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The use of two low cost methods for the prediction of the inner-shellscontribution to the correlation energy is analyzed. The Spin-Component-Scaledsecond order M{\o}ller-Plesset perturbation theory (SCS-MP2) wasreparameterized for the prediction of such contributions. The best results arefound when only the same spin term is considered (SSS-MP2). The CoupledElectron Pair Approximation (CEPA) using the domain based local pair naturalorbital approximation (DLPNO) was also studied for the same purpose. Themethods were tested on the W4-11 test set using basis sets up to quadruple zetaquality. The SSS-MP2 proved to be a marked improvement upon MP2 decreasing theroot-mean-square-error (RMSE) from 0.443 to 0.302 kcal/mol. The RMSE ofDLPNO-CEPA/1 in the test set is only 0.147 kcal/mol and its computational costis very low considering the intended applications. Furthermore, a linearcombination of both methods decreased the RMSE to 0.118 kcal/mol.

Prediction of the inner-shell contribution to the correlation energy  through DLPNO-CEPA/1 and Scaled same-spin second order M{\o}ller-Plesset  perturbation theory