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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[.]
ECS Journal of Solid State Science and Technology, (6) M3113-M3115 (2017) M3113 JSS FOCUS ISSUE ON NANOCARBONS—IN MEMORY OF SIR HARRY KROTO Computational Comparison of the Water-Dimer Encapsulations into D2 (22)-C84 and D2d (23)-C84 Zdenˇek Slanina,a,z Filip Uhl´ık,b Shigeru Nagase,c Takeshi Akasaka,a Ludwik Adamowicz,d and Xing Lua,∗ 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)-C84 and D2d (23)-C84 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)-C84 and D2d (23)-C84 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 (H2 O)2 @D2 (22)-C84 is higher than for (H2 O)2 @D2d (23)-C84 , 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 C70 with encapsulated water dimer1 represents a further example of fullerene endohedrals prepared2–5 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 common6,7 in fullerene science, even in its prehistoric times8,9 before the C60 breakthrough observation10 in 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 atomic11–15 and molecular16,17 nitrogen Endohedrals with rare gas atoms, in particular with He, were produced using18,19 high temperatures (650o C), high pressures (3000 atm) and a catalyst Such fullerene encapsulations of non-metals have been computed,20–25 too This paper continues in the research line with calculations on two C84 endohedrals containing encapsulated water dimer 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.39 The water dimer formation is described by the usual dimerization equilibrium constant K p,2 in terms of the partial pressures of the components: Calculations (H2 O)2 (g) + D2d (23) − C84 (g) (H2 O)2 @D2d (23) − C84 (g), 26 C84 has twenty four isolated-pentagon rule (IPR) isomers, two major isomers of D2 and D2d symmetries are conventionally labeled as 22 and 23, respectively, or D2 (22)-C84 and D2d (23)-C84 They belong to most abundant empty fullerenes besides C60 and C70 (some minor C84 isomers are also known27 ) The D2 and D2d species were prepared28 in a ratio of 2:1 and can be separated by recycling chromatography.29 The D2d structure has the lowest energy30 among the C84 IPR 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 computed31,32 as 60.3% while the D2d (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’s33 and cometary34,35 atmospheres Interestingly, it has been established through computations ∗ Electrochemical Society Member z E-mail: zdeneks@email.arizona.edu 2H2 O(g) (H2 O)2 (g), K p,2 [1] 40 In fact, the recent evaluation of 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 C84 cages (Figure 1) are similarly described by the encapsulation equilibrium constants K p,enc,i : (H2 O)2 (g) + D2 (22) − C84 (g) (H2 O)2 @D2 (22) − C84 (g), K p,enc,D2 K p,enc,D2d [2] [3] 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: K p,enc,D2 p(H2 O)2 @D2 (22)−C84 = p(H2 O)2 @D2d (23)−C84 K p,enc,D2d [4] as other partial pressures would cancel out in the arrangement The relative yields exhibit a useful feature that they not depend on water-vapor pressure or on the water-dimer population In fact, the stability measure defined by Eq is 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 Downloaded on 2017-03-06 to IP 80.82.77.83 address Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract) M3114 ECS Journal of Solid State Science and Technology, (6) M3113-M3115 (2017) Table I The M06-2X/6-31++G** water-dimer encapsulation energies Eenc,i into D2 (22)-C84 and D2d (23)-C84 Endohedrala E enc,i (kcal/mol) (H2 O)2 @D2 (22)-C84 (H2 O)2 @D2d (23)-C84 −17.37 −15.48 a See Figure Table II The K p,enc, D2 K p,enc, D2d ratios of the M06-2X/6-31++G** equilibrium constants for the water-dimer encapsulations into D2 (22)-C84 and D2d (23)-C84 at selected temperatures T T (K) K p,enc,D2 K p,enc,D2d 500.0 600.0 647.096a 1000.0 4.82 3.58 3.20 1.95 a The Figure The M06-2X/6-31++G** optimized structures of (H2 O)2 @D2 (22)C84 (top) and (H2 O)2 @D2d (23)-C84 (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 partition functions are of the usual rigid rotor and harmonic oscillator quality and the vibrational frequencies here are also from the M062X/6-31++G** approach Addition of the diffuse functions for complexes 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 frequencies (with an exception of the free water dimer) were only of