Nonlinear programming approach to locally constrained variational calculations

The standard variational problem is modified so that the local behavior of the wave function is indirectly incorporated into the optimum energy calculation. The minimum energy is determined subject to certain inequality constraints, formulated so that the reduced local energy is bounded above and below by a certain error, at different points in configuration space. This modified formulation of standard variational theory constitutes a problem in nonlinear programming. The gradient projection method has been employed to solve this problem. Calculations are carried out using the Hartree–Fock formalism for the ground state of the helium atom.