Rotational Motion and Nuclear Spin Interconversion of H2O

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Cite This: J. Phys. Chem. Lett. 2019, 10, 1306−1311

Rotational Motion and Nuclear Spin Interconversion of H2O Encapsulated in C60 Appearing in the Low-Temperature Heat Capacity Hal Suzuki,*,† Motohiro Nakano,‡ Yoshifumi Hashikawa,§ and Yasujiro Murata§ †

Department of Chemistry, Kindai University, 3-4-1 Kowakae, Higashiosaka, Osaka 577-8502, Japan Research Center for Structural Thermodynamics, Graduate School of Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan § Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan

J. Phys. Chem. Lett. Downloaded from pubs.acs.org by UNIV OF TEXAS AT DALLAS on 03/12/19. For personal use only.

‡

S Supporting Information *

ABSTRACT: The heat capacity of H2O encapsulated in fullerene C60 is determined for the first time at temperatures between 0.6 and 200 K. The water molecule in H2O@ C60 undergoes quantum rotation at low temperature, and the ortho-H2O and para-H2O isomers are identified by labeling the rotational energy levels with the nuclear spin states. A rounded heat capacity maximum is observed at ∼2 K after rapid cooling due to splitting of the rotational JKaKc = 101 ground state of ortho-H2O. This anomalous feature decreases in magnitude over time, reflecting the conversion of ortho-H2O to para-H2O. Time-dependent heat capacity measurements at constant temperature reveal three nuclear spin conversion processes: a thermally activated transition with Ea ≈ 3.2 meV and two temperature-independent tunneling processes with time constants of τ1 ≈ 1.5 h and τ2 ≈ 11 h.

R

the C60 cage and the protons to be spatially disordered, even at 8 K.8 Inelastic neutron scattering (INS) and far-infrared (FIR) spectroscopy at 5 K have identified several low-energy excitations, which are assigned to transitions between the quantum rotational states of H2O.9,10 The INS peaks at ΔE = ±2.3 and ±2.9 meV are assigned to transitions between the ground state of para-H2O (000) and the split ground states of ortho-H2O (101a and 101b). The temperature variation of the INS peaks indicates that the lower sublevel of ground-state ortho-H2O (101a) is doubly degenerate (g = 2), whereas the upper sublevel (101b) is nondegenerate (g = 1).10 FIR peaks at 2.5 and 7.0 meV are assigned to excitation from the ground to the first and second excited states of ortho-H2O, respectively.9 These peaks decrease in intensity with time, which is attributed to the nuclear spin conversion of ortho- to para-H2O with an estimated time constant, τ, of ∼12 h at 3.5 K. The rotational energy level diagram proposed on the basis of these spectroscopic studies is shown in Figure 1b. The kinetics of the nuclear spin conversion also has been investigated by nuclear magnetic resonance (NMR) spectroscopy, which indicates that the conversion does not proceed exponentially with time.11,12 Despite these efforts, little is known about the thermodynamic properties of H2O@C60. In this Letter, we

otational quantum states are coupled with nuclear spin states in symmetrical molecules with equivalent and identical atoms such as H2, H2O, and CH4.1 In H2, for example, the parity of the rotational quantum number, J, depends on the total nuclear spin, I, i.e., J is even for I = 0 (para-H2) and odd for I = 1 (ortho-H2). Because the interconversion between para- and ortho-H2 is extremely slow in the absence of a paramagnetic catalyst, the two nuclear spin isomers can be treated as different compounds.2 The quantum mechanical features of H2 rotation are evident in lowtemperature heat capacities, a property that is highlighted in many statistical thermodynamics textbooks as a good example of quantum statistics applied to molecular systems.3 H2O also has para and ortho isomers, whose rotational states are designated by JKaKc, where J is the total angular momentum quantum number, and Ka and Kc are the projections of J onto the principal a and c axes, respectively. para-H2O (I = 0) has an even value of Ka + Kc, whereas Ka + Kc is odd for ortho-H2O (I = 1). The quantum rotation of H2O has not been more widely investigated compared to that of H2 because H2O molecules do not rotate freely in the crystalline phase below 273 K.4−6 We recently synthesized a new compound comprising a H2O molecule encapsulated in fullerene C60 (H2O@C60),7 which opens the possibility to observe the quantum rotation of H2O at low temperature (Figure 1a). Some physical investigations have been carried out on H2O@C60. Single-crystal X-ray diffractometry shows the O atom to be located at the center of © XXXX American Chemical Society

