Abstract We discuss two examples (antiferromagnetic order in transition metal oxides and van der Waals interaction) where density functional theory (DFT) seems to fail in giving an appropriate description of the actual physical situation. We analyze whether or not this failure reflects only a shortcoming of the approximations to the exchange‐correlation functionals that are commonly used. It is shown that the well‐known incapability of DFT to yield the correct antiferromagnetic (AF) moment and insulating properties of CoO and stoichiometric La2CuO4 may be indicative of a more fundamental deficiency, namely, absence of an exact noninteracting V‐representability of the spin densities in AF materials. By enlarging and reducing the self‐consistent DFT spin densities by an appropriate amount and simultaneously keeping the total densities fixed, one can turn CoO and La2CuO4 into insulators with the correct AF moments. We also discuss the ground‐state energy of two noble gas atoms of radius R0 at a distance R ≫ 2R0, for which situation an exact DFT should yield a 1/R6‐dependence for the difference between the total energy of the bi‐atom and the two atoms at infinite separation. Even if one improves the local density approximation to the exchange‐correlation energy by gradient corrections, this dependence remains outside the current practical framework of DFT. We report and practically check a simple idea as to how this difficulty can be overcome. The method we develop also might prove useful in actually calculating the above defect spin densities for critical AF materials. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004Abstract We discuss two examples (antiferromagnetic order in transition metal oxides and van der Waals interaction) where density functional theory (DFT) seems to fail in giving an appropriate description of the actual physical situation. We analyze whether or not this failure reflects only a shortcoming of the approximations to the exchange‐correlation functionals that are commonly used. It is shown that the well‐known incapability of DFT to yield the correct antiferromagnetic (AF) moment and insulating properties of CoO and stoichiometric La2CuO4 may be indicative of a more fundamental deficiency, namely, absence of an exact noninteracting V‐representability of the spin densities in AF materials. By enlarging and reducing the self‐consistent DFT spin densities by an appropriate amount and simultaneously keeping the total densities fixed, one can turn CoO and La2CuO4 into insulators with the correct AF moments. We also discuss the ground‐state energy of two noble gas atoms of radius R0 at a distance R ≫ 2R0, for which situation an exact DFT should yield a 1/R6‐dependence for the difference between the total energy of the bi‐atom and the two atoms at infinite separation. Even if one improves the local density approximation to the exchange‐correlation energy by gradient corrections, this dependence remains outside the current practical framework of DFT. We report and practically check a simple idea as to how this difficulty can be overcome. The method we develop also might prove useful in actually calculating the above defect spin densities for critical AF materials. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

International Journal of Quantum ChemistryJan 1, 20049 citations

Modern Density Functional Theory

Viraht Sahni

Springer tracts in modern physicsJan 1, 202247 citations

Density-functional derivative discontinuities at the maximum number of bound electrons

Daniel Whitenack, Yu Zhang, Adam Wasserman

For every electronic many-body Hamiltonian with a one-body potential that goes to zero at infinity, there is a maximum number of bound electrons ( ${J}_{\mathrm{max}}$ ) that can be sustained in the system with an infinite lifetime. At this integer ${J}_{\mathrm{max}}$ , the derivative discontinuity in the exact energy of ensemble density functional theory (DFT) is ill defined. However, we investigate the derivative discontinuity of the energy within the framework of density functional resonance theory [D. L. Whitenack and A. Wasserman, Phys. Rev. Lett. 107, 163002 (2011)], which reduces to ground-state DFT as a coordinate scaling parameter is taken to zero, and find that the exact exchange-correlation potential experiences discontinuous jumps at integer particle numbers, including ${J}_{\mathrm{max}}$ . For integers below ${J}_{\mathrm{max}}$ the jump is purely real because of the real shift in the chemical potential. At ${J}_{\mathrm{max}}$ , the jump has a nonzero imaginary component reflecting the metastability of the system upon addition of one more electron. In addition, the magnitude of the derivative discontinuity at ${J}_{\mathrm{max}}$ is larger than would have been expected by simply setting the affinity to zero.For every electronic many-body Hamiltonian with a one-body potential that goes to zero at infinity, there is a maximum number of bound electrons (${J}_{\mathrm{max}}$) that can be sustained in the system with an infinite lifetime. At this integer ${J}_{\mathrm{max}}$, the derivative discontinuity in the exact energy of ensemble density functional theory (DFT) is ill defined. However, we investigate the derivative discontinuity of the energy within the framework of density functional resonance theory [D. L. Whitenack and A. Wasserman, Phys. Rev. Lett. 107, 163002 (2011)], which reduces to ground-state DFT as a coordinate scaling parameter is taken to zero, and find that the exact exchange-correlation potential experiences discontinuous jumps at integer particle numbers, including ${J}_{\mathrm{max}}$. For integers below ${J}_{\mathrm{max}}$ the jump is purely real because of the real shift in the chemical potential. At ${J}_{\mathrm{max}}$, the jump has a nonzero imaginary component reflecting the metastability of the system upon addition of one more electron. In addition, the magnitude of the derivative discontinuity at ${J}_{\mathrm{max}}$ is larger than would have been expected by simply setting the affinity to zero.

Physical Review AApr 5, 20125 citations

Density Functional Theory: Basic Results and Some Observations

Walter Kohn

Springer eBooksJan 1, 19855 citations

For every electronic many-body Hamiltonian with a one-body potential that goes to zero at infinity, there is a maximum number of bound electrons (

{J}_{\mathrm{max}}

) that can be sustained in the system with an infinite lifetime. At this integer

{J}_{\mathrm{max}}

, the derivative discontinuity in the exact energy of ensemble density functional theory (DFT) is ill defined. However, we investigate the derivative discontinuity of the energy within the framework of density functional resonance theory [D. L. Whitenack and A. Wasserman, Phys. Rev. Lett. 107, 163002 (2011)], which reduces to ground-state DFT as a coordinate scaling parameter is taken to zero, and find that the exact exchange-correlation potential experiences discontinuous jumps at integer particle numbers, including

{J}_{\mathrm{max}}

. For integers below

{J}_{\mathrm{max}}

the jump is purely real because of the real shift in the chemical potential. At

{J}_{\mathrm{max}}

, the jump has a nonzero imaginary component reflecting the metastability of the system upon addition of one more electron. In addition, the magnitude of the derivative discontinuity at

{J}_{\mathrm{max}}

is larger than would have been expected by simply setting the affinity to zero.