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6.10 Coupled-Cluster Methods

6.10.3 Second-Order Approximate Coupled Cluster Singles and Doubles (CC2)

(February 4, 2022)

The equations for the second-order approximate coupled cluster singles and doubles model (CC2) 206 are similar to the CCSD equations with the doubles amplitude equations approximated as:

ECC2=Φ0|H^exp(T^1+T^2)|Φ0 (6.38)
0=Φia|H¯+[H¯,T^2]|Φ0 (6.39)
0=Φijab|H¯+[F^,T^2]|Φ0 (6.40)

where the similarity-transformed Hamiltonian with the exponential function of the single excitation cluster operator is given by:

H¯=exp(-T^1)H^exp(T^1) (6.41)

CC2 energies are available in Q-Chem, and are requested by setting the keyword METHOD to CC2. Closed and open-shell references (RHF/UHF/ROHF) are available, as well as the frozen core option. The RI approximation (RI-CC2) can be applied by specifying an auxiliary basis set. Furthermore, complex-valued calculations, CAP (Complex Absorbing Potentials) and CBF (Complex Basis Functions), are available for CC2 and RI-CC2 calculations (see Section 7.10.9 for details). CC2 available in libgmbpt

Another implementation of CC2 is available in libgmbpt.429 A partitioned form of the CC2 equations is employed which eliminates the need to store double amplitudes. The resolution of the identity (RI) approximation for two-electron integrals can also be invoked to reduce the CPU time needed for calculation and I/O of these integrals.

This implementation can be invoked in Q-Chem using the keyword METHOD CC2 and setting CCMAN2=-1. As of the moment, this implementation is not yet optimized.