Validating additive correction schemes against gradient‐based extrapolations

Abstract

The use of additive correction schemes to obtain structures and vibrational frequencies of increasingly larger molecules is becoming more common. Such approaches, based on the cubic extrapolation formula applied directly to the quantity of interest, have been successfully validated only at the highest levels of computational accuracy: for coupled cluster methods with comparably large basis sets. Here, a systematic validation of geometries and vibrational frequencies is carried out, including more affordable and relevant levels of theory, such as the Møller‐Plesset perturbation theory applied with smaller basis sets. Comparisons of such additive schemes against the more rigorous gradient‐based extrapolation are presented. The cbs() routine of the open‐source quantum‐chemistry package Psi4 has been extended for this purpose. The results confirm that geometries and frequencies of covalently bound species obtained with additive correction schemes are in an excellent agreement with the results of gradient‐based extrapolations. However, when applied to systems involving noncovalent interactions, the errors due to such schemes are significantly larger. In general, we propose the application of gradient‐based extrapolations, as they incur no extra cost compared to additive schemes.

PSI4 1.4: Open-source software for high-throughput quantum chemistry

“…Automated Composite and Many-Body Computations. Psi4 provides a simple and powerful user interface to automate multi-component computations, including focalpoint [93][94][95] approximations, complete-basis-set (CBS) extrapolation, basis set superposition corrections, [96][97][98] and many-body expansion (MBE) treatments of molecular clusters. These capabilities can all be combined to obtain energies, gradients, or Hessians, as discussed below in Sec.…”

Xe⋯OCS: relatively straightforward?

“…Basis set incompleteness at the CCSD(T)/ [3,4]-z level is about B50 mÅ in the very weakly bound ArÁ Á ÁAr complex, and decreases to B5 mÅ for a more strongly bound complex, such as NH 3 Á Á ÁHF. 53 The effect of increasing basis set size in the d(T) component of the MP2+d(T) recipe is shown in Fig. 7, in the left panel.…”

“…Notably, additive terms obtained from the differences of augmented and unaugmented 3-z calculations that are used in various extrapolation recipes do not perform well for noncovalent complexes. 53,54 Therefore CCSD(T) computations with augmented 4-z basis sets might be unavoidable. Unfortunately, the currently available set of ''aug-cc-pwCVnZ''-quality basis sets is limited to the first two periods in the main group and first row transition metals, and appropriate density fitting basis sets are also unavailable.…”

Optimal diffuse augmented atomic basis sets for extrapolation of the correlation energy

“…Using a quadratic fit, the full CBS equilibrium geometry has been predicted. It should be added that extrapolation of molecular properties such as the geometry based on additive correction schemes or gradient‐based methods have also been suggested, but they may lack the physical motivation stemming from the asymptotic behavior of the energy described earlier in the article. For the bond distances, the CBS extrapolation scheme proposed here is shown to outperform the raw oAV t Z and AV T Z statistics when compared with both experimental and AV5Z data.…”

“…It should be added that extrapolation of molecular properties such as the geometry based on additive correction schemes or gradient-based methods have also been suggested, [75] but they may lack the physical motivation stemming from the asymptotic behavior of the energy described Experimental data from reference, [76] except for H 2 O 2 , [77] and HNO that are from somewhere else. [78] earlier in the article.…”