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In computational chemistry, it is extremely common to freeze the core electrons after an initial Hartree-Fock calculation, meaning that the core electrons are left out of any treatment of the electron correlation. Which orbitals are considered core depends on the atom, but for the second row, it usually just means the 1s electrons are not correlated.

This is an intuitive approximation, as one would expect that correlation of the valence electrons would have the greatest effect on any actual chemistry.

Now, clearly one can imagine situations where freezing the core electrons is a very bad idea. One such case is if you were interested in modelling x-ray spectroscopy. I am less interested in this type of example as this is almost just a user error, and hence I would consider this a somewhat trivial example.

So, to be concrete, are there any known examples in which treatment of correlation of the core electrons results in a qualitative change in the modelling of a process which is primarily mediated by the valence electrons?

My guess is if there is an example it occurs in the third row and beyond.

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    $\begingroup$ It's also very bad for NMR properties, but I assume that falls under "trivial" too. :) $\endgroup$ – orthocresol Mar 3 '20 at 0:23
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    $\begingroup$ @orthocresol haha ya I think so. Obviously it's good to know those things though. Maybe it is worth highlighting those cases? $\endgroup$ – jheindel Mar 3 '20 at 6:00
  • $\begingroup$ Somewhat non-trivial-ish but the relative energy of DMSO and its structural isomer, Me-O-S-Me (methyl methanesulfenate), is significantly affected (and just alllmost qualitatively impacted) when considering frozen (with a standard basis set) vs. fully correlated calculations. $\endgroup$ – LordStryker Aug 6 '20 at 20:52
  • $\begingroup$ @LordStryker I would say that's exactly the kind of thing I'm interested in. Is that published somewhere? Or do you have numbers? I'd be interested to see more of what causes that change. $\endgroup$ – jheindel Aug 7 '20 at 19:39
  • $\begingroup$ @jheindel Ask me in a couple months. Hopefully I'll have a DOI to send you. ;) $\endgroup$ – LordStryker Aug 7 '20 at 20:39
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The frozen core approximation (FCA) falls apart whenever you need orbital relaxation of the core to accurately describe your system. From a theory-based argument, there are multiple electronic structure methods which rely on this (CCSD, orbital optimized methods) to better account for correlation effects. However, given that the core orbitals do not change appreciably during most processes (ionization, binding, standard chemical reactions), the error introduced by the FCA is all but completely cancelled (you can still get sub kcal/mol accuracy with the FCA).

However, one case where it rears its head is when you're trying to calculate the single-point energy of a system. In this case, the FCA will get in the way of recovering (for example) the full CI result in the full basis set limit.

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