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6.11 Coupled-Cluster Methods

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

(September 1, 2024)

The equations for the second-order approximate coupled cluster singles and doubles model (CC2) 232 Christiansen O., Koch H., Jørgensen P.
Chem. Phys. Lett.
(1995), 243, pp. 409.
Link
are similar to the CCSD equations with the doubles amplitude equations approximated as:

ECC2=Φ0|H^exp(T^1+T^2)|Φ0 (6.50)
0=Φia|H¯+[H¯,T^2]|Φ0 (6.51)
0=Φijab|H¯+[F^,T^2]|Φ0 (6.52)

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) (6.53)

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).

6.11.4.1 CC2 available in libgmbpt

Another implementation of CC2 is available in libgmbpt. 493 Hattig C., Weigend F.
J. Chem. Phys.
(2000), 113, pp. 5154.
Link
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 using the keyword METHOD=CC2 and setting CCMAN2=-1. As of the moment, this implementation is not yet optimized.

An implementation of stochatic resolution of indentity to CC2 (sRI-CC2) is also available in libgmbpt for ground state energy calculations by setting SRI=1 and modest SRI_NTHETA for the number of stochatic orbitals. Look through the samples for details. sRI-CC2 for excited energy (including singlet and triplet) will be soon released after solving some storage bugs.