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

Abstract

Metallic solids are an enormously important class of materials, but they are a challenging target for accurate wave function-based electronic structure theories and have not been studied in great detail by such methods. Here, we use coupled-cluster theory with single and double excitations (CCSD) to study the structure of solid lithium and aluminum using optimized Gaussian basis sets. We calculate the equilibrium lattice constant, bulk modulus, and cohesive energy and compare them to experimental values, finding accuracy comparable to common density functionals. Because the quantum chemical "gold standard" CCSD(T) (CCSD with perturbative triple excitations) is inapplicable to metals in the thermodynamic limit, we test two approximate improvements to CCSD, which are found to improve the results.

How the Exchange Energy Can Affect the Power Laws Used to Extrapolate the Coupled Cluster Correlation Energy to the Thermodynamic Limit

“…There has been a recent push toward developing wave function-based methods such as coupled cluster theory for solids. − A long-term goal of this work is to provide highly accurate energy calculations for materials design. Coupled cluster has been growing in popularity for solid state calculations due to its ability to obtain the correlation energy (i.e., E total – E HF , where E HF is the Hartree–Fock energy) in a versatile and systemically improvable way.…”

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.…”

“…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 41,47 or on each system under study, 46,48,49 and recent works have demonstrated the success of such approaches for producing Gaussian basis sets with better behavior. approaches obviously hinderor forfeittransferability and reproducibility.…”

Integral-Direct Hartree–Fock and Møller–Plesset Perturbation Theory for Periodic Systems with Density Fitting: Application to the Benzene Crystal

“…Recent years have witnessed a rapid growth of interest in leveraging systematically improvable wave function-based quantum chemistry methods to study challenging problems in materials science. − These simulations, often performed using periodic boundary conditions, are computationally expensive because of the large simulation cells or dense k -point meshes needed to reach the thermodynamic limit ,,, (TDL) and the large one-particle basis sets needed to reach the complete basis set (CBS) limit. ,− As in molecular calculations, the evaluation and storage of the electron-repulsion integrals (ERIs) represent a major computational bottleneck − in Hartree–Fock (HF) and low-order perturbation (e.g., the second-order Møller–Plesset perturbation theory, MP2) calculations, including simulations using Kohn–Sham density functional theory , (KS-DFT) with hybrid − and double-hybrid − exchange-correlation functionals. In ref , the commonly used density fitting (DF) technique − was adapted for periodic systems to reduce the computational cost of handling the periodic ERIs.…”