A Resolution-Of-The-Identity Implementation of the Local Triatomics-In-Molecules Model for Second-Order Møller−Plesset Perturbation Theory with Application to Alanine Tetrapeptide Conformational Energies

Abstract

In this work, we incorporate the resolution-of-the-identity (RI) approximation into the theoretical framework of the local triatomics-in-molecules (TRIM) second-order Møller-Plesset (MP2) perturbation theory model. The resultant model, RI-TRIM MP2, emerges as a robust fourth-order methodology that extends the regime of practical MP2 calculations. With RI-TRIM MP2, correlation energy corrections can easily be obtained for systems that contain more than 125 heavy atoms with a computational timing cost less than those of the prerequisite self-consistent field procedure and popular density functional theory (DFT) alternatives. In this work, the chemical performance of RI-TRIM MP2 is numerically assessed against untruncated RI-MP2 and DFT (B3LYP) in determining the relative energies of 27 different alanine tetrapeptide conformations at the cc-pVXZ (X = D, T, and Q) levels and the results are T → Q extrapolated to the complete basis set limit. As the quality of the basis set employed increases, we report a significant reduction in the error introduced by the RI-TRIM approximation; at the cc-pVDZ level, the root mean-square (RMS) relative error was found as 0.192 kcal/mol and is decreased to an almost negligible 0.040 kcal/mol at the T → Q extrapolated complete basis set limit. Basis set dependence was investigated by computing the RMS (max) deviations from the extrapolated RI-MP2/cc-pV(TQ)Z data set found as 0.377 (0.944) kcal/mol (MP2/cc-pVTZ) and 0.250 (0.591) kcal/mol (TRIM MP2/cc-pVTZ). These deviations are chemically significant when compared against the conformer energy differences, suggesting that to obtain reliably converged relative conformational energies, computations must be done using the cc-pVTZ and cc-pVQZ basis sets followed by extrapolation to the cc-pV(TQ)Z limit. The findings reported herein also provide the first computational evidence demonstrating that the TRIM model approaches exactness as the one-particle basis approaches completeness.