ARTICLE pubs.acs.org/JPCA
Spectroscopy of HF and HF-Containing Clusters in Solid Parahydrogen Yuki Miyamoto,*,† Hiroki Ooe,† Susumu Kuma,‡ Kentarou Kawaguchi,† Kyo Nakajima,‡ Itsuo Nakano,§ Noboru Sasao,‡ Jian Tang,† Takashi Taniguchi,‡ and Motohiko Yoshimura§ †
Graduate School of Natural Science and Technology, Okayama University, Tsushima-naka 3-1-1 Kita-ku Okayama 700-8530, Japan Research Core for Extreme Quantum World, Okayama University, Tsushima-naka 3-1-1 Kita-ku Okayama 700-8530, Japan § Faculty of Science, Okayama University, Tsushima-naka 3-1-1 Kita-ku Okayama 700-8530, Japan ‡
ABSTRACT: We report measurements of FT-IR absorption spectroscopy of HF, DF, and their clusters in solid parahydrogen (pH2). The observed spectra contain many absorption lines which were assigned to HF monomers, HF polymers, and clusters with other species, such as N2, O2, orthohydrogen (oH2), etc. The rotational constants of HF and DF monomers were determined from the cooperative transitions of the vibration of solid pH2 and the rotation of HF and DF. Small reduction of the rotational constants indicates that HF and DF are nearly free rotors in solid pH2. Time dependence of the spectra suggests that HF and DF monomers migrate in solid pH2 and form larger polymers, probably via tunneling reactions through high energy barriers on inserting another monomer to the polymers. The line width of HF monomers in solid pH2 was found to be 4 cm1, which is larger than that of other hydrogen halides in solid pH2. This broad line width is explained by rapid rotational relaxation due to the accidental coincidence between the rotational energy of HF and the phonon energy with maximum density of states of solid pH2 and the rotationaltranslational coupling in a trapping site.
I. INTRODUCTION Spectroscopy of HF and its clusters has been extensively investigated in both experimental111 and theoretical works.1223 This is because HF molecules provide a prototype for hydrogenbonded systems. In particular, HF dimers as one of the simplest systems have attracted the greatest interest.37,1216 Hydrogen bond interconversion of dimers causes the tunneling splitting in their spectra and has been considered as one of the primary processes of cluster dynamics.24 Larger cyclic polymers have been observed in agreement with the minimum energy structures predicted in theoretical calculations.1518 Spectroscopy and dynamics of HF dimers and larger clusters were reviewed by M. Quack and M. A. Suhm.24 HF monomers, polymers, and clusters with other species in condensed phases have been also studied in many works.2544 Infrared absorption spectra of the monomer and polymers, and HF-N2, HF-H2, HF-O2, etc., in solid Ar and solid Ne were reported previously.2534 The matrix isolation technique has been a useful method for spectroscopy of unstable molecules including radicals and clusters.45,46 However, strong interactions with rare gas matrices make it difficult to perform a high resolution spectroscopy and detailed studies of subtle interactions and dynamics in solids. Quantum matrices such as solid pH24765 and helium nanodroplets3544,66 are proven to be excellent environments for the high-resolution spectroscopy of cold molecules. In general, molecules embedded in these quantum matrices exhibit quantized rotational states and extremely long lifetimes of vibrationrotation excited states, which makes the line widths of the rovibrational transitions of molecules narrow in these quantum matrices. Furthermore, the small cage effect of solid pH2 allows r 2011 American Chemical Society
