Computational Chemistry 4.18 - Functional Variation
Short lecture on variational minimization of the energy functional in quantum mechanics.
Just as the linear variational method can be derived from differentiating coefficients in a basis set expansion, so to do we arrive at this result by minimizing the first variation of an energy functional. This video goes through the derivation where we set the first variation of the energy equal to zero, including an additional term to enforce an orthonormal spin orbitals as the variations occur. This results in an expression where the Hamiltonian matrix acting on the basis function coefficient eigenvector equals the molecular energy times the overlap matrix acting on the same vector.
Notes Slide: https://i.imgur.com/7SjbYhg.png
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