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An old mail archive says that, in the usually used basis sets, polarisation functions are treated by a single-Gaussian treatment even for valence double-zeta basis sets.

A priori, I've done a few NBO calculations on some simple magnesium compounds, say the cubic magnesium oxide tetramer anchored to the sum of ionic radii, on Gaussian. The results seem to indicate that the 3p electrons on magnesium are treated as Rydberg, i.e. polarisation, functions on that package. This effect exists on Q-Chem as well, leading to my general conclusion that the np orbitals of lighter group 2 elements beryllium and magnesium are generally treated in the usual basis sets as polarisation functions that are not necessarily accurate and represented by a single Gaussian function, no matter the rest of the basis set's accuracy(i.e. the number of zetas).

However, there do exist circumstances where e.g. a 2p orbital of beryllium act as "legitimate" valence orbitals(such as these cases), in which case the treatment of the 2p orbitals of beryllium as Rydberg orbitals should not lead to accurate results. The last paper is behind a paywall that my institution is not affiliated with so I could not check if the authors of the article used "specialised" basis sets(no prizes for guessing out the meaning of the word "specialised" here); even if they did, these basis sets would likely be not directly accessible in the "vanilla" versions of the commonly used quantum chemistry packages and are thus hard to actually use.

My question now follows- do the basis sets included in (some or all) the "vanilla" versions of the commonly used quantum chemistry packages treat the np functions of the two lighter group 2 elements by the same way as they treat the rest of the valence(e.g. by a double-zeta for def2-SVP and by a triple-zeta for 6-311G(d))?; if not, are there any basis sets that do treat them as such available over-the-counter, should that be the right word here, in the literature?

P.S. My question also holds for the np functions of transition metals, which Gaussian treats as valence but Q-Chem treats as polarisation. To quote the quotes on Wikipedia, "Fe(−4), Ru(−4), and Os(−4) have been observed in metal-rich compounds containing octahedral complexes [MIn6−xSnx]; Pt(−3) (as a dimeric anion [Pt–Pt]6−), Cu(−2), Zn(−2), Ag(−2), Cd(−2), Au(−2), and Hg(−2) have been observed (as dimeric and monomeric anions; dimeric ions were initially reported to be [T–T]2− for Zn, Cd, Hg, but later shown to be [T–T]4− for all these elements) in La2Pt2In, La2Cu2In, Ca5Au3, Ca5Ag3, Ca5Hg3, Sr5Cd3, Ca5Zn3(structure (AE2+)5(T–T)4−T2−⋅4e−), Yb3Ag2, Ca5Au4, and Ca3Hg2; Au(–3) has been observed in ScAuSn and in other 18-electron half-Heusler compounds. See Changhoon Lee; Myung-Hwan Whangbo (2008). "Late transition metal anions acting as p-metal elements". Solid State Sciences. 10 (4): 444–449. Bibcode:2008SSSci..10..444K. doi:10.1016/j.solidstatesciences.2007.12.001. and Changhoon Lee; Myung-Hwan Whangbo; Jürgen Köhler (2010). "Analysis of Electronic Structures and Chemical Bonding of Metal-rich Compounds. 2. Presence of Dimer (T–T)4– and Isolated T2– Anions in the Polar Intermetallic Cr5B3-Type Compounds AE5T3 (AE = Ca, Sr; T = Au, Ag, Hg, Cd, Zn)". Zeitschrift für Anorganische und Allgemeine Chemie. 636 (1): 36–40. doi:10.1002/zaac.200900421.", surely some of these entities, such as Ag(-II) and Au(-II), indicate meaningful participation of the np orbitals of the transition metals silver and gold as "genuine" valence orbitals.

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    $\begingroup$ Some formatting may help the post readability. $\endgroup$
    – Poutnik
    Aug 18, 2022 at 7:32

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It is certainly commonplace for orbitals outside the usual valence set to be included in molecular orbital calculations these days. One of the most famous examples actually involves calcium as the alkaline earth metal, with $3d$ as an "extra" subshell [1]. In the "inverse sandwich" complex $\ce{[(thf)3Ca\{μ-C6H3-1,3,5-Ph3\}Ca(thf)3]}$, calcium $3d$ orbitals with the correct symmetry are held to overlap with otherwise antibonding orbitals of the organic ligand surrounding the dicalcium core, thus stabilizing these orbitals through forming calcium-carbon bonds. This enables electron transfer into these orbitals and the resultant emergence of calcium(I) in the core.

Reference

  1. Sven Krieck, Helmar Görls, Lian Yu, Markus Reiher, and Matthias Westerhausen (2009). "Stable 'Inverse' Sandwich Complex with Unprecedented Organocalcium(I): Crystal Structures of [(thf)2Mg(Br)-C6H2-2,4,6-Ph3] and [(thf)3Ca{μ-C6H3-1,3,5-Ph3}Ca(thf)3]". J. Am. Chem. Soc. 131, 8, 2977–2985. https://doi.org/10.1021/ja808524y
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  • $\begingroup$ Is the 3d orbital of calcium represented by the same number of zetas as the 4s one in the basis set used? The whole point of my question was that. $\endgroup$ Aug 21, 2022 at 5:55

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