Toward the limits of predictive electronic structure theory: Connected quadruple excitations for large basis set calculations

The general inclusion of the T-4 operator into the coupled cluster equation s requires an n(10) computational procedure, and n(9) in the lowest order, as in the CCSDTQ-1 (coupled cluster singles, doubles, triples, and lowest o rder quadruples) method. Coupled cluster methods with full inclusion of sin gles, doubles, triples, and an efficient noniterative inclusion of connecte d quadruples (CCSDT(Q(f))) have been introduced in [J. Chem. Phys. 108, 922 1 (1998)]. Since the connected quadruple part in the latter method scales a s n(7) (CCSDT itself is n(8)) it offers an attractive route to assess the c onnected quadruple contribution for larger basis sets. We present a detaile d description of the Q(f) algorithm with explicit algebraic formulas for th e spin-orbital formalism as well as for a nonorthogonal spin adapted approa ch. The method has been applied to obtain the equilibrium geometry and harm onic frequencies for the C-2 molecule for a sequence of correlation consist ent polarized (core) valence (cc-p(C)VXZ, X=D,T,Q,5) basis sets. For the la rgest basis sets, cc-pCVQZ and cc-pV5Z, the connected quadruple excitations lower the harmonic frequency by 10 cm(-1) and raise the bond length by 0.0 014 Angstrom, providing results that agree with experiment to 3 cm(-1) and 0.0003 Angstrom. (C) 2001 American Institute of Physics.