Improved electron-molecule scattering calculations with the relativistic optical-potential method

We present a computational framework for electron-molecule scattering that is intended as a step toward a more accurate and unified description over a broad energy range relevant to applications. The approach combines a spherical complex optical potential (SCOP), constructed from multiconfiguration Dirac-Fock atomic densities via a group-additivity scheme, with a partial-wave solution of the Dirac equation. Methane (CH₄) and silane (SiH₄) are used as benchmark targets because of their simple tetrahedral structure and well-documented cross sections. The comparison among exchange models is used to highlight the sensitivity of predicted cross sections to the target model potential and the need for improved model descriptions. In addition, the present Dirac-based implementation is benchmarked against our existing [Joshipura et al., Phys. Rev. A, 2004, 69, 022705] nonrelativistic optical-potential treatment that employs the Numerov method to solve the Schrödinger equation, allowing us to quantify both relativistic kinematic and spinor effects. Although relativistic effects on integral cross sections are minimal, the Dirac treatment has a pronounced impact on the phase shifts and large-angle differential cross sections. Among the exchange models tested, the modified Furness-McCarthy exchange shows the most consistent agreement with benchmark data and represents a clear improvement over our earlier group-additivity SCOP results. This enhancement lays the groundwork for extending the method to larger and strongly polar molecules.