the M06-2X/6-31G** quality.25 Let 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 energies E enc,i with inclusion of the basis set superposition error (BSSE/CP2) and so-called steric correction40,42,43 are given in Table I The BSSE/CP2 term reduces the energy gain upon encapsulation by 3.96 and 4.02 kcal/mol for the D2 (22)-C84 and D2d (23)-C84 cage, respectively critical temperature The steric correction is applied in order to reflect the cage distortion - 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 encapsulation, namely by 2.69 and 3.25 kcal/mol for the D2 (22)-C84 and D2d (23)-C84 species, respectively In fact, the water-dimer distortion represents a larger part of the steric correction The potential-energy changes upon encapsulation E 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 Table II The calculated ratios show that the water-dimer encapsulation into the D2 (22)-C84 cage exhibits a higher yield over the D2d (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 evaluations for the sole D2 (22)-C84 species.25 The applied temperatures are likely to go over the critical point (when saturation is not possible 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 (Figure 1) which is otherwise trans for the free species However, in the D2 (22)-C84 case 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 Table III The encapsulates in various endohedrals undergo relatively Table III The M06-2X/6-31++G** structural parametersa in the water-dimer (H2 O)2 species HOa [Å] Od Oa [Å] free (H2 O)2 (H2 O)2 @D2 (22)-C84 (H2 O)2 @D2d (23)-C84 1.916 1.756 1.747 2.877 2.705 2.681 Oa Od H [◦ ] 5.892 10.24 12.92 a HO a - hydrogen bond (Oa - acceptor-monomer oxygen); Od Oa distance between oxygen atoms of donor (Od ) and acceptor monomer; Oa Od H - deviation from linearity Downloaded on 2017-03-06 to IP 80.82.77.83 address Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract) ECS Journal of Solid State Science and Technology, (6) M3113-M3115 (2017) Table IV The M06-2X/6-31++G** rotational constants A, B, C [GHz] for the C84 endohedrals with the water-dimer Endohedrala A B C (H2 O)2 @D2 (22)-C84 (H2 O)2 @D2d (23)-C84 0.044133 0.042925 0.042536 0.042458 0.041200 0.042453 a See Figure free motions which is responsible for reconstruction of the cage symmetries, as documented by NMR spectroscopy The fully optimized (H2 O)2 @C84 aggregates exhibit just C1 static symmetry However, in order to reflect the fast internal motions, it is more realistic to describe the aggregates by the effective dynamic D2 or D2d symmetry This type of yield evaluation should be also performed for (H2 O)2 @C70 in order to clarify its relative production in comparison with encapsulation into the C84 cages Incidentally, the recent final confirmation44 of C60 in the interstellar space via electron spectroscopy allows to search there for fullerene cages with some encapsulates, too (though C60 itself is too small45 to accommodate the water dimer) As rotational spectroscopy could also be used for detection of such endohedrals in the interstellar space, Table IV presents the computed rotational constants A, B, C for both C84 cages 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)-C84 is a better candidate for high temperature and high pressure water-dimer encapsulation as the yield for (H2 O)2 @D2 (22)-C84 is higher compared to (H2 O)2 @D2d (23)-C84 - the yield ratio decreases with increasing temperature, however, for high temperatures is 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J Saykally, Chem Phys Lett., 633, 13 (2015) 50 W T S Cole, J D Farrell, D J Wales, and R J Saykally, Science, 352, 1194 (2016) Downloaded on 2017-03-06 to IP 80.82.77.83 address Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract) ... difference for the water dimer The steric correction reduces further the already BSSE/CP2 corrected energy gain upon encapsulation, namely by 2. 69 and 3 .25 kcal/mol for the D2 (22 ) -C8 4 and D2 d (23 ) -C8 4... 3.96 and 4. 02 kcal/mol for the D2 (22 ) -C8 4 and D2 d (23 ) -C8 4 cage, respectively critical temperature The steric correction is applied in order to reflect the cage distortion - it includes the difference... enc,i (kcal/mol) (H2 O )2 @D2 (22 ) -C8 4 (H2 O )2 @D2 d (23 ) -C8 4 −17.37 −15.48 a See Figure Table II The K p,enc, D2 K p,enc, D2 d ratios of the M06-2X/6-31++G** equilibrium constants for the water- dimer