CompChem.04.01 Ab Initio Hartree-Fock Theory: Basis Sets and LCAO Wave Functions

[@CarrieMK]

I’m dyslexic, so having you explain everything clearly is immensely helpful. I can’t thank you enough!

[@ChemProfCramer]

You're very welcome! So glad you've found useful.

[@natalieschindler5884]

Best explanation ever !!thank you so much!

[@ChemProfCramer]

You're very welcome! Thanks for letting me know.

[@sephirot1313]

Should we use diffuse functions for zwitterions? What about non-covalent interactions among subunits, like a non-covalent bounded dimer? Should we prefer 6-311G* over 6-31+G*? (Given the fact 6-311+G* cannot be used due to the computational cost) I also want to express my gratitude for this excellent course that taught me everything I know about electronic structure, a topic I have always wanted to avoid and now enjoy.

[@ChemProfCramer]

If you know some portion of your molecule has a strong concentration of negative charge (as would be true for a zwitterion), it is indeed probably a good idea to include diffuse functions, and perhaps more important than making a further split in the valence space. Of course, you can always assess those basis set effects by taking an additive approach (i.e., "best energy" = [ method/triple-zeta + ( method/augmented-double-zeta - method/double-zeta ) ]. As for non-covalent interactions, in the ABSENCE of strong concentrations of negative charge, probably better to have a triple-valence shell than to add augmentation functions, but that only goes so far -- if you can afford a still larger basis set, at some point having the diffuse functions is likely to be better than further decontracting the valence space. (And thanks for the kind words on the content!)

[@sahibhasan8373]

Thank you very much, Doctor.

[@Learning432]

Dear Prof., hi. You are working nicely and enthusiastically. Make a video explaining how to choose the appropriate hybrid functional & basis set for specific transition metals for inorganic clusters like [XM12O40]n-, Polyoxometalates (POMs) are clusters of units of oxoanions of transition metals, such as Mo, W, V and Nb.

[@ChemProfCramer]

My video making days seem past, alas, but I can offer a text answer that you might find helpful. The "easy" part of your question has to do with basis set. Since you want to model an anion (and possibly one with polyanionic character) adding diffuse functions will be critical. My personal preference leans towards minimally augmented Karlsruhe-type basis sets (e.g., ma-def2-TZVPP, which one can certainly afford for most single point calculations, although one might need to scale back a bit for geometry optimizations, depending on the size of the system). As for functional, that's much more difficult, frankly. I don't think there is a consensus in the field on that front where different transition metals are involved (especially if any are open-shell, although that's usually less of an issue for POMs). My usual recommendation would be to pick 3 or 4 "modern", widely-used functionals, and assess whether the properties in which you are interested are sensitive to choice of functional. If so, then you're in for some work benchmarking (perhaps against a wave-function theory approach where you think you can extrapolate to complete results) to try to decide which is more accurate. If not, then you can proceed with any one of those functionals with some degree of confidence that you do not have a pathological case.

[@alirezasadeghifar3815]

beautifully explained!! Thank you!

[@monagoda5378]

So what is the answer of the last example ?

[@gloriamariacastanedavalenc6177]

thank you so much! great explained!

[@Szczotii]

Excellent lecture! Thank you 😊

[@vigneshwarankannan4999]

Can you please suggest some python packages or any other software where I can use it to solve nuclear attraction integrals ? Where do I find program codes (python preferrably) and algorithms for computational chemistry problems ?

[@ChemProfCramer]

PySCF sunqm.github.io/pyscf/

[@sunrisesunshine684]

Hi Chris youre vedios are so amazing and helpful ,i need yr help please! I need how to find thé expressions of the elements of the square matrix of Fock, recovry (s) & coefficients!??

[@fredyalexanderhoyosariza4693]

Dr. Chris Cramer about the exercise, the polarization functions are degenerate functions? in that case, which are the bases? are these organized like the valence orbitals, for instance like in 3-31G with one tight and three primitives, and one loose with 1 primitive? would be the same for each one of the polarization functions: d0, d1, d2, d3, d4, d5, px, py, oz, each one with 2 basis functions and 4 primitives?

[@ChemProfCramer]

For the early basis sets (like 6-31G(d), for example), there was only a single basis function per degenerate set. Thus, for each of the d functions, a single exponent is used for the set of the d orbitals. For more modern basis sets, the typical way to balance a basis is to decrease the number of functions by one as one moves out from the valence space. Thus, if the valence is triple zeta for a first-row atom, it would be typical to use 2 d functions and 1 f function. The construction of the functions when there is more than one from linear combinations of primitives varies from basis set to basis set -- one simply has to look that up.

[@fredyalexanderhoyosariza4693]

I believe that I understand a little more, Thank you very much, Dr. Cramer

[@samaarn]

Amazing, thanks a lot!

[@ChemProfCramer]

you're very welcome!

[@MrBeastlypro96]

So 6-31+g and 6-31g* are not the same basis set?

[@ChemProfCramer]

No, they are not. The “*” implies d polarization functions on atoms otherwise limited to s and p. The notation should be regarded as archaic at this point, though, and 6-31G(d) is preferred. The “+” notation implies diffuse s and p functions on heavy atoms. In more modern basis sets, the notation is generally not to add a “+” symbol but to precede the basis set with the prefix “aug-”.

[@saeedahmadvand2712]

Hello Dr. Cramer, I didn't understand how we obtain virtual orbitals form LCAO, while the number of orbitals is the same as electrons?

[@ChemProfCramer]

The number of molecular orbitals is NOT equal to the number of electrons (except possibly by accident when using a small basis set, and even then there would be virtual orbitals unless every electron is unpaired). The number of MOs is equal to the number of basis functions employed in the basis set. So, bigger and bigger basis sets lead to more and more virtual MOs, since the occupied MOs are always the same, and dictated by the number of paired and unpaired electrons. The virtual MOs are solutions to the eigenvalue equation, but have higher energies than those that are occupied if occupation occurs according to an aufbau principle of filling low-energy orbitals first.

[@user-ci8lg7zw2h]

Chris Cramer Dear Dr. Cramer, I donnot get that why the number of basis functions is 1 for the 1s corelevel orbital, 2 for 2s valence orbital (at 27:46 in the video)? what is the difference between basis set and basis function?

[@a22258461]

Thanks