MAGNETIC-FIELD DENSITY-FUNCTIONAL THEORY

We discuss the formal basis and general advantages of magnetic-field-a nd-density functional theory (BDFT) for the ground-state magnetic prop erties of many-electron systems. The ground-state density rho(r) and t he magnetic field B(r) are the variables appearing in the energy funct ionals that are the fundamental elements of BDFT. This is in contrast to the energy functionals of current-and-density functional theory (CD FT), the most general density-functional way of treating systems in a magnetic field, where the variables are rho(r) and the ground-state pa ramagnetic current j(p)(r). Explicit calculations of magnetic properti es have already been made that can be recognized as belonging to the B DFT paradigm, which this work therefore puts on a formal foundation. T here are also aspects of BDFT discussed here that may make it an attra ctive alternative to the more general CDFT in some situations. In part icular, we show that Kohn-Sham equations may be derived that use purel y real orbitals and for which the energy does not separate into para- and diamagnetic contributions. We also show that in BDFT the zero-fiel d electron density alone is sufficient to calculate the energy to seco nd order in the magnetic field. Thus calculation of, e.g., diamagnetic susceptibilities or chemical shifts can in principle be made directly from zero-field electron distributions, without any need for the calc ulation of first-order corrections.