Accurate Hartree-Fock energy of extended systems using large Gaussian basis sets

Calculating highly accurate thermochemical properties of condensed matter via wave-function-based approaches (such as, e.g., Hartree-Fock or hybrid functionals) has recently attracted much interest. We here present two strategies providing accurate Hartree-Fock energies for solid LiH in a large Gaussian basis set and applying periodic boundary conditions. The total energies were obtained using two different approaches, namely, a supercell evaluation of Hartree-Fock exchange using a truncated Coulomb operator and an extrapolation toward the full-range Hartree-Fock limit of a Padé fit to a series of short-range screened Hartree-Fock calculations. These two techniques agreed to significant precision. We also present the Hartree-Fock cohesive energy of LiH (converged to within sub-millielectron volt) at the experimental equilibrium volume as well as the Hartree-Fock equilibrium lattice constant and bulk modulus.

Figure 1

(Color online) Convergence of the SR-HF energy (a.u.) of a LiH unit cell containing four LiH ion pairs at experimental lattice constant $\left(4.084\text{Å}\right)$ with decreasing screening parameter $\omega$ involved in the short-range Coulomb interaction. Gaussian results for each $\omega$ are represented by crosses. The line shows the [7/7] Padé fit to the numerical data (see text for details). The inset gives SR-HF energies for $\omega ∊\left[0;0.1\right]\text{a}\text{.u}{\text{.}}^{-1}$ as well as the extrapolated value for $\omega =0$ in Hartree atomic units.

Figure 2

(Color online) Murnaghan equation of state (red/gray line) for LiH obtained using the HF approximation. Each of the seven points corresponds to the extrapolated least-squares fit of 31 screened HF energies to a Padé approximant of order [7/7] (see text for details).