Random phase approximation with exchange for an accurate description of crystalline polymorphism
Maria Hellgren, Lucas Baguet
Abstract
We determine the correlation energy of BN, ${\mathrm{SiO}}_{2}$, and ice polymorphs employing a recently developed random phase approximation with exchange (RPAx) approach. The RPAx provides larger and more accurate polarizabilities as compared to the random phase approximation (RPA), and captures the 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 $\ensuremath{\alpha}$-quartz and stishovite in ${\mathrm{SiO}}_{2}$, and layered and cubic BN. Furthermore, a reliable ${({\mathrm{H}}_{2}\mathrm{O})}_{2}$ 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 a higher computational cost than RPA, we observe a faster convergence with respect to the number of eigenvalues in the response function.