# Why is the trans-effect of nitrile ion (cyanide) weaker than acetonitrile (methyl cyanide) in octahedral chromium complexes?

I was reading a paper which built a series of trans-philicity (a term they coined to indicate both kinetic trans-effect and thermodynamic trans-influence) from extensive calculations. And I found that in the series, $$\ce{:\!CN-}$$ is shown to have a weaker trans effect than $$\ce{MeC#N \!:}$$ [1] (Note: this is for octahedral complexes)

However, this trend seems odd to me, because I cannot explain it in terms of electron donating and withdrawing capacities. I had heard that the trans-effect is strongest in ligands which were either strong $$\sigma$$-donor or strong $$\pi$$-acceptor or a combination of both. This is why $$\ce{CN-}$$, $$\ce{CO}$$ etc. have very strong trans-effects.

Now, in the experimental trans-effect series that is commonly found in inorganic textbooks, we have: $$\ce{H2O < NH3 < ... < CO < CN-}$$ $$\ce{NH3}$$ is near the very beginning of the series. $$\ce{MeC#N}$$ should be a worse $$\sigma$$-donor than $$\ce{NH3}$$ (as the lone pair is in an $$\mathrm{sp}$$-orbital). It also seems unlikely that $$\ce{MeCN}$$ will be a better $$\pi$$-acceptor than $$\ce{CN-}$$ because $$\ce{MeCN\!:}$$ binds via the more electronegative $$\ce{N}$$ while $$\ce{:\!CN-}$$ binds with the less electronegative $$\ce{C}$$ (which would mean the tendency to accept electron density in the $$\pi$$-orbitals should be lower for $$\ce{MeCN}$$).

So, I don't understand how it is possible to have the trans-effect order $$\ce{CN- < MeCN}$$. Is there any explanation for this?

Reference:

[1]. A. C. Tsipis, "Building trans-philicity (trans-effect/trans-influence) ladders for octahedral complexes by using an NMR probe", Dalton Trans. 2019, 48, 1814-1822 (DOI: 10.1039/C8DT04562C).

According to the reference mentioned in the question (Ref.1):

The term ‘trans-influence’, being a long-established concept of broad relevance in the realm of inorganic chemistry, was defined first in 1966 by Pidcock et al. as the ability of ligand L in a complex to weaken the metal–ligand bond trans to itself. This ground-state phenomenon should be distinguished from the kinetic phenomenon called the ‘trans-effect’, which is the effect of coordinated ligand L upon the rate of substitution reactions of the ligand in trans-position to L.
Note: Pidcock et al. 1966: Ref.2

Considering the high sensitivity of the $$\ce{^{13}C}$$-$$\mathrm{NMR}$$ isotropic shielding tensor elements to small structural/electronic changes, the authors of Ref.1 have published a reliable trans-philicity ladder for octahedral $$\ce{[Cr(CO)5L]^{−/0/+}}$$ complexes using $$\ce{^{13}C}$$-$$\mathrm{NMR}$$ isotropic shielding tensor elements. In $$\ce{[Cr(CO)5L]^{−/0/+}}$$ complex, $$\ce{L}$$ represents a wide variety of ligands (50 ligands) commonly used in coordination and organometallic chemistry. Briefly, all $$\ce{^{13}C}$$-$$\mathrm{NMR}$$ isotropic shielding tensor elements and other parameters have been calculated using PBE0/Def2-TZVP(Cr)∪6-31G(d,p)(E)/PCM and PBE0/Def2-TZVP(Cr)∪6-311++G(d,p)(E)/PCM computational protocols set in dichloromethane solution where the latter protocol is more sophisticated than the former.

I think, major drawback in this publication is the lack of experimental date to support the calculations. For instance, the authors admit that to the best of their knowledge, experimental data for $$\delta \ \ce{^{13}C}$$-$$\mathrm{NMR}$$ chemical shifts of $$\ce{[Cr(CO)5L]^{−/0/+}}$$ complexes are available only for the $$\ce{Cr(CO)6}$$ complex and the “free” $$\ce{CO}$$ ligand, which are $$212$$ and $$\pu{184.4 ppm}$$, respectively.

