Completeness-optimized basis sets: Application to ground-state electron momentum densities

Abstract

In the current work we apply the completeness-optimization paradigm [P. Manninen and J. Vaara, J. Comput. Chem. 27, 434 (2006)] to investigate the basis set convergence of the moments of the ground-state electron momentum density at the self-consistent field level of theory. We present a black-box completeness-optimization algorithm that can be used to generate computationally efficient basis sets for computing any property at any level of theory. We show that the complete basis set (CBS) limit of the moments of the electron momentum density can be reached more cost effectively using completeness-optimized basis sets than using conventional, energy-optimized Gaussian basis sets. By using the established CBS limits, we generate a series of smaller basis sets which can be used to systematically approach the CBS and to perform calculations on larger, experimentally interesting systems.

Automatic algorithms for completeness‐optimization of Gaussian basis sets

“…(19) can be optimized using standard approaches. [72] In our preceding work [56,57] using ERKALE, [58,59] the exponents were optimized using the Nelder-Mead simplex method, [73] which we found to consistently yield much smaller s l values than the previously used stochastic scheme. [72] In our preceding work [56,57] using ERKALE, [58,59] the exponents were optimized using the Nelder-Mead simplex method, [73] which we found to consistently yield much smaller s l values than the previously used stochastic scheme.…”

“…[56] and [57], production-level basis sets were produced by choosing a maximal error allowed for the property for each level of the basis set. [56] and [57], production-level basis sets were produced by choosing a maximal error allowed for the property for each level of the basis set.…”

“…This question was answered affirmatively by Manninen and Vaara, [44] who suggested a procedure for a systematical approach to the CBS limit; namely, completeness-optimization. [56,57] As a heuristic rule of thumb from these studies, nf CO basis sets yield results of (n 1 1)f EO quality (for properties other than the energy). The procedure can also be applied to forming auxiliary basis sets in an identical fashion.…”

“…[56] and [57]) has been based on a manual approach, where the trials are performed by hand, implying a significant amount of tedious repetitive work and ample opportunity for error. To our knowledge, all of the work on CO basis sets so far (except for that in Refs.…”

Nuclear spin-spin coupling in a van der Waals-bonded system: Xenon dimer

“…Completeness-optimized primitive basis sets have been used to obtain results close to the basis-set limit for magnetic 32,33,[35][36][37] and magneto-optic properties, 38,39 as well as electron momentum densities. 40 In particular, Refs. 36, 37, and 39 have extended the application of the method to elements beyond the first row, xenon in two of the cases.…”