us to use it as a reaction field and study chemical reactions at low temperature, including tunneling-reactions.5052 He nanodroplet studies in combination with the pendular spectroscopy performed by R. E. Miller et al.3544 revealed the structure and dynamics of HF monomers, polymers, and clusters with other species in the superfluid helium environment. Their time scale to trace the dynamics was limited in the millisecond range. On the contrary, solid pH2 matrices provide us enough long time of days and more to investigate slow dynamics such as tunneling5052 and nuclear spin relaxation.5861 Previously, infrared absorption spectra of HX (X = Cl,53 Br,54 CN55) in solid pH2 were reported. As far as we know, however, HF in solid pH2 matrix has not been studied in detail. These molecules have relatively large permanent electric dipole moments (HF 1.8 D, HCl 1.1 D, HBr 0.8 D, and HCN 3.0 D in gas phase)67 and easily form polymers and clusters with other species. Spectroscopy of the weakly bonded clusters trapped stably in solid pH2 is beneficial not only for understanding of the cluster structures and dynamics but also for studies on the nature of the quantum solid. Recently, several works on clusters in solid pH2 have been reported.5659 In this paper, we report absorption spectra of HF monomers and polymers (HF)n in solid pH2 and discuss the IR dynamics. The rotational constants of HF and DF, and the matrix shifts of the monomers and polymers were determined, indicating that these values are close to those in the gas phase. The relatively Received: August 3, 2011 Revised: November 2, 2011 Published: November 02, 2011 14254
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Figure 1. FTIR absorption spectra of HF (top panel) and DF (bottom panel) in solid pH2. Traces (a) and (c) show the spectra just after sample preparation and (b) and (d) the spectra 1 day after the preparation. Different horizontal scales are used in the top and bottom panels.
broad monomer line width we observed is discussed in relation to the phonon distribution in the matrix and the rotationtranslation coupling in a trapping site. The time dependence of the spectra indicates the possibility of migration of HF molecules. Also the spectroscopic data of other HF containing clusters in solid pH2 observed in this study are presented.
II. EXPERIMENTAL SECTION The pH2 crystals were prepared in a way similar to that described in previous papers.63,64 Briefly, normal hydrogen (nH2) was converted into pH2 with a purity better than 99.95% by passing the nH2 through a magnetic catalyst Fe(OH)O kept at about 14 K. Crystals were grown by spraying the sample gas on a BaF2 substrate cooled to 3.6 K in a closed cycle refrigerator cryostat. Mixing ratio of HF/pH2 was 10100 ppm. HF gas was generated inside a gas line by two ways: (1) heating KFHF up to about 200 °C; (2) reaction with F2 gas and residual water. Sample crystals made by the method 2 contained residual F2 while most of water was eliminated at a cold trap set in the gas line. For the DF experiment, D2O vapor was introduced into the gas line, and substantial HF was also contained in the sample because of residual H2O. Samples which contained about 0.1% of oH2, N2, O2, and CO2 were prepared for the study of the corresponding binary clusters with HF. IR absorption spectra were observed by an FTIR spectrometer (Nicholet 6700 FT-IR) with a liquid-N2-cooled MCT detector, a KBr beam splitter and a Glober IR light source with a resolution of 0.125 cm1. Time dependence of the spectra was recorded from just after deposition to after 12 days. III. RESULTS Figure 1 shows observed spectra of HF (top panel) and DF (bottom panel) containing samples. Traces (a) and (c) of Figure 1
