The general inclusion of the T-4 operator into the coupled cluster equations 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 order quadruples) method. Coupled cluster methods with full inclusion of singles, doubles, triples, and an efficient noniterative inclusion of connected quadruples (CCSDT(Q(f))) have been introduced in [J. Chem. Phys. 108, 9221 (1998)]. Since the connected quadruple part in the latter method scales as n(7) (CCSDT itself is n(8)) it offers an attractive route to assess the connected quadruple contribution for larger basis sets. We present a detailed description of the Q(f) 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 C-2 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 Angstrom, providing results that agree with experiment to 3 cm(-1) and 0.0003 Angstrom.