Platinum, gold, and silver standards of intermolecular interaction energy calculations

Abstract

High-accuracy noncovalent interaction energies are indispensable as data points for potential energy surfaces and as benchmark values for improving and testing more approximate approaches. The preferred algorithm (the gold standard) for computing these energies has been the coupled-cluster method with singles, doubles, and perturbative triples [CCSD(T)] converged to the complete basis set (CBS) limit. However, gold-standard calculations are expensive as correlated interaction energies converge slowly with the basis set size, and establishing the CBS limit to better than 0.05 kcal/mol typically requires a CCSD(T) calculation in a basis set of at least triple-zeta quality. If an even higher accuracy is required (for example, for the assignment of complicated high-resolution spectra), establishing a superior platinum standard requires both a precisely converged CCSD(T)/CBS limit and the corrections for the core correlation, relativistic effects, and higher-order coupled-cluster terms at least through the perturbative quadruple excitations. On the other hand, if a triple-zeta CCSD(T) calculation is not feasible but a double-zeta one is, it is worthwhile to look for a silver standard that provides the most accurate and consistent approximation to the gold standard at a reduced computational cost. We review the recent developments aimed at (i) increasing the breadth and diversity of the available collection of gold-standard benchmark interaction energies, (ii) evaluating the best computational strategies for platinum-standard calculations and producing beyond-CCSD(T) potential energy surfaces for spectroscopic and scattering applications of the highest precision, and (iii) improving the accuracy of the silver-standard, double-zeta-level CCSD(T)/CBS estimates through the use of explicit correlation and midbond basis functions. We also outline the remaining challenges in the accurate ab initio calculations of noncovalent interaction energies.

Recent developments in symmetry‐adapted perturbation theory

“…Noncovalent interactions are not only ubiquitous, but they are also absolutely necessary to describe many physical, chemical, and biochemical phenomena, ranging from thermodynamics of nonideal gases to spectroscopy and scattering cross sections of interstellar complexes to the performance and selectivity (including enantioselectivity) of molecular catalysts to the secondary, tertiary, and quaternary structure of proteins, the double‐helix structure of DNA, and the interaction between enzymes and their substrates (or inhibitors). Thus, theoretical and experimental investigations of noncovalent interactions are published in very large quantities, and various aspects of these interactions have been reviewed in this journal and elsewhere …”

“…The supermolecular CCSD(T) treatment in a basis set that is sufficiently converged to the complete basis set (CBS) limit has been termed the gold standard of interaction energy calculations. Moreover, higher‐accuracy (platinum) and lower‐accuracy (silver) standards have also been designated and thoroughly benchmarked, and these standards are also based on the CC methodology …”

Non-Covalent Interactions Atlas Benchmark Data Sets 2: Hydrogen Bonding in an Extended Chemical Space

“…1 Important points at the dissociation curve (the equilibrium geometry and the closest point) are computed at the "gold level" with MP2/CBS extrapolated 20 from aug-cc-pVQZ and aug-cc-pV5Z basis sets, and the CCSD(T) correction is computed in the heavy-aug-cc-pVTZ basis. 21 It is now widely agreed that a true "gold-standard" CCSD(T)/CBS benchmark requires the CCSD(T) correction computed in the triple-zeta basis, 2,3,22 and this study shows that the basis sets used to obtain the MP2/CBS term should also be as large as possible. The remaining points were computed at the "silver level" with MP2/CBS extrapolated from aug-cc-pVTZ and aug-cc-pVQZ basis sets and CCSD(T) correction calculated in the aug-cc-pVDZ basis set.…”

“…This setup balances high accuracy and a cost still applicable to large data sets. [2][3][4] Bromine and iodine are treated slightly differently in order to account for effects specific to heavier elements. 5 The complete protocol is outlined below; additional information can be found in the paper introducing the NCIA project.…”

The Leiden Atomic and Molecular Database (LAMDA): Current Status, Recent Updates, and Future Plans

“…As these systems often have the particularity of being adequately represented by a single electronic configuration, the use of mono-configurational ab initio methods like the coupled-cluster methods [34] are preferably used for the determination of the PESs. The coupled-cluster method with single, double, and perturbative triple substitution [CCSD(T)] is considered as the gold-standard [33,35]. The explicitly-correlated CCSD(T)-F12 approaches [36] are nowadays the methods of choice for PES generation since they allow the use of small atomic basis sets while maintaining high accuracy.…”