CCSD approximation size-consistent methods

There have been a number of correction algorithms formulated over the years to help improve this size consistency problem but they do not entirely resolve it °. Another means of introducing size consistency is by a quadratic approximation, QCISD. The approach achieves this size consistency by sacrificing its variational character. It can be considered as a simplified approximate form of CCSD (see below) the method may cease to remain size consistent on going to higher levels of substitution. ... 

The CCD, CCSD, CCSD(T), and CCSDT methods are size consistent but not variational. Analytic gradients are available for these methods. Often, the frozen-core (FC) approximation is used in CC calculations. Here, excitations of inner-shell electrons are omitted. 

Pople and co-workers developed the nonvariational quadratic configuration-interaction (QCI) method, which is intermediate between the CC and Cl methods. The QCI method exists in the size-consistent forms QCISD, which is an approximation to CCSD, and QCISD(T), which is similar to CCSD + T(CCSD). QCISD(T) has given excellent results for correlation energies in many calculations and is available as an option in Gaussian [J. A. Pople, M. Head-Gordon, and K. Raghavachari, J. Chem. Phys., 87, 5968 (1987) 90, 4635 (1989) K. Raghavachari and G. W. Trucks, /. Chem. Phys., 91, 1062, 2457 (1989) J. Paldus et al., J. Chem. Phys., 90, 4356 (1989)]. 

The methods of coupled clusters with single- and double-excitation terms (CCSD), CCSD with noniterative triples [CCSD(T)], and the closely related approximate method of quadratic Cl (QCISD) and QCISD with noniterative triples [QCISD(T)] have been used to study a few hydrogen-bonded complexes. These methods are size-consistent, infinite-order methods, and as such are deemed to be most reliable. Unfortunately, CCSD(T) is computationally the most expensive method, and is not feasible for routine use on larger systems. CCSD(T) is, however, the correlation method which should be used for benchmarking purposes in small complexes, and the method of choice for difficult cases. 

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