Received: February 2, 2019 Accepted: March 5, 2019 Published: March 5, 2019 1306

DOI: 10.1021/acs.jpclett.9b00311 J. Phys. Chem. Lett. 2019, 10, 1306−1311

Letter

The Journal of Physical Chemistry Letters

Figure 1. (a) Molecular structure of H2O@C60 and (b) proposed rotational energy level diagrams of H2O encapsulated in C60.9

Figure 2. (a) Heat capacity (Cp) of H2O@C60 between 0.6 and 200 K (red symbols). The dashed curve is the heat capacity of empty C60. The inset is a double-logarithmic plot of Cp below 40 K illustrating the shoulder at ∼2 K. (b) Excess heat capacity (ΔCp) of H2O@C60 obtained by subtracting the Cp of empty C60 (red symbols). The dotted blue curve is the translational heat capacity (Ctrans) of H2O calculated using the Einstein model (ΘE = 124 K). The dashed black curve is the sum of the rotational heat capacity (Crot) and Ctrans calculated assuming that the conversion of ortho- to para-H2O is rapid. The solid green curve is the Ctrans + Crot sum calculated assuming that the ortho-to-para conversion is slow and that the fraction of ortho-H2O (ϕ) is constant and equal to 0.75.

split sublevels of the ortho-H2 ground state.14 However, the size of the H2O@C60 anomaly is much smaller than that of H2@C60. Figure 2b shows the excess heat capacity (ΔCp) of H2O@ C60 obtained by subtracting the Cp of vacant C60. Because the crystal structure of H2O@C60 is almost the same as that of empty C60,8 ΔCp is regarded to equal the Cp of H2O given that the internal modes of C60 and H2O are independent of one another. Because H2O is triatomic, nine molecular degrees of freedom contribute to the heat capacity, but the contributions from high-frequency intramolecular vibrations (symmetric stretching, 3657 cm−1; bending, 1595 cm−1; antisymmetric stretching, 3756 cm−1)15 are negligible below 200 K. The remaining contributions arise from translational and rotational motion, i.e., ΔCp ≈ Ctrans + Crot. The dotted blue curve in Figure 2b represents the translational heat capacity (Ctrans) calculated using the Einstein model. Because the diameter of H2O (∼3.38 Å)16 is comparable to the inner diameter of the C60 cage (∼3.7 Å), the translational motions of H2O are approximated by threedimensional harmonic vibrations. The Einstein temperature (ΘE) is estimated to be 124 K from the results obtained for

present the initial report and interpretation of the lowtemperature heat capacities of H2O@C60. H2O@C60 was synthesized by the published procedure.7 The compound was purified by high-performance liquid chromatography (HPLC) followed by recrystallization from o-xylene solution. The heat capacity was measured using a relaxation calorimeter PPMS (Quantum Design) at temperatures between 0.6 and 200 K. The heat capacity of pure C60 was measured for comparison. The experimental heat capacities (Cp) are shown in Figure 2a. The measurements were conducted from low to high temperature immediately after the samples were rapidly cooled (dT/dt ≈ −10 K min−1) to the lowest temperature. The Cp of H2O@C60 is significantly greater than that of pure C60 over the entire temperature range due to the contributions from H2O. No peak-like anomaly is observed, which indicates that the orientational order−disorder transition of H2O caused by dielectric interactions13 does not occur in this temperature range. The inset of Figure 2a shows a double-logarithmic plot of Cp below 40 K, where a shoulder is observed at ∼2 K. The shoulder resembles the Schottky-like anomaly observed for H2@C60 that is attributed to thermal excitation between the 1307


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Figure 3. (a) Excess heat capacities obtained by subtracting the Cp following 48 h annealing at 2.5 K. The data of samples annealed at 2.5 K for 1.5, 3, 6, 12, and 24 h show that the magnitude of the excess Cp and the shape of the Cp curves change with annealing time. (b,c) Cpara (dotted blue curves), Cortho (dashed green curves), and Cpara − Cortho (solid red curves) of H2O calculated from the rotational energy level scheme in Figure 1b. The degeneracies of the split ortho-H2O ground state (101) are shown as insets in each panel.

