Imperial College London

Henry Rzepa

A recently published review on
hypervalency\[cite\]10.1039/C5SC02076J\[/cite\] introduced a very simple
way of quantifying the effect. One of the molecules which was suggested
to be hypervalent using this method was diazomethane. Here I take a
closer look.

The new method is called the **valence electron equivalent γ**. It is
defined as* "the formal shared electron count at a given atom, obtained
by any combination of valid ionic and covalent resonance forms that
reproduces the observed charge distribution"*. These atom charge maps
can be obtained from various kinds of quantum mechanical calculation;
the one adopted in the review was Bader's QTAIM analysis.

Three resonance forms used to estimate γ for the atoms in diazomethane
are shown below. According to
Durrant\[cite\]10.1039/C5SC02076J\[/cite\], "*if γ(X) \> 8, neither form
of the octet rule is obeyed and the atom is hypervalent"*. His procedure
gives γ(N) = **10** (table 3 and also structure
**27a**\[cite\]10.1039/C5SC02076J\[/cite\]), suggesting that the third
resonance form shown below is the most appropriate.

[![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane.svg){.aligncenter
.size-large .wp-image-19253 decoding="async"
width="450"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane.svg)

As a result, the nitrogen is to be considered hypervalent, with five
formal covalent bonds and hence a ten shared-electron valence shell. If
such hypervalence is to be considered as more than just a convenient
representation and to have a deeper underlying foundation, similar
conclusions should ideally emerge from other ways of analysing the
wavefunctions for such species. Here I try the NBO (Natural Bond
Orbital) and ELF (Electron localization Function) analyses of two types
of wavefunction using both DFT (density functional
theory) ωB97XD/Def2-TZVPP and multi-reference CASSCF(12,12)/Def2-TZVPP
Hamiltonians.^‡^

Firstly, the NBO method, which localizes electron pairs. There are four
bonding NBOs associated with the **central** nitrogen and a modest
contribution from a fifth, the terminal nitrogen lone pair
(bottom).![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-NBO-N-886x1024.jpg){.aligncenter
.size-large .wp-image-19271 decoding="async" width="400"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-NBO-N-886x1024.jpg 886w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-NBO-N-260x300.jpg 260w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-NBO-N-768x888.jpg 768w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-NBO-N.jpg 1186w"
sizes="(max-width: 886px) 100vw, 886px"}

The carbon has four NBOs comprising one "non-bonding lone pair", two
C-Hs, a C-N and one partial C-N (bottom). This partitioning can be
quantified using Wiberg atom **bond** indices: C, 3.716; N 3.802; N
2.907 (the C-N and N=N bond orders are 1.425 and 2.368). Note that the
"non-bonding carbon lone pair" would not contribute to the C **bond**
index, which is already **3.72**. Is numerical evidence perhaps emerging
that the carbon may exceed the octet in its valence shell? In contrast,
the central nitrogen, with a bond index of 3.802, but not having any
associated "non-bonding lone pair", does not look to exceeding the
octet. It seems well short of achieving γ(N) = 10, equivalent to a bond
index of 5 as shown in the resonance form above.

![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-NBO-C-833x1024.jpg){.aligncenter
.size-large .wp-image-19269 decoding="async" width="400"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-NBO-C-833x1024.jpg 833w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-NBO-C-244x300.jpg 244w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-NBO-C-768x944.jpg 768w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-NBO-C.jpg 1269w"
sizes="(max-width: 833px) 100vw, 833px"}

Now for ELF, which is derived from the electron density and the basin
locations from its kinetic energy density. The values are the
integrations for the individual ELF basins, of which 0.498\*2 = 0.996 is
the monosynaptic basin for the carbon lone pair noted above. The total
for this carbon comes to **8.16**, the adjacent nitrogen 6.59 and the
terminal nitrogen 7.52e. 

![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-DFT_ELF-1024x574.jpg){.aligncenter
.size-large .wp-image-19258 decoding="async" width="400"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-DFT_ELF-1024x574.jpg 1024w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-DFT_ELF-300x168.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-DFT_ELF-768x431.jpg 768w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-DFT_ELF.jpg 1730w"
sizes="(max-width: 1024px) 100vw, 1024px"}
![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-CAS_ELF-1024x441.jpg){.aligncenter
.size-large .wp-image-19257 decoding="async" width="400"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-CAS_ELF-1024x441.jpg 1024w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-CAS_ELF-300x129.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-CAS_ELF-768x331.jpg 768w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane-CAS_ELF.jpg 1947w"
sizes="(max-width: 1024px) 100vw, 1024px"}

The CASSCF(12,12) values are respectively are **8.18**, 6.50 and 7.50e,
which are very similar. So these two types of electron partitioning show
no evidence that the central nitrogen has γ(N) = 10; it's actually
\~6.5, which is a long way short of 10! However, γ(C) = \~8.2, which
**does** exceed the octet, if only very modestly. Perhaps this can best
be summarised with the following representation based on the bond
orders, which indicates three shared covalent bonds to carbon, a partial
(dashed) C-N interaction and a lone pair implied by the minus sign, the
total of which exceeds γ(C) = \~8. It all boils down really to whether
that "lone pair" of electrons on the carbon is truly a non-bonding
electron pair or whether it should be considered a fully covalent pair
associated also with the nitrogen. Certainly, there appears to be no
evidence from NBO or ELF that this is the
case.[![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane1.svg){.aligncenter
.size-large .wp-image-19273 decoding="async"
width="150"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/12/diazomethane1.svg)

The next logical question to ask is whether the effect can be
"optimised" such that γ(C) \> 8 or even \>\> 8. I will address this in
the next post.

------------------------------------------------------------------------

^‡^FAIR data for all calculations is available at
DOI: [10.14469/hpc/3476](https://doi.org/10.14469/hpc/3476)

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A recently published review on hypervalency[cite]10.1039/C5SC02076J[/cite] introduced a very simple way of quantifying the effect. One of the molecules which was suggested to be hypervalent using this method was diazomethane. Here I take a closer look.

Rogue Scholar Beiträge

Are diazomethanes hypervalent molecules? Probably, but in an unexpected way!