J. Phys. Chem. 1996, 100, 4413-4419
4413
Near-Infrared and Visible Spectroscopy of CH3D in Liquid Argon Solutions Victor M. Blunt, Ansgar Brock, and Carlos Manzanares I.* Department of Chemistry, Baylor UniVersity, Waco, Texas 76798 ReceiVed: September 29, 1995; In Final Form: December 22, 1995X
The near-infrared and visible spectra of CH3D in liquid argon solutions have been measured around 95 K. The fundamental and overtones, ∆V ) 1, 2, 3, 4, and 5 around the C-H stretch and ∆V ) 1, 2, and 3 of the C-D stretch, are reported. Combination bands between 3500 and 5000 cm-1 (∆V ) 3/2) and between 6500 and 7600 cm-1 (∆V ) 5/2) of the C-H stretching vibration were also measured. Measurements were made using a cryostat, a low-temperature cell, and a Fourier transform IR and near-IR spectrometer. Visible spectra were recorded with a photoacoustic spectrometer employing resonant continuous wave laser excitation and piezoelectric detection. Spectra in solutions are greatly simplified compared to the gas phase. This simplification is attributed to a narrowing of the rotational distribution at low temperatures and partial hindering of the rotational motion of sample molecules. Peak positions are systematically red-shifted with respect to the gas phase, and the magnitude of the shift increases with the vibrational quantum number. Numerous transitions unobserved in the gas phase carry oscillator strength in solution; thus, significant intensity redistribution occurs in the solution environment. The harmonic frequency and anharmonicity were obtained from a Birge-Sponer fit of the C-H vibrations, and the interbond coupling parameter was obtained from the observed splitting of the fundamental C-H stretch. These three parameters were used with a harmonically coupled anharmonic oscillator model to calculate frequencies and assign absorption bands.
Introduction The infrared, near-IR, and visible absorption spectra of CH3D in the gas phase have been investigated in several laboratories. The most recent studies correspond to the fifth overtone (∆V ) 6) of the C-H stretching region.1,2 Ginsburg and Barker3 obtained the IR bands and compared them with the calculated frequencies of Dennison and Johnston.4 A reinvestigation of the spectrum was done by Wilmshurst and Bernstein.5 The C-D rotation-vibration band was studied by Boyd and Thompson.6 Absolute intensities of the infrared bands were calculated by Hiller and Stralley.7 The rotational structure of the Raman bands was obtained by Richardson et al.8 Some absorptions in the near-infrared and visible regions have been studied in connection to the presence of CH3D in the atmosphere of the outer planets (Saturn, Uranus, Neptune).9 The rotationvibration spectrum of the 9201 cm-1 band was studied by Childs and Jahn.10,11 The rotationally resolved absorption spectra in the regions around 11 931, 10 405, and 9389 cm-1 have been investigated by Danehy et al.12 The ∆V ) 6 overtone spectrum of CH3D at room temperature shows a very congested spectrum where C-H overtone and combination bands overlap. Our approach to simplify vibrational absorption bands is to study the overtone spectra of the molecule in diluted argon solutions at 90 K. In this way, the contributions from rotational transitions and hot bands are reduced because of the low temperature and the hindering of the rotation in the presence of the solvent. Although the information about rotational transitions is lost, some vibrational bands hidden under the congested room temperature absorption can be observed. Liquid argon shows very weak interactions with the host molecule, so the frequency shifts of the absorption bands are small compared with the pure sample in the gas phase. Also, the integrated intensities of the fundamental bands of the dilute argon solution are within 15% of the gas phase values; the small difference is due to the dielectric constant of the X
Abstract published in AdVance ACS Abstracts, February 15, 1996.
