Vibrational overtone spectroscopy of CH2D2 in liquid argon solutions

Chemical Physics ELSEVIER

Chemical Physics 209 (1996) 79-90

Vibrational overtone spectroscopy of CHRD 2 in liquid argon solutions Victor M. Blunt, Nairmen Mina-Camilde, David L. Cedefio, Carlos Manzanares I * Department of Chemistry, Baylor University, Waco, TX 76798, USA

Received 28 September 1995

Abstract

The spectra of the fundamental and overtones of the C - H (v = 1-5) and C - D (Av = 1, 2, 3) stretches of CH2D 2 have been measured in liquid argon solutions at temperatures between 94 and 101 K. Absorption in the visible was obtained with a low temperature cell and a resonant continuous wave laser technique with acoustic detection. Absorptions in the IR and near-IR were observed with a Fourier transform spectrophotometer. To interpret the experimental results, overtone transitions are described in terms of the local mode model. The harmonically coupled anharmonic oscillator (HCAO) model was used to determine the overtone energy levels and assign the absorption bands to vibrational transitions. The linewidths of the fundamental and overtone transitions are discussed in terms of rotational relaxation for the fundamental bands and vibrational relaxation in the form of dephasing for the overtones.

1. Introduction

Recently, supersonic expansion methods have been used to study overtone transitions at low temperatures with the resulting simplification of the absorption bands [1-7]. We have developed a different method to study overtone transitions at low temperatures which involves the study of the sample in cryogenic liquid solutions at temperatures around 90 K [8-12]. The solubility of the sample in a cryogenic liquid (Ar or N 2) is usually in the order of parts per million. Because of this, the solute molecules behave as essentially isolated, surrounded by a solvent that interacts only weakly with the solute. The fundamental and overtone spectra of the molecules in cryogenic solutions show a decrease in

* Corresponding author.

band overlap due to elimination of hot bands and a reduction in the rotational envelope. This is due to the low temperatures and the hindering of the rotation in the presence of the solvent. It is possible under these conditions to obtain more accurate vibrational terms than from the gas phase spectra of molecules with unresolved rotational structure. Cryogenic solvents show 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. In this paper the C - H fundamental and overtone spectra of C H 2 D 2 are studied in Ar solution around 90 K. There is very little information on the near-IR and visible spectroscopy of methane-d 2 in the literature. Perry et al. [13] published the only existing report on the fifth overtone of CD 2H 2. The fundamental vibrations of methane-d 2 in the gas phase have been investigated by Bernstein and Wilmshurst

0301-0104/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0301-0104(96)00118-8

80

V.M, Blunt et a l . / Chemical Physics 209 (1996) 79-90

[14] at low resolution. Hiller and Straley [15] studied the intensities of the fundamental bands. Rotational resolution studies of some fundamental, first overtone, and combination bands between 2000 and 3100 cm-1 have been reported [16,17]. In addition, rotationally resolved spectra of lower frequency fundamental bands have been analyzed [18-23]. A study of C - H overtone transitions of CH2D 2 in the near-IR and visible is interesting because it allows testing of local mode theories that include coupling between C - H modes. A previous local mode calculation of CH2X 2 (X = CI, Br, I) molecules has been reported [24] at room temperature.

Methane-d2 (0.017% in Ar)

0.50

~6

0.40

o= ~<

0.30

0.20

.o3

x)4+~9

0.10

L.

2. Experimental 0.oo

The experimental technique and low temperature cryostat have been described in detail previously [10]. In order to obtain the acoustic resonant frequency of the system, the acoustic signal as a function of the modulation frequency of the laser was obtained for a 10% solution of CDEH 2 in liquid argon at 108 K. The dye laser was tuned to the Av = 5 absorption maximum at 13758 cm -1 and the modulation frequency was varied. Measurements were done with 115 mW of dye laser power. The strongest resonance was located at 114 kHz. The position of the strongest resonance frequency was found to be inversely proportional to temperature. This is in agreement with the fact that the speed of sound in liquid argon increases when the temperature decreases [25]. Photoacoustic spectrum. Methane-d 2 (99.5%) and argon (99.99%) were purchased from MSD Isotopes and Matheson, respectively, and used without further purification. The photoacoustic spectrum of the C - H absorption around Av = 5 was measured. The laser dye pyridine 2 was used to cover the region of interest (13000 to 14500 c m - t ) . The dye laser output was modulated at 114 kHz. The spectrum of a 10% solution of CH2D 2 in liquid argon was recorded at three different temperatures: 108, 101 and 96 K. The peak position did not change with temperature over this small temperature range. FTIR and near-IR spectra. The spectra in liquid argon solutions were obtained with the sample cell inside a cryostat. Path length cells of 10, 4.8, and 1.9

