ECS Journal of Solid State Science and Technology, 6 (6) M3113 M3115 (2017) M3113 JSS FOCUS ISSUE ON NANOCARBONS—IN MEMORY OF SIR HARRY KROTO Computational Comparison of the Water Dimer Encapsulations[.]
Trang 1ECS Journal of Solid State Science and Technology, 6 (6) M3113-M3115 (2017) M3113
JSS FOCUSISSUE ONNANOCARBONS—INMEMORY OFSIRHARRYKROTO Computational Comparison of the Water-Dimer Encapsulations
into D2(22)-C84and D2d(23)-C84 Zdenˇek Slanina, a,z Filip Uhl´ık, b Shigeru Nagase, c Takeshi Akasaka, a Ludwik Adamowicz, d and Xing Lu a, ∗
a State Key Laboratory of Materials Processing and Die & Mould Technology, School of Material Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
b Department of Physical and Macromolecular Chemistry, Charles University, Faculty of Science, Praha 2, Czech Republic
c Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan
d Department of Chemistry and Biochemistry, University of Arizona, Tucson, Arizona 85721-0041, USA
The water dimer encapsulations into D2 (22)-C 84and D 2d(23)-C 84 fullerenes are evaluated The encapsulation energy is computed
at the M06-2X/6-31++G** level and it is found that the energy gain upon encapsulation into the D2 (22)-C 84and D 2d(23)-C 84
cages is −17.37 and −15.48 kcal/mol, respectively Encapsulation equilibrium constants are computed using partitions functions
based on the M06-2X/6-31++G** molecular data The yield for (H 2 O) 2@D2 (22)-C 84 is higher than for (H 2 O) 2@D 2d(23)-C 84 ,
however, the yield ratio decreases with increasing temperature and for high temperatures is close to 2:1 The M06-2X/6-31++G**
computed rotational constants are presented for a possible use in detection of the water-dimer endohedrals by rotational spectroscopy
in laboratory or interstellar space.
© The Author(s) 2017 Published by ECS This is an open access article distributed under the terms of the Creative Commons
Attribution Non-Commercial No Derivatives 4.0 License (CC BY-NC-ND, http://creativecommons.org/licenses/by-nc-nd/4.0/ ),
which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is not changed in any
way and is properly cited For permission for commercial reuse, please email: oa@electrochem.org [DOI: 10.1149/2.0201706jss ]
All rights reserved.
Manuscript submitted December 12, 2016; revised manuscript received January 31, 2017 Published February 8, 2017.This paper
is part of the JSS Focus Issue on Nanocarbons – In Memory of Sir Harry Kroto.
The very recent production of C70with encapsulated water dimer1
represents a further example of fullerene endohedrals prepared2 via
organic synthesis Moreover, it offers a stabilized, conserved water
dimer (though influenced by the carbon cage) that can be used for
various spectral characterizations of the prototype hydrogen-bonded
aggregate It also represents an interesting observed species for further
computational studies, this experiment-theory symbiosis being always
quite common6 , 7in fullerene science, even in its prehistoric times8 , 9
before the C60breakthrough observation10in 1985
In addition to the water1 , 2 , 5 and hydrogen molecule3 , 4 containing
endohedrals, also encapsulations of other non-metal species inside
the fullerene cages have been studied, for example atomic11 – 15and
molecular16 , 17nitrogen Endohedrals with rare gas atoms, in particular
with He, were produced using18 , 19high temperatures (650oC), high
pressures (3000 atm) and a catalyst Such fullerene encapsulations
of non-metals have been computed,20 – 25too This paper continues in
the research line with calculations on two C84endohedrals containing
encapsulated water dimer
Calculations
C84has twenty four26isolated-pentagon rule (IPR) isomers, two
major isomers of D2 and D 2d symmetries are conventionally
la-beled as 22 and 23, respectively, or D2(22)-C84 and D 2d(23)-C84
They belong to most abundant empty fullerenes besides C60and C70
(some minor C84isomers are also known27) The D2and D 2dspecies
were prepared28in a ratio of 2:1 and can be separated by recycling
chromatography.29The D 2dstructure has the lowest energy30among
the C84IPR isomers, however, owing to entropy effects it is still less
populated For example, at a temperature of 1000 K, the D2(22)-C84
isomer is computed31 , 32as 60.3% while the D 2d(23)-C84 species as
only 34.2% in the IPR isomeric mixture
The water dimer has also been vigorously studied as an H-bond
model and also as a component of Earth’s33and cometary34 , 35
atmo-spheres Interestingly, it has been established through computations
∗Electrochemical Society Member.
