By about C17H36, the geometry of “cold-isolated” unbranched saturated alkenes is supposed not to contain any fully anti-periplanar conformations.

Imperial College London

Henry Rzepa

By about C~17~H~36~, the geometry of "cold-isolated" unbranched
saturated alkenes is supposed not to contain any fully anti-periplanar
conformations. \[cite\]10.1002/anie.201202894\[/cite\] Indeed, a
(co-crystal) of C~16~H~34~ shows it to have two-gauche
bends.\[cite\]10.1002/chem.200801428\[/cite\]. Surprisingly, the longest
linear alkane I was able to find a crystal structure for,
C~28~H~58~ appears to be fully
extended\[cite\]10.1107/S0108768191011059\[/cite\],\[cite\]10.1107/S0567740876005025\[/cite\]
(an early report of a low quality structure for
C~36~H~74~\[cite\]10.1107/S0365110X5600111X\[/cite\] also appears to
show it as linear).^‡^ Here I explore how standard DFT theories cope
with these structures.

I start with noting the use of a TZVP basis set. In a recent
article\[cite\]10.1039/C3SC53416B\[/cite\] we noted that the
basis-set-superposition-errors for this basis were about a quarter of
that for the standard Pople-type 6-311G(d,p) basis that I tend to use
for modelling in this blog. This matters, since the relative energy of a
folded-conformation *vs* an extended linear one might depend on the
quality of the basis set and its inherent BSSE. The DFT method is the
classical B3LYP. I also modelled C~58~H~118~ as the hydrocarbon as being
well beyond the region anticipated above for folding of the chain to
have started (no, there is no crystal structure). The geometries of
linear and bent forms are shown below.

[![003](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/03/003.jpg){.aligncenter
.size-full .wp-image-12216 decoding="async" width="400"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/03/003.jpg 838w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/03/003-300x17.jpg 300w"
sizes="(max-width: 838px) 100vw, 838px"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/03/003.jpg)[![001](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/03/001.jpg){.aligncenter
.size-full .wp-image-12205 decoding="async" width="400"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/03/001.jpg 807w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/03/001-300x205.jpg 300w"
sizes="(max-width: 807px) 100vw, 807px"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/03/001.jpg)

The relative free energy of the V-shaped bent
form\[cite\]10.6084/m9.figshare.978501\[/cite\] emerges as 3.5 kcal/mol
**higher** than the linear
form\[cite\]10.6084/m9.figshare.978502\[/cite\]. Now, to add a Grimme-D3
dispersion correction to the energies. The V-shape of the bent form now
adopts the hairpin mode,\[cite\]10.6084/m9.figshare.978832\[/cite\] and
its energy is now 2.5 kcal/mol **lower** than the linear
form.\[cite\]10.6084/m9.figshare.978833\[/cite\]

[![002](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/03/002.jpg){.aligncenter
.size-full .wp-image-12215 decoding="async" width="400"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/03/002.jpg 1040w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/03/002-300x53.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/03/002-1024x181.jpg 1024w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/03/002-900x159.jpg 900w"
sizes="(max-width: 1040px) 100vw, 1040px"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/03/002.jpg)

Note in the above the very slight strange oscillation (kink) that
appears about 11 atoms away from the hairpin bend. I repeated this with
the wB97XD DFT procedure (in which dispersion is implicit) and found the
same result.

As triple-ζ basis quality modelling of molecules with \>100 atoms
becomes increasingly common, it is worth repeating yet again that the
model should always contain dispersion (and solvent if appropriate)
corrections as default. Indeed, it is probably also worth
re-investigating much early modelling (by this I mean modelling done ten
or more years ago) to see if such corrections significantly influence
the conclusions.\[cite\]10.1039/C3SC53416B\[/cite\]

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

^‡^The searches cannot be carried out according to the formula
C~n~H~2n+2~, but must be done individually for the value of n. I gave up
at C~50~.

::: {.wp_orcid_field}
[https://orcid.org/0000-0002-8635-8390](https://orcid.org/0000-0002-8635-8390){target="_blank"
rel="author"}
:::


By about C
<sub>
 17
</sub>
H
<sub>
 36
</sub>
, the geometry of “cold-isolated” unbranched saturated alkenes is supposed not to contain any fully anti-periplanar conformations.

Messaggi di Rogue Scholar

Modelling the geometry of unbranched alkanes.