were taken just after preparing samples, and traces (b) and (d) of Figure 1 were after 1 day. Many sharp lines between 2300 and 2400 cm1 are due to atmospheric CO2 absorption. The frequencies and assignment of the observed transitions were summarized in Table 1. Broad absorptions at 3970.8 and 3948.7 cm1 on (a) of the top panel in Figure 1 are very similar to the R(0) and “induced” Q pattern of HBr in solid pH2.54 The Q transition of hydrogen halides is generally forbidden in the gas phase, but has been observed in many matrix experiments2729,54,68 and explained as the transition “induced” by the matrix environment.6872 By comparison with the HF spectrum, broad absorption at 2908.1 cm1 was assigned to DF R(0) transition and 2898.0 cm1 was to the induced Q line. These assignments also agree with those in other matrices. The intensity ratio of R(0) to Q line of DF is quite different from that of HF, which will be discussed later. In Figure 1, many sharp lines were observed from 3800 to 3950 cm1 and some broad absorption lines below 3800 cm1. These lines were assigned to (HF)n polymers, and the complexes of HF with residual gases such as oH2, F2, N2, O2, CO2, and H2O as discussed below. It is obvious in Figure 1 (b) that intensities of some lines varied over time. After 1 day from the sample production, the monomer peaks were decreased and some additional broad absorption lines emerged below 3800 cm1. This is probably due to diffusion of monomer HF and growth of larger polymers as previously observed in rare gas matrices.2729 The diffusion effect was observed at 11 K in Ne matrix27 and above 16 K in Ar matrix.28,29 The fact that the diffusion can be observed at 3.6 K in solid pH2 may suggest the “softness” of solid pH2. Figure 2 shows the spectra of samples which contain some amount of other molecules. Trace (a) is spectrum of a sample without any additives. Traces (b)(g) correspond to the spectra of samples containing about 0.1% of oH2, O2, F2, N2, CO2, and 14255
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Table 1. Frequencies, Line Widths, and Assignments of Observed Absorption Lines of HF (DF)/pH2a
Figure 2. FTIR spectra of HF/pH2 sample with contaminates. (a) no intentional addition, (b)(g) correspond to sample with enriched oH2, O2, F2, N2, CO2, and H2O, respectively. Many sharp lines on traces (a) and (g) (>3575 cm1) are atmospheric water peaks.
a
Transition frequencies in the gas phase are also listed. For (HF)2 and (DF)2, frequencies of a few dominant peaks were listed. The asterisk and double asterisk indicate the values in Ne matrices and Ar matrices, respectively. The notation RQ1 (00) indicates transition to v = 1, J = 1, n = 0 from v = 0, J = 0, n = 0 and QR1(00) to v = 1, J = 0, n = 1 from v = 0, J = 0, n = 0.
H2O, respectively. The oH2, O2, and N2 were intentionally mixed with samples. The samples for not only trace (d) but also trace (c) of Figure 2 contained F2 because F2 gas was used as a HF source. For the H2O spectrum, we chose the spectrum which has the strong H2O monomer absorption near 3700 cm1 as a residual gas. In traces (b)(g), strong sharp lines appeared at frequencies specific to each contaminant and were assigned to the cluster of HF with each contaminant. The frequencies and assignments are summarized in the Table 1. Our assignments agree with those in rare gas matrices.2534 The order of frequency shift is H2O > CO2 > N2 > F2 > O2 > oH2, which indicates the strength of interaction with the matrix. H2O is the only molecule possessing a permanent electric dipole moment among them, which is the reason of the large matrix shift. The shifts of other clusters are almost in the order of polarizability of corresponding molecules (the order of F2 and O2 is inverted). The line width of these clusters is of the order of 0.1 cm1 except for the H2O cluster (about 2 cm1). The broad line of H2O clusters may be explained by rapid relaxations via the strong hydrogen bond between HF and H2O. N2, O2, and F2 clusters have only single sharp lines with no structure, while oH2, CO2 and H2O complexes have satellites. The absorption structures of the oH2 cluster will be discussed below. The structures of the CO2 and H2O clusters may be due to the difference of the geometric structures and/or the trapping sites in solid pH2. The
Figure 3. Spectra of HF/pH2 with different oH2 concentration. (a) ∼0.1%, (b) ∼1%, and (c) >1%. (c)0 Spectra of sample c after 1 day from sample preparation.