z E-mail: zdeneks@email.arizona.edu
that the dimer mole fraction36 – 38 in saturated water vapor increases with increasing temperature It may be a surprising result but in fact
it can easily be rationalized While the equilibrium constant for the dimer formation decreases with temperature, the saturated pressure increases and actually grows faster.39The water dimer formation is
described by the usual dimerization equilibrium constant K p ,2in terms
of the partial pressures of the components:
In fact, the recent evaluation40of the water dimerization constant (G3&MP2/AUG-cc-pVQZ level) reaches nearly perfect agreement with the available experimental data
The dimeric-water encapsulations into both C84cages (Figure1) are similarly described by the encapsulation equilibrium constants
K p ,enc,i:
(H2O)2(g) + D2(22) − C84(g)
(H2O)2@D2(22) − C84(g) , K p,enc,D2 [2]
(H2O)2(g) + D 2d(23)− C84(g) (H2O)2@D 2d(23)− C84(g) ,
The relative yields of both encapsulates (here represented by the
ratio of their partial pressures p - see Eq.4) can actually be estimated using the ratio of equilibrium constants (2) and (3), especially if the starting amount of both empty fullerenes (or more precisely, their amounts in the equilibrium gas phase) would be the same:
p (H2O)2@D2(22)−C84
p (H2O)2@D 2d(23)−C84
= K p ,enc,D2
K p ,enc,D 2d
[4]
as other partial pressures would cancel out in the arrangement The relative yields exhibit a useful feature that they do not depend on water-vapor pressure or on the water-dimer population In fact, the stability measure defined by Eq.4is basically given by ratios of the partition functions for two isomeric pairs and thus, it allows for a convenient cancellation-out of related contributions, especially of at least part of the anharmonic corrections
Trang 2M3114 ECS Journal of Solid State Science and Technology, 6 (6) M3113-M3115 (2017)
Figure 1 The M06-2X/6-31++G** optimized structures of (H2 O) 2@D2
(22)-C 84 (top) and (H 2 O) 2@D 2d(23)-C 84 (bottom).
All the molecular parameters needed for the construction of the
equilibrium constants on the base of partition functions are computed
here with the Gaussian program package.41
Results and Discussion
The structural and energy data for the encapsulation equilibrium
constants are calculated using the M06-2X density functional with
the standard 6-31++G** basis set (M06-2X/6-31++G**) The
par-tition functions are of the usual rigid rotor and harmonic oscillator
quality and the vibrational frequencies here are also from the
M06-2X/6-31++G** approach Addition of the diffuse functions for
com-plexes with large distances is desirable, however, it brings rather large
demands on computational resources, especially for the vibrational
calculations Therefore, in the previous computations the
frequen-cies (with an exception of the free water dimer) were only of the
M06-2X/6-31G** quality.25Let us note in addition, that the simpler
M06-2X/6-31G** approach (in contrast to the M06-2X/6-31++G**
level used here) is not able to produce the trans conformation known
for the free water dimer
The M06-2X/6-31++G** encapsulation energiesE enc,iwith
in-clusion of the basis set superposition error (BSSE/CP2) and so-called
steric correction40 , 42 , 43are given in TableI The BSSE/CP2 term
re-duces the energy gain upon encapsulation by 3.96 and 4.02 kcal/mol
for the D2(22)-C84and D 2d(23)-C84cage, respectively
Table I The M06-2X/6-31++G** water-dimer encapsulation energiesE enc ,i into D2 (22)-C 84and D 2d(23)-C 84
a See Figure 1
Table II The K K p ,enc,D2
p ,enc,D2d ratios of the M06-2X/6-31++G**
equilibrium constants for the water-dimer encapsulations into
D2 (22)-C 84and D 2d(23)-C 84at selected temperatures T
p ,enc,D2d
a The critical temperature.
