Constraint Satisfaction in Local and Gradient Susceptibility Approximations: Application to a van der Waals Density Functional

We show how charge conservation and reciprocity can be built into local density or gradient approximations for density-density response functions (susceptibilities). We apply these ideas to derive from first principles a variant of the Rapcewicz-Ashcroft formula for the van der Waals interaction. We also discuss how improved formulas may be obtained.