0022-3654/96/20100-4413$12.00/0
solvent. Because of the simplification of the absorption bands using this technique, it is easier to obtain their position. Vibrational assignments can be done by comparison with calculated results using theoretical models. Another important aspect of the studies is related to the understanding of the constituents of the surface and atmosphere of Titan, the largest satellite of Saturn.13 A joint US-European (Cassini-Huygens) mission to explore Saturn is expected to reach Titan in the year 2004. An atmospheric probe (Huygens) will be released to descend to the surface of Titan, whose temperature is around 95 K. This probe will collect visible and near-IR spectra of the atmosphere and the surface. Liquid methane, nitrogen, and argon are important components of the surface of Titan. Our experiments are designed to obtain the IR, near-IR, and visible spectra of CH3D in liquid argon solutions at 95 K, which could provide laboratory data to compare with the information gathered by the Cassini-Huygens mission. Experimental Section The experimental technique has been described in detail.14 Briefly, the output beam of a continuous wave argon ion laser operating in the all lines mode is used to pump a dye laser. The power of the pump beam is 5 W. An acoustooptic modulator system (modulator and driver) is used to modulate the dye laser beam as a square wave. Wavelength tuning of the dye laser (1 cm-1 bandwidth) is accomplished with a birefringent filter driven by a stepper motor. The stepper motor is controlled with a microcomputer. The modulated output of the dye laser is directed along the length of a cryostat and a low-temperature photoacoustic cell. The piezoelectric transducer is coupled into a high-impedance preamplifier. The signal from the combination piezoelectric detector and preamplifier is fed to a lock-in amplifier. The modulated dye laser beam passes through the cell and is detected with a fast silicon photodiode and processed with another lock-in amplifier. The reference signal for both lock-in amplifiers is obtained from a © 1996 American Chemical Society
4414 J. Phys. Chem., Vol. 100, No. 11, 1996
Figure 1. Absorption spectrum of the fundamental (∆V ) 1) C-H stretch of CH3D in the gas phase at 298 K. Pressure is 91 Torr. The cell path length is 4.8 cm.
square wave signal generator which also supplies the modulation signal to the driver input of the acoustooptic modulator. Normalization of the photoacoustic signal is achieved by dividing the output voltages of both lock-in amplifiers. A microcomputer controls the dye laser wavelength scan and digitizes and stores the normalized signal as a function of the wavelength for further analysis. The cryostat and low-temperature cells have been described.14 Methane-d1 (99.5%) and argon (99.99%) were purchased from MSD Isotopes and Matheson, respectively, and used without further purification. The photoacoustic spectrum of a 10% solution of CH3D in liquid argon was recorded at 93 K. The laser dye pyridine 2 was used to cover the region of interest (13 000-14 500 cm-1). The dye laser output was modulated at 130 kHz. The fundamental C-H stretching vibration of CH3D in liquid argon solution (0.036%) at 96 K and in the gas-phase (pressure ) 91 Torr) were recorded with a 1.9 cm path length cell using a FT-IR spectrophotometer. The resolution was 1 cm-1 in the range 2500-4000 cm-1. The near-IR absorbance spectra were recorded at 94 K in liquid argon solution (0.16-0.31%) in the range 4000-10 000 cm-1 with a resolution of 4 cm-1. The Fourier transform spectrophotometer in the near-IR operates with a PbSe detector, a tungsten light source, and a quartz beam splitter. The spectra in liquid argon solutions were obtained with the sample cell inside a cryostat. A 10 cm path length cell was used for transitions above 4000 cm-1. Results Spectra were deconvoluted with Lorentzian bands in order to extract the pure local mode bands. Each plot consists of an experimental curve and calculated curves obtained by summing individual Lorentzian bands. The spectra of CH3D in the gas phase at 300 K and in liquid argon solution at 97 K, around the C-H stretching fundamental (∆V ) 1), are shown in Figures 1 and 2. The first overtone (∆V ) 2) of the C-D stretching vibration and combination bands between 4000 and 4600 cm-1 (∆V ) 3/2) are shown in Figure 3. The spectrum around the first overtone (∆V ) 2) of the C-H stretching vibration in liquid argon solution is shown in Figure 4. The second overtone (∆V ) 3) of the C-D stretching vibration is shown in Figure 5. Combination bands between 6600 and 7600 cm-1 (∆V ) 5/2) are shown in Figure 6. The second overtone (∆V ) 3) of the
Blunt et al.
Figure 2. Absorption spectrum of the fundamental (∆V ) 1) C-H stretch of CH3D in liquid argon solution at 96 K. The concentration is 3.6 × 10-4 mole fraction. The cell path length is 1.9 cm.
Figure 3. Absorption spectrum of CH3D around first overtone (∆V ) 2) of the C-D stretching vibration and around the C-H combination band region (∆V ) 3/2) between 4000 and 4600 cm-1 in liquid argon solution at 94 K. The concentration is 1.6 × 10-3 mole fraction. The cell path length is 10 cm.
