Holomorphic Density Functional Theory

Abstract

Self-consistent-field (SCF) approximations formulated using Hartree-Fock (HF) or Kohn-Sham Density Functional Theory (KS-DFT) both have the potential to yield multiple solutions. However, the formal relationship between multiple solutions identified using HF or KS-DFT remains generally unknown. We investigate the connection between multiple SCF solutions for HF or KS-DFT by introducing a parametrised functional that scales between the two representations. Using the hydrogen molecule and a model of electron transfer, we continuously map multiple solutions from the HF potential to a KS-DFT description. We discover that multiple solutions can coalesce and vanish as the functional changes, forming a direct analogy with the disappearance of real HF solutions along a change in molecular structure. To overcome this disappearance of solutions, we develop a complex-analytic extension of DFT - the "holomorphic DFT" approach - that allows every SCF stationary state to be analytically continued across all molecular structures and exchange-correlation functionals.

References in corpus (12)

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Cited by in corpus (3)

• Excited states, symmetry breaking, and unphysical solutions in state-specific CASSCF theory
• Excited-State-Specific Kohn-Sham Formalism for the Asymmetric Hubbard Dimer
• The uncharted space of non-Hermitian solutions to the Hartree-Fock and Kohn-Sham equations