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

Abstract 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 spin-component 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-ζ accuracy. With scaling parameters that are essentially inverted with respect to their original recommended values, namely, cOS = 0.40 and cSS = 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. Acknowledgements Funding for this work comes from a subcontract from Q-Chem Inc. as part of an NIH SBIR grant, with further support from the National Science Foundation. R.A.D. gratefully acknowledges useful discussions with Tobias Benighaus, Rohini Lochan, and Ryan P. Steele. M. H.-G. is a part-owner of Q-Chem Inc.