gpara,i (gortho,j) and εpara,i (εortho,j) are the degeneracy and energy level, respectively, of the rotational state i (j) of para-H2O (ortho-H2O). Crot,1 and Crot,2 were calculated using the degeneracy (g) and energy level (ε) data estimated in previous spectroscopic studies of H2O@C609 and of H2O in the gas phase.17 The degeneracy of the split ortho ground state, 101, was set at g = 2 for the lower 101a level and at g = 1 for the higher 101b level. The resultant Ctrans + Crot,1 (dashed black curve) and Ctrans + Crot,2 (ϕ = 0.75) (solid green curve) behaviors are plotted in Figure 2b. These two curves are almost identical above 60 K and similar to the experimental ΔCp results except at high temperature. Thus, the free-rotation picture of H2O encapsulated in the C60 cage seems plausible from the calorimetric point of view. The difference between the calculated and experimental values at high temperature may be due to the crystallinity of the samples or to correlations between the motions of H2O and C60, which are ignored in the analysis. The Ctrans + Crot,2 (ϕ = 0.75) curve agrees with the experimental data below 50 K, while the Ctrans + Crot,1 curve does not. This suggests that nuclear spin conversion is slower than the rate of Cp measurement, which typically requires 10 s per data point at 20 K. If the degeneracy of the split ortho ground state 101 is reversed (i.e., g = 1 for 101a and g = 2 for 101b), the curve of Ctrans + Crot,2 (ϕ = 0.75) deviates from the experimental ΔCp below 10 K (Figure S1). However, ϕ is not constant nor equal to 0.75 at this temperature due to the nuclear spin conversion. The nuclear spin conversion process was investigated by annealing the sample for different lengths of time at 2.5 K: the sample was first cooled from 45 to 2.5 K with cooling rate of dT/dt ≈ −10 K min−1, annealed at 2.5 K for 1.5, 3, 6, 12, 24, and 48 h, and then immediately cooled to 0.6 K, and finally, the Cp were measured from 0.6 to 40 K. The Cp curves obtained after annealing show a smaller shoulder at ∼2 K than does the curve of a rapidly cooled sample (Figure S2). The

H2@C60 (ΘE = 260 K) in the preceding work.14 Detail of the ΘE estimation is given in the Supporting Information. The rotational heat capacity (Crot) depends on the rate of nuclear spin conversion between ortho- and para-H2O. If the conversion is rapid and completed within a shorter time than that required to measure a single Cp data point, Crot is given by eq 1 Crot,1 = Zrot =

d l i d y| o o ln Zrot zzzo mNAkBT 2jjj } o dT n d T k {~

(1a)

rot, i / kBT )

∑ grot,ie(−ε

(1b)

i

where NA is Avogadro’s number, kB is the Boltzmann constant, Zrot is the rotational partition function, and grot,i and εrot,i are the degeneracy and energy level of the rotational state “i”, respectively. In this model, all thermal excitations between the ortho and para states are allowed. However, if the conversion is much slower than the time of the Cp measurement, thermal excitations between the ortho and para states are forbidden, and Crot is given by eq 2 | l d o i d yo ln Zpara zzz} NAkBT 2jjj m o o dT n k dT {~ d l y| i d o o +ϕ m NAkBT 2jjj ln Zorthozzz} o o dT n d T k {~

Crot,2 = (1 − ϕ)Cpara + ϕCortho = (1 − ϕ)

Zpara =

(2a)

para, i / kBT )

∑ gpara,ie(−ε i

Zortho =

ortho, j / kBT )

∑ gortho,je(−ε j

(2b)

where ϕ is the fraction of ortho-H2O, Zpara (Zortho) is the rotational partition function of para-H2O (ortho-H2O), and 1308


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between 1.8 and 40 K as plots of ln τ against T−1. The conversion rates above 13 K, which are reproduced by a singleexponential function, show clear Arrhenius-type behavior. The conversion rates below 13 K, which are fitted by a doubleexponential function, are temperature-independent. The fit of the data above 13 K to the Arrhenius equation

excess heat capacity traces obtained after subtracting the Cp of a sample annealed for 48 h (Figure 3a) show positive peaks at ∼2 and ∼7 K, a zero-crossing at ∼10 K, and negative values above 10 K. The size of the peaks becomes smaller with increasing annealing time, but the zero-crossing temperature never changes. The shape of the excess Cp curve for the rapidly cooled sample (red symbols in Figure 3a) resembles that of a model calculation with a doubly degenerate upper sublevel 101b (Figure 3b), i.e., the peak at ∼2 K is larger than that at ∼7 K. However, the excess Cp of the sample annealed for 24 h resembles that of the model calculation with a doubly degenerate lower sublevel 101a (Figure 3c). Here, the peaks at ∼2 and ∼7 K are of comparable size. This trend is seen more clearly upon comparing the Cp changes during the early and late stages of the conversion (Figure S3). These results indicate the presence of two distinct H2O with different energy level diagrams and different conversion rates. The excess Cp of the rapidly cooled sample (Figure 3a) is about 5 times smaller than those of the calculated ones (Figure 3b,c), indicating that the fraction of ortho-H2O is ϕ ≈ 0.2 for the rapidly cooled sample. The time variation of Cp at constant temperature was investigated to confirm the above suggestion. Samples were rapidly cooled (−10 K min−1) from 45 K to a target temperature, and Cp was measured for up to several 10s of hours at that temperature. Typical examples of the time variation in Cp at 1.85 and 15 K are shown in Figure S4. The results above 13 K are well reproduced by a single-exponential function Cp(T ) = C0 + C1e−t / τ1

