Classical molecular dynamics simulations of hydrogen plasma, employing quantum pseudopotentials such as the Kelbg pseudopotential, provide a computationally efficient alternative to fully quantum methods. This approach avoids the high cost of ab initio quantum simulations while enabling the study of dynamic properties and time evolution in dense partially ionized plasmas. However, classical methods often fail to properly account for the quantum exchange correlations that govern the behavior of electrons. In this work, we systematically investigate the stability of classical hydrogen plasma using the standard and improved Kelbg pseudopotentials and molecular dynamics across the range of coupling parameters Γ=0.25–2.5. We demonstrate that both pseudopotentials lead to unphysical clustering of electrons with identical spin projections at Γ0.5, resulting in a complete system collapse at Γ≥1.0. This artifact, clearly visible in radial distribution functions and energy evolution, manifests itself as an unphysical peak at distances below the thermal de Broglie wavelength, reflecting the failure of the pairwise pseudopotential to reproduce fermionic exchange effects. Our analysis establishes Γ≈0.5 as the upper limit of applicability for these classical approaches. The results highlight a critical gap in current methodologies and provide a clear motivation for the development of physically justified corrections that explicitly emulate quantum exchange effects.
Onegin et al. (Wed,) studied this question.