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LMInorg

Member

Registered: 2022-09-29

Posts: 3

Fukui indices for high spin inorganic species

Hello Prof.,

I am calculating condensed Fukui indices (using NBO populations via Gaussian) for a series of inorganic complexes, in order to compare the relative electrophilicities of the metal centers, and the relative nucleophilicites of their ligands.

My problem is that I am not sure which multiplicity I should assign after adding r removing one electron. For instance, if we consider a d7 octahedral complex that is high spin (here a quartet), according to the ligand field theory, we have two filled t2g orbitals, one singly-occupied t2g orbitals, and two singly-occupied eg* orgbitals.

When calculating f+ indices, I need to add one electron, but I don’t know if I should calculate the energy of a quintet or of a triplet, i.e. adding one alpha or one beta electron, respectively. If we add one alpha electron, it will most likely spread over the ligand and the metal, but if we add one beta electron, it will, unsurprisingly, mostly locate on the metal center, on the third t2g orbital which was previously singly-occupied. This yields huge differences in terms of Fukui indices, one method giving f+ = 0.4, and the other f+ = 0.8 ; for the metal center.

So which of them should I use? Or should we use the average of both values, i.e. f+ = 0.55 ? Or do Fukui indices become meaningless in that case and they are not a good method to study the nucleophilic and electrophilic areas of such complexes?

Thanks in advance for your advice/comments on that matter, and thank you for your time dedicated to this forum, which is an amazing resource for all computational chemistry students.

Best regards!

sobereva

Tian Lu (Multiwfn developer)

From: Beijing

Registered: 2017-09-11

Posts: 1,830

Website

Re: Fukui indices for high spin inorganic species

If there is no special reason that Fukui function must be used, I would suggest using averaged local ionization energy (ALIE) to predict relative nucleophilicites among ligand atoms, please Section 4.12.2 of Multiwfn manual, and you do not need to respectively calculate two different states. Also, Multiwfn supports orbital weighted Fukui function and dual descriptor, see Sections 3.100.16.3 and 4.100.16.2 of Multiwfn manual for introduction and examples, respectively, they work well for systems with (quasi-)degenerate frontier MOs, and you only need to calculate wavefunction of N state.

f+ often doesn't work well for predicting relative local electrophilicities, even the very simple Hirshfeld atomic charge performs better, see Theoretical Chemistry Accounts (2019) 138:124 for comparison.

If you insist on using f+, and you are not sure about spin multiplicity of ground state of N+1 state, the best way is calculating energies of different spin states and adopt the wavefunction with lowest energy.

LMInorg

Member

Registered: 2022-09-29

Posts: 3

Re: Fukui indices for high spin inorganic species

Thank you for your prompt reply.
Actually, I am more interested in studying the nucleophilicities of the ligands, so f- but this is more or less the same story.
I like your idea of considering only the lower energy wavefunction (for either f+ or f-, I believe) to calculate the Fukui indices.
But I am not restrained to use the Fukui function, so I will look into the concept of ALIE as you suggested.
Would you say that for a given series of similar complexes, the use of f- would still be worth considering?

sobereva

Tian Lu (Multiwfn developer)

From: Beijing

Registered: 2017-09-11

Posts: 1,830

Website

Re: Fukui indices for high spin inorganic species

Using f- is still useful, or at least, you can compare it with e.g. ALIE to further consolidate the local reactivity estimation.

LMInorg

Member

Registered: 2022-09-29

Posts: 3

Re: Fukui indices for high spin inorganic species

I will indeed try both and see if I see a similar trend in my studies.
Thanks alot, once again!