Random phase approximation with exchange for an accurate description of crystalline polymorphism

TL;DR

This paper demonstrates that the RPAx method improves the accuracy of correlation energy calculations for crystalline polymorphs, effectively predicting relative energies and phase behaviors of materials like SiO2, BN, and ice.

Contribution

The study introduces and applies the RPAx approach, showing it provides more accurate polarizabilities and correlation energies than RPA, especially for complex polymorphic systems.

Findings

RPAx yields more accurate polarizabilities than RPA.

Improved prediction of relative energies between polymorphs.

Comparable results to high-level methods like coupled cluster and QMC.

Abstract

We determine the correlation energy of BN, SiO$_2$ and ice polymorphs employing a recently developed RPAx (random phase approximation with exchange) approach. The RPAx provides larger and more accurate polarizabilities as compared to the RPA, and captures effects of anisotropy. In turn, the correlation energy, defined as an integral over the density-density response function, gives improved binding energies without the need for error cancellation. Here, we demonstrate that these features are crucial for predicting the relative energies between low- and high-pressure polymorphs of different coordination number as, e.g., between $\alpha$-quartz and stishovite in SiO$_2$, or layered and cubic BN. Furthermore, a reliable (H$_2$O)$_2$ potential energy surface is obtained, necessary for describing the various phases of ice. The RPAx gives results comparable to other high-level methods such as coupled cluster and quantum Monte Carlo, also in cases where the RPA breaks down. Although higher computational cost than RPA we observe a faster convergence with respect to the number of eigenvalues in the response function.