Self-consistent molecular orbital methods. XVIII. Constraints and stability in Hartree–Fock theory

Constraints that may be applied to the spin orbitals used in Hartree–Fock theory are classified and discussed. Once a constrained stationary wavefunction has been obtained by a self-consistent procedure, it may be tested for stability both internally (with constraints remaining) and externally (with some constraints removed). Methods for carrying out these tests are presented. In addition, a general technique is described for further energy minimization following detection of an instability.