I

900

1360

I

1820

I

I

I

2280

I

I

2740

3200

Wavenumber(cm-i) Fig. 1. Fundamental spectrum of CD2H 2 in liquid argon at 96 K. The concentration is 1.7X 10 -4 mole fraction. The cell path length is 1.9 cm.

cm were used for transitions above and below 5000 cm -1, respectively. The fundamental bands of CD2H 2 in liquid argon solution (0.017%) at 96 K and in the gas phase (pressure = 91 Torr) at 298 K, were recorded with a resolution of 1 cm-~ in the range 500 to 3500 cm -~. The NIR absorbance spectra of CD2H 2 in liquid argon solutions (0.18 to 0.39% mole fractions) were recorded in the range 3500 to 10000 cm -~ at 94 K. The near-IR absorbance spectra were recorded with a resolution of 4 cm- t. The Fourier transform spectrophotometer in the near-IR operates with a PbSe detector, a tungsten light source, and a quartz beam splitter.

3. R e s u l t s

The fundamental spectrum of CD2H 2 in liquid argon from 900 to 3200 cm-~ is shown in Fig. 1. The gas phase spectrum at 298 K, around the C - H stretching fundamental (Av = 1) is shown in Fig. 2. The spectrum in liquid argon solution at 96 K, around the C - H stretching fundamental (Av = I) is shown in Fig. 3. The Av = 3 / 2 manifold is shown in

V.M. Blunt et al./ ChemicalPhysics 209 (1996) 79-90

81

Methane-d2 (0.017 % in Ar)

Methane-d2 (gas) 300 K 1.00

0.60

I10)_

0.53 0.80 o c

0.45

I10)+ ot"

0.60

¢1 .,0

o xl < 0.40

0.38

0.30

.D

<( 0.23 0.15

0.20 ....

0.08 0.00 2800

. . . . . 2880

i

2960

3040

i

3120

i

0.00

i

,

2870

3200

,

2932

Fig. 4 and the first C - D overtone (Av = 2) is observed in this region as well. The region around the first C - H overtone (Av = 2) is shown in Fig. 5. Combination bands between 6700 and 7600 c m (Av = 5 / 2 ) are shown in Fig. 6. The second harmonic (Av = 3) of the C - H stretching vibration is shown in Fig. 7. The photoacoustic spectrum of the fourth C - H overtone (Av = 5) is shown in Fig. 8. The region around the second C - D overtone (Av = 3) is shown in Fig. 9. Spectra were deconvoluted with Lorentzian bands in order to extract the pure local mode bands. Each deconvoluted plot consists of an experimental curve at the top of the figure and calculated curves at the bottom, which are obtained by summing up individual Lorentzian bands. 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: 1 y=A (1) l+[(V-Vo)/b] 2) This function contains the peak height (A), the full width at half maximum (b), the frequency (u),

,

2994

3056

3118

3180

Wavenumber (cm-1)

Wavenumber (cm-1)

Fig. 2. Absorption spectrum of the fundamental (Av = 1) C-H stretch of CH2D2 in the gas phase at 298 K. Pressure is 91 Torr. The cell path length is 4.8 cm.

,

Fig. 3. Absorption spectrum of the fundamental (Av = 1) C - H su'etch of CH2D 2 in liquid argon solution at 96 K. The concentration is 1.7X 10-4 mole fraction. The cell path length is 1.9 cm. Experimental band (top). Dcconvoluted band (bottom). Methane-d2 (0.18 % in Ar)

I!0)- + x)4

0.40 0.35

0.30 O ¢:° 0.25

I10)++~ 3 I

0,20 <

0.15

0.t0 0.05 0.00 3700

3880

4060

4240

4420

4600

Wavenumber (crn-1)

Fig. 4. Absorption spectrum of CH2D2 around first overtone (Av = 2) of the C-D stxgtching vibration and around the C-H combination band region (Av = 3/2) between 3700 and 5000 cm-1 in liquid argon solution at 94 K. The concentration is 1.8× 10-3 mole fraction. The cell path length is 4.8 cm. Experimental band (top). Deconvolutedband (bottom).

82

V.M. Blunt et a l . / Chemical Physics 209 (1996) 79-90

Methane-d 2 (0.39 % in Ar)

0.14

Methane-d 2 (0.39 % in Ar)

I10)- +2~7

0.040

13o)±

0.12

to ¢.

£

0.030

Ill)

0.10

120)±

0,08

~ 0.020

o co 0.06 <

.13 <

..O

0.04

0.010

0.02 0.00 4800

i

I

5120

i

i

5440

i

i

i

5760

i

0.000 8400

i

6080

6400

8520

Wavenumber (cm-1)

8640

8760

, 9000

8880

Wavenumber(cm-1)

Fig. 5. Absorption spectrum around the first C - H overtone (Av = 2) of CH2D 2 in liquid argon solution at 94 K. The concentration is 3.9x 10 -3 mole fraction. The cell path length is 10 cm. Experimental band (top). Deconvolutext band (bottom).

