Electronic-structure calculations for nonisothermal warm dense matter

Warm dense matter (WDM) is an exotic state of matter that is inherently difficult to model theoretically, due to the fact that the thermal Coulomb coupling and quantum effects are comparable in magnitude and must be treated on equal footing, foregoing the employment of conventional methods from either plasma physics or condensed-matter physics. Our work focuses on describing electronic states present in a transient, nonisothermal WDM state, where electrons become hot and ions remain cold, during the first 10–100 fs after the irradiation of a solid sample with an intense femtosecond x-ray pulse. We present a methodology, combining the finite-temperature Hartree-Fock-Slater approach with the Bloch-wave approach within a periodic atomic lattice, implemented in a new toolkit, xcrystal. In xcrystal, electronic states are represented in a hybrid basis comprising plane waves and localized core orbitals on a radial pseudospectral grid. This hybrid basis ensures a high numerical efficiency as highly localized states need not be described using plane waves. Additionally, these core orbitals are responsive to the presence of delocalized plasma electrons through an interwoven optimization between inner-shell and outer-shell electronic states employed in xcrystal. Therefore, not only does xcrystal model the plasma electrons efficiently, it also allows for access to inner-shell modifications at high electronic temperatures. To benchmark our method, we calculate K-shell threshold energies of x-ray-excited solid-density aluminum as well as the ionization potential depression and show their agreement with experiment. In comparing our method with other theoretical models, we conclude that the incorporation of optimized inner-shell orbitals is essential to obtain accurate results, and we find that the inclusion of the full crystal structure has a limited effect. Furthermore, we obtain temperature-dependent band structure predictions at WDM conditions, up to temperatures of 100 eV, which, to the best of our knowledge, are the first of their kind for this nonisothermal system. We expect that our proposed methodology will aid in the theoretical description of nonisothermal WDM, as well as advance the understanding of this exotic state of matter.