τ1 = τ0 + Ae−Ea / kBT

yields an activation energy of Ea ≈ 3.2 meV, which is comparable to the energy difference between the ground and first excited states of ortho-H2O (i.e., 2.2−2.8 meV for 101 ↔ 110, Figure 1b). The temperature-independent time constants below 13 K are estimated to be τ1 ≈ 1.5 and τ2 ≈ 11 h. From these results, we conclude that H2O@C60 is characterized by two nuclear spin conversion processes. One is thermally active; the other is thermally inactive. The former process is dominant at temperatures above 13 K, where the rate-limiting step may be thermal excitation from the 101 to 110 state of ortho-H2O. The temperature-independent conversion at low temperature is due to some tunneling, which is often observed in the spin relaxation of single molecular magnets (SMMs).18−21 H2O tunneling involves direct transition from the 101 ground state of ortho-H2O to the 000 ground or 111 first excited state of para-H2O. The tunneling has fast (τ1 ≈ 1.5 h) and slow (τ2 ≈ 11 h) components, consistent with the effect of annealing on the Cp curves (Figure 3a). Molecules existing having different configurations within the 101 ground state display different nuclear spin conversion rates. The faster time constant, τ1, corresponds to the energy level diagram in Figure 3b, where the higher-energy 101b sublevel is doubly degenerate. The slower time constant, τ2, corresponds to the scheme in Figure 3c, where the lower 101a sublevel is doubly degenerate. It should be noted that this “two-molecule model” also explains the preceding INS results, wherein an additional 101a′ sublevel is observed.10 It is our interpretation that 101a and 101a′ correspond to the lower sublevels of two molecules, where 101a is singly degenerate and 101a′ is doubly degenerate. The higherenergy sublevel partner of 101a′, which would be designated as 101b′, may explain the excess width of the INS peak of 101b. The temperature dependence of the INS peak for the 101a ́ → 000 transition also is explained by this model. However, we note that the two-molecule model conflicts with the interpretation provided by the NMR study of the kinetics of nuclear spin conversion in H2O@C60, wherein the nonexponential feature of the conversion is attributed to a second-order spinconversion process.11 The time-dependent Cp behavior also was analyzed by this second-order model, but the result was not as satisfactory as that with the double-exponential model (Figure S4). The reason for the disagreement is not clear at present. It should be noted that decay curves of the doubleexponential model and the second-order model are similar to each other, and it is difficult to distinguish one from the other. For further investigation, studies on D2O@C60 may shed light on this issue because the isotope substitution sometimes makes a significant change to the kinetics of nuclear spin conversion.22 In summary, we have conducted an initial determination of the heat capacity of H2O encapsulated in a C60 cage (H2O@ C60) below 200 K. The H2O molecules rotate quantum mechanically in the carbon cage even at very low temperature. This contrasts with the behavior of [Li+@C60](PF6−), in which the C60-encapsulated Li+ ion localizes in two positions below 100 K and exhibits antiferroelectric ordering below 24 K.23−26

(3)

where C0 and C1 are the coefficients and τ1 is the time constant. However, the results below 13 K were not fitted by this function but reproduced by a double-exponential function Cp(T ) = C0 + C1e−t / τ1 + C2e−t / τ2

(5)

(4)

where C0, C1, and C2 are the coefficients and τ1 and τ2 are the time constants. Figure 4 shows the time constants collected

Figure 4. Temperature dependence of the time constant of nuclear spin conversion from ortho- to para-H2O. The natural logarithms of the time constant (ln τ) are plotted versus inverse temperature (T−1). The data above 13 K are fitted to an Arrhenius equation (solid line). The data below 13 K are temperature-independent. 1309