C-H vibration is shown in Figure 7. The fourth harmonic (∆V ) 5) of the C-H vibration, recorded with the photoacoustic spectrometer, is shown in Figure 8. Since the observed spectra show overlapping bands, the peaks were separated into individual bands by computer deconvolution. The generally adopted procedure for extracting peak positions and areas from the spectra is by fitting them with line shape functions possessing adjustable parameters. The spectra were deconvoluted using the Lorentzian function
y ) A[1/[(1 + (ν - ν0)/b]2)]
(1)
This function contains the peak height (A), the full width at half-maximum (b), the frequency (ν), and the band origin (ν0). The band shape equation allows the reproduction of spectral
CH3D in Liquid Argon Solutions
Figure 4. Absorption spectrum around the first C-H overtone (∆V ) 2) of CH3D in liquid argon solution at 94 K. The concentration is 3.1 × 10-3 mole fraction. The cell path length is 10 cm.
Figure 5. Absorption spectrum around the second C-D overtone (∆V ) 3) of CH3D in liquid argon solution at 94 K. The concentration is 3.1 × 10-3 mole fraction. The cell path length is 10 cm.
features. Several runs with varying initial conditions were performed to make sure that the optimization was not excessively biased by the set of initial parameters (A, b, and ν0). We chose not to interrupt the fitting routine to adjust parameters manually during the fit. The fitting routine uses a modified nonlinear least-squares optimization algorithm.15 Discussion Frequencies of fundamental vibrational transitions of CH3D have been studied by several groups.3,5,7,8 Methane-d1 belongs to the point group C3V and has six fundamental vibrations: three totally symmetric (A1) and three doubly degenerate (E) modes, all of which are infrared-active.16 The frequencies and symmetries of the various fundamental modes are listed in Table 1. The local mode parameters, harmonic frequency (ω), and anharmonicity (ωx) were obtained from a fit of C-H (D) overtones to the Birge-Sponer equation:
J. Phys. Chem., Vol. 100, No. 11, 1996 4415
Figure 6. Absorption spectrum of CH3D around the C-H combination band region between 6500 and 7700 cm-1 (∆V ) 5/2) in liquid argon solution at 94 K. The concentration is 3.1 × 10-3 mole fraction. The cell path length is 10 cm.
Figure 7. Absorption spectrum around the second C-H overtone (∆V ) 3) of CH3D in liquid argon solution at 94 K. The concentration is 3.1 × 10-3 mole fraction. The cell path length is 10 cm.
∆E/V ) ω - (V + 1)ωx
(2)
The local mode parameters for the C-H bond of CH3D in argon solution are ω(C-H) ) 3108.3 cm-1 and ωx(C-H) ) 60.7 cm-1. For C-D, the local mode parameters are ω(C-D) ) 2260.8 cm-1 and ωx(C-D) ) 30.5 cm-1. Both C-H and C-D transitions gave a linear fit with the fundamental C-H (D) stretch included. Interbond coupling splits the fundamental C-H vibration into symmetric (|100, A1〉) and antisymmetric (|100, E〉) states. The interbond coupling parameter (λ) is determined from experimental peak positions and the following equations:
ν(|100, E) ) ω - 2ωx - λ
(3)
ν(|100, A1) ) ω - 2ωx + 2λ
(4)
For the ∆V ) 2 set of transitions, the symmetric states are given
4416 J. Phys. Chem., Vol. 100, No. 11, 1996
Blunt et al.
Figure 8. Laser photoacoustic spectrum around the fourth C-H overtone (∆V ) 5) of CH3D in liquid argon solution at 93 K. The concentration is 1.0 × 10-1 mole fraction.
