9024
dx.doi.org/10.1021/ja201786y |
J. Am. Chem. Soc. 2011, 133, 9023–9035
Journal of the American Chemical Society
ARTICLE
pressures of 20
À25 GPa, at which point chemical reaction
between benzene units is supposed to take place. In this phase
diagram, one sees only phases I (Pbca) and II (P2
1
/c), and IV as a
possible high-temperature variant of phase II. No indications of
II
ÀIII and IIIÀIII
0
phase transitions were found in the work of
Ciabini et al. The same research group in 2001 presented results
di
ffering from their 2005 measurements; they confirmed then
that the transition between phases II and III (P2
1
/c) is at 4.8 GPa,
and the transition from phase III to III
0
is at 11.2 GPa. This study
also presumed a phase V in the high-temperature region. In their
early work, Ciabini et al. used the same notation as Thi
ery and
L
eger.
A reviewer has pointed out to us that the apparent di
fferences
between the two phase diagrams are likely the consequences of
technical improvements that occurred between the two experi-
ments. Synchrotron-based di
ffraction experiments and FTIR
spectra on both unannealed and annealed samples
6
allowed
one to understand the metastability of phase I on pressurizing
the sample at room temperature. These results are consistent
with those previously reported by Piermarini et al.
8
and recently
con
firmed by single-crystal diffraction studies by Katrusiak,
Podsiad
zo, and Budzianowski.
9
We thank the reviewer for his
or her guidance here.
To summarize, Thi
ery and Leger’s phase II
5
is not found
in subsequent studies, and their phase III (phase II of Ciabini
et al.
6,7
) is the only stable one at high pressure.
Theoretically, several high-pressure benzene phases were
predicted by Raiteri et al.
10
utilizing a metadynamics method.
Seven phases labeled as I, I
0
, II, III, III
0
, IV, and V, in the notation
used by Thi
ery and Leger, were proposed on the basis of this
crystal structure prediction method. Phases I (Pbca), II (P4
3
2
1
2),
and III (P2
1
/c) were reproduced by the metadynamics. Phases I
0
,
III
0
, IV, and V were predicted to crystallize in Cmca, C2/c, Pbam,
and P2
1
space groups, respectively. However, no enthalpy pro
file
as a function of pressure was presented for the phases calculated.
In the present work we study carefully benzene over a range of
pressures up to 300 GPa. We provide a possible explanation for
the complexities observed in benzene at high pressure, and we pay
attention to the electronic properties of benzene phases in the
context of our strategy of alloying enhancing metallization.
11
À13
Before beginning the story, we need to mention an essential
limitation in what we do, one that limits comparison to experi-
mental reality. We are unable to study e
ffectively amorphous
structures. Clearly, benzene under pressure gives rise to amor-
phous, partially or fully saturated, materials, not that these are
well characterized.
14,15
Their formation is clearly nucleated, and a
legitimate question is whether the regular benzene or saturated
structures (for, as we will see, we
find such) are relevant to what is
observed. We will return below to the experimental work and the
dilemma of interpretation that is a problem for experiment as
well as theory here.
’ THEORETICAL METHODS
The density functional theory (DFT) calculations employed in this
paper are based on the plane wave/pseudopotential approach using the
computer program VASP (Vienna Ab-initio Simulation Package)
16,17
employing the PBE exchange and the projected-augmented wave
(PAW)
18,19
method. The energy cuto
ff for the plane-wave basis was
set to 600 eV. The Brillouin zone was sampled by an automatic mesh of
60 points (converted to Monkhorst
ÀPack meshes on the basis of the
structures
’ unit cell). Relaxation of the electronic degrees of freedom was
stopped when the total (free) energy and the band structure energy
changed between two steps by less than 1
 10
À6
. A conjugate-gradient
algorithm was used to relax the ions into their instantaneous ground
state. We allowed all structural parameters (atomic position, lattice
constants) to relax; each structure was reoptimized twice to check
reproducibility. All atoms are fully relaxed until the Hellmann
À
Feynman forces is less than 0.01 eV/Å. The evolutionary algorithms
USPEX
20
À22
and XtalOpt
23
were employed to
find the lowest energy
structures.
We might note also that zero-point energies are not included in these
calculations; they should be very similar in all the benzene structures
considered here, as all of them have the same bonding patterns.
For MD annealing simulation, only the
Γ k-point was used, with an
energy cuto
ff of 600 eV. Since the CH stretching motion has a period of
11
À12 fs, a 1 fs time step is utilized.
Dynamical stability was checked by phonon calculations carried out using
the linear-response method in the Quantum-ESPRESSO code. Pseudopo-
tentials for H and C were also generated by a Troullier
ÀMartins norm-
conserving scheme; the structural parameters and electronic structures at
both ambient and high pressures obtained with these were comparable with
the results obtained from standard VASP pseudopotentials.
There are inherent limitations in this approach, voiced well in the
following comment by a reviewer:
“[This] model considers one solid
phase only and therefore cannot describe genuine thermodynamic
transitions between phases of equal free energy. There is a wide literature
Figure 1.
Phase diagrams of benzene: (a) suggested by Thi
ery and Leger
5
and (b) proposed by Ciabini et al.
6,7