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

(December 20, 2021)

The equations for the second-order approximate coupled cluster singles and doubles model (CC2) 206 Christiansen O., Koch H., Jørgensen P.
Chem. Phys. Lett.
(1995), 243, pp. 409.
are similar to the CCSD equations with the doubles amplitude equations approximated as:

 $E_{\mathrm{CC2}}=\langle\Phi_{0}\left|\hat{H}\exp\left(\hat{T}_{1}+\hat{T}_{2}% \right)\right|\Phi_{0}\rangle$ (6.38)
 $0=\left\langle{\Phi_{i}^{a}\left|{\bar{H}}+\left[{\bar{H}},\hat{T}_{2}\right]% \right|\Phi_{0}}\right\rangle$ (6.39)
 $0=\left\langle{\Phi_{ij}^{ab}\left|{\bar{H}}+\left[\hat{F},\hat{T}_{2}\right]% \right|\Phi_{0}}\right\rangle$ (6.40)

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

 $\bar{H}=\exp\left(-\hat{T}_{1}\right)\hat{H}\exp\left(\hat{T}_{1}\right)$ (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).

## 6.10.3.1 CC2 available in libgmbpt

Another implementation of CC2 is available in libgmbpt. 429 Hattig C., Weigend F.
J. Chem. Phys.
(2000), 113, pp. 5154.
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.