Fig. 7. Absorption spectrum around the second C - H overtone (Av = 3) of CH2D 2 in liquid argon solution at 94 K. The concentration is 3.9× l0 -3 mole fraction. The cell path length is l0 cm. Experimental band (top). Deconvoluted band (bottom).

Methane-d 2 (0.39 % in Ar) Methane-d 2 (10 % in Ar)

120)++~3

0.024

150)+

9.0

12°)++ ~5

8.0 0.018

=¢- 7.0 D <~ 6.0

Q)

to ¢. ¢1 0#) 0.012 ¢1 <

~

5.0

g •-

4.0

ffl

o_ 3.0

0.006

<

2.0 1.0

0.000

i

5700

6880

7060

7240

i

7420

i

i

7600

Wavenumber (cm-1) Fig. 6. Absorption spectrum of CH2D 2 around the C - H combination band region between 6700 and 7600 c m - l (Av = 5 / 2 ) in liquid argon solution at 94 K. The concentration is 3.9x 10 -3 mole fraction. The cell path length is 10 cm. Experimental band (top). Deconvoluted band (bottom).

0.0 13300

,

13480

13660

13840

14020

,

14200

Wavenumber (cm "1) Fig. 8. Laser photoacoustic spectrum around the fourth C - H overtone (Av = 5) of CH2D 2 in liquid argon solution at 101 K. The concentration is 1.0× 10-J mole fraction. Experimental band (top). Dcconvoluted band (bottom).

V.M. Blunt et aL/ Chemical Physics 209 (1996) 79-90

Methane-d 2 (0.39 % in Ar)

molecule has nine fundamental vibrational modes [26]: four o f type A t , two B l, two B2, and one o f A 2. Fig. 1 presents a spectrum o f CHED 2 in liquid argon that shows all the infrared active bands. All modes are IR active except v 5. The band maxima and symmetries of the fundamental modes are listed in Table 1, which also presents the measured fundamental frequencies o f CHED 2 in liquid argon, as well as the integrated intensities to be discussed in the next section. Table 2 presents the measured frequencies of the pure C - H local mode transitions with Av = 1, 2, 3, and 5 and their integrated intensities. The notation for assignments, as well as calculated frequencies shown in Table 2, will be discussed next. The local mode parameters, harmonic frequency (to) and anharmonicity ( t o x ) were obtained from a fit o f the energy o f the fundamental C - H vibration (average of v I and v 6) and overtones to the B i r g e - S p o n e r equation:

120i±+ 2~4 /~ 130)'±

0.000

o.oo8 0.007

~ 0.006 0.006

=0 0.004 < o.oo3

0.002 0.001 0.000

6100

.

.

6240

.

.

.

6380

.

.

6520

.

6660

83

6800

Wavenumber (crn'1) Fig. 9. Absorption spectrum around the second C - D overtone

(Av = 3) of C H 2 D 2 in liquid argon solution at 94 K. The concentration is 3.9X 10-3 mole fraction. The cell path length is 10 cm. Experimental band (top). Deconvoluted band (bottom).

and the band origin (u0). The band shape equation allows the reproduction o f spectral features.

4. Discussion Dideuterated methane is an asymmetric top molecule, and belongs to the point group C2v. The

AEIv = to- (v + 1)tog.

(2)

The local mode parameters for the C - H bond of CH3D in argon solution are: t o ( C - H ) = 3110 + 3 c m - l and to x ( C - H ) -- 59.9 + 0.7 c m - 1. A harmonically coupled anharmonic oscillator ( H C A O ) calculation was done using the three parameters (to, tox, and h ) and the matrices listed in Ref. [24]. The parameter h represents the interbond coupling. The local mode theory states that C - H and C - D vibrations are represented by Inl,n 2 ) and [nl,n2 Y, respectively, where the subscripts 1 and 2 refer to equivalent bonds. The + subscript refers to symmetric and anti-symmetric vibrational states. Interbond coupling

Table 1 Fundamental vibrational frequencies of methane-d2 in the gas phase and in liquid argon; integrated intensities (Gi) in liquid argon Assignment

Symmetry

Mode

Frequency/gas

Frequency/liq. Ar

G~(atm-a cm-2)

ut .o2 .o3 .o4 lo5 v6 u7 us 1°9

AI AI AI At

C-H 2 s-stretch C - D 2 s-stretch C H 2 s-bend CD2 s-bend C - H 2 twist C - H 2 a-stretch C - H 2 rock C - D 2 a-stretch C-H 2 wag

2974 2202 1436 1033 1329 3013 1090 2234 1234

2971 2198 1432 1030 3007 1082 2229 1233

9.21 4.01 6.37 5.53 29.64 15.92 4.64 13.92

A2

B~ Bt B2 BE

Gas phase frequencies from Ref. [26]. The mode v5 is infrared inactive.