TABLE 1: Fundamental Vibrational Frequencies of CH3D assignt
sym
mode
freq (cm-1)
ν1 ν2 ν3 ν4 ν5 ν6
A1 A1 A1 E E E
C-H s-stretch C-D stretch C-H3 s-bend C-H a-stretch C-H3 a-bend C-D bend
2973 2200 1300 3017 1471 1155
by the equations
|200; A1〉 |110; A1〉
[
2ω - 6ωx 2(2)1/2λ 2ω - 4ωx + 2λ 2(2)1/2λ
]
(5)
Eigenvalues 1 and 2 are obtained by diagonalizing the matrix above, and the corresponding wave functions are Ψ(2) ) b|110, A1〉 - a|200, A1〉, where a and b are components of the eigenvectors. If the basis functions are weakly coupled, i.e., a . b or vice versa, then Ψ(1) ≈ |110, A1〉 and Ψ(2) ≈ |200, A1〉. Off-Diagonal Coupling. The interbond coupling parameter λ can be separated into two components: a kinetic energy coupling term (γ) and a potential energy coupling term (φ). The interbond coupling parameter is given by the following equation17
λ ) (γ - φ)ω
(6)
where ω is the familiar harmonic frequency. The value of λ can be calculated from the following equation if the HCH bond angle θ is known17
γ ) 1/2 cos θ(1 + MC/MH)-1
(7)
where MC and MH are the carbon and hydrogen atomic masses. Using the bond angle of methane and eqs 6 and 7, the values for γω and φω were determined to be 39.9 and 23.9 cm-1, respectively. These values imply that kinetic energy coupling is more significant, but the symmetric stretch is shifted to higher energy by Fermi resonance. This has the effect of making λ larger and φω smaller. The HCAO parameters, harmonic frequency (ω ) 3108.3 cm-1), anharmonicity (ωx ) 60.7 cm-1), and interbond coupling
parameter (λ ) -16 cm-1), were substituted into HCAO matrices derived by Halonen and Child for the C3V point group.18 Matrices were diagonalized on a VAX mainframe computer. The experimental and calculated frequencies are listed in Table 2, along with the full width at half-maximum (fwhm) and absolute difference between gas phase and solution peaks. The C-D oscillator states are denoted by |n〉. Assignment of Overtone Spectral Features. ∆V ) 1. The gas-phase spectrum shown in Figure 1 is heavily congested by rotational transitions and consists of three main spectral features around 3017, 2973, and 2914 cm-1. Rotational structure is not fully resolved at this resolution, but R-branch structure can be identified in the region 3040-3120 cm-1. In solution, the spectrum of Figure 2 shows a very significant reduction in rotational congestion because fewer rotational levels are populated at low temperature. The absence of rotational structure allows unambiguous identification of band heads. The most prominent peak is located at 3013 cm-1 and is assigned to |100; E〉, while the shoulder on the low-energy side at 2965 cm-1 is assigned to |100; A1〉. These two peaks are interpreted on the basis of the HCAO model as arising from interbond coupling of equivalent C-H bonds. The high-energy side of the strongest fundamental band shows the remains of the R branch (around 3047 cm-1). Some controversy exists over the assignment of |100; E〉, this is thought to be in Fermi resonance with the first overtone of ν5.5 Wilmshurst and Bernstein reported the unperturbed position of |100; E〉 as 2945 cm-1 while peaks at 2914 and 2973 cm-1 were associated with the Fermi dyad. The peak at 2904 cm-1 was assigned to 2ν5. The sapphire windows have a cutoff around 2000 cm-1; hence, the C-D fundamental was not observed. ∆V ) 3/2. Seven bands are observed in the spectrum of Figure 3, most of which are very intense. The first harmonic of the C-D stretch is located at 4338 cm-1. It is relatively weak and was assigned with the aid of calculated gas-phase frequencies.18 Most bands are combinations of the one quantum each of C-H stretch and a low-frequency mode. ∆V ) 2. A single band is expected at this level of excitation if the most rigid assumptions of the local mode theory hold, but taking interbond