Researchers Samuel Poncé and Xavier Gonze from the Université Catholique de Louvain in Belgium have published a study that delves into the intricacies of calculating the total energy of solids, molecules, and nanostructures. Their work, titled “In search of the electron-phonon contribution to total energy,” was published in the journal Physical Review B.
The study focuses on refining the Born-Oppenheimer (BO) approximation, a widely used method in first-principles calculations that separates the nuclear and electronic motions in a system. This approximation is crucial for understanding the energy landscape of materials, which is essential for predicting stable forms of materials and their magnetic properties.
Poncé and Gonze provide an exact formulation for the total energy using BO electronic wavefunctions and identify additional energy contributions beyond the primary electronic and vibrational (phononic) ones. These contributions become significant when dealing with small energy differences, such as those encountered in predicting stable polymorphs or describing magnetic energy landscapes.
The researchers list these additional contributions, which appear in a perturbative expansion in powers of the inverse fourth root of a typical nuclear mass. Among these, the electron-phonon contribution to the total energy, denoted as E^elph, first appears at the fourth order. The electronic inertial mass contributes at the sixth order. The study clarifies that the sum of the Allen-Heine-Cardona zero-point renormalization of eigenvalues over occupied states is not the electron-phonon contribution to the total energy but a part of the phononic contribution.
Poncé and Gonze implemented the computation of the lowest-order E^elph and found it to be small but non-negligible, amounting to 3.8 meV per atom in the case of diamond and its hexagonal polymorph. They also estimated the electronic inertial mass contribution and confirmed the size-consistency of all computed terms.
For the energy industry, this research could have practical applications in the development of new materials for energy storage, conversion, and transmission. A more accurate understanding of the total energy of materials can lead to the discovery of new polymorphs with enhanced properties, such as better conductivity, higher stability, or improved magnetic characteristics. This, in turn, can contribute to the development of more efficient and sustainable energy technologies.
Source: Physical Review B
This article is based on research available at arXiv.