DENSITY-MATRICES AND DENSITY FUNCTIONALS IN STRONG MAGNETIC-FIELDS

The equation of motion for the first-order density matrix (1DM) is con structed for interacting electrons moving under the influence of given external scalar and vector potentials. The 1DM is coupled there to th e 2DM by means of the electron-electron interaction. This equation is then employed to obtain the differential virial equation for interacti ng electrons moving in a magnetic field of arbitrary strength. Suitabl e integration leads back to the virial theorem derived recently by Erh ard and Gross. The exchange-correlation scalar potential of the curren t-density functional theory of Vignale and Rasolt is derived in two fo rms, in terms of 1DMs and 2DMs and their noninteracting-system counter parts, involving also (in a linear way) the vector potentials: externa l and exchange-correlation (xc) ones in the first form, and the xc one in the second form. An equation is obtained also for determining the corresponding xc vector potential in terms of the same DMs and the ext ernal vector potential. Approximate exchange-only scalar and vector po tentials are proposed in terms of noninteracting 1DM. Finally the Hart ree-Fock 1DM for atoms and molecules in magnetic fields is shown to sa tisfy the same equation of motion as the fully interacting 1DM. [S1050 -2947(97)06312-9].