84

V.M. Blunt et al. / Chemical Physics 209 (1996) 79-90

splits the fundamental C - H vibration into symmetric (110)+) and anti-symmetric ( l l 0 ) - ) states. The interbond coupling parameter h = - 1 9 + 1 cm -1 was determined from experimental peak positions and the following equations: ~,(110)-) = t o - 2 t o g - A

(3)

~,(110)+) = t o - 2tox + A

(4)

For the Av = 2 polyad, the symmetric states are not given by simple equations but by an energy matrix: '20)+ [ 2 t o - 6 t o x Ill) -2X

-2A ] 2 t o - 4tox "

(5)

Eigenvalues e 1_and e 2 are obtained by diagonalizing the matrix shown above, and the corresponding wavefunctions are ~ ( g l ) = a l l l ) + bl20)+ and g'(e 2) = b i l l ) - a120)+, where a and b are components of the eigenvectors. If the basis functions are weakly coupled, i.e. a >> b then ~ ( e 1) ~-Ill) and

q'(e2) = 120)+.

4.1. Assignment of C-H spectral features Av ---- 1. As shown in Fig. 2, the Q branch of the asymmetric stretch dominates the gas phase room temperature spectrum of the C - H fundamental, while the symmetric state, which is much less intense and

rotationally congested, is on the low frequency side of the Q branch. To the left of the band there is a dense thicket of rotational lines (from 2960 to 2975 cm- I ). The rotational structure is perturbed by Coriolis resonances, and has been thoroughly analyzed by Deroche and Guelachvili [22]. In the solution spectrum shown in Fig. 3 (2870 to 3180 c m - l ) , the rotational lines disappear and two bands are observed; the more intense one was assigned to I10)_ and the weaker one to I10)+. The I10)- band contour is slightly asymmetric on the high energy side; this represents a wash-out R branch structure. Av = 3 / 2 . Combination bands are observed in this region shown in Fig. 4 (3700-4600 c m - t ) . The assignments for the two main bands are shown in Fig. 4 and the rest of the assignments are presented in Table 3. The region can be divided into two groups of transitions. The low frequency group shows a main band assigned as I10)- + ~4, with two shoulders. On the low energy side of the main band is the combination I10)+ + v 4, and on the high energy side, the combination I10)- + v 7. Three bands are located to the high frequency end of Fig. 4. The first is possibly the first overtone of the C - D stretch and will be discussed in the next section, it can also be the combination I10) _ + ~5. The remaining bands are combinations of the symmetric (ll0)+) or the asymmetric ([10)_) stretching vibration and ~3.

Table 2 Calculated and experimental vibrational frequencies, full width at half maximum (fwhm), and integrated intensities (Gi) of pure C - H local mode bands of methane-d 2 in liquid Ar v

Assignment

HCAO (liq. Ar)

Obs. (gas)

1 1

I10)+ II0)-

2971 3009

2974 3013

2

120)+ 120)-

3 4 5

fwhm

G i (arm- l c m - 2 )

2971 3007

21 34

9.21 29.64

5850 5861

5864

38

4.2 x 10 -2

130) +

8607

130)140)+.

8606

8605

58

5.9 x 10 -2

140)_/

11238 13756

90

150)+. 150)_/

13749

Obs. (in liq. Ar)

V.M. Blunt et a l . / Chemical Physics 209 (1996) 79-90

85

Table 3 Calculated and experimental vibrational frequencies, full width at half maximum (fwhm), and integrated intensities (G i) of methane-d 2 in liquid Ar Obs. b (gas)

Obs. (in liq. At)

fwhm

G i (arm- i) c m - z

2202 2234 2974 3013

2198 229 2917 3007 4000 4037 4090

20 27 21 34 16 38 50

4.01 4.64 9.21 29.64 0.24 2.27 0.93

4338 4366

4332

62

0.32

4407 (4445) (5037) (5075) (5189)

4419 4468 5037 5097 5198

30 44 20 24 36

0.70 0.22 1.8 × 10- 3 7.1 × 10 -3 0.14

110)++°4+°9 I10)'- + I10)-

5238 5243

5247

36

8.2 X 10 -2

2 2 2 2 2

110)-+`07 +`09 110) + + 209 110)-+`05 +`09 I10) + + 2"05 I10) - + 2"03

(5333) (5439) (5572) (5629) (5829)

5311 5435 5552 5627 5811

44 66 44 36 40

2.6× 4.3 × 1.6 × 8.9 X 6.5X

2

120) + 120) -

5850 5861

5864

38

4.2 × 10 -2

2

111)

5991

C-D C-D C-D C-D 5/2 5/2 5/2 5/2 5/2 5/2 5/2 5/2 3

120)'± + 2v 4 ]30)'+ 120)'± + 2v7 121Y±

(6568)