The steric correction is applied in order to reflect the cage distor-tion - it includes the difference between the energy of the carbon-cage geometry simply taken from a treated endohedral and the energy of the related fully-optimized empty fullerene cage, and also the respective energy difference for the water dimer The steric correction reduces further the already BSSE/CP2 corrected energy gain upon
encapsu-lation, namely by 2.69 and 3.25 kcal/mol for the D2(22)-C84 and
D 2d(23)-C84species, respectively In fact, the water-dimer distortion represents a larger part of the steric correction
The potential-energy changes upon encapsulationE enc,i are just the first step in the relative yields evaluations Only after evaluations
of the related encapsulation standard enthalpy and entropy changes
one can get the related encapsulation equilibrium constants K p,enc,i Their ratios at selected temperatures are presented in TableII The calculated ratios show that the water-dimer encapsulation into the
D2(22)-C84 cage exhibits a higher yield over the D 2d(23)-C84 case though the difference in the yields is decreasing with the increasing temperature Still, both cages should be a promising target for an application of a high temperature and high pressure technique18 – 20
for the water-dimer encapsulations as already indicated with
evalu-ations for the sole D2(22)-C84species.25 The applied temperatures are likely to go over the critical point (when saturation is not pos-sible and pressures become arbitrary) The high temperatures (and
a catalyst) allow for a temporary window in the cage, yet they cannot be too high in order to prevent a larger cage destruction (and also water dissociation)
Interestingly enough, the cage presence influences the water dimer conformation (Figure1) which is otherwise trans for the free species However, in the D2(22)-C84case the encapsulated trans arrangement
is higher in energy only by 0.08 kcal/mol Other structural parameters
of the water dimer are also influenced by the encapsulation as seen in TableIII The encapsulates in various endohedrals undergo relatively
Table III The M06-2X/6-31++G** structural parameters a in the water-dimer.
(H 2 O) 2 species HOa[Å] OdOa[Å] OaOdH [◦]
a HOa - hydrogen bond (Oa - acceptor-monomer oxygen); OdOa -distance between oxygen atoms of donor (Od) and acceptor monomer;
OaOdH - deviation from linearity.
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Table IV The M06-2X/6-31++G** rotational constants A, B, C
[GHz] for the C 84 endohedrals with the water-dimer.
(H 2 O) 2@D2 (22)-C 84 0.044133 0.042536 0.041200
(H 2 O) 2@D 2d(23)-C 84 0.042925 0.042458 0.042453
a See Figure 1
free motions which is responsible for reconstruction of the cage
sym-metries, as documented by NMR spectroscopy The fully optimized
(H2O)2@C84aggregates exhibit just C1static symmetry However, in
order to reflect the fast internal motions, it is more realistic to describe
the aggregates by the effective dynamic D2or D 2dsymmetry
This type of yield evaluation should be also performed for
(H2O)2@C70 in order to clarify its relative production in
compari-son with encapsulation into the C84 cages Incidentally, the recent
final confirmation44of C60in the interstellar space via electron
spec-troscopy allows to search there for fullerene cages with some
encap-sulates, too (though C60itself is too small45to accommodate the water
dimer) As rotational spectroscopy could also be used for detection
of such endohedrals in the interstellar space, TableIVpresents the
computed rotational constants A, B, C for both C84cages with the
encapsulated water dimer, showing that they are rather different for
the two aggregates (however, in the interstellar space the species can
be in an ionized form)
In conclusion, the calculations show that D2(22)-C84is a better
candidate for high temperature and high pressure water-dimer
en-capsulation as the yield for (H2O)2@D2(22)-C84is higher compared
to (H2O)2@D 2d(23)-C84- the yield ratio decreases with increasing
temperature, however, for high temperatures is yet close to 2:1 The
calculations also suggest that still larger water aggregates46 – 50could
be encapsulated and studied for suitably larger nanocarbons
Acknowledgments
The reported research has been supported by the National
Thou-sand Talents Program of China, the NSFC (numbers 21171061 and
51472095), and the Program for Changjiang Scholars and
Inno-vative Research Team in University (IRT1014); an early phase of
the research line was supported by the Alexander von
Humboldt-Stiftung and the Max-Planck-Institut f¨ur Chemie (Otto-Hahn-Institut)
An access to the MetaCentrum (LM2010005) and CERIT-SC
(CZ.1.05/3.2.00/08.0144) computing facilities is acknowledged, too
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