An alternative derivation of orbital-free density functional theory
- URL: http://arxiv.org/abs/2211.14441v1
- Date: Sun, 20 Nov 2022 22:16:08 GMT
- Title: An alternative derivation of orbital-free density functional theory
- Authors: Russell B. Thompson
- Abstract summary: Polymer self-consistent field theory techniques are used to derive quantum density functional theory.
The equations are shown to be equivalent to Kohn-Sham density functional theory.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Polymer self-consistent field theory techniques are used to derive quantum
density functional theory without the use of the theorems of density functional
theory. Instead, a free energy is obtained from a partition function that is
constructed directly from a Hamiltonian, so that the results are, in principle,
valid at finite temperatures. The main governing equations are found to be a
set of modified diffusion equations, and the set of self-consistent equations
are essentially identical to those of a ring polymer system. The equations are
shown to be equivalent to Kohn-Sham density functional theory, and to reduce to
classical density functional theory, each under appropriate conditions. The
obtained non-interacting kinetic energy functional is, in principle, exact, but
suffers from the usual orbital-free approximation of the Pauli exclusion
principle in additional to the exchange-correlation approximation. The
equations are solved using the spectral method of polymer self-consistent field
theory, which allows the set of modified diffusion equations to be evaluated
for the same computational cost as solving a single diffusion equation. A
simple exchange-correlation functional is chosen, together with a
shell-structure-based Pauli potential, in order to compare the ensemble average
electron densities of several isolated atom systems to known literature
results. The agreement is excellent, justifying the alternative formalism and
numerical method. Some speculation is provided on considering the time-like
parameter in the diffusion equations, which is related to temperature, as
having dimensional significance, and thus picturing point-like quantum
particles instead as non-local, polymer-like, threads in a higher dimensional
thermal-space. A consideration of the double-slit experiment from this point of
view is speculated to provide results equivalent to the Copenhagen
interpretation.
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