Exact differential equation for the density and ionization energy of a many-particle system
Abstract
The ground-state density n of a many-electron system obeys a Schrödinger-like differential equation for n12(r-->), which may be solved by standard Kohn-Sham programs. The exact local effective (nonexternal) potential, veff(r-->), is displayed explicitly in terms of wave-function expectation values, from which veff(r-->)>=0 for all r-->. A derivation for n as | r--> |-->∞ implies that this new effective potential tends asymptotically to zero, as does the exact Kohn-Sham potential, with the highest occupied eigenvalue as the exact ionization energy. A new exact expression is also presented for the exchange-correlation hole density ρxc(r-->, r-->') about an electron at r-->, as | r--> |-->∞.
- Publication:
-
Physical Review A
- Pub Date:
- November 1984
- DOI:
- 10.1103/PhysRevA.30.2745
- Bibcode:
- 1984PhRvA..30.2745L
- Keywords:
-
- Differential Equations;
- Electron Density (Concentration);
- Electron Energy;
- Ionization;
- Particle Theory;
- Eigenvalues;
- Ground State;
- Integral Equations;
- Wave Functions;
- Atomic and Molecular Physics