7.10.15 Approximate EOM-CC Methods

Approximate EOM-CCSD models with $T$-amplitudes obtained at the MP2 level offer reduced computational cost compared to the full EOM-CCSD since the computationally demanding $𝒪(N^6)$ CCSD step is eliminated from the calculation. Two methods of this type are implemented in Q-Chem. The first is invoked with the keyword METHOD = EOM-MP2. Its formulation and implementation follow the original EOM-CCSD(2) approach developed by Stanton and coworkers. ¹²⁰⁵ Stanton J. F., Gauss J.
J. Chem. Phys.
(1995), 103, pp. 1064. Link The second method can be requested with the METHOD = EOM-MP2T keyword and is similar to EOM-MP2, but it accounts for the additional terms in $\overline{H}$ that appear because the MP2 $T$-amplitudes do not satisfy the CCSD equations. EOM-MP2 ansatz is implemented for IP/EA/EE/SF energies, state properties, and interstate properties (EOM-EOM, but not REF-EOM). EOM-MP2t is available for the IP/EE/EA energy calculations only.

These are very light-weight EOM methods in which the EOM problem is solved in the singles block and the effect of doubles is evaluated perturbatively. The $\overline{H}$ is evaluated by using either CCSD or MP2 amplitudes, just as in the regular EOM calculations. The EOM-MP2-S(D) method, which is similar in level of correlation treatment to SOS-CIS(D), is particularly fast. These methods are implemented for IP and EE states. For valence states, the errors for absolute ionization or excitation energies against regular EOM-CCSD are about 0.4 eV and appear to be systematically blue-shifted; the EOM-EOM energy gaps look better. The calculations are set as in regular EOM-EE/IP, but using METHOD = EOM-CCSD-SD(D) or METHOD = EOM-MP2-SD(D). State properties and EOM-EOM transition properties can be computed using these methods (reference-EOM properties are not yet implemented). These methods are designed for treating core-level states. ¹¹¹⁵ Sadybekov A., Krylov A. I.
J. Chem. Phys.
(2017), 147, pp. 014107. Link

Note:  These methods are still in the experimental stage.