Internal Rotation of Methane Molecules in Large Clusters - American

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Internal Rotation of Methane Molecules in Large Clusters Mikhail N. Slipchenko, Hiromichi Hoshina, Daniil Y Stolyarov, Boris Sartakov, and Andrey F. Vilesov J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.5b02548 • Publication Date (Web): 10 Dec 2015 Downloaded from http://pubs.acs.org on December 11, 2015

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The Journal of Physical Chemistry Letters

Internal Rotation of Methane Molecules in Large Clusters

Mikhail N. Slipchenko,a)b) Hiromichi Hoshina,a)c) Daniil Stolyarov,a)d) Boris G. Sartakov,e) and Andrey F. Vilesova)*

J. Phys. Chem. Lett. manuscript December 6, 2015

a) Department of Chemistry, University of Southern California, Los Angeles, CA 90089, USA b) Present address: School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA c) Present address: Terahertz Sensing and Imaging Research Team, RIKEN; 519-1399 AramakiAoba, Aoba-ku, Sendai, Miyagi, 980-0845, Japan d) Present address: Graphene Laboratories, 4603 Middle Country Rd., Room 111, Calverton, NY 11933 e) General Physics Institute, RAS, Vavilov str. 38, 119991 Moscow, Russia.

*Corresponding author: Email: [email protected]

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Abstract Methane is one of the very few substances that show rotation of individual molecules in the crystalline phase. Here we explore the evolution of the rotation spectrum of methane from single molecules to clusters containing up to about 4×103 molecules. The clusters were assembled in He droplets at T = 0.38 K and studied via infrared laser spectroscopy in the ν3 region of the methane molecules. Well resolved rotational structure in the spectra was observed in clusters containing up to about 50 molecules. We have concluded that in distinction to the crystals molecular rotation in methane clusters is confined to the surface and is enabled by low coordination of the molecules. On the other hand the molecules in the cluster’s interior are in amorphous state wherein the rotation is quenched. These results demonstrate that even at very low temperature the surface of the methane clusters remains fluxional due to quantum effects.

Keywords: methane, clusters, He droplets, rotation, infrared spectra

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Molecules in the gas phase are free to rotate and have quantized energy and angular momentum. Due to small energy separation between the rotational energy levels, the rotation of most substances is quenched by intermolecular interaction in the solid phase. Hydrogen and methane present the only known exceptions to this rule and continue showing rotational spectrum in the solid state.1-2 This effect is related to the large rotational constant of the molecules of 59.3 cm-1 3 and 5.2 cm-1,4 respectively, as well as weak intermolecular interaction, and high symmetry of the crystalline environment. Both molecules also possess nuclear spin isomers. Because the nuclear spin of methane has a long relaxation time, the methane molecules can be found in the states with rotational quantum number J = 1 and 2 even at very low temperatures. In crystalline methane at low temperature (T < 20 K), for every four CH4 molecules, three are locked by intermolecular interaction and one is subjected to a crystal field of high symmetry, Oh, and remains rotating.2,5-6 Recently, the study of rotation in liquid and solid hydrogen has been extended to clusters.7-8 However, very little is known on the molecular rotation in methane clusters. Methane is a spherical top molecule, which has been extensively studied via infrared spectroscopy in the gas phase,4,9-11 in He droplets,12-14 in matrix,15-16 in solid,2,5-6 and in films.17 Methane aerosol particles of few nanometer diameter were generated in collisional cooling cell and investigated via infrared spectroscopy,18 however, no rotational structure in the spectra was observed. Here, we present the study of methane in clusters of different size via infrared spectroscopy in the range of the ν3 - band. The spectra indicate that molecular rotation persists on the surface of methane clusters and makes it possible to estimate the coordination number and the fraction of the molecules on the surface of the clusters. The spectra of methane dimers and small clusters of n < 6 are reported in Ref. 19 Methane clusters were assembled in helium droplets. In this molecular beam technique1921

single molecules are captured by the droplet sequentially and recombine in its interior at 3



