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ARTICLE
pressure. It is not clear what barrier might be considered a cuto
ff
for labeling a material as a rotational solid. If we choose a barrier
of less than 0.5 eV, then only at pressures below 20 GPa would
the rotational solid description be warranted.
Phase Transformations Rear Their Heads.
To provide some
focus for our studies, we concentrate from this point on phases III
and V, whose enthalpy is shown over a still wider enthalpy range
in Figure 5. Note that we have switched from relative enthalpy to
absolute; this makes it easier to spot phase transitions.
Given the computed stability of phase V at pressures >40 GPa,
we examined this phase
first. Phase V evolves from P2
1
at
ambient pressure to P2
1
/c at elevated pressure. Above 80 GPa,
phase V spontaneously undergoes in our calculations a pressure-
induced chemical transformation to a curious polymeric phase
we have labeled
“polymer I”. The discontinuity is apparent in
Figure 5. Figure 6 shows two views of polymer I at 100 GPa. One
sees in this structure one-dimensional arrays, with all carbons
tetracoordinate. These CH needles or tubes contain
five-, six-,
and eight-membered rings. They could be thought of as one-
dimensional arrays of C
6
H
6
rings bridged to each other by three
σ bonds on one side and three on the other. The CÀC distances
are in the range of 1.42
À1.57 Å. The closest H 3 3 3 H distance
between the CH tubes is 1.56 Å. The calculated band gap of
polymer I at 100 GPa is around 5 eV (see SI), indicating that
polymer I should be transparent. This is not surprising, given the
four-coordinate C structure. The gap remains at higher pressures.
We began to wonder if this transformation could occur at a
lower pressure. First, we extended the pressure
“backward” on
polymer I, studying it a pressures lower than 80 GPa. The
tetracoordinate, saturated structure is dynamically stable, as
determined by a phonon analysis, and at all pressures is more
stable than phase V!
We then looked at the dynamic stability of molecular phase V
gauged by phonon calculations, now at lower pressures. At 10, 20,
and 50 GPa, phase V is dynamically unstable. Following the
imaginary frequencies of vibration, one comes again to polymer I.
This four-connected CH structure is the harbinger of what is
to come
—“saturated”, four-connected carbon structures must be
considered for benzene under pressure, for they are often more
stable than molecular analogues. No claim of novelty here
—
Nicol and Yin entitled a 1984 paper,
“Organic Chemistry at High
Pressure: Can Unsaturated Bonds Survive 10 GPa?
”
31,32
One
had better also worry about kinetics, set by the barriers between
structures.
We return to phase III, the most stable molecular phase
calculated for benzene in the pressure range of 7
À40 GPa, as
Figure 3b shows. This phase remains molecular up to much
higher pressures than any other benzene phase. Phonon disper-
sion calculations show that phase III is dynamically stable up to
190 GPa; for phase III a pressure-induced chemical transforma-
tion, without thermal activation, occurs only above
∼200 GPa.
The phase transformation that does occur in phase III at
∼200
GPa is a drastic one. Above this pressure we
find polymer II,
whose structure is shown in Figure 7. Polymer II is a stacking of
CH sheets containing four-, six-, and eight-membered carbon
rings bonded with H atoms on both sides. All carbons in this
structure are four-coordinate. The C
ÀC distances are in the
range of 1.36
À1.43 Å at 210 GPa; for calibration the CÀC
distance in diamond at 210 GPa is 1.412 Å, so the polymer II
distances are normal. The original six-membered rings are
actually discernible in the polymer structure
—one way to
describe the two-dimensional network is as the product of a
Figure 6.
Two views of polymer I at 100 GPa. On the left is a side view, on the right a top one.
Figure 5.
Calculated absolute enthalpy curve of benzene for phases III
and V as a function of pressure (up to 300 GPa).
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J. Am. Chem. Soc. 2011, 133, 9023–9035
Journal of the American Chemical Society
ARTICLE
(formally forbidden) 2
þ2 dimerization of a chain of benzenes,
along with a 1,4-polymerization to give a sheet.