Table 2. Frequencies of Absorption Lines which Were Assigned to Clusters between HF and oH2 wavenumber (cm1)
assignment
3932.9
oH2-HF
3931.9
(oH2)2-HF
3930.9
(oH2)3-HF
3929.7
(oH2)4-HF
3928.8 3927.7
(oH2)5-HF (oH2)6-HF
3926.8
(oH2)7-HF
absorption intensities of the clusters increase through time due to the HF diffusion. Figure 3 shows spectra of samples with different oH2 concentrations near the monomer region. Trace (a) is a spectrum of the sample with the lowest concentration of about 0.01%, and traces (b) and (c) are of ∼1% and >1%, respectively. Trace (c0 ) is a spectrum of the concentrated sample after 1 day from the sample preparation. In trace (a), a single line at 3932.9 cm1 was observed, and a series of red-shifted sharp peaks was in trace (b). Furthershifted broad absorption emerged in trace (c). This behavior is similar to that observed on the spectra of CH3F-(oH2)n in solid pH2,58 where equally spaced, red-shifted sharp lines correspond 14256
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Figure 4. Spectra of samples with different HF concentration. The HF concentration becomes large from bottom to upper, as 0.1, 15, and 30 ppm.
to clusters with increasing n. In the same manner, we assigned the 3932 cm1 line to HF-oH2 and the multipeaks to HF-(oH2)n. In trace (b), it is possible to distinguish up to HF-(oH2)7. The transition frequencies of these lines were summarized in Table 2. The almost constant spacing of 1 cm1 supports our assignment. The broad absorption in trace (c) is attributable to larger clusters. In trace (c0 ), the absorption of the large clusters decreased while that of HF-oH2 and HF-(oH2)2 increased. This suggests that oH2 in the clusters was converted to pH2 by a magnetic field gradient around nearby oH2 and/or HF, as is the case in CH3F-(oH2)n.58 The R(0) monomer peak shows an additional blue tail with the oH2 concentration increased as seen in trace (b). The oH2 concentration dependence suggests the possibility to assign this tail to the rotation of HF interacting with nearby oH2. The assignment of HF polymers was done by (1) HF concentration dependence of spectra, (2) comparison with assignments in the gas phase5,9 and He nanodroplets,38 and (3) time dependence of absorption intensities. Figure 4 shows spectra of different HF concentration samples. The concentration increases from the bottom to the upper trace. Several sharp lines from 3820 to 3840 cm1 increase with a rise of HF concentration. Furthermore, there are some lines which emerge in the high concentration spectra around 3900 cm1. It is known that HF dimers have two vibrational modes at 3 μm region; free HF stretching (ν1) and hydrogen-bonded HF stretching (ν2).3,4 The band origin of ν1 and ν2 in gas phase is 3930.9 (3930.5) cm1 and 3868.3 (3867.4) cm1, respectively (the values in parentheses are for the counterpart of tunneling splitting)4 so that the two bunches of lines were assigned to the two vibrational modes of HF dimers: 3830 cm1 to the ν2 mode and 3900 cm1 to the ν1 mode. The matrix shift for each mode is 3040 cm1, which is in agreement with the matrix shift of R(0) transition of monomers. The intensity of the ν2 is more than 10 times larger than the ν1. This indicates the infrared intensity enhancement induced by hydrogen bonding, as is the case in other matrices.2729,36 The top panel of Figure 5 shows the absorption spectra of HF polymers in gas phase and He nanodroplets taken from reference 38. The numbers indicate the size of cyclic polymers which were predicted to be the most stable structures in calculations.1518,38 The “4 + 1” means a pentamer consisting of a tetramer ring and a hydrogen-bonded fifth molecule, which was observed only in
Figure 5. Panel (a) shows spectra of HF polymers in gas phase and He droplets taken from ref 38. Numbers show the size of the polymers. Panel (b) shows spectrum at the same region in solid pH2.