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temperature of 0.38 K.20,22-28 Helium droplets having average size in the range of NHe = 3.0×103 to 1.8×106 are obtained, upon expansion of the 4He gas through a 5 µm nozzle at pressure of P0 = 20 bar at temperatures in the range of T0 = 16 to 9 K, respectively.20-21 The helium droplets capture multiple methane molecules in a pickup cell. The average number of the captured molecules is determined from the pickup pressure and the average droplet size as described in Ref. 19 The infrared laser beam obtained from the optical parametric oscillator - amplifier system (Laser Vision, repetition rate - 20 Hz, linewidth - 0.25 cm-1 or 1 cm-1, pulse energy about 5 mJ, pulse duration - 7 ns), is aligned antiparallel to the He droplet beam. 19,26-28 The total flux of the He droplet beam is detected by a quadrupole mass filter, which is adjusted to transmit all masses larger than M = 6 amu. The absorption of the laser radiation by the embedded clusters leads to a transient decrease of the mass spectrometer signal,27 which is recorded by a fast digitizer.

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10 5 0

= 4200

g) = 450

2

f)

0

= 145

10

e)

0

= 36

1

d)

0 10

= 25

5 0

c) = 3.5

2 0

b)

0.5

R(0)

Q P(2)

= 0.3 R(1)

P(1)

a)

0.0 3000

3010

3020

Wavenumber, cm

3030

3040

-1

Figure 1. Spectra of the (CH4)n clusters in He droplets. Average number of methane molecules captured by the droplets is shown in each panel. Trace a) was recorded with spectral resolution of 0.25 cm-1 while the other traces with 1 cm-1. Curves in the bottom of panels b) – g) represent fits of the spectra by Gaussian functions, where continuous red and dashed blue (color online) curves correspond to molecules on the surface and volume of the clusters, respectively, see the text.

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Figure 1 shows the spectra of methane clusters of different average size, , as indicated in each panel. The strong lines in the trace (a) at = 0.3 are assigned to rotational-vibrational transitions of single methane molecules.14 Based on the correlation between the spectral patterns of single methane molecules and of clusters in Fig. 1, we assigned the prominent features in the spectra of the clusters to the P(1), Q and R(0) ro-vibrational lines of the ν3 band of CH4 molecules. The observation of the lines indicates that methane molecules with rotational quantum numbers J < 2 execute internal rotation in clusters. This assignment is also supported by the observation of the internal rotation in small (n < 6) clusters.19 Because the dominant fraction of the molecules in clusters is located on the surface, see Fig. 2, surface molecules must be responsible for the observed rotational structure in the spectrum. With increase of the cluster size, the spectra gradually shift towards the low frequencies and the rotational contour of the band shrinks, see Fig. 1 (a - e). Traces (c - e) show that the spectral intensity in the range of the P(1) line relative to that of the Q line is larger in larger clusters, which indicates a contribution from some new spectral peak (in addition to the P(1) line) at about ν = 3011 cm -1. The spectra of the very large clusters in Fig. 1 (f, g) appear as a superposition of a strong structure less band and a weak band on its high frequency side. We assigned the strong band at ν = 3011 cm-1 to the methane molecules in the interior volume of the cluster, which will be referred to as V-band. The band with the well resolved P-Q-R rotational structure in the smaller clusters is assigned to the molecules on the surface of the clusters and will be referred to as S-band. Red and blue dashed lines in Fig. 1 represent the fits of the spectral features by up to five Gaussian functions corresponding to P(1), Q, R(0), and R(1) lines of the S-band and to the Vband, respectively. The relative intensities of the P(1), Q, R(0), and R(1) lines in the fits were fixed to the values in free single molecules 3:11:15:15,14 as it follows from the spin statistics and the strengths of P, Q and R transitions in CH4. The width of the R(1) line increases upon increase 6


