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Numerous online references say that $\ce{SCN-}$ has two resonance structures: Structures 1 and 2

I am wondering why this structure is not also possible?

Structure 3

I expect structure 3 to be rare because of the high formal charges, but shouldn't it be included as a possible resonance structure?

Furthermore, there is disagreement about whether structure 1 or structure 2 is more common. I would expect structure 2 to be more common because the negative charge is on the more electronegative N atom. However, this worksheet says that structure 1 is more common. On the other hand, this video says that structure 2 is more common. Which should it be?

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    $\begingroup$ What do you mean my "more common"? $\endgroup$ – Raditz_35 Feb 20 '18 at 15:55
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First I must note the improper use of the terms common and rare as we are not to answer which structure most frequently occurs. I consider this as due to not carefully chosen words.

We have to predict which of the above sketched limiting structure is the more stable or, precisely, the most important one,e.g. that entering the molecular orbital with higher weight.

The one you proposed is indeed possible and you also know why is not the major contributor, and even not a major one.

Usually, as you said, discerning between structures with a formal charge is done by placing it according to the elements electronegativity.

In our case this rule points to structure 2, with the negative charge on nitrogen.

However, examining the energy of the corresponding bonds we note that 2 is a cumulene, which is not a particularly stable configuration around a carbon atom.

Opposite in 1, a stable C-N triple bond is attained, with the big sulphur atom still capable to spread electron density over itself.

We are therefore facing a case in which is not very easy to answer, and myself I will have to doubt.

As matter of the fact I remember that 1 is indeed the major contributor. In SCN anion the negative charge is about 50 % on sulphur and 30 % on the nitrogen side. But on the values I can be wrong.

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I performed a quick calculation on the DF-BP86/def2-SVP level of theory and analysed it with Natural Resonance Theory (from the Natural Bond Orbital Theory). This results in the following major contributors to this wave function: $$\left[ \underset{(1)}{\overset{67.49\%}{\ce{^-S-C#N}}} \ce{<->} \underset{(2)}{\overset{21.25\%}{\ce{S=C=N^-}}} \right]$$

The third contributor is a weird structure with a 'long-distance-bond' between the sulfur and the nitrogen with $7.22\%$. All other contribution are neglected/discarded.

While your structure 3 is indeed a valid contributor, its actual contribution will be very small. Forcing the program to use it as a structure, it resulted in an error, as it was unable to match the orbitals to that structure. The reason for that is likely that the overlap between the sulfur and the carbon is too poor to actually be considered a good contributor. This would also explain the smaller contribution of the second structure.

Here are the localised (according to NBO) molecular orbitals:

nbo orbitals of SCN-

(Colour code: blue/orange - occupied molecular orbital [Lewis]; red/yellow - virtual molecular orbital [unorccupied, non-Lewis])

The total contributions in terms of atomic orbitals to the above:

     (Occupancy)   Bond orbital / Coefficients / Hybrids
 ------------------ Lewis ------------------------------------------------------
   8. (1.98209) LP ( 1) S  1            s( 79.86%)p 0.25( 20.13%)d 0.00(  0.01%)
   9. (1.77474) LP ( 2) S  1            s(  0.00%)p 1.00( 99.91%)d 0.00(  0.09%)
  10. (1.77474) LP ( 3) S  1            s(  0.00%)p 1.00( 99.91%)d 0.00(  0.09%)
  11. (1.96342) LP ( 1) N  3            s( 52.42%)p 0.91( 47.54%)d 0.00(  0.04%)
  12. (1.99743) BD ( 1) S  1- C  2
               ( 44.86%)   0.6698* S  1 s( 20.64%)p 3.81( 78.61%)d 0.04(  0.75%)
               ( 55.14%)   0.7425* C  2 s( 51.41%)p 0.94( 48.47%)d 0.00(  0.12%)
  13. (1.99846) BD ( 1) C  2- N  3
               ( 41.02%)   0.6404* C  2 s( 48.44%)p 1.06( 51.48%)d 0.00(  0.08%)
               ( 58.98%)   0.7680* N  3 s( 48.02%)p 1.08( 51.75%)d 0.00(  0.23%)
  14. (1.99735) BD ( 2) C  2- N  3
               ( 43.98%)   0.6632* C  2 s(  0.00%)p 1.00( 99.91%)d 0.00(  0.09%)
               ( 56.02%)   0.7485* N  3 s(  0.00%)p 1.00( 99.80%)d 0.00(  0.20%)
  15. (1.99735) BD ( 3) C  2- N  3
               ( 43.98%)   0.6632* C  2 s(  0.00%)p 1.00( 99.91%)d 0.00(  0.09%)
               ( 56.02%)   0.7485* N  3 s(  0.00%)p 1.00( 99.80%)d 0.00(  0.20%)
 ---------------- non-Lewis ----------------------------------------------------
  16. (0.01904) BD*( 1) S  1- C  2
               ( 55.14%)   0.7425* S  1 s( 20.64%)p 3.81( 78.61%)d 0.04(  0.75%)
               ( 44.86%)  -0.6698* C  2 s( 51.41%)p 0.94( 48.47%)d 0.00(  0.12%)
  17. (0.01384) BD*( 1) C  2- N  3
               ( 58.98%)   0.7680* C  2 s( 48.44%)p 1.06( 51.48%)d 0.00(  0.08%)
               ( 41.02%)  -0.6404* N  3 s( 48.02%)p 1.08( 51.75%)d 0.00(  0.23%)
  18. (0.22011) BD*( 2) C  2- N  3
               ( 56.02%)   0.7485* C  2 s(  0.00%)p 1.00( 99.91%)d 0.00(  0.09%)
               ( 43.98%)  -0.6632* N  3 s(  0.00%)p 1.00( 99.80%)d 0.00(  0.20%)
  19. (0.22011) BD*( 3) C  2- N  3
               ( 56.02%)   0.7485* C  2 s(  0.00%)p 1.00( 99.91%)d 0.00(  0.09%)

               ( 43.98%)  -0.6632* N  3 s(  0.00%)p 1.00( 99.80%)d 0.00(  0.20%)

On the terminology. Alchimista already explained most of this, however, I cannot stress enough: There is no such thing as a most stable resonance structure. Therefore when you say common, you probably mean large contribution to the wave function, and when you say rare, you probably mean little contribution. None of the resonance structures can be independent from each other, as they are all hypothetical.

Please read more about that here: What is resonance, and are resonance structures real?

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