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(8) Aoyagi, S.; Hoshino, N.; Akutagawa, T.; Sado, Y.; Kitaura, R.; Shinohara, H.; Sugimoto, K.; Zhang, R.; Murata, Y. A Cubic Dipole Lattice of Water Molecules Trapped inside Carbon Cages. Chem. Commun. 2014, 50, 524−526. (9) Beduz, C.; Carravetta, M.; Chen, J. Y. C.; Concistrè, M.; Denning, M.; Frunzi, M.; Horsewill, A. J.; Johannessen, O. G.; Lawler, R.; Lei, X.; et al. Quantum Rotation of Ortho and Para-water Encapsulated in a Fullerene Cage. Proc. Natl. Acad. Sci. U. S. A. 2012, 109, 12894. (10) Goh, K. S. K.; Jiménez-Ruiz, M.; Johnson, M. R.; Rols, S.; Ollivier, J.; Denning, M. S.; Mamone, S.; Levitt, M. H.; Lei, X.; Li, Y.; et al. Symmetry-Breaking in the Endofullerene H2O@C60 Revealed in the Quantum Dynamics of Ortho and Para-Water: a Neutron Scattering Investigation. Phys. Chem. Chem. Phys. 2014, 16, 21330− 21339. (11) Mamone, S.; Concistrè, M.; Carignani, E.; Meier, B.; Krachmalnicoff, A.; Johannessen, O. G.; Lei, X.; Li, Y.; Denning, M.; Carravetta, M.; et al. Nuclear Spin Conversion of Water inside Fullerene Cages Detected by Low-Temperature Nuclear Magnetic Resonance. J. Chem. Phys. 2014, 140, 194306. (12) Meier, B.; Kouřil, K.; Bengs, C.; Kouřilová, H.; Barker, T. C.; Elliott, S. J.; Alom, S.; Whitby, R. J.; Levitt, M. H. Spin-Isomer Conversion of Water at Room Temperature and Quantum-RotorInduced Nuclear Polarization in the Water-Endofullerene H2O@C60. Phys. Rev. Lett. 2018, 120, 266001. (13) Cioslowski, J.; Nanayakkara, A. Endohedral Fullerites: A New Class of Ferroelectric Materials. Phys. Rev. Lett. 1992, 69, 2871−2873. (14) Kohama, Y.; Rachi, T.; Jing, J.; Li, Z.; Tang, J.; Kumashiro, R.; Izumisawa, S.; Kawaji, H.; Atake, T.; Sawa, H.; et al. Rotational Sublevels of an Ortho-Hydrogen Molecule Encapsulated in an Isotropic C60 Cage. Phys. Rev. Lett. 2009, 103, 073001. (15) Shimanouchi, T. Tables of Molecular Vibrational Frequencies Consolidated Vol. I; National Bureau of Standards, 1972; pp 1−160. (16) Edward, J. T. Molecular Volumes and the Stokes-Einstein Equation. J. Chem. Educ. 1970, 47, 261. (17) Tennyson, J.; Zobov, N. F.; Williamson, R.; Polyansky, O. L.; Bernath, P. F. Experimental Energy Levels of the Water Molecule. J. Phys. Chem. Ref. Data 2001, 30, 735−831. (18) Yamabayashi, T.; Katoh, K.; Breedlove, K. B.; Yamashita, M. Molecular Orientation of a Terbium(III)-Phthalocyaninato DoubleDecker Complex for Effective Suppression of Quantum Tunneling of the Magnetization. Molecules 2017, 22 (1−11), 999. (19) Aubin, S. M. J.; Dilley, N. R.; Pardi, L.; Krzystek, J.; Wemple, M. W.; Brunel, L.-C.; Maple, M. B.; Christou, G.; Hendrickson, D. N. Resonant Magnetization Tunneling in the Trigonal Pyramidal MnIVMnIII 3 Complex [Mn4O3Cl(O2CCH3)3(dbm)3]. J. Am. Chem. Soc. 1998, 120, 4991−5004. (20) Sangregorio, C.; Ohm, T.; Paulsen, C.; Sessoli, R.; Gatteschi, D. Quantum Tunneling of the Magnetization in an Iron Cluster Nanomagnet. Phys. Rev. Lett. 1997, 78, 4645−4648. (21) Cadiou, C.; Murrie, M.; Paulsen, C.; Villar, V.; Wernsdorfer, W.; Winpenny, R. E. P. Studies of a Nickel-based Single Molecule Magnet: Resonant Quantum Tunnelling in an S = 12 Molecule. Chem. Commun. 2001, 2666−2667. (22) Niki, K.; Kawauchi, T.; Matsumoto, M.; Fukutani, K.; Okano, T. Mechanism of the Ortho-Para Conversion of Hydrogen on Ag Surfaces. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, 201404. (23) Matsuo, Y.; Okada, H.; Ueno, H. New Directions in Li@C60 Research: Physical Measurements Endohedral Lithium-Containing Fullerenes: Preparation, Derivatization, and Application; Springer Singapore: Singapore, 2017; pp 129−140. (24) Aoyagi, S.; Tokumitu, A.; Sugimoto, K.; Okada, H.; Hoshino, N.; Akutagawa, T. Tunneling Motion and Antiferroelectric Ordering of Lithium Cations Trapped inside Carbon Cages. J. Phys. Soc. Jpn. 2016, 85, 094605. (25) Suzuki, H.; Ishida, M.; Yamashita, M.; Otani, C.; Kawachi, K.; Kasama, Y.; Kwon, E. Rotational Dynamics of Li+ Ions Encapsulated in C60 Cages at Low Temperatures. Phys. Chem. Chem. Phys. 2016, 18, 31384−31387.

