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

Abstract

The general inclusion of the T4 operator into the coupled cluster equations requires an n10 computational procedure, and n9 in the lowest order, as in the CCSDTQ-1 (coupled cluster singles, doubles, triples, and lowest order quadruples) method. Coupled cluster methods with full inclusion of singles, doubles, triples, and an efficient noniterative inclusion of connected quadruples (CCSDT(Qf)) have been introduced in [J. Chem. Phys. 108, 9221 (1998)]. Since the connected quadruple part in the latter method scales as n7 (CCSDT itself is n8) it offers an attractive route to assess the connected quadruple contribution for larger basis sets. We present a detailed description of the Qf algorithm with explicit algebraic formulas for the spin–orbital formalism as well as for a nonorthogonal spin adapted approach. The method has been applied to obtain the equilibrium geometry and harmonic frequencies for the C2 molecule for a sequence of correlation consistent polarized (core) valence (cc-p(C)VXZ, X=D,T,Q,5) basis sets. For the largest 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 0.0014 Å, providing results that agree with experiment to 3 cm−1 and 0.0003 Å.