When compared the calculations of $$\delta \ \ce{^{13}C}$$-$$\mathrm{NMR}$$ chemical shifts of the $$\ce{Cr(CO)6}$$ complex and the “free” $$\ce{CO}$$ ligand employing the two computational protocols, the PBE0/Def2-TZVP(Cr)∪6-31G(d,p)(E)/PCM predicted $$\delta \ \ce{^{13}C}$$-$$\mathrm{NMR}$$ chemical shifts of $$210.2$$ and $$\pu{186.1 ppm}$$, respectively for two compounds, while the protocol PBE0/Def2-TZVP(Cr)∪6-311++G(d,p)(E)/PCM) predicted $$\delta \ \ce{^{13}C}$$-$$\mathrm{NMR}$$ chemical shifts of $$226.8$$ and $$\pu{197.6 ppm}$$, respectively for the same two compounds:

$$\begin{array}{l|cc} \hline \text{Compound} & \ce{\delta \ ^{13}C} \text{ (calculated)}^1 & \ce{\delta \ ^{13}C} \text{ (calculated)}^2 & \ce{\delta \ ^{13}C} \text{ (experimental)} \\ \hline \ce{Cr(CO)6} \text{ (complex)} & \pu{210.2 ppm} & \pu{226.8 ppm} & \pu{212.0 ppm} \\ \ce{CO} \text{ ('free' ligand)} & \pu{186.1 ppm} & \pu{197.65 ppm} & \pu{184.4 ppm} \\ \hline \end{array}\\ ^1 \text{From protocol PBE0/Def2-TZVP(Cr)∪6-31G(d,p)(E)/PCM;} \\ ^2\text{ From protocol PBE0/Def2-TZVP(Cr)∪6-311++G(d,p)(E)/PCM.}$$

Evidently, the GIAO/PBE0/Def2-TZVP(Cr)∪6-31G(d,p)(E)/PCM computational protocol is a better performer in the calculation of the $$\ce{^{13}C}$$-$$\mathrm{NMR}$$ spectra of $$\ce{[Cr(CO)5L]^{−/0/+}}$$ complexes than that of PBE0/Def2-TZVP(Cr)∪6-311++G(d,p)(E)/PCM one. Nevertheless, the differences of the calculated $$\Delta\sigma \ \ce{^{13}C}$$-$$\mathrm{NMR}$$ descriptors of trans-philicity for the complexes using either protocol were minimal.

Yet the authors have mentioned that:

It can be seen that the $$\mathrm{NMR}$$ trans-philicity ladders constructed by the two computational protocols are similar with some minor local reversed orders in the trans-philicity series of similar ligands. The PBE0/Def2-TZVP(Cr)∪6-31G(d,p)(E)/PCM computational protocol predicts for the $$\ce{NCR}$$ ligands the order: $$\ce{NCH \gt NCPh \gt NCMe}$$, while the PBE0/Def2-TZVP(Cr)∪6-311++G(d,p)(E)/PCM computational protocol predicts the order: $$\ce{NCMe \gt NCPh \gt NCH}$$. Consideration of the $$\sigma$$-donor and $$\pi$$-acceptor abilities of the $$\ce{NCR}$$ ligands supports the order predicted by the PBE0/Def2-TZVP(Cr)∪6-31G(d,p)(E)/PCM computational protocol.

Thus, I could argue that the difference in two protocols make this difference than actual situation. Unless we have experimental data to support the finding, it is just speculation.

Reference:

1. A. C. Tsipis, "Building trans-philicity (trans-effect/trans-influence) ladders for octahedral complexes by using an NMR probe", Dalton Trans. 2019, 48, 1814-1822 (DOI: 10.1039/C8DT04562C).
2. A. Pidcock, R. E. Richards, and L. M. Venanzi, "$$\ce{^{195}Pt–^{31}P}$$ nuclear spin coupling constants and the nature of the trans-effect in platinum complexes," J. Chem. Soc. A 1966, 1707–1710 (DOI: https://doi.org/10.1039/J19660001707).
• I don't understand how this answers the question? I was asking about the difference between CN- and MeCN. MeCN has a higher trans-philicity than CN- with both basis sets. Is there any experimental data you know about the trans-effect of MeCN vs CN- that disproves the order from the calculation? Otherwise your answer is just explaining what's written in the paper. Jun 4 '21 at 7:51
• @ Shoubhik R Maiti: Before you question, did you read the paper? It was stated that two protocols give opposite results. Thus, none is conclusive. That's what I said in my answer. Please read the paper first. Jun 4 '21 at 16:13
• Of course I read the paper, that's why I mentioned it in the question. The two protocols give different results for RCN groups, but I am not asking about the order of that. (And HCN is not the same as CN-, they are different ligands in the paper) In both protocols the order of CN- and MeCN is the same. Are you arguing that because the methods predict different order for RCN ligands, the whole series is questionable? Jun 4 '21 at 19:33
• Did you have any other evidence that it is different than what the paper said? Jun 4 '21 at 19:43
• Well, seems like I misunderstood your question. I'll see some evidence to add. Jun 4 '21 at 19:51