Saturated CH Polymers Are More Stable than Benzene
Phases.
At this point we have an interesting mystery before us
—
two (so far) polymeric four-coordinate structures, polymers I
and II, are more stable than any benzene structure. To an organic
chemist, used to the archetype of benzene, this is a surprise. It
should not be.
Let us construct a way to think of this problem, sketched in
Scheme 1. In the
first step in a Gedankenexperiment, the benzene
is
“dearomatized”; in the second step, the resulting cyclohexa-
triene converts to a saturated polymer.
There is a range of values of the energetic value of aromaticity.
Following Shaik and co-workers,
33
we use the larger value in the
literature, a so-called
“vertical” resonance energy, ∼65 kcal/mol,
to create from benzene a cyclohexatriene with all aromaticity
removed. To reach one of the saturated CH polymorphs from
such a
“dearomatized” cyclohexatriene involves the further
conversion of three CdC bonds to three σ CÀC bonds inside
the benzene hexagon, and three more
σ CÀC bonds outside, as
sketched in Scheme 1.
The second (
π) bond of any double bond is energetically
worth less than a single bond. This is not a number one can
measure directly. One estimate of the preference comes from the
heat of reaction of three ethylenes (C
2
H
4
) to cyclohexane
(C
6
H
12
), a process in which in fact three
π bonds are converted
to three
σ bonds (see Scheme 2). That heat is experimentally
À67 kcal/mol.
34
Another way to estimate the energy of breaking a
π bond is to
look at the energy of rotating the two CH
2
groups in ethylene 90
°
out-of-plane (
∼65 kcal/mol
35
), and to compare that to a CC
σ
bond strength (
∼90 kcal/mol
36
). That would lead to a slightly
larger estimate of
À75 kcal/mol for three bonds.
The sum of the two heats for processes A and B is 65
À 67
(or
À 75) = À2 (or À8) kcal/mol C
6
H
6
. We will see that this is
not a bad estimate.
Graphanes.
The needle-like structures of polymer I and the
sheets of polymer II contain four-, five-, and eight-membered
rings. One can do better in the organic chemistry of saturated
systems (which is what we have before us) so far as angle strain is
concerned. We therefore began at this point to look at graphanes,
CH sheets with all six-membered rings.
Graphane is a fully saturated CH hydrocarbon conceptually
derived from a single graphene sheet. This structure was
first
computed in 2003 by Sluiter and Kawazoe,
37
and in 2007 by Sofo
et al.,
38
and synthesized in an approach to a pure form in 2009 by
Elias et al.
39
(see also the earlier work from the Brus group
40
).
Our work on the system is described in detail elsewhere.
41
There
are actually many isomeric single-sheet graphanes (see the
enumeration in refs 18 and 22); the four we have found that
are more stable than benzene are shown in Figure 8.
Two of these sheets may be derived by taking single-layer slices
from the cubic diamond structure, three from hexagonal diamond.
Sheet B also occurs (not for carbon) in many inorganic compounds,
such as BaIn
2
,
42
TiNiSi,
43
or EuAuSn,
44
as a planar motif in a three-
dimensional structure. The all-chair sheet A and boat sheet C have
forerunners in the CF literature;
45
À47
sheets B and D have also
been suggested for CH by others.
48,49
In our own work
41
we have
also come on some new sheets, but none so stable as the four shown.
Figure 7.
Di
fferent views of polymer II at 210 GPa: (a) 3D structure of polymer II, (b) side view of a single layer in polymer I, and (c) top view of the
single layer.
Scheme 1. Schematic Formation of a Four-Coordinate C
Polymer from Benzene
a
a
Hydrogens are omitted from this portrayal.
Scheme 2. Reaction of Three Ethylenes to Cyclohexene: A
Model for Three CdC Bonds Converting to Six CÀC Bonds