Take a look at all the following molecules: $\ce{SO3^{2-}}$, $\ce{SO2}$, $\ce{SO4^2-}$, $\ce{PF5}$ and many more you can add. In all these there is a controversy of one of these two types:

  1. Is formal charge more important than octet rule - as to justify hypervalency- on determining Lewis structure? As a rule I'd say the answer is no. For example in $\ce{SO2}$,$\ce{SO3}$, $\ce{SO4^2-}$, Do calculations show it?

  2. What is the central atom hybridization? For example, in $\ce{PF5}$ (see here). Does it involve d-orbitals?

In any case, both previous statements are related to the d-orbitals energy.

There is -at least- one straightforward way to answer the question:

  • Calculate* the Molecular Orbitals and see which of previous options fit better (the use of d-orbitals or the non use of them). *sure some can be found in some papers.

So the question is:

Are there theoretical studies of many concrete examples as to remark that d orbitals don't play any relevant role in covalent bonding?

  • $\begingroup$ Sorry, can you clarify your question? What info are you looking for that is not in the related posts? $\endgroup$ – Greg Sep 24 '18 at 16:15
  • $\begingroup$ @Greg look at the title, I think the posts below show $d$ orbitals are not important in covalent bonds. I ask what is the Evidence. $\endgroup$ – santimirandarp Sep 24 '18 at 17:20
  • 2
    $\begingroup$ Some related pub.: 1. Gillespie, R. Coord. Chem. Rev. 2002, 233-234, 53–62. DOI: 10.1016/S0010-8545(02)00102-9 2. Gillespie, R. Inorg. Chem. 1995, 34 (4), 978–979. DOI: 10.1021/ic00108a032 3. Smith, D. J. Chem. Educ. 2005, 82 (8), 1202. DOI: 10.1021/ed082p1202 4. Jensen, W. J. Chem. Educ. 2006, 83 (12), 1751. DOI: 10.1021/ed083p1751 5. Halgren, T. J. Am. Chem. Soc. 1977, 99 (21), 6793–6806. DOI: 10.1021/ja00463a002 $\endgroup$ – Martin - マーチン Sep 25 '18 at 13:58
  • $\begingroup$ Is this only meant to be about supposedly hypervalent compounds of main group elements? $\endgroup$ – orthocresol Sep 25 '18 at 20:14
  • $\begingroup$ Why don't you look for studies that do show a significant d orbital contribution to covalent bonding. Proving nonexistence is hard. $\endgroup$ – Karl Sep 27 '18 at 20:28