He droplets. The bottom panel shows the spectrum of the HF/pH2 sample taken after 1 day from sample preparation. The spectrum of the bottom panel is similar to the gas phase spectrum below 3400 cm1 and to the He droplets spectrum above 3400 cm1. From comparison with them, we concluded that absorption at 3705, 3427, 3270, 3216, and 3179 cm1 were assigned to 37 cyclic polymers, respectively. There are two lines at 3586 and 3468 cm1 corresponding to “4 + 1” polymers. The peak at 3370 cm1 can contain the absorption of “4 + 1” polymers, which may be overlapped with the broad absorption of larger clusters. It was difficult to distinguish the line corresponding to the 3174 cm1 He droplets line because of the overlap with larger (n > 7) clusters absorption. The “4 + 1” polymers have another weak vibrational mode at 3876.1 cm1 in He nanodroplets.38 However, we observed no corresponding line in pH2. This may be because of weak intensity of the mode. Matrix shifts of the 37 polymers in solid pH2 are 7, 18, 32, 24, and 34 cm1, respectively,9 increasing basically with a rise in polymer size. This is probably because the larger geometric size makes the interaction with the environment stronger. As described above, the absorption intensity of monomer HF decreases and that of larger polymers increases through time due to the diffusion of HF. Therefore, the time dependence of spectra is an additional confirmation of the assignment of (HF)n. The time dependence of absorption intensities of the assigned polymers is shown in Figure 6. The intensities of monomer and dimer absorption monotonically decrease and those of trimers and tetramers increase in several hours, and then the latter start to decrease. Large HF polymers (n > 4) increase on a longer time scale. These behaviors agree with our assignments and the assumption of growth of larger clusters by migration of HF. The migration rate depends on sample conditions. High density of HF or contaminants suppresses the migration while irradiation of IR light from the FTIR spectrometer enhances it. Difference in n distribution of polymers between He droplets and solid pH2 seems to be interesting. In He nanodroplets, larger cyclic polymers with n > 4 were not observed,38 while strong 14257
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Figure 6. Time dependence of normalized peak intensity of absorption of cyclic-(HF)n (n = 17). The largest intensity of each line was normalized to be unity.
absorption of the hexamer and larger polymers were observed in solid pH2, as with in the gas phase. The barrier for converting the cyclic tetramer and monomer (4 + 1) to the cyclic pentamer was estimated to be 100 cm115,38 so that it is difficult to form the cyclic pentamer in the He nanodroplets at 0.4 K and in the millisecond time scale; thus the “4 + 1” polymers were observed. In solid pH2, however, the cyclic pentermers and the larger polymers can be formed through tunneling reactions because of long interaction time in the solid. The line width of (HF)n (n > 2) transition is typically a few cm1 and, on the contrary, that of dimer is ∼0.2 cm1. Furthermore, the dimer transitions show complicated structures. These differences suggest that dynamics of the dimers is somehow different from both the monomers and the larger clusters. Absorption of the trimer also splits to two components. It may be due to the different geometrical structures. By comparing with spectra of HF/pH2, the assignment of absorption of DF/pH2 samples was partially done (traces (c) and (d) of Figure 1). Sharp lines at 2885.8 and 2885.2 were assigned to DF-oH2 and DF-(oH2)2. This assignment was also confirmed by the fact that intensities of these two line decrease through time due to the oH2 conversion described above. The lines at 2883.5, 2882.9, 2856.7, and 2845.3 cm1 were assigned to DF-O2, DF-F2, DF-N2, and DF-CO2, respectively. The lines around 2810 cm1 were assigned to DF dimers. The structure of absorption spectra in this region, however, is more complicated than that in HF dimers because both DF-DF and HF-DF dimers contribute to the spectra. The absorption of trimers, tetramers, pentamers, and hexamers was found to be at 2720, 2535, 2438, and 2404 cm1, respectively.
