configuration interaction with singles and doubles (CISD) uses a linear combination of the reference Slater determinant and singly and doubly excited determinants. Its many-electron trial state is therefore not restricted to one determinant; the orbitals may be held fixed while the configuration coefficients are varied.
Kohn-Sham equations in density functional theory use an auxiliary one-electron Hamiltonian whose effective potential depends on the density. Its orbitals construct a density representing an interacting electronic system; this is distinct from explicitly diagonalizing a large many-electron determinant Hamiltonian.[ref]
Self-Consistent Equations Including Exchange and Correlation Effects by Walter Kohn and Lu Jeu Sham. 1965, pp. A1133–A1135, ground-state effective one-electron formulation
molecular mechanics evaluates a parametrized potential of atomic positions, with terms such as bond stretching, angle bending, torsion and nonbonded interactions. electrons are represented implicitly through the fitted force field, rather than by electronic orbitals, a density or an electronic wavefunction. This example is different from both preceding electronic methods.
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