1519
J . Phys. Chem. 1986, 90, 1519-1524 cn (OH,), = --(Dkj),,
C,
5
( 2 ) Solvent-Fixed
+ -(Dkm),,
(j # m,n)
(A37)
Cmvm
Cm
(j # m,n)
(A47)
or in one equation
.... . .
k # n I+n
('443)
anL
1
(L;), = cicj ( 1 - Sni) x
or in one equation
6ni(l - 6 n j ) af:
6dnj
k+n
af(LC),
+ R2 ( a n )k # n
zaFaf(LB), (A44)
/#n
These explicit equations also show that the ORR are preserved in changing solvents.
SPECTROSCOPY AND STRUCTURE Binary Overtone and Combination Band Intensities of Methyl Fluoride Shigeo Kondo,* Yoshinori Koga, and Taisuke Nakanaga National Chemical Laboratory f o r Industry, Tsukuba Research Center, Yatabe, Ibaraki 305, Japan (Received: May 30, 1985)
Integrated intensities of the binary overtone and combination bands of CH3F and CD3F have been calculated by using the experimental first derivatives and theoretical second derivatives of the dipole moment as well as the recently reported cubic force constants. They were compared with the experimental values obtained with the pressure broadening technique. A marked agreement was obtained between the calculated and measured intensities. Many terms of the second derivatives of the dipole moment have been determined from the observed band intensities by subtracting the contribution of the mechanical anharmonicity. These values have been compared with those obtained from analysis of the effective dipole moment in the excited vibrational states.
Introduction General expressions have kn developed for the band intensities of two quantum transitions by Secroun, Barbe, and Jouve,] and by Yao and Overend.2 According to these expressions, analysis (1) Secroun, C.; Barbe, A.; Jouve, P. J . Mol. Spectrosc. 1973, 45, I.
0022-3654/86/2090-1519$01.50/0
of the overtone and combination band intensities requires extremely accurate information O n the anharmonic force Constants (2) (a) Yao, S. J.; Overend, J. Spectrochim. Acta, Part A 1976, 32, 1059. (b) Overend, J. J . Chem. Phys. 1976.61, 2878. (c) Overend, J. "Vibrational Intensities in Infrared and Raman Spectroscopy"; Person, W. B., Zerbi, G., Eds.; Elsevier: Amsterdam, 1982; p 203.
0 1986 American Chemical Society
1520 The Journal of Physical Chemistry, Vol. 90, No. 8, 1986 of the molecule. However, even where only the cubic force constants are concerned, it has been extremely difficult to obtain reliable values for molecules which have more than three atoms. Recently, however, it was found that really reliable anharmonic force constants can be obtained by refining the anharmonic a b initio force field using the experimental spectroscopic constants for such molecules as methyl chloride) and methyl flu0ride.j In a previous paper, binary overtone and combination band intensities of methyl chloride have been investigated for the purpose of, above all, demonstrating the feasibility of determining the dipole moment function up to second order of appr~ximation.~The analysis has been carried out very successfully. The predictability of the infrared intensities of binary transitions has been demonstrated to be excellent for this molecule. It was found that except for the fundamentals the more intense ones were all due to two quantum transitions, and a few ternary transitions observed in the spectrum were all in Fermi resonance with the fundamentals and/or two quantum tran~itions.~This is important because the absorption intensities of two quantum transitions can be calculated by using only the cubic force constants, whereas the calculation of its intensities for ternary transitions requires detailed information on the quartic force constants as well. Then, it may be almost impossible to acquire the necessary information to carry out the analysis. The present paper deals with a similar analysis on methyl fluoride. The purpose of the study is again threefold; first, to confirm the feasibility of determining the dipole moment function up to second order of approximation in this five-atomic molecule; second, to determine the individual terms of the dipole moment function from the infrared intensities; and third, to examine the predictability of the infrared intensities of binary overtone and combination bands. For methyl fluoride the fundamental band intensities of CH3F and CD3F have already been analyzed to determine the values of the first derivatives of the dipole moment with respect to the normal coordinates,6 