Sum rules for exchange and correlation energy functional in the current-density functional theory

Various kinds of sum rules for the exchange-correlation energy functional E-xc[rho, j(p)] of the current-density functional theory (CDFT) are investigated systematically. A set of new sum rules is obtained by considering the behavior of the correlation energy functional under a nonuniform coordinate scaling of electrons. In addition, we derive another set of sum rules which give the upper and the lower limits of E-xc[rho, j(p)]. These sum rules can be employed as a constraint in developing an approximate form for E-xc[rho, j(p)].