IV. DISCUSSIONS A. Spectral Structure and Rotational Constants of Monomers. In this study we observed only the R(0) transition for the
monomer absorption at 4 K because of the large rotational energy of HF except for the “induced Q” line. The line shape and its physical mechanism of hydrogen halides in rare gas matrices have been discussed in detail.6872 According to ref 72, there are two main origins of the Q lines. One is an interaction between the dopants, another is a rotation-translation coupling (RTC).6971 In the former case, the interaction with nearby, but not adjacent,
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Figure 7. FTIR spectra of HF and DF in solid pH2 between 4130 to 4195 cm1 with (a) HF 0.1 ppm (b) HF 30 ppm, (c) HF 15 ppm + DF 12 ppm.
dopants hinders the rotation and induces the Q lines. Intensity of this type of Q line should strongly depend on dopant concentration. Actually, they were observed in relatively concentrated samples which contained the dopants of ∼1% or more and showed the concentration dependence.72 However, the concentration of HF in our experiments was at most 100 ppm and the intensity ratio of the Q line with the R(0) did not depend on the concentration. Thus the Q line in our experiments is not originated from the interaction between dopants but from RTC, which probably causes a density-independent Q line. In the RTC picture, an additional eccentric motion of the dopant due to separation between the center-of-mass and the “center of interaction” is responsible for the Q lines. Heteronuclear molecules trapped in matrix rotate about not only the center-of-mass but also the “center of interaction” which is determined by the interaction between dopants and matrices. This introduces the coupling of the rotational and translation motion of the dopants, resulting in additional angular momentum coupled with the rotation of dopants (RTC). As a result, the eigenstates and eigenenergies of the system are designated by mainly two quantum numbers, J, n, where the J corresponds to the molecular rotation and the n corresponds to the oscillational motion of the dopant molecule around the center of interaction which couples to J via RTC. Friedmann and Kimel6971 suggested that only a state Jn = 00 is occupied at low temperature and a strong R(0) = RQ(00) transition from Jn = 00 to Jn = 10 and weaker “RTC” transitions such as Q R(00) from Jn = 00 to 01 should be observed. The designations mean ΔJΔn (Jinitial ninitial). The intensity of this type of the Q lines is thought to behave in the same way of that of the R(0) transition when sample concentration changes, as contrasted to the former case. Thus we concluded that observed Q line is assigned to the RTC transition Q R1(00) (v = 1r0, J = 0r0, n = 1r0). One of the important parameters that govern the RTC is ξ = ν/B, where ν is the frequency of the oscillation motion of the center-of-mass in the cell and B is the rotational constant.6971 Because the interactions of HF and DF with the matrix are expected to be approximately the same, the frequency ν is determined by only reciprocal square root of the mass. The rotational constant of DF is about a half of that of HF. As a result, ξ of DF is estimated to be about two times larger than that of HF. The strong QR1(00) of DF may be attributed to this large RTC. 14258
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Table 3. Frequencies and Assignments of Observed Absorption Lines in the Q1 Regiona wavenumber (cm1)
assignment
4189
Q 1(0)[pH2] + R Q(00)[HF]
4172 4166
Q 1(0)[pH2] + R Q(00)[DF] Q 1(0)[pH2] + Q R(00)[HF]
4162
Q 1(0)[pH2] + Q R(00)[DF]
4151
Q 1(0)[pH2] induced by HF(DF)
a
The upper four lines are assigned to the cooperative transition of the pH2 vibration and the HF rotation or translation. The notation R Q(00) indicates the transition to J = 1, n = 0 from J = 0, n = 0 and the Q R(00) to J = 0, n = 1 from J = 0, n = 0 in the ground vibrational state.
