Kohn-Sham Formulation Of Density Functional Theory Research Articles

Extension of the Kohn-Sham formulation of density functional theory to finite temperature

Based on Mermin's extension of the Hohenberg and Kohn theorems to non-zero temperature, the Kohn-Sham formulation of density functional theory (KS-DFT) is generalized to finite temperature. We show that present formulations are inconsistent with Mermin's functional containing expressions, in particular describing the Coulomb energy, that defy derivation and are even in violation of rules of logical inference. More; current methodology is in violation of fundamental laws of both quantum and classical mechanics. Based on this feature, we demonstrate the impossibility of extending the KS formalism to finite temperature through the self-consistent solutions of the single-particle Schrödinger equation of T>0. Guided by the form of Mermin's functional that depends on the eigenstates of a Hamiltonian, determined at T=0, we base our extension of KS-DFT on the determination of the excited states of a non-interacting system at the zero of temperature. The resulting formulation is consistent with that of Mermin constructing the free energy at T>0 in terms of the excited states of a non-interacting Hamiltonian (system) that, within the KS formalism, are described by Slater determinants. To determine the excited states at T=0 use is made of the extension of the Hohenberg and Kohn theorems to excited states presented in previous work applied here to a non-interacting collection of replicas of a non-interacting N-particle system, whose ground state density is taken to match that of K non-interacting replicas of an interacting N-particle system at T=0. The formalism allows for an ever denser population of the excitation spectrum of a Hamiltonian, within the KS approximation. The form of the auxiliary potential, (Kohn-Sham potential), is formally identical to that in the ground state formalism with the contribution of the Coulomb energy provided by the derivative of the Coulomb energy in all excited states taken into account. Once the excited states are determined, the minimum of the free energy within the KS formalism follows immediately in the form of Mermin's functional, but with the exact excited states in that functional represented by Slater determinants obtained through self-consistency conditions at the zero of temperature. It is emphasized that, in departure from all existing formulations, no self-consistency conditions are implemented at finite T; as we show, in fact, such formulations are rigorously blocked.

Computationally simple, analytic, closed form solution of the Coulomb self-interaction problem in Kohn–Sham density functional theory

We have developed and tested in terms of atomic calculations an exact, analytic and computationally simple procedure for determining the functional derivative of the exchange energy with respect to the density in the implementation of the Kohn–Sham formulation of density functional theory (KS-DFT), providing an analytic, closed-form solution of the self-interaction problem in KS-DFT. We demonstrate the efficacy of our method through ground-state calculations of the exchange potential and energy for atomic He and Be atoms, and comparisons with experiment and the results obtained within the optimized effective potential (OEP) method.

Kohn-Sham formulation of density-functional theory

We rederive the Kohn-Sham formulation of density-functional theory by considering it as a special case of the mapping of the physical density to that of a Slater determinant with an arbitrarily chosen density. It follows that the application of the variational principle requires an additional constraint, with a Lagrange multiplier function that modifies the effective local potential. The Kohn-Sham theory is then regained in the limit of the vanishing Lagrange multiplier. We then study the possibility of applying a similar idea to a formulation, proposed recently by the authors, in terms of the density matrix rather than the density; it follows from well-known relations that this cannot be done.

Energy-density relationships for the treatment of ion solvation within density-functional theory.

Useful energy-density relationships, connected with the embedding of singly charged postive or negative atomic ions in polar solvents, are developed. The insertion of the atomic charged system into the polarizable host is modeled through successive isoelectronic processes at the nucleus, involving a varying nuclear charge. In this way, the controversial procedure of selecting appropriate ionic radii, involved in the calculation of solvation energies through the Born formula, is avoided and replaced by integration in [0,\ensuremath{\infty}]. The approximate expressions, derived from a variational procedure proposed by Levy [J. Chem. Phys. 68, 5298 (1978); 70, 1573 (1979)], are reformulated within the nuclear-transition-state model. The classical reaction field expression for the insertion energy is recovered. The quality of the approximations made are discussed within the frame of the Kohn-Sham formulation of density-functional theory.

Theoretical investigation of (111) stacking faults in aluminium

Abstract We have investigated (111) stacking faults in aluminium using the Kohn-Sham formulation of density-functional theory (DFT) along with plane-wave expansions for the Kohn-Sham functions and pseudopotentials to describe the interactions between the Kohn-Sham functions and the ions. We find that the energies of the intrinsic, extrinsic and twin stacking faults are 161, 151 and 74 mJ m-2 respectively. These values are in reasonable agreement both with estimates based on experimental observations and with values obtained from previous calculations also based on DFT. In addition, we have considered relaxations of the atoms within the stacking-fault region and find that this has a negligible effect on the stacking-fault energies.