Computational Chemistry 4.20 - Canonical Hartree-Fock Equations
Short lecture on the canonical Hartree-Fock equations for molecular systems.
For a given molecular Hamiltonian, there are an infinite number of sets of spin orbitals which are equally valid solutions to the Schrodinger equation. We can transform any set of orbitals into any other with the appropriate unitary matrix, through a procedure called a unitary transformation. All molecular properties are invariant to the choice of spin orbital set we ultimately make. In the previous video, we saw the Hartree-Fock equations in their non-canonical form, where every orbital contributes the the result of the Fock operator acting on a spin orbital. In canonical form, the set of Lagrange multipliers form a diagonal matrix, and the spin orbitals are pseudo-eigenfunctions of the Fock operator. For a given Hamiltonian, there exists exactly one such set of canonical spin orbitals.
Notes Slide: https://i.imgur.com/33W2WxW.png
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