It is worth mentioning that the Q R1(00) do not lie at the vibrational origin but blue-shifted by kinetic energy of the eccentric motion and the rotational constants in solid pH2 could not be determined solely by RQ1(00) and Q R1(00). Anderson et al.53 have reported the cooperative pH2HCl transition in solid pH 2 , Q 1 (0)[pH 2 ] + R0 (0)[HCl], and Q 1(0)[pH2] + S0(0)[HCl], which are simultaneous transitions of pure vibration of pH2 and pure rotation of HCl. Figure 7 shows the absorption spectra of a dilute HF/pH2 sample (trace (a)), concentrated HF/pH2 sample (trace (b)), and HF+DF/pH2 sample (trace (c)) in the Q 1 region of H2. The transition frequencies and their assignment of observed lines in this region are summarized in Table 3. The rising edge from ∼4180 cm1 is the phonon band Q R of solid pH2. Weak absorption at 4153 cm1 in trace (a) is the well-known Q 1(0) transition of pH2 induced by neighbor oH2.4749 In trace (b), three broad absorption lines were observed at 4151, 4166, and 4189 cm1. In trace (c), additional lines were at 4162 and 4172 cm1. The absorption at 4151 cm1 was assigned to Q 1(0) of pH2 induced by nearby HF molecules from analogy with HCl.53 The difference between the Q 1(0)[HF-induced] and broad absorption at 4189 cm1 was 38 cm1. The rotational constant of HF in gas phase is 20.6 cm1,2 so that if the rotational constant in solid pH2 is similar to that in gas phase, the broad line can be assigned to Q 1(0)[pH2] + RQ(00)[HF]. Thus the effective rotational constant in the ground vibrational state of HF in solid pH2 was determined to be 19 cm1. This value is ∼90% of that in the gasphase value, which indicates that HF is nearly a free rotor in solid pH2. The 4172 cm1 line was similarly assigned to Q 1(0)[pH2] + RQ(00)[DF], and the rotational constant of DF was obtained to be 11 cm1, while the value in gas phase is 10.9 cm1. The absorption at 4166 cm1 in trace (b) and 4162 cm1 in trace (c) is assigned to Q 1(0)[pH2] + Q R(00) of HF and DF monomers, respectively, assuming that the energy difference between (J = 0, n = 1) and (J = 1, n = 0) in the ground state is similar to that in the vibrationally excited state. In fact, the energy difference in the ground state between Q 1(0)[pH2] + Q R(00) and the Q 1(0)[pH2] + RQ(00) (23 cm1 for HF, 10 cm1 for DF) agrees well with that in the excited state, i.e., the difference between Q R1(00) and RQ1(00) (22.1 cm1 for HF, 10.1 cm1 for DF). These assignments mean that there are RTC states also in the ground state and support our hypothesis that observed “Q” lines are blue-shifted from the origin and attributed to the RTC. It is found that the effective rotational constant in the excited state can be estimated from the HF-(oH2)n structures as follows. As described above, CH3F-(oH2)n show a series of almost equally spaced peaks next to the vibrational band origins of CH3F in solid pH2.58 A
Figure 8. Line width of R(0) in pH2 vs rotational constant (in gas phase) of HF (DF), HCl (DC1),53 HBr (DBr),54 and HCN.55
recent analysis of the rovibrational spectrum of CO in solid pH2 showed a peak assigned to the CO-oH2 clusters, which overlapped with the CO monomer band origin peaks.62 Therefore, the band origin of the monomer was estimated to be at the frequency corresponding to n = 0 assuming that frequency difference between HF-(oH2)n with adjacent n is constant. The frequency difference between adjacent n is about 1 cm1, and the transition frequency of HF-oH2 is 3932.9 cm1, so that the band origin was estimated to be 3934 cm1 and the rotational constant in the excited state was 18 cm1. The rotational constants of HF in gas phase are 20.6 and 19.8 cm1 in the ground state and v = 1 excited state,2 respectively. The ratio between the rotational constant in v = 0 and v = 1 in solid pH2 is 0.95 and agrees with that in gas phase. Similarly, the band origin and the rotational constant of DF were determined to be 2286 cm1 and 11 cm1, respectively. Thus the rotational constants of DF in v = 1 and v = 0 were determined to be the same and those in gas phase are also nearly identical with the values of 10.9 cm1 (v = 0) and 10.6 cm1(v = 1).73 It is curious that HF and HBr have the Q lines but HCl does not.53,54 It may be due to the different relation of parameters such as the rotational constants, the frequency of the translational motion etc., however, further quantitative