Energy of a many-electron system in an ensemble ground-state, versus electron number and spin: piecewise-linearity and flat plane condition generalized
arxiv(2023)
摘要
Description of many-electron systems with a fractional electron number
N_tot and fractional spin M_tot is of great importance in
physical chemistry, solid state physics and materials science. In this Letter,
we provide an exact description of the zero-temperature ensemble ground state
of a general, finite, many-electron system, and characterize the dependence of
the energy and the spin-densities on both N_tot and
M_tot, when the total spin is at its equilibrium value. We
generalize the piecewise-linearity principle and the flat-plane condition and
determine which pure states contribute to the ground-state ensemble. We find a
new derivative discontinuity, which manifests for spin variation at constant
N_tot, as a jump in the Kohn-Sham potential. We identify a
previously unknown degeneracy of the ground state, such that the total energy
and density are unique, but the spin-densities are not. Our findings serve as a
basis for development of advanced approximations in density functional theory
and other many-electron methods.
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