Systematic Gaussian basis‐set limit using completeness‐optimized primitive sets. A case for magnetic properties

Abstract

We discuss the connection between the completeness of a basis set, measured by the completeness profiles introduced by Chong (Can J Chem 1995, 73, 79) at a certain exponent interval, and the possibility of reproducing molecular properties that arise either in the region close to the atomic nuclei or in the valence region. We present a scheme for generating completeness-optimized Gaussian basis sets, in which a preselected range of exponents is covered to an arbitrary accuracy. This is done by requiring Gaussian functions, the exponents of which are selected without reference to the atomic structure, to span the range with completeness profile as close to unity as wanted with as few functions as possible. The initial exponent range can be chosen suitable for calculations of molecular energetics or other valence-like properties. By extending the exponent range, properties requiring augmentation of the basis at a given angular momentum value and/or in a given distance range from the nucleus may be straightforwardly and systematically treated. In this scheme a universal, element-independent exponent set is generated in an automated way. The relation of basis-set completeness and performance in the calculation of magnetizability, nuclear magnetic shielding, and spin-spin coupling is tested with the completeness-optimized primitive sets and literature basis sets.

ERKALE—A flexible program package for X‐ray properties of atoms and molecules

“…Conventional basis sets are energy optimized, which tends to overemphasize the tightly bound region and neglect the diffuse area. [104] Manninen and Vaara introduced completenessoptimization of basis sets [105] as a systematical as well as practical approach to the complete basis set limit. Indeed, many molecular properties have been found to converge faster with completeness-optimized basis sets than with conventional, energy optimized basis sets.…”

“…Indeed, many molecular properties have been found to converge faster with completeness-optimized basis sets than with conventional, energy optimized basis sets. [105][106][107][108] As well as the Kruununhaka basis set tool kit, [109] ERKALE can be used to plot completeness profiles and generate completeness-optimized primitive sets.…”

“…In the completeness optimization paradigm, the primitives in each angular momentum shell in the basis set are optimized so that the resulting completeness profile is as close to unity as possible in the exponent range α ∈ [α 1 , α 2 ] that is relevant for the computed property [105] † † . The optimization in ERKALE is performed by minimizing the measure (34) where n = 1 corresponds to maximization of the area of completeness (as done in Refs.…”

“…The optimization in ERKALE is performed by minimizing the measure (34) where n = 1 corresponds to maximization of the area of completeness (as done in Refs. [105][106][107][108]) and n = 2 to minimization of the root mean square deviation from completeness. The completeness-optimization of the basis set using Eq.…”

“…ERKALE performs the minimization using the Nelder-Mead simplex algorithm [110] as implemented in GSL, [62] which in our calculations systematically provided better optimized basis sets (smaller τ n ) than the stochastic differential evolution algorithm [111] used in previous work. [105] The modeling of excitation spectra discussed in the following subsections requires rather large basis sets to be used to obtain satisfactorily converged results. X-ray absorption and Xray Raman calculations (see Core electron excitations section) often use the IGLO-III basis set [112] for describing the excited atom, whereas Casida calculations for valence excitations often use the Sadlej basis set.…”