Material-Specific Optimization of Gaussian Basis Sets against Plane Wave Data

Abstract

Since in periodic systems, a given element may be present in different spatial arrangements displaying vastly different physical and chemical properties, an elemental basis set that is independent of physical properties of materials may lead to significant simulation inaccuracies. To avoid such a lack of material specificity within a given basis set, we present a material-specific Gaussian basis optimization scheme for solids, which simultaneously minimizes the total energy of the system and optimizes the band energies when compared to the reference plane wave calculation while taking care of the overlap matrix condition number. To assess this basis set optimization scheme, we compare the quality of the Gaussian basis sets generated for diamond, graphite, and silicon via our method against the existing basis sets. The optimization scheme of this work has also been tested on the existing Gaussian basis sets for periodic systems such as MoS 2 and NiO, yielding improved results.

Ground-State Properties of Metallic Solids from Ab Initio Coupled-Cluster Theory

“…In periodic solids, increasing the size of the basis set by brute force frequently leads to linear dependencies, quantified by an overlap matrix with large condition number, and concomitant numerical issues. Following similar works, ,− here we optimize these basis functions for each solid by minimizing the cost function where E HF is the Hartree–Fock (HF) energy, E c (2) is the second-order Møller–Plesset perturbation theory (MP2) correlation energy, S is the periodic overlap matrix of the GTO basis, and γ = 10 –4 E h . For this basis set optimization, we sampled the Brillouin zone with a uniform mesh of N k = 2 3 k -points (Li) or N k = 1 3 k -points (Al), including the Γ point; with these boundary conditions, the system is gapped and thus MP2 provides a well-defined and computationally affordable correlation energy.…”

Correlation-Consistent Gaussian Basis Sets for Solids Made Simple

“…In contrast to Dunning’s original approach, we use these primitives for all zeta levels, with the final valence basis differing only in the number of uncontracted functions (however, see section for a modification of this procedure for group VI elements to group VIII elements). We emphasize that the reference periodic system serves only as a guide for choosing an appropriate valence basis and is not used in the optimization of any parameters, unlike in previous works based on eq . ,− As we will see in the numerical results (Section ), our scheme maintains the important atomic electronic structure of a basis set, which is crucial for its transferability and high accuracy.…”

“…One way to mitigate the linear dependency issue is reoptimizing the Gaussian exponents ζ i and contraction coefficients c i of existing basis sets based on a cost function, such as ,− the minimization of which trades some of the energy ( E ) for a lower condition number of the basis set overlap matrix S to the extent controlled by the developer-selected parameter γ > 0. Such a cost function can be minimized on a paradigmatic system that exhibits the linear dependency of concern , or on each system under study, ,, and recent works have demonstrated the success of such approaches for producing Gaussian basis sets with better behavior. − However, aside from the extra cost associated with frequent basis set reoptimization, such approaches obviously hinderor forfeittransferability and reproducibility.…”

Approaching the Basis Set Limit in Gaussian-Orbital-Based Periodic Calculations with Transferability: Performance of Pure Density Functionals for Simple Semiconductors

“…[13][14][15][16] The use of GTOs to reach the thermodynamic limit (TDL) of solids often faces numerical difficulties associated with overcompleteness of GTOs that leads to a severe linear dependency among basis functions towards the TDL. [17][18][19][20] Nonetheless, many studies have employed Gaussian basis sets either using those developed for molecular calculations, those developed for periodic mean-field calculations, 19,20 or those optimized system-specifically without much in the way of transferability guarantees [21][22][23] .…”