120) + + `04 120) - + `07 120) + + `09

(6883) (6951) (7084)

120) + + `05 120) + + lo3

(7179) (7286)

]20) _ + `03 + `09

8531

5991 6333 6402 6454 6514 6569 6822 6881 6933 7072 7120 7183 7273 7384 8558

38 66 60 54 40 73 25 44 79 42 26 66 58 46 18

8.6 X 10 -2 4.7 × 10 -3 1.5 X 10- 2 7.2' 10- 3 7.5 X 10- 3 5.4 X 10- 3 1.0 × 10- 3 1.1 X 10 -2 1.6 × 10- 2 1.2 × 10- 2 1.9X 10 -3 3.8 X 10 -2 3.0 X 10 -2 1.0× 10 -2 1.2 X 10 -3

3

130> + 130>-

8607 8606

8605

58

5.9 x 10 -2

3 3 3 5

111> + 2`05 121)121) + 140) + u 4 + `05

(8649) 8818 8893 13600

8661 8840 8887 13590

84 34 42 78

7.0 X 10- 3 2.1 X 10 -3 1.7 x 10 -3 0.13 c

13749

13756

90

0.83 c

v

Assignment

C-D

I10)'.

C-D

II0)'_

1 1 3/2 3/2 3/2

I10)+ I10) 110)++`04 I10)- + `04 110) - + `07

2917 3009 (4004) (4042) (4099)

110)- + v5 120)'+ 3/2 3/2 2 2 2

110) + + 110) - + I1O) + + I10) _ + I10) - +

2

5 5 5 5 5

150) +

15o)_ 141)141) + 132) 132) +

}

`03 `03 2`04 2`0,, 2`07

HCAO a (liq. At)

(6432) 6456 (6546)

14221 14226 14429 14538

a The values in bracket are the sum of frequencies calculated from the HCAO model and gas-phase frequencies. b Observed gas-phase frequencies for Av = 1 were taken from Ref. [26]. c Relative intensities.

10 -2 10 -2 10- 2 10- 3 10 -2

86

V.M. Blunt et al./ ChemicalPhysics 209 (1996) 79-90

Av = 2. Fig. 5 (4800-6400 cm-1) shows eleven bands are observed at this level of excitation. The pure overtone 120)+ is predicted to be split into a doublet with a separation of 10 c m - 1 . The doublet is n o t observed probably because of the weak intensity of the 120)+ band, which could be hidden below the combination band I 1 0 ) - + 2~ 3. The 120) ± is shown at 5864 cm- 1 in Fig. 5. The doublet is clearly visible in the spectra of the halogen analogs [24]. The local mode-local mode combination state l11), which is shown in Fig. 5, is observed at 5991 cm -1. This corresponds to a transition in which one quantum of energy is deposited in each C - H bond. Most bands are combinations of the fundamental plus two quanta of bending or rocking motion. The strongest one in this region is the 1 1 0 ) _ + 2 u 7 at 5198 cm -1. The band at 5247 cm-1 deserves special attention; it can be assigned to 1 1 0 ) + + ~ 4 + ~ 9 or I10)'-+110)- . The latter state corresponds to the simultaneous excitation of a C - D and a C - H vibration. Av = 5 / 2 . The strongest transitions with assignments are shown in Fig. 6 (6700-7600 cm-1). Most assigned transitions are combinations of 120)_ or 120) + and a quantum of bending vibration. The two possible assignments for the band at 7072 cm-1 are: ]20)+ + ~9 or [11) + UT. Table 3 shows the complete s e t of assignments and their frequencies. Av = 3. This region is shown in Fig. 7 (8400-9000 cm- 1). Local mode states 130)+ and 130)- are predicted to be less than a wavenumber apart. The most intense peak (8605 cm- i ) is assigned the unresolved doublet. Even at this level, local mode-local mode combination states 121)+ and 121)_ are still split by off-diagonal coupling terms, which is the same trend observed for dihalomethanes [24]. In addition to the three local mode states, two local mode-normal mode combinations are present on either side of 130) ±. The 120)- + ~3 + u9 state is on the low energy side and the I l l ) + 2 u 5 state is on the high energy side of the 130) ~, respectively. A u = 5. Two bands are observed in Fig. 8 (13300-14200 cm -1) at this level. The peak at 13756 cm- ~ is assigned to the pure local mode state 150) ±. The transition to the left of 150) ± is assigned as 140)±+ u4 +us. Perry et al. used laser photoacoustic spectroscopy to investigate the fifth harmonic of methane-d 2 in the gas phase [13]. Two bands can be seen in the Av = 6 gas phase spectrum

but the lack of information about transitions in the near-IR prevented the authors from making other assignments except for the 160) ± band. 4.2. Assignment of C - D spectral features

