Computational Chemistry 4.19 - Minimum Determinant Energy

Short lecture on minimization of the Hartree-Fock energy by functional variation of spin orbitals.

When we take a Slater determinant of occupied spin orbitals and vary these orbitals to minimize the molecular energy, the resulting expression involves the Fock operator. First we set the molecular energy to the expectation value of the Hamiltonian operator acting on the Slater determinant (the wavefunction). We then define a Lagrangian which constrains the spin orbitals to remain orthonormal as they are varied. This Hermitian expression expands into many terms as we apply the product rule to both one-electron and two-electron integrals. Refactoring the results ultimately provides a the non-canonical Hartree-Fock equations, where the Fock operator acting on a spin orbital is equal to a sum of a column vector of Lagrange multipliers multiplied by all occupied spin orbitals. We shall see in the next video how this can be transformed into canonical, pseudo-eigenvalue form.

Notes Slide: https://i.imgur.com/X1jy9nf.png

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