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of the cluster size until it disappears in the noise at n > 50. Because in the spectra of the large clusters (n > 50) the P(1), Q and R(0) lines have a strong overlap with the dominant V-band the fit to five Gaussian functions becomes ambiguous. Nevertheless, the R(0) line can still be identified as a shoulder around 3020 cm-1 in Fig. 1 (f, g) and was used to estimate the intensity of the S-band. Figure 2 shows the ratio of the S-band intensity to the total intensity of the ν3 band, which gives the fraction of the molecules on the surface of the clusters, F, versus cluster size. For comparison, the values of F for the liquid drop

29-30

and for the cubo-octahedral cluster,31 which

exemplifies close packed cluster, with filled shells are shown in Fig. 2 by the dashed line and the open diamonds, respectively.

It is seen that the measured values of F follows the size

dependence for a close packed cluster within the accuracy of the measurements. Hence, we concluded that methane clusters formed in He droplets at T=0.38 K have a compact structure.

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Fraction of the surface molecules


1

0.1

10

100

1000

10000

Cluster size,

Figure 2. Measured ratio of the S-band intensity to the total ν3 band intensity vs. average cluster size – filled squares. The fraction of surface molecules according to the liquid drop model and in the cubo-octahedral clusters having surface molecule counted as filled outer shells are shown by the dashed line and the open diamonds, respectively.

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Vibrational frequecy / cm

a) 3020 in aerosole, phase I in aerosole, amorphous in aerosole, phase II in solid, phase I

S-band

3015

V-band 3010

6

b)

-1

BS / cm

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-1

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4

In solid phase II 2

0

0

10

1

10

2

10

3

4

10

10

solid CH4

Figure 3. Vibrational frequency and rotational constant of CH4 in clusters of different size. Panel (a): Frequency of the Q – line of the S-band (filled triangles) and of the V-band (filled squares). Panel (b): Effective rotational constant of the CH4 molecules on the surface of the clusters, BS. Corresponding values in phase I and phase II of solid methane and in methane aerosol particles are shown on the right hand side of each panel by open symbols, see the legend and the text for more explanations.

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Fig. 3(a) shows the cluster size dependence of the frequency of the Q line of the S-band and of the maximum of the V-band, which give the vibrational frequency of the surface and volume molecules, respectively. Recent study18 of the methane aerosol particles (n ≈ 104) in the collision cooling cell at T = 21 K has shown that particles are initially formed in an amorphous phase, which, within about five minutes, turns into phase I or into phase II (at lower temperature). The ν3 frequencies (band widths) in amorphous phase, phase I, and phase II were found to be of 3010.5 cm-1 (9 cm-1), 3011.5 cm-1 (12 cm-1), and 3010.2 cm-1 (6 cm-1), respectively,18 see Fig. 3(a). The close proximity of the frequency in the bulk phases to that of the V-band at 3011 cm-1 shows that the coordination number of methane molecules in the volume of the clusters is close to that in the solid, i.e., about 12. In addition, the intermolecular distances in the clusters should be similar to those in the methane solid. The vibrational shift of the S-band at = 50 with respect to the ν3 frequency in free molecule is about 50% of the corresponding shift of the V-band. The shift should approximately scale with the number of the nearest neighbor molecules. Therefore, we have concluded that the average coordination number of the surface molecules in the clusters is about 6. For comparison, the average coordination numbers on the (100) surface of a solid and on the surface of a large cubo-octahedral cluster with filled shells are 9 and 8.4, respectively.31 The CH4 clusters in He droplets likely grow by addition of molecules one by one to random points on cluster’s surface, a process which result in porous clusters, if molecules are immobilized upon the impact, see Ref.