In general, C - D overtones are weaker than C - H overtones, therefore identification is difficult. This is further compounded if transitions are located in regions where strong local mode-normal mode combination of C - H bands occur. Consequently, the assignments given below are tentative. Based on our results with CH 4 [29], CH3D [30], and CHD 3 [8], it is assumed that the region shown in Fig. 9 (61006800 cm -1) corresponds to C - D transitions. Liquid CH 4 does not show any transitions in the range from 6100 to 6700 cm -1, but CHD 3 and CH3D show their second C - D overtones in this region. Local mode parameters for CH2D 2 a r e n o t known, but the harmonic frequency (~o(C-D)) could be estimated assuming a value for the anhannonicity constant approximately equal to the values obtained for CHD 3 and CH3D ( t o x ( C - D ) - - 31 c m - l ) . Using Eq. (2) with v = 1, the average energy of the symmetric and asymmetric states (ll0)'±) at 2214 cm -1, and the anharmonicity constant, it is possible to estimate the parameter o~(C-D) -- 2276 c m - 1. With these param-

100

80 P

g 8o ,,

40 2O

0

h

I

,

I

~

I

l

2

3

4

5

6

Vibrational Quantum Number (v) Fig. 10. Line width (fwhm) of CH2D 2 in liquid argon versus vibrational quantum number v.

V.M. Blunt et al. / Chemical Physics 209 (1996) 79-90

eters we predict the energies of the states 120)'+ and 130)'± at 4366 and 6456 c m - 1, respectively. A v = 2. The first C - D overtone is expected somewhere in the Av = 3 / 2 C - H region. A peak observed at 4332 cm-L is the closest to the first C - D overtone (120)'±). This transition can also be assigned as I 1 0 ) - + v 5. The latter is probably more accurate in view of the difference between intensities of the C - H and C - D stretching vibrations. Av = 3. The second C - D harmonic of CD2H 2 is expected somewhere around 6456 cm -1. The transition at 6454 cm- ~ is tentatively assigned to 1300)'±. Other bands are probably combination bands involving the state 120)'+ and the overtones 2u 4 and 2~ 7. The band at 6569 c m - l could be assigned to the state 121)' ±.

4.3. Band strengths The band strength of a transition from the ground to a vibrational state i, in units of atm-~ cm -2 is given by [27] G i "=

- ~ f a ( ~ ) d~, a(~) = In

,

(6)

where (P) is the absorbance, p is the pressure in atmospheres at 300 K, and L is the path length. The integrated intensities (G i) of the deconvoluted bands according to Eq. (6) are presented in Table 1 for all the fundamental bands. Table 2 shows the integrated intensities for the pure C - H fundamental and overtones. It can be observed that the integrated intensities associated with the states ]20)± and ]30)± are very similar in magnitude. The reason is because for Av = 2, the transition from local mode to normal mode is occurring and several combination states borrow intensity from the pure local mode. The closest states to 120) ± are ]10)_ + 21o3 and [11). The most intense transition in the Av = 2 region (see Fig. 5) corresponds to the state I10)_+ 2u 7 with an integrated intensity Gi = 0.14. Table 3 shows the integrated intensities in liquid argon for all the bands measured between 2900 and 9000 cm -j. The C - H absorbance for the region around Av = 5 is not known and only the relative intensities are reported for this region. Bulanin [28] reported that integrated intensities of dilute cryo-solutions, in the absence of

87

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 by [28] (;soI = Gga~( n2 + 2)Z/9n,

(7)

where n = 1.222 is the refractive index of the pure liquid argon at 90 K. The total integrated intensity of the C - H fundamental in gas-phase and in liquid argon solution is 28.55 and 38.72 cm -2 atm -1, respectively. The ratio (;soI to Ggas is 1.36 compared to 1.11 from Eq. (7). The difference with respect to the expected value could be due to the instrumental resolution (1 cm -~) used to obtain the gas phase band in our experiment, giving an integrated intensity below the true value. It can also be due to interactions between CH2D 2 and the solvent Ar. We measured the ratio (Gsol/Ggas) for several different initial pressures and the result was always similar to the one reported. We also found that the ratio (Gsol/Ggas) is larger for CH 4 in At.

