Constraints for hierarchies of many electron distribution functions

Some inequalities that constrain the reconstruction of k-electron distribution functions from lower-order distribution functions are presented. These inequalities are related to the N-representability conditions on electron distributions functions and they have two basic types: (1) general N-representability inequalities, which are very powerful but difficult to apply and (2) generalized “Davidson” inequalities, which are less powerful but which may be more facile in computational implementations. A constraint on the exchange-correlation hole is also presented.