To assess the limits of single-reference coupled-cluster (CC) methods for potential-energy surfaces, several methods have been considered for the inclusion of connected quadruple excitations. Most are based upon the factorized inclusion of the connected quadruple contribution

(Q_{f})

[J. Chem. Phys. 108, 9221 (1998)]. We compare the methods for the treatment of potential-energy curves for small molecules. These include CCSD

(T Q_{f})

, where the initial contributions of triple (T) and factorized quadruple excitations are added to coupled-cluster singles (S) and doubles (D), its generalization to

CCSD (\tilde{T} {\tilde{Q}}_{f})

, where instead of measuring their first contribution from orders in H, it is measured from orders in

\tilde{H} = e^{- (T_{1} + T_{2})} H e^{(T_{1} + T_{2})}

; renormalized approximations of both, and CCSD(2) defined in [J. Chem. Phys. 115, 2014 (2001)]. We also consider CCSDT,

CCSDT (Q_{f})

, CCSDTQ, and CCSDTQP for comparison, where T, Q, and P indicate full triple, quadruple, and pentuple excitations, respectively. Illustrations for

F_{2}

, the double bond breaking in water, and

N_{2}

are shown, including effects of quadruples on equilibrium geometries and vibrational frequencies. Despite the fact that no perturbative approximation, as opposed to an iterative approximation, should be able to separate a molecule correctly for a restricted-Hartree–Fock reference function, some of these higher-order approximations have a role to play in developing new, more robust procedures.

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