coupling into consideration, four bands are expected. A total of 16 bands are observed in the spectrum of Figure 4. Clearly, such a large number of bands indicates that the normal mode picture is more appropriate for this level. The oscillator strength for this polyad is distributed among many states, contrary to the predictions of the local mode theory. HCAO calculations predict that the first C-H harmonic is split into |200; E〉 and |200; A1〉, but these states are too close to be resolved. The |200; A1〉 state is dominated by other transitions. This argument is supported by the intensity distribution of the fundamental. Local mode states corresponding to simultaneous excitation of two oscillators are also observed, and peaks at 5972 and 6016 cm-1 were assigned to |110; A1〉 and |110; E〉, respectively. The |110; E〉 is by far the most intense at this level. The region from 6175 to 6575 cm-1 is shown in Figure 5. The band at 6418 cm-1 is the second overtone of the C-D vibration (13〉). The remainder of the bands in this region were assigned to combinations of one quantum of the fundamental C-H vibration and two quanta of low-frequency vibrations or one quantum of C-D vibration. ∆V ) 5/2. The spectrum is shown in Figure 6. The band at 7281 cm-1 is the most intense and can be assigned to either a combination of a C-D stretch or C-H stretch and a bending mode. The latter was preferred because C-H overtones are in general more intense than C-D overtones. The band at 6997
CH3D in Liquid Argon Solutions
J. Phys. Chem., Vol. 100, No. 11, 1996 4417
TABLE 2: Calculated and Observed (cm-1) Vibrational Frequencies, Line Widths (fwhm), and Frequency Shifts (∆ν) of CH3D in Liquid Ar V
assignt
1 1 1 3/ 2 3/ 2 3 /2 3/ 2 3/ 2 3/ 2 3 /2 3/ 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
HCAOa (liq Ar)
2ν5 |100; A1〉 |100; E〉 2ν3 + ν5 |100; A1〉 + ν6 |100; E〉 + ν6
2955 3003 (4071) (4110) (4158)
|100; E〉 + ν3 |2〉 (C-D) |100; A1〉 + ν5 |100; E〉 + ν5 |1〉 + 2ν6
(4303) 4338 (4426) (4474) (4510)
|100; A1〉 + |1〉 |100; E〉 + |1〉
(5155) (5203)
|100; E〉 + 2ν6
(5313)
|2〉 + ν6 |100; A1〉 + 2ν3 |100; A1〉 + ν6 + ν5 |100; E〉 + 2ν3 |100; A1〉 + ν3 + ν5 |100; E〉 + ν3 + ν5 |200; A1〉 |200; E〉 |100; A1〉 + 2ν5 |100; A1〉 |100; E〉
(5493) (5555) (5581) (5603) (5726) (5774) 5833 5849 (5897) 5961 5993
|2〉 + 2ν6
obs (in liq Ar)
2914 2973 3017
}
|3〉 (C-D)
2 5/ 2
obsb (gas)
6430 (6648)
∆ν
fwhm
V
2904 2965 3013 4053 4110 4159 4205 4305 4338 4430 4465 4494 5096 5120 5157 5211 5254 5302 5357 5453 5531 5581 5612 5758 5790
10 8 4
18 28 26 28 22 38 80 26 41 18 28 30 28 20 28 34 76 24 36 38 68 26 48 28 46
5/ 2 5/ 2 5/ 2 5/ 2 5/ 2 5 /2 5/ 2 5/ 2 5 /2 5/ 2
5848
8
5895 5972 6016 6223 6284 6329 6418 6450 6659
8 2
8 6
12
40 62 24 52 26 20 40 38 78 58
3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 5 5 5 5
HCAOa (liq Ar)
assignt
|200; A1〉 + ν6 |200; E〉 + ν6
(6988) (7004)
|200; E〉 + ν3 |100; E〉 + ν3 |2〉 + |100; E〉 |100; A1〉 + 2ν6 |100; E〉 + ν5 |200; E〉 + 2ν3 or |4〉(C-D) |300; A1〉 |300; E〉 |210; A1〉 0.745 |210; 2E〉 0.65 |210; 1E〉 0.738 |210; 1E〉 + 0.667 |210; 2E〉 |111; A1〉
(7149) (7293) (7341) (7432) (7464) 8448 8433 8588 8590 8782
} }
} }
obsb (gas)
8617
obs (in liq Ar)
∆ν
fwhm
6758 6907 6970 6997 7051 7143 7281 7362 7417 7460
42 24 50 60 60 44 54 70 24 40
8406
32
8593
24
86
8777
14
8815
8823
44
8870
8885
30
8977 9021
|500; A1〉 |500; E〉 |400〉 + 2ν3 |410; A1〉 |410; E〉 |410; E〉 |320; A1〉 |320; E〉 |320; E〉 |311; A1〉 |311; E〉 |221; E〉 |221; E〉
}
13613 13714 (13812) 14172 14184 14212 14398 14440 14462 14537 14573 14686 14767
13753
13723 13814
42 30
94 116
a
The values in parentheses are the sum of frequencies calculated from the HCAO model and gas-phase frequencies. b The observed gas-phase frequencies for ∆V ) 1 were taken from ref 5; for ∆V ) 3 (C-D) from ref 18; for ∆V ) 3 (C-H) from refs 10 and 11; and for ∆V ) 5 from ref 9.