32

and references therein. The formation of the compact

cluster core indicates that CH4 molecules remain mobile upon attachment and that the clusters experience some relaxation during the process of growth, even at very low temperature of T = 0.38 K in He droplets. Fig. 3(b) shows the dependence of the effective rotational constant of methane molecules calculated as: 10


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BS =

ν ( R(0)) − ν ( P(1)) , 4 × (1 − ζ 3 )

(1)

where the numerator is the frequency difference between the maxima of the R(0) and P(1) lines, and ζ3= 0.048 is the Coriolis vibration-rotation interaction constant for the ν3 mode in free methane molecules.4

The value of BS for =50 is about 3.0 cm-1 is smaller than the rotational

constant in the free CH4 molecules of 5.2 cm-1,4 and in the Oh sites5,33 in the crystal of about 4.4 cm-1,34 as a result of the anisotropic interaction with the neighbor molecules. To illustrate the hindering of the molecular rotation due to anisotropy of the interaction potential, we conducted the numerical simulation of the energy levels for the two dimensional rotation of CH4 around one of C-H bonds. The effective rotation potential was modeled as 0.5·V·(1-cos(3φ)), where V is the height of the potential barrier and φ is the rotation angle. The factor of two reduction in the energy difference between the two lowest rotational levels was calculated to be at V ≈ 50 cm-1. V ≈ 100 cm-1 could be obtained based on the analytical approximation

34

of the energy levels of

methane molecule in the tetrahedral potential.35 For comparison, the barrier for the rotation of the methane molecule in a dimer was calculated to be about 30 cm-1.36 Thus, the decrease of the effective rotational constant in Fig. 3(b) is consistent with the increase of the coordination number of the surface molecules with the cluster size. The V-band revealed no rotational structure. The ν3 band of the ordered molecules in the bulk low temperature crystalline phase II has a peak at 3008.5 cm-1.5-6 The rest of the molecules occupy highly symmetric Oh sites5,33 and rotate nearly freely. These molecules have an effective rotational constant of about 4.4 cm-1,34 which is larger than 3.0 cm-1 as found in the ≈ 50 clusters in this work, see Fig. 3(b). The infrared spectrum of the CH4 molecules in the Oh sites has P(1), Q and R(0) lines at 3004, 3011, and 3020.3 cm-1, respectively.5-6 The spectra in Fig. 1 do not show the presence of these lines, indicating that the clusters formed in He droplets are not 11



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in crystalline phase-II. Therefore, we concluded that the large clusters assembled in the helium droplets likely stay in the amorphous form during the time of flight of about 5 ms. The lack of the phase II in small clusters is also in agreement with inelastic neutron scattering studies of methane in porous glasses.37-38 In these works, it was shown that sharp free rotor peaks of methane molecules at 8.7 cm-1 only appear in the energy loss spectra if the diameter of the pores was larger than about 10 nm, whereas in smaller pores, the molecules are disordered. The largest clusters studied here have a diameter of about 7 nm, which is below the threshold size. Very recently, quantum vortices were found in droplets larger than about 200 nm in diameter.39-40 The presence of multiple vortices results in formation of multiple track shaped clusters41 in the droplet which should have much larger F values as compared with the compact single clusters. Consistent agreement of the measured F values and those calculated for single compact clusters, serves as a circumstantial evidence of the absence of vortices in droplets with diameter of less than 100 nm in this work. Concluding, we studied the structure of the clusters of methane molecules formed at low temperature in helium droplets via infrared spectroscopy.

We found that the clusters are

amorphous in the interior, where the methane molecules are locked due to the high coordination in cages of low symmetry. On the other hand the molecules on the clusters’ surface show rotation characterized by reduced effective rotational constant. For comparison, in para-hydrogen clusters intermolecular interaction leads to formation of the rotational energy band that encompasses all the molecules of the clusters.7-8 Our previous study indicated considerable inter-mixing of the internal rotational states in CH4 dimers. Similar effect in larger clusters will cause the formation of the rotational band confined to a spherical slab on the surface of the clusters. The presented results call for further theoretical investigations of the rotational energy levels in this unique system. 12


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Acknowledgement This material is based upon work supported by the National Science Foundation under grant CHE-1362535. The authors thank Becklin Davis for careful reading of the manuscript.

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Internal Rotation of Methane Molecules in Large Clusters - American

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