Third-order Douglas-Kroll relativistic coupled-cluster theory through connected single, double, triple, and quadruple substitutions: applications to diatomic and triatomic hydrides

Coupled-cluster methods including through and up to the connected single, double, triple, and quadruple substitutions have been derived and implemented automatically for sequential and parallel executions by an algebraic and symbolic manipulation program TCE (TENSOR CONTRACTION ENGINE) for use in conjunction with a one-component third-order Douglas-Kroll approximation for relativistic corrections. A combination of the converging electron-correlation methods, the accurate relativistic reference wave functions, and the use of systematic basis sets tailored to the relativistic approximation has been shown to predict the experimental singlet-triplet separations within 0.02 eV (0.5 kcal/mol) for five triatomic hydrides (CH2, NH2+, SiH2, PH2+, and AsH2+), the experimental bond lengths (re or r0) within 0.002 angstroms, rotational constants (Be or B0) within 0.02 cm(-1), vibration-rotation constants (alphae) within 0.01 cm(-1), centrifugal distortion constants (De) within 2%, harmonic vibration frequencies (omegae) within 8 cm(-1) (0.4%), anharmonic vibrational constants (xomegae) within 2 cm(-1), and dissociation energies (D0(0)) within 0.02 eV (0.4 kcal/mol) for twenty diatomic hydrides (BH, CH, NH, OH, FH, AlH, SiH, PH, SH, ClH, GaH, GeH, AsH, SeH, BrH, InH, SnH, SbH, TeH, and IH) containing main-group elements across the second through fifth rows of the periodic table. In these calculations, spin-orbit effects on dissociation energies, which were assumed to be additive, were estimated from the measured spin-orbit coupling constants of atoms and diatomic molecules, and an electronic energy in the complete-basis-set, complete-electron-correlation limit has been extrapolated in two ways to verify the robustness of the results: One assuming Gaussian-exponential dependence of total energies on double through quadruple zeta basis sets and the other assuming n(-3) dependence of correlation energies on double through quintuple zeta basis sets.