cm-1 is the combination of the |200; E〉 and the fundamental ν6. Other assignments are listed in Table 2. ∆V ) 3. The spectrum is shown in Figure 7. Only five transitions are observed, bringing this level closer in line with the predictions of the local mode theory. The HCAO model predicts six bands. The intensity distribution is different compared to the first harmonic because for this level the pure local mode state carries most of the oscillator strength. In the gas phase the state |300〉 is very congested.10 In solution, the pure local mode is located at 8593 cm-1. The calculated values for |300; A1〉 and |300; E〉 are very close in energy and are both assigned to this transition. The band in solution at 8406 cm-1 on the low-energy side of |300〉, and previously unreported, is assigned to |200; E〉 + 2ν3. It could also be assigned to the third C-D overtone (14〉). The bands on the high-energy side of |300〉 are |210〉 states and have not been reported in the gas phase. In the gas phase, a band with clearly visible P- and R-branch structure was observed10,11 at 9021 cm-1. ∆V ) 5. The only previous investigation of this level was by Bardwell and Herzberg.9 They were unable to resolve the peaks in this region. The fourth harmonic of CH3D was recorded with the photoacoustic spectrometer. More details are seen in the solution spectrum where the fourth overtone consists of three closely spaced overlapping bands. The two at higher intensity were assigned to the pure overtone |500〉, located at 13 723 cm-1, and a combination band |400〉 + 2ν3 at 13 814 cm-1.
The third overtone was not studied because the Fourier transform spectrophotometer cannot detect such a weak absorption at the concentrations used. It was equally difficult to study this transition with the photoacoustic spectrometer because nearIR dyes have short tuning ranges. Herzberg and Bardwell reported several bands at this level.9 Perry and Zewail recorded the gas-phase photoacoustic spectrum of CH3D (∆V ) 6).1,2 Rotational congestion prevented any spectral features from being assigned. One would expect more details to be revealed in the solution spectrum, but the laser power of our experimental setup is not enough to detect the weak transitions. Band Strengths. The band strength of a transition from the ground to a vibrational state i, in units of atm-1 cm-2, is given by19
()
I0 1 a(ν˜ ) dν˜ a(ν˜ ) ) ln (8) ∫ pL I where a(ν˜ ) is the absorbance, p is the pressure in atmospheres at 300 K, and L is the path length. Bulanin20 reported that integrated intensities of dilute cryosolutions, in the absence of intermolecular interactions, are within 15% of gas-phase values, the small difference being attributed to the dielectric constant of the solvent. The relationship between gas-phase and solution intensities is given by20 Gi )
Gsol ) Ggas(n2 + 2)2/9n
(9)
where n is the refractive index of the pure liquid argon. The
4418 J. Phys. Chem., Vol. 100, No. 11, 1996
Blunt et al.
Figure 9. (a) Shift in peak position of CH3D in liquid argon versus vibrational quantum number V. (b) Line width (fwhm) versus vibrational quantum number V.
intensity of the C-H stretch (asymmetric and symmetric) in solution is 56.54 cm-2 atm-1. The gas-phase value measured in this work is 42.6 cm-2 atm-1. The ratio of Gsol to Ggas is 1.33 compared to 1.11 obtained from eq 9. Knudtson and Weitz19 reported significant deviations from eq 7 for the fundamental and overtone of HCl in liquid xenon solution and suggested that intermolecular interaction between HCl and Xe affects the dipole moment. There is no intensity data for gasphase overtones of CH3D for comparison with solutions, but the close agreement between observed and calculated values for the ratio Gsol/Ggas indicates that interactions between CH3D and Ar are weak. Frequency Shifts. The shift in the C-H peak position of CH3D as a function of the vibrational quantum number is shown in Figure 9a. Compared to the gas-phase spectra, bands are systematically shifted to lower energy (red shift) in liquid argon solution, in agreement with the work of Bulanin on IR spectra of molecules in solutions of argon, nitrogen, and oxygen.20 This shift has been attributed to the formation of loose cages at low temperatures. The frequency shift increases with quantum number. Bulanin reported that the shifts of overtone and combination bands correlate well with the sum of fundamentals involved. In Figure 9a the fundamental transition is represented by two points, the symmetric and asymmetric C-H stretch. The shift of the symmetric C-H stretch is twice that of the asymmetric C-H stretch. A semiempirical formula relating the shift in vibrational frequency of a dipole to the dielectric constant of the medium is given by21