studies are desired for precise understanding. B. Line Width of HF Monomers. The R(0) line width of HF is 4 cm1 and large compared with other hydrogen halides in solid pH2.53,54 It may be due to the large electric dipole moment of HF. However, the line width of HCN, whose electric dipole moment is larger than that of HF, in solid pH2, is about 0.1 cm155 so that it seems to be difficult to explain the large line width of HF with only the magnitude of the electric dipole moment. It was reported that the line width in He nanodroplets can be explained by rotational relaxation enhanced by phonons of the droplets.74 When a rotational energy is near the maximum of phonon density distribution of media, the line width becomes large because the rotational energy is easily transferred to the media and the relaxation is enhanced. Figure 8 shows line widths of R(0) vs rotational constants of hydrogen halides and HCN in solid pH2. The phonon density distribution of solid pH2 has the maximum at 40 cm1,75 which is accidentally coincident with the rotational energy of HF. As a result, rotational relaxation of HF is enhanced and the line width becomes large. This explanation agrees with the three observations as below. (1) The similarity of 14259
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The Journal of Physical Chemistry A the line width between the vibrational transition R Q1(00) and the cooperative rotational transition Q 1(0)[pH2]+R Q(00) indicates that the rotational relaxation is the dominant process of the relaxation. (2) The line width does not depend on the sample temperature from 3.5 to 4.9 K, which suggests that the line width is determined by the population relaxation because line width due to dephasing strongly depend on the sample temperature in solid pH2.65 (3) The line width of small clusters is narrow because clusters cannot rotate or have small rotational constants in solid pH2. It is clearly seen in Figure 8 that the line widths of HF, HBr, and their deuterized species are larger than those of HCl, DCl, and HCN. This probably indicates the RTC also contributes to the rapid relaxation because the spectra of the former show the induced Q line while those of the latter do not.5355,62 By assumption that the observed line width is a sum of the contributions of the phonon density effect and the RTC effect, the RTC effect part can be roughly estimate to be a deviation from the line width only with the phonon density effect indicated by a broken line in Figure 8 (large error is expected in HF). The RTC effect part in HF and HBr is about 1 cm1, while that of DF and DBr is 3.5 and 1.5 cm1, respectively, which qualitatively agrees with the large RTC and the consequential large intensities of Q line of the deuterized species.
V. CONCLUSIONS The absorption lines observed in FT-IR spectra of HF(DF)/ pH2 samples were assigned to HF and DF monomers, polymers and clusters with other species, oH2, O2, F2, N2, CO2, and H2O. HF and DF were found to migrate in solid pH2 even at 3.6 K and form the larger cyclic polymers through the tunneling reactions. The metastable polymers “4 + 1” with a tetramer ring and a hydrogen-bonded fifth molecule was also observed as in the case of the He nanodroplets experiments. Monomer Q transition was found to be attributed to the RTC effect. The rotational constants of the monomers in the ground vibrational state were determined from the cooperative pH2 + HF(DF) transitions. Small reduction of the rotational constants indicates that the monomers are nearly free rotors in solid pH2. The rotational constants in the exited vibrational state were also determined using the evenly spaced HF-(oH2)n clusters peaks. The line width of HF was found to be large compared to other hydrogen halides and qualitatively explained by the relation between the phonon density distribution of solid pH2 and the rotational energy of HF and the RTC. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This research was partially supported by Grant-in-Aid for Scientific Research on Innovative Areas Extreme Quantum World Opened up by Atoms (Grant Nos. 21104002 and 21104003) from the Ministry of Education, Culture, Sports, Science, and Technology. ’ REFERENCES (1) Hedderich, H. G.; Frum, C. I.; Engleman, R., Jr.; Bernath, P. F. Can. J. Chem. 1991, 69, 1659.
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