CompChem.05.02 Density Functional Theory: Early Approximations

[@suphalsen7711]

sir, your lectures are excellent. Your book on computational chemistry and this lecture series on DFT make life simpler. Thank you, sir.

[@ChemProfCramer]

Thanks for letting me know that you've found the materials helpful! Positive feedback always a pleasure.

[@abiramikathiravan4079]

Thanks a lot for making this wonder more transparent.

[@ChemProfCramer]

You're very welcome.

[@baaam2482]

Dear Dr. Cramer, thank you for these wonderful lectures, so that even an organic chemist can (partly) understand it :). I have a short question: What is the difference between a functional and an operator? Because both of them take a function as argument. Thanks in advance

[@ChemProfCramer]

I think I would offer that all functionals are operators, but not all operators are functionals. For instance, if _f_ is defined to operate on real numbers x to map them to 2x, that's perfectly legitimate, but the argument of _f_ is not itself a function, and hence _f_ is not a "functional". Hope that's not obfuscating!

[@baaam2482]

@@ChemProfCramer Thank you very much

[@brendanmuscutt5001]

Thank you. Superb Video. Do you have a Video where you explain the exchange energy? I just dont get it.

[@abhisek.kole.1]

Thank you, sir. Very Very useful video. Love it!!!!!!

[@ChemProfCramer]

My pleasure -- thanks for letting me know it was useful for you.

[@dariomiric2958]

Great video :) Do you know some source or the name of Slater's paper where I can study the derivation of the exchange energy expression? I can't find good sources so far.

[@ChemProfCramer]

I believe the best sources would be: J. C. Slater, Phys. Rev. 81, 385 (1951), ibid. 82, 538 (1951).

[@dariomiric2958]

Thank you, professor.

[@keshav822]

Amazing sir Thanks a lot!

[@saeedahmadvand2712]

Hello Dr. Cramer, The expression for electron density looks like the wave-function itself, am I right? Because it's the summation over probability density (psi squared) multiplied by density matrix!

[@ChemProfCramer]

That's why you want to watch the erratum... (kzbin.info/www/bejne/pYmyd5uOm7N8sM0)

[@saeedahmadvand2712]

This is what I found for electron density in Wikipedia! It's slightly different from your definition!

[@archanasampath3221]

Very Useful video! :) Thankyou Sir :)

[@ChemProfCramer]

+Archana Sampath very glad you found it useful (with the erratum...)

[@kamalgurnani924]

Does the word UEG not mean that the density of electrons should be uniform? Other than this, I did not understand the meaning of the 'assumed' variational principle. Could anyone please guide me?

[@ChemProfCramer]

1) Yes, UEG implies a "gas" with the same density everywhere, for which an energy can be determined analytically. When used in a molecular sense, that means that for any given volume element dV, you take the energy to be the same as would be the case for a UEG having the (average) density found within that volume elements. 2) Assuming a variational principle lets one use variational calculus to find stationary-point solutions to the energy equation. However, there is no proof that the minimum in energy is actually an upper bound to the correct energy -- hence, the variational principle is merely assumed, not established.

[@kamalgurnani924]

​@@ChemProfCramer Thanks for the prompt responses. I had learned DFT through the other sources but this presentation is actually making those connections clearer.