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Is using the effective core potential (ECP) and Gaussian basis set simultaneously in ab initio calculation a valid approach? For example, is it correct to use ECP for one of the atoms and, instead of a basis set which is optimized for ECP, to take a normal Gaussian basis set (say, 6-31G) when we perform calculations for a molecule with a Hartree–Fock method?

P.S. I know technically I can do it in the quantum chemistry packages (for example, I have checked it in MOLPRO), but I don't know whether it is valid physically.

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Sure, it can be valid physically. You can use the full-electron basis set, like 6-31G*, and the ECP with associated basis set, like Lanl2dz, for instance, in calculations of transition metal compounds or compounds with heavier non-metals (Sb, Te, etc.) as an example. Important here would be to compare results obtained with available experimental data (such as bond distances/angles, reaction energies, UV-vis spectra, etc.) or results of similar calculations in order to see if the simultaneous use of ECP and full-electron basis sets is valid and would not give you some weird results.

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Using a basis set that is not designed for the effective core potential is not a good idea. The problem is that an ECP is designed to produce the effective potential of core electrons, and an all-electron basis set will include basis functions meant to model the core electrons. At best, those core basis functions are poorly optimized for your problem. At worst, you will run into SCF convergence problems.

I always recommend to use ECPs with basis sets designed specifically for them.

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    $\begingroup$ Thanks for your useful answer. You mentioned, the corresponding basis set is optimized for core electrons. So, If I add some diffusion function on those basis set (to improve the description of the continuum in my system), is it valid physically or not? $\endgroup$
    – milad behrooz
    Sep 16, 2020 at 8:49
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    $\begingroup$ A normal all-electron basis set will include the minimum number of basis functions for the core electrons, but multiple basis functions for each outer valence orbital. Also possibly higher angular momentum functions (polarization) and low exponent functions (diffuse). If your all-electron basis set does not have diffuse functions it might be quite helpful to add them, as they often improve accuracy. Beware that diffuse functions often increase computational cost and cause SCF problems more than other functions, especially on condensed systems. That's why they are often not included by default. $\endgroup$
    – Hayden S
    Sep 20, 2020 at 5:35

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