4.4. Linewidths and dynamics of relaxation A plot of fwhm as a function of vibrational quantum number v is shown in Fig. 10. Line widths increase linearly with v. For Av = 1, the widths of [10)+ and [10)_ are shown. Information about the dynamics of relaxation in dilute liquid solutions is usually obtained from infrared and raman spectroscopies, or by time resolved picosecond (or femtosecond) laser spectroscopy [31]. The time correlation function of an infrared band contains information about molecular reorientation and vibrational relaxation [32-34]. If the approximation is made that the rotational and vibrational contributions to the time correlation function are independent of each other, it is possible to write the total time correlation function of an infrared band as the product of contributions due to rotational reorientation and vibrational relaxation. In this approximation, the width of the absorption band is a sum of the rotational and vibrational contributions [32]. If rotational reorientation is the main broadening mechanism present, the Fourier transform of the

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V.M. Blunt et al. / Chemical Physics 209 (1996) 79-90

spectral band is related to the second and fourth spectral moments. The second spectral moment depends on the moment of inertia of the molecule and represents free rotation of the molecule in the solvent. The fourth spectral moment may be used to obtain an estimate of the mean squared torque exerted on the molecule [33]. If vibrational relaxation is dominant, it can be attributed to two processes: (1) 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. (2) Dephasing, which is the frequency modulation due to a variable environment of the molecule [34]. This process is very important in the case of diluted solutions. In the dephasing mechanism, the vibrational frequency in solution is dependent on the intermolecular potential to which the molecule is subjected. Two limiting cases are considered: (1) a slow modulation limit where 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 linewidth is large; (2) a fast modulation limit where the variation of the potential is too rapid to let the molecule follow it. In this case, the observed profile is Lorentzian and the linewidth is small. Considering the linewidth of overtones, the slow modulation limit predicts Gaussian bands and a linear dependence with the vibrational quantum number (v). The fast modulation limit predicts Lorentzian bands and a quadratic (v 2) dependence with the vibrational quantum number. Studies of the dynamics of rotational relaxation in solution have been done for fundamental bands of linear molecules, spherical, and symmetric rotors [32]. For asymmetric rotors, a few studies of rotational relaxation in solution have been published due to the difficulties interpreting the results. This is the case of a study of CH2Br 2 in solution [35]. In our study of CH2D 2 there is an apparent linear dependence of the linewidth with vibrational quantum number which indicates the possibility of a dephasing mechanism in the slow modulation limit. At the same time all the observed bands are Lorentzian, indicating a dephasing mechanism in the fast modulation limit. It is also possible that we have not measured enough overtones to show a quadratic increase in the linewidth. We are presently calculat-

ing the time correlation functions of the fundamental and overtone bands of CH2D 2 and using rotational and dephasing models to explain the relaxation of the molecule. Initial results indicate that the relaxation of the fundamental bands is mainly due to rotational relaxation while the increase in overtone linewidth can be attributed to vibrational relaxation through the dephasing mechanism.

4.5. C H 2 D 2 and other methanes The spectra of liquid phase CH2D 2 around Ao = 5 can now be compared with the solution spectra obtained for CDaH, CHAD, and C H 4. The CDaH spectrum in solution [8], shows two bands that are assigned to the pure [5) and 14) + 2v 5 in agreement with the gas phase result obtained by Perry et al. [13]. The spectrum obtained for CHED 2 shown in Fig. 8, presents two bands similar to the CDaH spectrum. The main transition is slightly asymmetrical on the high energy side but it is not clear that there is a hidden transition on this side of the band. The CHaD and CH 4 spectra in gas phase and in solution are more congested compared to CD2H 2 and CDaH around the same region [13]. In solution, both CH 4 and C H 3 D [29,30], show at Ao =-5, a central band with two clear shoulders on both sides, which are local mode-normal mode combination bands. The fundamental band of CH2D 2 shows the separation between the C - H symmetric and antisymmetric bands. This result is used to determine the interbond coupling parameter k = - 19 + 1 cm -~ , which is in very good agreement with the gas phase result [13] of - 18.2 cm -j . The interbond coupling parameters that were obtained for CHAD, and CH 4 were - 1 6 and - 25 cm - I , respectively. The C - H harmonic frequencies and anharmonicities of CH2D 2 in the gas phase are 3110 and - 5 8 cm-1, respectively, and for CDaH 3106 and - 5 7 . 9 cm -1, respectively [13]. These results are in excellent agreement with the liquid argon solution results. The harmonic frequencies and anharmonicities of CH2D 2 in liquid argon are 3110 and - 5 9 . 9 cm -~, respectively, and for CDaH in liquid argon, 3104 and - 5 8 . 8 cm -1, respectively [30].

V.M. Blunt et a l . / Chemical Physics 209 (1996) 79-90

The results obtained for the linewidths of C H 2 D 2 , CH3D and CHD 3 seem to indicate linear dependence of the increase in iinewidth with vibrational quantum number. At Av = 5 the linewidth is around 90 cm - l for all the molecules except CH 4 which is 104 cm-1. The relaxation times are essentially the same for all the molecules at Av = 1 and for CH 4, the linewidth increases faster compared to the deuterated methanes from Av = 2-6. A better comparison of linewidths will be done in a future publication where the time correlation functions of the fundamental and overtone bands of the four molecules will be presented and rotational and dephasing models will be used to explain the relaxation of these molecules.

