16 research outputs found
Functional Derivative of the Zero Point Energy Functional from the Strong Interaction Limit of Density Functional Theory
We derive an explicit expression for the functional derivative of the
subleading term in the strong interaction limit expansion of the generalized
Levy--Lieb functional for the special case of two electrons in one dimension.
The expression is derived from the zero point energy (ZPE) functional, which is
valid if the quantum state reduces to strongly correlated electrons in the
strong coupling limit. The explicit expression is confirmed numerically and
respects the relevant sum-rule. We also show that the ZPE potential is able to
generate a bond mid-point peak for homo-nuclear dissociation and is properly of
purely kinetic origin. Unfortunately, the ZPE diverges for Coulomb systems,
whereas the exact peaks should be finite.Comment: 12 pages, 7 figure
Kohn-Sham equations with functionals from the strictly-correlated regime: Investigation with a spectral renormalization method
We re-adapt a spectral renormalization method, introduced in nonlinear
optics, to solve the Kohn-Sham (KS) equations of density functional theory
(DFT), with a focus on functionals based on the strictly-correlated electrons
(SCE) regime, which are particularly challenging to converge. Important aspects
of the method are: (i) the eigenvalues and the density are computed
simultaneously; (ii) it converges using randomized initial guesses; (iii) easy
to implement. Using this method we could converge for the first time the
Kohn-Sham equations with functionals that include the next leading term in the
strong-interaction limit of density functional theory, the so-called zero-point
energy (ZPE) functional as well as with an interaction-strength-interpolation
(ISI) functional that includes both the exact SCE and ZPE terms. This work is
the first building block for future studies on quantum systems confined in low
dimensions with different statistics and long-range repulsions, such as
localization properties of fermions and bosons with strong long-range repulsive
interactions in the presence of a random external potential
Fermionic statistics in the strongly correlated limit of Density Functional Theory
Exact pieces of information on the adiabatic connection integrand
, which allows to evaluate the exchange-correlation energy
of Kohn-Sham density functional theory, can be extracted from the leading terms
in the strong coupling limit (, where is the
strength of the electron-electron interaction). In this work, we first compare
the theoretical prediction for the two leading terms in the strong coupling
limit with data obtained via numerical implementation of the exact Levy
functional in the simple case of two electrons confined in one dimension,
confirming the asymptotic exactness of these two terms. We then carry out a
first study on the incorporation of the fermionic statistics at large coupling
, both numerical and theoretical, confirming that spin effects enter
at orders
Large coupling-strength expansion of the M{\o}ller-Plesset adiabatic connection: From paradigmatic cases to variational expressions for the leading terms
We study in detail the first three leading terms of the large
coupling-strength limit of the adiabatic connection that has as
weak-interaction expansion the M{\o}ller-Plesset perturbation theory. We first
focus on the H atom, both in the spin-polarized and the spin-unpolarized case,
reporting numerical and analytical results. In particular, we derive an
asymptotic equation that turns out to have simple analytical solutions for
certain channels. The asymptotic H atom solution for the spin-unpolarized case
is then shown to be variationally optimal for the many-electron spin-restricted
closed-shell case, providing expressions for the large coupling-strength
density functionals up to the third leading order. We also analyze the H2
molecule and the uniform electron gas
Kinetic Correlation Functionals from the Entropic Regularization of the Strictly Correlated Electrons Problem
In this work, we study the entropic regularization of the strictly correlated electrons formalism, discussing the implications for density functional theory and establishing a link with earlier works on quantum kinetic energy and classical entropy. We carry out a very preliminary investigation (using simplified models) on the use of the solution of the entropic regularized problem to build approximations for the kinetic correlation functional at large coupling strengths. We also analyze lower and upper bounds to the Hohenberg-Kohn functional using the entropic regularized strictly correlated electrons problem
Kohn-Sham equations with functionals from the strictly-correlated regime:Investigation with a spectral renormalization method
We re-adapt a spectral renormalization method, introduced in nonlinear optics, to solve the Kohn-Sham (KS) equations of density functional theory, with a focus on functionals based on the strictly-correlated electrons (SCE) regime, which are particularly challenging to converge. Important aspects of the method are: (i) the eigenvalues and the density are computed simultaneously; (ii) it converges using randomized initial guesses; (iii) easy to implement. Using this method we could converge for the first time the Kohn-Sham equations with functionals that include the next leading term in the strong-interaction limit of density functional theory, the so called zero-point energy (ZPE) functional as well as with an interaction-strength-interpolation functional that includes both the exact SCE and ZPE terms. This work is the first building block for future studies on quantum systems confined in low dimensions with different statistics and long-range repulsions, such as localization properties of fermions and bosons with strong long-range repulsive interactions in the presence of a random external potential