-Hartree-Fock treatment [F. Wang, J. Gauss, and C. van Wullen, J. Chem. Phys. 129, 064113 (2008)], and an implementation is reported at the coupled-cluster singles and doubles (CCSD) level as well as at the CCSD level augmented by a perturbative treatment of triple excitations [CCSD(T)]. The applicability of the developed analytic second-derivative techniques is demonstrated by computing harmonic and fundamental frequencies for PtH(2), PbH(2), and HgH(2) with the required cubic and semidiagonal quartic force fields obtained by numerical differentiation of the analytically evaluated quadratic force constants. Spin-orbit coupling effects are shown to be non-negligible for the three considered molecules and thus need to be considered in the case of high-accuracy predictions. (C) 2009 American Institute of Physics. [doi:10.1063/1.3245954]