A scaled explicitly correlated F12 correction to second-order Møller–Plesset perturbation theory

Abstract

An empirically scaled version of the explicitly correlated F12 correction to second-order Møller–Plesset perturbation theory (MP2-F12) is introduced. The scaling eliminates the need for many of the most costly terms of the F12 correction while reproducing the unscaled explicitly correlated F12 interaction energy correction to a high degree of accuracy. The method requires a single, basis set dependent scaling factor that is determined by fitting to a set of test molecules. We present factors for the cc-pVXZ-F12 (X = D, T, Q) basis set family obtained by minimizing interaction energies of the S66 set of small- to medium-sized molecular complexes and show that our new method can be applied to accurately describe a wide range of systems. Remarkably good explicitly correlated corrections to the interaction energy are obtained for the S22 and L7 test sets, with mean percentage errors for the double-zeta basis of 0.60% for the F12 correction to the interaction energy, 0.05% for the total electron correlation interaction energy, and 0.03% for the total interaction energy, respectively. Additionally, mean interaction energy errors introduced by our new approach are below 0.01 kcal mol−1 for each test set and are thus negligible for second-order perturbation theory based methods. The efficiency of the new method compared to the unscaled F12 correction is shown for all considered systems, with distinct speedups for medium- to large-sized structures.

Regularized Second-Order Møller–Plesset Theory: A More Accurate Alternative to Conventional MP2 for Noncovalent Interactions and Transition Metal Thermochemistry for the Same Computational Cost

“…The first major development was the spin-component scaled MP2 (SCS-MP2), which was shown to significantly improve MP2 for TM complexes as well as main group chemistry by a heuristic scaling of same-spin and opposite-spin correlation contributions. ,, SCS-MP2 was also successful for dispersion interactions on smaller conjugated hydrocarbons although different scaling parameters were required . The scaled opposite spin MP2 approach (SOS-MP2) also improved thermochemical results relative to MP2, and reduced the computational cost from to . , For dispersion interactions, a similar approach was recently applied to MP2-F12; alternatively, attenuating the long-range part of the MP2 correlation energy was also quite successful. ,− We note other approaches based on adiabatic connection theory. , …”

Efficient Exploitation of Numerical Quadrature with Distance-Dependent Integral Screening in Explicitly Correlated F12 Theory: Linear Scaling Evaluation of the Most Expensive RI-MP2-F12 Term

“…Usually, density fitting (DF) techniques further improve performance by decomposing 4c2e integrals into three-center-two-electron (3c2e) and two-center-two-electron (2c2e) integrals, thus drastically reducing the prefactor of the evaluation. Nowadays, DF/CABS-RI F12 approaches are well-established and feature a wide range of methods and variations, i.e., in perturbation theory, ,,− coupled-cluster theory, ,− the random-phase-approximation (RPA), − multireference approaches, − and even in density functional theory (DFT) design. , …”

Highly Efficient and Accurate Computation of Multiple Orbital Spaces Spanning Fock Matrix Elements on Central and Graphics Processing Units for Application in F12 Theory

“…These elements, denoted in the following as F12-type Fock matrix elements, need to be evaluated for multiple orbital spaces introduced by the strong orthogonality operator Q̂ 12 , which notably increases the number of required basis functions. In general, the formally quartic-scaling evaluation of the direct and exchange contributions to F12-type Fock matrices is thus substantially more demanding than the evaluation of normal Fock matrices and frequently represents an extremely expensive step in applications of F12 theory. ,, Efficient evaluation is thus highly beneficial since a series of theories require these elements, among them the complementary auxiliary basis set (CABS) singles correction, , explicitly correlated second-order Møller–Plesset perturbation theory (MP2-R12/F12), ,,,− coupled cluster-F12 (CC-F12), ,,− multireference-F12 (MR-F12), − and other explicitly correlated approaches. − Previous works applied RI ,,,, and seminumerical integral approaches but focused primarily on other aspects of F12 theory, not the investigation of their influence on accuracy and efficiency. Motivated by these circumstances, we transferred our recently introduced RI-J and sn-LinK methods to F12 theory.…”