26 research outputs found
Local reduced-density-matrix-functional theory: Incorporating static correlation effects in Kohn-Sham equations
We propose a novel scheme to bring reduced density matrix functional theory
(RDMFT) into the realm of density functional theory (DFT) that preserves the
accurate density functional description at equilibrium, while incorporating
accurately static and left-right correlation effects in molecules and keeping
the good computational performance of DFT-based schemes. The key ingredient is
to relax the requirement that the local potential is the functional derivative
of the energy with respect to the density. Instead, we propose to restrict the
search for the approximate natural orbitals within a domain where these
orbitals are eigenfunctions of a single-particle hamiltonian with a local
effective potential. In this way, fractional natural occupation numbers are
accommodated into Kohn-Sham equations allowing for the description of molecular
dissociation without breaking spin symmetry. Additionally, our scheme provides
a natural way to connect an energy eigenvalue spectrum to the approximate
natural orbitals and this spectrum is found to represent accurately the
ionization potentials of atoms and small molecules
Density inversion method for local basis sets without potential auxiliary functions: inverting densities from RDMFT
A density inversion method is presented, to obtain the constrained, optimal, local potential that has a prescribed asymptotic behaviour and reproduces optimally any given ground-state electronic density. This work builds upon the method of [Callow et al., J. Chem. Phys., 2020, 152, 164114.] and differs in the expansion of the screening density in orbital basis element products instead of basis functions of an additional auxiliary set. We demonstrated the method by applying it to densities from DFT, Hartree–Fock, CAS-SCF and RDMFT calculations. For RDMFT, we demonstrate that density inversion offers a viable single-particle description by comparing the ionization potentials for atomic and molecular systems to the corresponding experimental values. Finally, we show that with the present method, accurate correlation potentials can be obtained from the inversion of accurate densities
Reply to “Comment on ‘Nonanalyticity of the optimized effective potential with finite basis sets’ ”
A correction for the Hartree-Fock density of states for jellium without screening
We revisit the Hartree-Fock (HF) calculation for the uniform electron gas, or jellium model, whose predictions—divergent derivative of the energy dispersion relation and vanishing density of states (DOS) at the Fermi level—are in qualitative disagreement with experimental evidence for simple metals. Currently, this qualitative failure is attributed to the lack of screening in the HF equations. Employing Slater’s hyper-Hartree-Fock (HHF) equations, derived variationally, to study the ground state and the excited states of jellium, we find that the divergent derivative of the energy dispersion relation and the zero in the DOS are still present, but shifted from the Fermi wavevector and energy of jellium to the boundary between the set of variationally optimised and unoptimised HHF orbitals. The location of this boundary is not fixed, but it can be chosen to lie at arbitrarily high values of wavevector and energy, well clear from the Fermi level of jellium. We conclude that, rather than the lack of screening in the HF equations, the well-known qualitative failure of the ground-state HF approximation is an artifact of its nonlocal exchange operator. Other similar artifacts of the HF nonlocal exchange operator, not associated with the lack of electronic correlation, are known in the literature