and the anharmonic force field has been obtained as described above.4 Therefore, detailed analysis of the overtone and combination band intensities should be possible. In the present study, improvement of the first derivatives of the dipole moment has been carried out first. Then the absorption band intensities of the binary overtones and combinations have been calculated by using these improved first derivatives and theoretical second derivatives of the dipole moment as well as the reported cubic force constants. The calculated band intensities have been used to confirm, if available in the literature,'-I' or to determine the vibrational assignments of the observed bands. On the other hand, the experimental band intensities have been obtained by the pressure broadening technique. Wherever the isolated band intensities were available, the corresponding second derivatives of the dipole moment have been determined. They are compared with the values derived from the effective dipole moment in the excited vibrational states, where available.4
Experimental Section The sample gases of C H 3 F and CD3F were purchased from Takachiho Chemical Co. and Merck Sharp 8.z Dohme Co. Canada, respectively. The purity of CH3F was stated as 98% and that of CD3F was 99 atom %. Inspection of the full range of the (3) Kondo, S.; Koga, Y . ; Nakanaga, T. Bull. Chem. Soc. Jpn. 1985, 58, 65. (4) Kondo, S. J . Chem. Phys. 1984, 81, 5945. (5) Kondo, S.; Koga, Y . ;Nakanaga, T.; Saeki, S. Bull. Chem. Soc. Jpn. 1984, 57, 16. (6) (a) Barrow, M.; Mckean, D. C . Proc. R . Soc. London, Ser. A 1952, 218, 27. (b) Russell, J. W.; Needham, C. D.; Overend, J. J . Chem. Phys. 1966, 45, 3383. (c) Kondo, S.; Saeki, S. J . Chem. Phys. 1982, 76, 809. (7) Jones, E. W.; Popplewell, R. J. L.; Thompson, H. W. Proc. R. Soc. London, Ser. A 1966, 290, 490. (8) Champion, J. P.; Robiette. A. G.; Mills, I . M.; Graner, G . J . Mol. Spectrosc. 1982, 96, 422. (9) Betrencourt, M. Spectrochim. Acta, Part A 1982, 38A, 8 11. (10) Smith, W. L.; Mills, I . M. J . Mol. Spectrosc. 1963, 11, 1 1 . ( I 1 ) Pickworth. J.; Thompson, H. W. Proc. R. SOC.London. A 1954, 222, 443.
Kondo et al.
0 6 -
3000
3100
2900
2800
W a v e n u m b e r / cm-'
Figure 1. Observed and calculated spectra of
u I and u4 region of CH3F. (a) Observed spectrum with sample pressure of 2.99 X IO' Pa in a 6-cm cell under a total pressure of 1.1 1 X IO6 Pa with nitrogen. Resolution of 0.25 cm-I was used. (b) Calculated spectrum.
TABLE I: Fundamental Band Intensities (in km/mol) for Methyl Fluoride band CH,F 1'1
"2 1'3
"4
"3 "6
L
v:
2966.25d 1459.40e 1048.61f 3005.8Id 1467.82' 1182.359
0.047d -0.250e 0.2849
BobsdC
20.30 0.92 100.93 53.28 8.98 2.74
(70) (25) (308) (122) (11) (07)
CDlF "I
"2
u3 u4 "S
"6
2090.77h 1 134.63' 992.29 2258.44h 107 2.3 9' 911.49'[
O.18Oh -0.297' 0.242'[
17.05 (38) 36.7 ( 1 . 1 ) 65.1 (1.5) 39.06 (81) 4.5 (0.5)' 5.2 (0.3)'
In cm-l. bCoriolis zeta constant. cPresent measurement unless otherwise stated; numbers in parentheses a r e uncertainties. dChampion et al., ref 8. 'Escribano et al., ref 13. fFreund et al., ref 14. gSmith et al., ref 10. hJones et al., ref 7. 'Caldow et al., ref 15. 'Duxbury et al., ref 16. kDuxbury et al., ref 17. 'Kondo et al., ref 6c.
infrared spectra of these gases confirmed the stated sample purities. Spectra were all observed with a Nicolet Model 7199 FT-IR spectrophotometer with a mercury-cadmium telluride detector. Optical resolution of 0.25 cm-' was used (maximum path difference of 4 cm, with Happ-Genzel apodization). For intensity measurements, a 6-cm high-pressure cell with KBr windows was used under a total pressure of 1.11 X lo6 Pa with nitrogen as a broadening gas. In order to investigate rotational fine structure for some of the bands, a conventional 10-cm glass body cell was used. The sample pressure was measured with an MKS Baratron Type 220, which covers a pressure range of 1.333 X lo5 to 1.333 X lo2 Pa with a stated accuracy of 0.25% of reading. Integration of the absorption band area was carried out in a manner similar to ref 12 according to the equation
Bi= ( l / n l )
1
band i
In ( T o / T )dv
where n is the sample concentration (mol/m3), I is the optical path length (m), and T a n d Toare the transmittance values of the cell with and without the sample gas, respectively. The band intensity is given in units of km/mol.
