CompChem.03.04 Semiempirical Molecular Orbital Theory: Slater Determinants and Hartree-Fock Theory

[@solsticetwo3476]

As usual, a great lecture!

[@ChemProfCramer]

you're very kind -- glad you found it useful.

[@marko6489]

19:46 - Density matrix.

[@solsticetwo3476]

Hi. The first term in integral at 10:20 should be the complex conjugated of phi_j

[@ChemProfCramer]

at some stage in the series, I say that "for notational simplicity, I'm only going to use real orbitals from here on out" which is, of course, generally fine as long as you don't need momentum eigenfunctions...

[@durhamsmith6165]

First off thanks for the amazing video series. Is there a place I can check the answer for the question posed at the end of the video? I have written it out but I want to make sure I have got it correct.

[@ChemProfCramer]

I don't think I ever did it -- to be honest, it would be quite horrible -- better done in lines of code than in formal mathematical notation. Mind you, if you've done it, kudos! You'd have wanted to refer to a basic quantum textbook for the cartesian formulations of the various atomic orbitals.

[@blender2day849]

why dont we skip electronic structure calculation before optimisation is achieved (Do the electronic structure calculation only after optimised geometry achieved )

[@ChemProfCramer]

One needs the derivative of the energy with respect to atomic movement in order to optimize the geometry, so computing the energy itself is a necessary first step.

[@solsticetwo3476]

Hi. Some questions. Considering that this determinant has the same structure than the Secular one: 1. The mu set of orbitals are the complex conjugated of the nu set, right? I mean, mu_i=nu_i* 2. If so, can I assume lambda_i =sigma_i* ? 3. In both, the coulumb and exchage energies, left side is for electron 1 and right side for electron 2? 4. Why there are now two sub indices for the coefficients 'a'? Before, for a given Energy, there was just one coefficient per basis function. THANKS FOR ANY COOMENT.

[@ChemProfCramer]

1. See previous answer about using real orbitals. 2. No, the integrals run over all basis functions and different Greek letters are different indices. These integrals have no physical meaning -- they must simply be computed because the MOs have been expanded in terms of those basis functions. 3. For a chemist, yes. Turns out physicists use a different notational convention, but that's not super important. 4. First coefficient runs over basis functions, second coefficient runs over MOs (each MO has its own energy, also indexed by that coefficient, and unique expansion coefficients multiplying the basis functions).

[@solsticetwo3476]

Chris Cramer Thank Dr. Cramer for your fast reply. Yes, the confusion came from the several levels of 'objects' involved : the multi-electron wavefunction is defined by the Slater determinant of N Molecular Orbitals (MO), which each in turn is formed by a lineal combination of Atomic Orbitals (basis).