Density-functional theory with effective potential expressed as a mapping of the external potential: Applications to open-shell molecules

Abstract

In this paper we apply the direct-mapping density-functional theory (DFT) to open-shell systems, in order to get many-electron wave functions having the same transformation properties as the eigenstates of the exact Hamiltonians. Such a case is that of spin, where in order to get the magnetic properties, the many-particle states must be eigenstates not only of S(z) but also of S2. In this theory the Kohn and Sham [Phys. Rev. A 140, 1133 (1965)] potential is expressed directly as a mapping of the external potential. The total energies of the molecules calculated were satisfactory as their relative deviations (deltaEE) from the exact Hartree-Fock ones were of the order of 10(-4). This accuracy is much higher than that of the standard DFT in its local exchange potential approximation. This method does not need an approximate density as input, as the effective potential is derived directly from the external potential.

A density difference based analysis of orbital-dependent exchange-correlation functionals

“…To minimize computational difficulties that are often encountered in the application of the finite basis set OEP procedure to both the exchange-only energy functional 8,12,14,[52][53][54][55][56] and that including correlation 18,24 , which are the manifestation of the well-known instability associated with numerical solutions of Fredholm integral equations of the first kind, we use the same carefully chosen uncontracted basis sets to represent both the orbitals and potentials in our procedure 8,17,24,27,51 . These issues have been discussed extensively in the literature and several schemes have been proposed for managing this problem 12,14,52-57 .…”

Nonanalyticity of the optimized effective potential with finite basis sets

“…In the last section, the notation "λ → 0" merely implies use of Eqs. (16), (28, and (43) to calculate the finite basis x-OEP, with the cutoff for the null-space of A determined as described. Strictly, λ cannot take values lower than the small but nonzero eigenvalues in the null-space of A.…”

“…Several attempts have been made to overcome these issues [13][14][15][16][17][18][19][20] but with limited success so far. As a result and despite promise, interest in OEP has diminished.…”

Highly Excited States from a Time Independent Density Functional Method

“…The potential preserves symmetry properties of the exact eigenstates and has proven to be successful for the ground state calculations of different characteristic atoms and molecules [34,37,38] and for low-lying excited states [1,2]. Therefore it is natural to try this potential for highly excited state calculations.…”

“…Before discussing results of calculations, we should point out that our x-COEP implementation employs a parameterized form of V eff proposed in [36] and further developed in [37,38] where an effective potential is a direct mapping of the external potential V ext and for N-electron atoms takes the form:…”