Results and Discussion A . Improvement of the Fundamental Band Intensities. A detailed analysis has been made to determine finally the signs of ( d P / d q i ) in ref 6c. However, since all the fundamental band intensities for CH3F and some for CD3F were remeasured in the present study, we have revised the values of (dP/dqi). The def(12) For example, see: Kondo, S.; Saeki, S. J . Chem. Phys. 1981, 74,6603.
The Journal of Physical Chemistry, Vol. 90, No. 8, 1986 1521
Binary Overtone and Combination Band of Methyl Fluoride
1
0.24
0.1
I,
4
n
TABLE 11: Summary of P/ Values (in D) CH3F CD3F p," obsd" calcdb obsd" calcd6 PI' -0.0933 (23)' -0.0840 -0.0886 (28)" -0.0925 P,' 0.0155 (42) 0.0675 0.1594 (24) 0.2136 P3' 0.2756 (85) 0.3028 0.2277 (26) 0.2196 P 4 ' -0.0824 (19) -0.1198 0.0818 (8) 0.1127 Psx 0.0489 (08) 0.0226 0.0407 (23) 0.0052 P6' 0.0301 (16) 0.0460 0.0473 (14) 0.0582
"Obtained from the intensity data in Table I. 6From 4-31G* calculation. CThe2u: intensity in Table 111 was added to u l . "The 2u: intensity in Table IV was added to u l .
1500
1600
1400
W a v e n u m b e r / cm-1
v6,15317
Figure 2. Observed and calculated spectra of u2 and vs region of CH3F. (a) Observed spectrum with sample pressure of 6.29 X lo3 Pa in a 6-cm cell under total pressure of 1.1 1 X lo6 Pa with nitrogen. Resolution of 0.25 cm-I was used. (b) Calculated spectrum for negative Coriolis
perturbation between v 2 and
of the ground vibrational state were used for 2v50, while the literature values were available for v I and v4.' For the v2 and v3 bands,15J6the intensities have been remeasured in this work. For v 5 and the intensities reported in ref 6 were employed. The fundamental band intensities are summarized in Table I. Table I1 shows the new values of the first derivatives of dipole moment. B. Predictions of the Binary Overtone and Combination Band Intensities. The general expressions for the integrated intensities of binary overtone and combination bands have been established in the l i t e r a t ~ r e .Therefore, ~ ~ ~ ~ ~ only a brief survey will be given below partly for the purpose of illustrating definitions of the physical quantities treated in this study. The dipole moment function is expanded as a Taylor series in the dimensionless normal coordinates as2
u5.
0.20 C U
O
0.0-
p = Po
n
+ CPA, + (1/2)CP,,q,qs + ... I
where P, denotes (dP/dq,),P, denotes (d2P/dq+3qs),etc. On the other hand, the potential function may also be expanded in dimensionless normal coordinates18
0.2-
0.0
(2)
IS
I
2300
I
I
I
2200
I
I
2100
W a v e number / cm-'
Figure 3. Observed and calculated spectra of v 1 and u4 region of CD,F. (a) Observed spectrum with sample pressure of 2.72 X lo3 Pa in a 6-cm cell under total pressure of 1. I 1 X lo6 Pa with nitrogen. Resolution of 0.25 cm-' was used. (b) Calculated spectrum.
inition of the normal coordinates employed here is the same as in ref 6c. As shown in Figure 1 , the spectrum of the 3000-cm-' region recorded under a pressurized condition shows a relatively simple feature in spite of the complex interactions revealed by Champion et aLs In this figure, three strong bands are apparent: two parallel bands and a perpendicular one. According to ref 8, the former are due to mixed states of v,, 2v2, and 2~50,while the latter is almost purely due to v4. The apparent intensities of these bands were obtained by a usual simulation technique.& They were tentatively assigned to v4, v I , and 2vS0bands. A simulation analysis was also carried out for the v2 and v5 band area, where the band parameters of ref 13 have been used. The result is shown in Figure 2 and Table I. Also for u3 and v6 bands,14.10the intensities have been remeasured in the present study as listed in Table I. Very complicated interactions are expected among the bands in the CD stretching region of CD,F as well. However, here again only four bands were apparent in the spectrum recorded under a pressurized condition. They are due to mixed states of several vibrational levels. They were tentatively assigned to v4, 2v?O, v l , and 2u3,of which the 2v3 band intensity was estimated by simply integrating the appropriate absorption area. In order to obtain the intensities for the former three bands, a simulation calculation was carried out as usual (Figure 3), where the parameter values (13) Escribano, R.; Mills, I. M.; Brodersen, S . J . Mol. Specfrosc. 1976, 61, 249. (14) Freund, S . M.; Duxbury, G.; Romheld, M.; Tiedje, J. T.; Oka, T. J . Mol. Spectrosc. 1974, 52, 38.