∆ν/ν ) C(D - 1)/(2D + 1)
(10)
where C is a constant and D is the dielectric constant of the solvent. The constant C depends on the first and second derivatives of the dipole moment and is usually obtained by fitting data to eq 10. This equation reproduces shifts for the fundamental and overtone of HCl in various solvents21 using C ) 0.06. Methane-d1 has not been studied in other solvents. Using eq 10 with the dielectric constant of liquid argon (D ) 1.53), the measured shifts in the C-H fundamental and overtones in liquid argon, and the corresponding gas-phase
frequencies (see Table 2), the calculated value of C is approximately 0.02. Overtone Line Widths. Line widths of the C-H stretching vibration of CH3D increase with vibrational quantum number as shown in Figure 9b. Two values of line width are shown for V ) 1 representing the symmetric and asymmetric C-H stretch. The deviation for V ) 3 is not known, but it is probably due to the presence of a hidden combination band in the main |300〉 transition. The reciprocal of the full width at halfmaximum is proportional to the lifetime τ of an excited state. Rotational transitions, combination bands, hot bands, and difference bands are all inhomogeneous line broadening mechanisms. Experiments reported here were performed at low temperatures. Therefore, thermal excitation of even the lowest vibrational mode is very unlikely; about 1 in 108 molecules populates the lowest vibrational state at 90 K. Thus, contributions from hot and difference bands can be ruled out. For the C-H fundamental, contributions from combination bands and part of the rotational structure (R branch) can be separated from the vibrational line shape by deconvolution; what remains is due to the Q branch. For higher levels, only combination bands can be removed. Inhomogeneous broadening does not explain the increase in fwhm with V, since overtone states sample the same ground state rotational distribution as the fundamental, and this is fixed for a given temperature. Time correlation functions of vibrational band profiles in liquids provide information about dynamic processes at the molecular level, particularly molecular reorientation and vibrational relaxation.22-24 If rotational relaxation is the main broadening mechanism present, it is possible to relate the Fourier transform of the spectral band to an autocorrelation function of a vector in the molecular fixed frame. It has been shown by Gordon23 that, for a vibrational band broadened mainly by rotational relaxation, the second spectral moment of the band [M(2)] is a constant at a given temperature. This constant reflects classical kinetic energy effects and is independent of the reorientation process. According to the theory, the fourth spectral moment of the band [M(4)] may be used to obtain an estimate of the mean-squared torque exerted on the molecule. The investigation of vibrational relaxation in liquids is usually done by measuring the isotropic Raman scattering or by timeresolved laser spectroscopy.25 Overtone bands are weak and are not easily observable using Raman techniques. In order to interpret infrared bands, a zero-order approximation of the time correlation function makes the rotational and vibrational contributions to the relaxation independent, and in some cases (dilute solutions) it is possible to write the following equation:26
ΦIR ) φv(t) φR(t)
(11)
where ΦIR is the time correlation function obtained from the infrared band, and φv(t) and φR(t) are the vibrational and rotational time correlation functions, respectively. In this approximation, the width of the absorption band is a sum of the contributions from rotational reorientation and the vibrational relaxation. Vibrational relaxation in liquids can be attributed to two processes: (a) The first is vibrational relaxation due to intra- or intermolecular energy transfer. This relaxation process is important in studies of pure liquids and is usually neglected in the case of very diluted solutions. (b) Dephasing is the vibrational frequency modulation due to variable environment of the molecule.27 This process is very important in the case of diluted solutions. The vibrational frequency in solution is dependent on the intermolecular potential to which the molecule is subjected. Two limiting cases are considered in vibrational dephasing: (1) The first case is a slow modulation limit where