The rotational energy level diagram of H2O proposed in previous spectroscopic studies has been confirmed except for the degeneracy of the split sublevels of the 101 ground state of ortho-H2O. The low-temperature heat capacity is timedependent due to nuclear spin conversion. Careful investigation of the kinetics of this conversion based on the time dependence of the heat capacity reveals one thermally activated and two thermally independent processes. The first process is characterized by an activation energy of ∼3.2 meV, which is comparable to the energy difference between the 101 and 110 states of ortho-H2O. The thermally inactive processes are attributed to tunneling involving direct transition from the 101 state of ortho-H2O to the 000 or 111 state of para-H2O. The two components of the temperature-independent conversion exhibit time constants of τ1 ≈ 1.5 and τ2 ≈ 11 h. There also are two distinct time-dependent Cp responses, both of which are well reproduced by an energy scheme with different degeneracies of the split sublevels of the ortho-H2O 101 ground state. All results are consistent with the presence of two types of H2O molecules in crystalline H2O@C60.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.9b00311. Description of experimental details, calculation of the heat capacity of H2O, and data analyses (PDF)

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AUTHOR INFORMATION

ORCID

Hal Suzuki: 0000-0001-7315-077X Motohiro Nakano: 0000-0002-2599-5740 Yoshifumi Hashikawa: 0000-0001-7834-9593 Yasujiro Murata: 0000-0003-0287-0299 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (KAKENHI) Grant Numbers 15K05404 and 17K19102.

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REFERENCES

(1) Hougen, J. T.; Oka, T. Nuclear Spin Conversion in Molecules. Science 2005, 310, 1913. (2) Matsumoto, M.; Espenson, J. H. Kinetics of the Interconversion of Parahydrogen and Orthohydrogen Catalyzed by Paramagnetic Complex Ions. J. Am. Chem. Soc. 2005, 127, 11447−11453. (3) Hill, T. L. An Introduction to Statistical Thermodynamics; Dover Publications, 1987. (4) Redington, R. L.; Milligan, D. E. Infrared Spectroscopic Evidence for the Rotation of the Water Molecule in Solid Argon. J. Chem. Phys. 1962, 37, 2162−2166. (5) Hama, T.; Kouchi, A.; Watanabe, N. Statistical Ortho-to-Para Ratio of Water Desorbed from Ice at 10 K. Science 2016, 351, 65. (6) Abouaf-Marguin, L.; Vasserot, A. M.; Pardanaud, C.; Michaut, X. Nuclear Spin Conversion of Water Diluted in Solid Argon at 4.2K: Environment and Atmospheric Impurities Effects. Chem. Phys. Lett. 2007, 447, 232−235. (7) Kurotobi, K.; Murata, Y. A Single Molecule of Water Encapsulated in Fullerene C60. Science 2011, 333, 613−616. 1310


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The Journal of Physical Chemistry Letters (26) Aoyagi, S.; Sado, Y.; Nishibori, E.; Sawa, H.; Okada, H.; Tobita, H.; Kasama, Y.; Kitaura, R.; Shinohara, H. Rock-Salt-Type Crystal of Thermally Contracted C60 with Encapsulated Lithium Cation. Angew. Chem., Int. Ed. 2012, 51, 3377−3381.

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Rotational Motion and Nuclear Spin Interconversion of H2O

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