Highly correlated calculations using optimized virtual orbital space with controlled accuracy. Application to counterpoise corrected interaction energy calculations

Abstract

ABSTRACT:In this work, we investigate the correlation between error introduced by truncation of optimized virtual orbital space (OVOS) on the MP2 level (Y MP2 ) with the error of the post-MP2 contributions, such as the CCSD-MP2 (i.e., Y CCSD ), CCSD(T)-MP2 (i.e., Y CCSD(T) ), or the (T) separately. We found a correlation between the Y MP2 and several other quantities, such as the percent of recovered optimization functional value in the HIGHLY CORRELATED CALCULATIONS USING OVOS truncated OVOS (OF%), or the aforementioned Y CCSD , Y CCSD(T) , Y (T), which is to good approximation linear in the logarithmic scale. These correlations open a possibility to control the accuracy of the post-MP2 calculations in the truncated OVOS, because the Y MP2 and the OF% are easily obtained, almost as a byproduct of the virtual orbital optimization. According to the results present in this work, knowledge of the Y MP2 or the OF% allows us to safely estimate the order of magnitude of the error of the post-MP2 corrections. To keep the accuracy of, for instance, CCSD(T) correlation energy calculated in the truncated OVOS within 1.10 −5 − 1.10 −6 Hartree error bars, we can typically reduce only a few percent of the OVOS, although this value increases slightly with enlarging the atomic orbital (AO) basis set and the number of inactive occupied orbitals. Still, even such a modest reduction can save more then a half of the computation time, compared with calculations in the full VOS. The situation is, however, much more favourable in case of counterpoise (CP) corrected calculations of interaction energy, where this methodology enables safe truncation of significant part of OVOS of monomers, resulting from the presence of the ghost AO. Dimension of such truncated OVOS essentially corresponds to CP-uncorrected calculations, thus leads to more than an order of magnitude speedup of calculation of monomers.

Benchmark Calculations of Interaction Energies in Noncovalent Complexes and Their Applications

“…Additionally, in the calculations of noncovalent interactions, these methods provide one very important advantage. When the counterpoise correction is used, the virtual space originating from the ghost basis functions in the calculations of the monomers can be substantially reduced without compromising the accuracy …”

A Theoretical Study of the X-Abstraction Reactions (X = H, Br, or I) from CH2IBr by OH Radicals: Implications for Atmospheric Chemistry

“…It is obvious, that this approach, when we directly control the absolute value of the error introduced by OVOS procedure [67] is slightly different from the traditional concept of OVOS applications. In typical OVOS calculations, we try to keep an absolute error of the method constant, but not necessarily negligible.…”

“…To reduce the computational costs, we have used the OVOS (optimized virtual orbital space) method with controlled accuracy [67]. In the OVOS method, introduced by Adamowicz et al [68,69] and reformulated later by Neogrády et al [70], we perform unitary transformation of the virtual space such that we try to accumulate most of the flexibility of the complete virtual orbital space (VOS) into selected smaller subspace.…”

“…These relations can be used for specific application of the OVOS method for more efficient evaluation of BSSE, where OVOS is applied exclusively to the subsystems [67,77]. Reducing the VOS to the size of the subsystem in BSSE calculations, we typically encounter an error of 10 −5 -10 −4 a. u.…”

Off‐center Gaussian functions: Applications toward larger basis sets, post‐second‐order correlation treatment, and truncated virtual orbital space in investigations of noncovalent interactions

“…In the case of noncovalent interaction investigations, where the counterpoise correction (CP) is often used to alleviate the basis set superposition error (BSSE), modified VO techniques can be used to eliminate weakly contributing, so called “ghost” basis functions. The CP calculations in the modified VOs of the interacting subsystems in the supersystem basis set are carried out for practically the same cost as using subsystem basis sets only . This methodology can also be used with a basis set containing off‐center Gaussian grids, where redundant (i.e., weakly contributing) s‐functions are eliminated after the orbital optimization procedure.…”