CH3D in Liquid Argon Solutions the variation of the intermolecular potential is sufficiently slow to let the molecule react to each value. In this case, the observed band profile is Gaussian and the line width is large. (2) The second is a fast modulation limit where the variation of the potential is too rapid to let the molecule follow it. In this case, the observed band profile is Lorentzian and the line width is small. Considering the line width of overtones, the slow modulation limit predicts a linear dependence with the vibrational quantum number (V). The fast modulation limit predicts a quadratic (V2) dependence with the vibrational quantum number.22 In a previous study,28 the dynamics of relaxation of fundamental bands of CH3D in different cryogenic solvents were interpreted in terms of pure rotational relaxation. The present study considers the C-H fundamental and overtones of CH3D in liquid argon. The vibrational line width of succesive harmonics is linear as a function of the vibrational quantum number (V). This result agrees with a dephasing mechanism in the slow modulation limit. The only problem is that the band profiles are not Gaussian. It is possible that the overtone bands are a combination of contributions from rotational relaxation and dephasing, with the dephasing mechanism becoming more important as the vibrational quantum number increases. We are presently obtaining the experimental time correlation functions and calculating the rotational time correlation functions of CH3D to determine its contribution to the fundamental and overtone relaxations. Comparison will be made with overtone studies that we have completed for CD3H and CH4 in argon solutions. Conclusion The spectra of C-H and C-D transitions of CH3D in liquid argon solutions have been investigated using Fourier transform IR and near-IR techniques, as well as visible absorption with acoustic detection. A narrowing of the rotational distribution occurs due to the low temperatures employed and the hindering of the rotation in the presence of the solvent. This allows the detection of small bands that are hidden in the congested room temperature spectra. Deconvolution of the bands with a Lorentzian function allowed the determination of peak positions and line widths of the individual transitions. The local mode parameters obtained for C-H and C-D transitions in liquid
J. Phys. Chem., Vol. 100, No. 11, 1996 4419 argon solution and the harmonically coupled anharmonic oscillator model were used to assign most of the bands found between 2500 and 13 000 cm-1. Rotational relaxation and dephasing are the main mechanisms to explain the fundamental and overtone line widths, respectively. Acknowledgment. This work was supported by the Robert A. Welch Foundation under Grant AA-1173. References and Notes (1) Perry, J. W.; Moll, D. J.; Kuppermann, A.; Zewail, A. H. J. Chem. Phys. 1985, 82, 1195. (2) Voth, G. A.; Marcus, R. A.; Zewail, A. H. J. Chem. Phys. 1984, 81, 5494. (3) Ginsburg, N.; Barker, E. F. J. Chem. Phys. 1935, 3, 668. (4) Dennison, D. M.; Johnston, M. Phys. ReV. 1935, 47, 93. (5) Wilmshurst, J. K.; Bernstein, H. J. Can. J. Chem. 1957, 35, 226. (6) Boyd, D. R. J.; Thompson, H. W. Proc. R. Soc. London 1953, A216, 143. (7) Hiller, R. E.; Straley, J. W. J. Mol. Spectrosc. 1960, 5, 24. (8) Richardson, E. H.; Brodersen, S.; Krause, L.; Welsh, H. L. J. Mol. Spectrosc. 1962, 8, 406. (9) Bardwell, J.; Herzberg, G. Astrophys. J. 1953, 117, 462. (10) Childs, W. H. J.; Jahn, H. A. Nature 1936, 138, 285. (11) Childs, W. H. J.; Jahn, H. A. Proc. R. Soc. London 1939, A169, 428. (12) Danehy, R. G.; Lutz, B. L.; Owen, T.; Scattergood, T. W.; Goetz, W. Astrophys. J. 1977, 213, L139. (13) Lunine, J. I. Chem. Eng. News 1995, 73, 40. (14) Manzanares, I. C.; Mina-Camilde, N.; Brock, A.; Peng, J.; Blunt, V. M. ReV. Sci. Instrum. 1995, 66, 2644. (15) Marquardt, D. J. Soc. Ind. Appl. Math. 1963, 11, 431. Levenberg, K. Q. Appl. Math. 1944, 2, 164. (16) Shimanouchi, T. Tables of Molecular Vibrational Frequencies, Consolidated Vol. 1; Natl. Bur. Stand. 1972, 39, 47. (17) Henry, B. R.; Tarr, A. W.; Mortensen, O. S.; Murphy, W. F.; Compton, D. A. C. J. Chem. Phys. 1983, 79, 2583. (18) Halonen, L.; Child, M. S. J. Chem. Phys. 1983, 79, 4355. (19) Knudtson, J. T.; Weitz, E. J. Chem. Phys. 1985, 83, 927. (20) Bulanin, M. O. J. Mol. Struct. 1973, 19, 59. (21) West, W.; Edwards, R. T. J. Chem. Phys. 1937, 5, 14. (22) Bratos, S.; Pick, R. M. Vibrational Spectroscopy of Molecular Liquids and Solids; Plenum: New York, 1980. (23) Gordon, R. G. AdV. Magn. Reson. 1968, 3, 1. (24) Oxtoby, D. W. Annu. ReV. Phys. Chem. 1981, 32, 77. (25) Laubereau, A.; Kaiser, W. ReV. Mod. Phys. 1978, 50, 607. (26) Oxtoby, D. W. J. Chem. Phys. 1978, 68, 5528. (27) Oxtoby, D. W. AdV. Chem. Phys. 1979, 40, 1. (28) Marsault, J. P.; Marsault-Herail, F.; Levi, G. Mol. Phys. 1977, 33, 735.
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