Imperial College London

Henry Rzepa

In the [previous
post](http://www.ch.imperial.ac.uk/rzepa/blog/?p=12204 "Modelling the geometry of unbranched alkanes."){target="_blank"},
I showed how modelling of unbranched alkenes depended on dispersion
forces. When these are included, a bent (single-hairpin) form of
C~58~H~118~ becomes lower in free energy than the fully extended linear
form. Here I try to optimise these dispersion forces by adding further
folds to see what happens.

[![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)

I had noted a small kink in the bent single-hairpin form (above, red
circle). What about making a full bend at that point? Such forms have
been previously investigated using OPLS-AA
mechanics\[cite\]10.1021/jp064811m\[/cite\], with the finding that such
a triple-hairpin conformation (below) was 9.7 kcal/mol **higher** in
energy than the single hairpin (above). OK, its got eight gauche-turns
more (four per bend, and which do cost energy), but it also has three
rather than just one row of close dispersion-stabilising contacts to
compensate. Using quantum rather than molecular mechanics
(B3LYP+D3/TZVP), I found that this triple-hairpin folded form was 3.2
kcal/mol higher in free energy than the single
hairpin.\[cite\]10.6084/m9.figshare.988335\[/cite\]

::: {#attachment_12244 .wp-caption .aligncenter style="width: 410px"}
![Click for
3D](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/C58-mismatched-paper-clip.jpg){.size-full
.wp-image-12244 decoding="async"
aria-describedby="caption-attachment-12244"
onclick="jmolInitialize('../Jmol/','JmolAppletSigned.jar');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2014/04/C58-paper-clip-2280.804620=3.2.log;vectors on;vectors 4;vectors scale 8.0;color vectors green;vibration 6;animation mode loop;');"
width="400"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/C58-mismatched-paper-clip.jpg 640w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/C58-mismatched-paper-clip-300x221.jpg 300w"
sizes="(max-width: 640px) 100vw, 640px"}

Click for 3D
:::

One folded at a slightly different point (below) was in fact higher 4.7
kcal/mol in energy that the single
hairpin,\[cite\]10.6084/m9.figshare.988334\[/cite\] indicating that
there is an optimum position for the bend.

::: {#attachment_12226 .wp-caption .aligncenter style="width: 410px"}
![Click for
3D](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/paper-clip-matched.jpeg){.size-full
.wp-image-12226 decoding="async"
aria-describedby="caption-attachment-12226"
onclick="jmolInitialize('../Jmol/','JmolAppletSigned.jar');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2014/04/C58-triple-hairpin-2280.802234=4.7.log;vectors on;vectors 4;vectors scale 8.0;color vectors green;vibration 6;animation mode loop;');"
width="400"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/paper-clip-matched.jpeg 688w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/paper-clip-matched-300x237.jpeg 300w"
sizes="(max-width: 688px) 100vw, 688px"}

Click for 3D
:::

I was convinced better folds could be found. So how about this
double-hairpin, but in three dimensions to form a **prism** so that each
chain has just as many contacts as the triple-hairpin, but is achieved
with two-fewer gauche-turns? Its free
energy\[cite\]10.6084/m9.figshare.988771\[/cite\] is ~~1.6~~ 2.5
kcal/mol **lower** than the single-hairpin. It did not feature in the
previous report\[cite\]10.1021/jp064811m\[/cite\] and hence represents a
new lowest-energy folding (the colour indicates three ribbons of
attractive non-covalent interactions, using the NCI technique). I would
point out that such "manual" searching for better folds is not really
sustainable; a statistical method would normally be used (MD or
Monte-Carlo).

::: {#attachment_12246 .wp-caption .aligncenter style="width: 410px"}
![Click for
3D](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/C58-triple.jpg){.size-full
.wp-image-12246 decoding="async"
aria-describedby="caption-attachment-12246"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2014/04/triple_den.cub.xyz;isosurface wp-content/uploads/2014/04/triple_den.cub.jvxl translucent;');"
width="400"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/C58-triple.jpg 552w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/C58-triple-300x100.jpg 300w"
sizes="(max-width: 552px) 100vw, 552px"}

Click for 3D
:::

A similarly folded version of the triple-hairpin can be made (below),
with more opportunity for five rows of close dispersion contacts. This
time however, the free energy is 1.9 kcal/mol higher than the single
hairpin\[cite\]10.6084/m9.figshare.988333\[/cite\] (but the position of
the fold does need to be optimised and perhaps a better one can be
found). This result does imply that there is an optimum balance between
the energy penalty of creating four gauche-turns per fold and the
additional energy stabilisation of the dispersion. Perhaps the triple
hair-pin above is close to that optimum?

::: {#attachment_12254 .wp-caption .aligncenter style="width: 410px"}
![Click for
3D](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/C58-quint.jpg){.size-full
.wp-image-12254 decoding="async"
aria-describedby="caption-attachment-12254"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2014/04/quint.cub.xyz;isosurface wp-content/uploads/2014/04/quint.cub.jvxl translucent;');"
width="400"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/C58-quint.jpg 617w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2014/04/C58-quint-300x159.jpg 300w"
sizes="(max-width: 617px) 100vw, 617px"}

Click for 3D
:::

Unfortunately no crystal structures for the higher linear alkanes have
been reported that would give us a reality check on any of these models.
Can it really be that difficult to crystallise such molecules?

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


In the previous post, I showed how modelling of unbranched alkenes depended on dispersion forces. When these are included, a bent (single-hairpin) form of C
<sub>
 58
</sub>
H
<sub>
 118
</sub>
becomes lower in free energy than the fully extended linear form. Here I try to optimise these dispersion forces by adding further folds to see what happens.

Rogue Scholar Beiträge

What is the best way of folding a straight chain alkane?