89

References

CH4,

5. Conclusion The spectra of C - H and C - D transitions of CH2D 2 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 argon solution and the anharmonically coupled anharmonic oscillator (HCAO) model were used to assign most of the bands found between 2500 and 13000 cm -1. Overtone linewidths are probably due to a dephasing mechanism, while fundamental linewidths are due to rotational relaxation.

Acknowledgements This work was supported by the Robert A. Welch Foundation under Grant No. AA-1173.

[1] M. Hipler and M. Quack, Chem. Phys. Letters 231 (1994) 75. [2] R.D.F. Settle and T.R. Rizzo, J. Chem. Phys. 97 (1992) 2823. [3] A. Campargue, M. Chenevier and F. Stoeckel, Chem. Phys. Letters 183 (1991) 153. [4] C. Douketis and J.P. Reily, J. Chem. Phys. 91 (1989) 5239. [5] E.R.T. Kerstel, K.K. Lehmann, T.F. Mentel, B.H. Pate and G. Scoles, J. Phys. Chem. 95 (1991) 8282. [6] M. Scotoni, A. Boschetti, N. Overhofer and D. Bassi, J. Chem. Phys. 94 (1991) 971. [7] R.H. Page, Y.R. Shen and Y.T. Lee, J. Chem. Phys. 88 (1988) 4621. [8] V.M. Blunt, A. Brock and C. Manzanares I, Ber. Bunsenges. Phys. Chem. 99 (1995) 520. [9] C. Manzanares I, J. Peng, N. Mina-Camilde and A. Brock, Chem. Phys. 190 (1995) 247. [10] C. Manzanares I, N. Mina-Camilde, A. Brock, J. Peng, V.M. Blunt, Rev. Sci. Instrum. 66 (1995) 2644. [11] A. Brock, N. Mina-Camilde and C. Manzanares I, J. Phys. Chem. 98 (1994) 4800. [12] C. Manzanares I, A. Brock, J. Peng and V.M. Blunt, Chem. Phys. Letters 207 (1993) 159. [13] J.W. Perry, D.J. Moll, A. Kuppermann and A.H. Zewail, J. Chem. Phys. 82 (1985) 1195. [14] J.K. Wilmshurst and H.J. Bemstein, Can. J. Chem. 35 (1957) 226. [15] R.E. Hiller and J.W. Straley, J. Mol. Spectry. 5 (1960) 24. [16] O.N. Ulenikov, A.B. Malikova, G.A. Sbevchenko, G. Guelachvili and M. Morillon-Chapley, J. Mol. Spectry. 154 (1992) 22; 149 (1991) 160. [17] W.B. Olson, H.C. Allen and E.K. Plyler, J. Res. Natl. Bur. Std. A 67 (1963) 27. [18] M. Akiyarna, T. Nakagawa and K. Kuchitsu, J. Mol. Specify. 64 (1977) 109. [19] J.C. Derocbe and G. Graner, J. Mol. Speetry. 62 (1976) 68. [20] J.C. Deroche, G. Graner and A. Cabana, J. Mol. Spectry. 57 (1975) 331. [21] J.C. Deroche and P. Pinson, J. Mol. Specify. 58 (1975) 229. [22] J.C. Deroche and G. Guelaehvili, J. Mol. Spectry. 56 (1975) 76. [23] M. Morillon-Chapey and C. Alamichel, Can. J. Phys. 51 (1973) 2189. [24] B.R. Henry, O.S. Mortensen and M.A. Mohammadi, J. Chem. Phys. 75 (1981) 4800. [25] S. Angus and B. Armstrong, IUPAC, Chem. Data Ser. No. 16. International thermodynamic tables of the fluid state, argon (Pergamon Press, New York, 1971). [26] T. Shimanouchi, Tables of Molecular Vibrational Frequencies, Consolidated, Vol. 1, Natl. Bur. Std. 39 (1972) 47. [27] J.T. Knudtson and E. Weitz, J. Chem. Phys. 83 (1985) 927. [28] M.O. Bulanin, J. Mol. Struct. 19 (1973) 59. [29] V.M. Blunt, D.L. Cedefio and C. Manzanares 1, Mol. Phys., to be published.

90

V.M. Blunt et a l . / Chemical Physics 209 (1996) 79-90

[30] V.M. Blunt, A. Brock and C. Manzanares I, J. Phys. Chem. 99 (1996) 520. [31] A. Laubereau and W. Kaiser, Rev. Mod. Phys. 50 (1978) 607. [32] S. Bratos and R.M. Pick, Vibrational spectroscopy of molecular liquids and solids (Plenum Press, New York, 1980).

[33] R.G. Gordon, Advan. Magn. Resort. 3 (1968) 1. [34] D.W. Oxtoby, Advan. Chem. Phys. 40 (1979) 1. [35] C.H. Wang, D.R. Jones and D.H. Christensen, J. Chem. Phys. 64 (1976) 2820.