Optimized spin-component scaled second-order Moller-Plesset perturbation theory for intermolecular interaction energies

The optimal set of scaling parameters that minimize the error between spin-component scaled (SCS-MP2) and scaled opposite spin (SOS-MP2) theories and CCSD(T) in computing intermolecular binding energies were determined using multivariate linear least squares analysis. Counterpoise corrected intermolecular binding energies among a diverse test set of hydrogen bonded, dispersion, and mixed complexes (S22 training set) were obtained using RI-MP2 theory and the cc-pVXZ (X D, T, and Q) and the extrapolated cc-pV(XY)Z (XY = D -> T, T -> Q) atomic orbital basis set series. Optimization of the opposite spincomponent scaling parameter yielded the SOS(MI)-MP2 model, with the ability to outperform RI-MP2 theory in obtaining accurate intermolecular binding energies among dispersion complexes with only fourth-order computational effort. At the extrapolated cc-pV(DT)Z and cc-pV(TQ)Z levels, for example, intermolecular binding energies among dispersion complexes were computed with RMS errors of 1.00 kcal/mol and 0.87 kcal/mol, respectively, thereby allowing for accurate treatment of prohibitively large molecular systems at a fraction of the computational cost associated with standard RI-MP2 calculations. With both spin-component scaling parameters optimized, the resultant model, SCS(MI)-MP2, emerged as a highly accurate methodology that simultaneously corrects the MP2 errors associated with hydrogen bonded and dispersion complexes. Computations at the extrapolated SCS(MI)-MP2/ cc-pV( DT) Z level yielded RMS errors of 0.31 kcal/mol, and therefore represented a computationally efficient method for obtaining intermolecular binding energies with quadruple-zeta accuracy. With scaling parameters that are essentially inverted with respect to their original recommended values, namely, c(OS) = 0.40 and c(SS) = 1.29, intermolecular binding energies computed at the SCS(MI)-MP2/cc-pV(TQ)Z level of theory were found to be within 0.25 kcal/mol of the highest level CCSD( T) benchmarks available to date. Surprisingly, it was found that scaling only the same spin-component of the MP2 energy (SSS(MI)-MP2) leads to significant decreases in the errors associated with MP2 theory in computing intermolecular binding energies. These findings, coupled with the earlier work on SOS-MP2 theory, strongly suggest that the MP2 description of bond energies contains a systematically underestimated opposite spin-component and a simultaneously overestimated same spin-component, while the reverse appears generally true for intermolecular interactions.