v / h c = (1/2)Cwrq12 + (1/6)CPrsrqrq,qr r
+ ...
(3)
IS1
where w, is rth normal frequency and prsPrsr is a cubic force constant. In order to evaluate matrix elements of the dipole moment operator for anharmonic vibrational wave functions, a contact transformation, T , may be used
P' = T P T ' (4) where T = exp(iXS). Then, the integrated intensities of binary transition bands may be expressed by the following equation A,, = 2.5066(2w,)dflQ,s122;(1 - e-2pwJ)
(5)
for a binary overtone band, and A,,, = 2.5066(ws
+ ws.)dflQ,,~12ZsZsr( 1 - e - s ( w ~ + w ~ () 6) )
for a binary combination band. Here, w, is the sth normal frequency, d f is the degeneracy of the upper vibrational state, fl is l / k T , 2, is the partition function for the sth normal vibration, 2, = 1 /{1 - exp(-flu,)), and Q,,, is the transition dipole moment. The numerical coefficient used here is for the case where w, is given in l/cm, Q,, and Qss,in D, and A,, and A,, in km/mol. In a symmetric-top molecule, the transition dipole moments are given by the effective second derivatives of the transformed dipole moment, Q,,",multiplied by numerical factors as f01lows:~
Qst= [(I /2)2"21 [p,t + CJ',~'~~,,,w5,/(4w,2
- w,z2)I
S'
= [ (1 /2)21/2]Q,,Z
(7)
+
QSS,'= ( l / 2 ) [ P s s r ' + ~ P P , ~ ~ ' ~ , , ~w,,)~ , ~ ~- /wp2)] ((~, S"
= ( 1 /2)Q,,'
(8)
(15) Caldow, G. L.; Halonen, L. 0. Mol. Phys. 1982, 46, 223. (16) Duxbury, G.; Freund, S. M.; Johns, J. W. C . J . Mol. Spectrosc. 1976, 62, 99. (17) Duxbury, G.; Freund, S. M. J . Mol. Spectrosc. 1977, 67, 219. (18) Mills, I. M. "Molecular Spectroscopy: Modern Research"; Rao, K. N., Mathews, C. W., Eds.; Academic: New York, 1972; pp 115-140.
Kondo et al. TABLE 111: Binary Overtone and Combination Band Intensities of CH3F (in km/mol) band UmD t-2 obsd' ured Id ured IId 21,,2
6000.78'
2u40
1
+ (u4 + us)2 (Uq + u s ) @ u> + u4 u .~ ,
1J(
? ? ? ? ? ?
U]
1'2
?
VI
lJ4
2u,
+
+ (u4 + U 6 ) 2
+ + ug u , + u4 u , + u,
U "i _ P
[,U A ~
0)
242 2uso u2
+ u5 (us + U6)2 ( u s + U6)0 + U6 u j + vg u2 + u ,
2u2
In these equations, all of the summations are unrestricted, so
xr
that E,, includes the term with s' = s and includes the term with t'= t, etc. However, the index s runs only over nondegenerate modes and the index t runs only over degenerate modes. The numerical subscripts on t for the other dipole moment expansion coefficients are as follows; P," = PtaX= Pfby,Prrz = Profa'= Prbfb', and Pfr,"= Pror,,"= -P,b,'bx = -P,,l,bY = -Prbt'aY.2c Similarly, the numerical subscripts on t for the other cubic force constants are as follows; 'Psff= 'Pstnt'o = Pssrbr'b; 'Pfr'r" = 'Pfot'af'a = -%r'br"b = -'Pfbr'af"b
- -'Ptbr'br"a.
18
According to these expressions, the mechanical anharmonic contribution to the intensities can be obtained if the normal-coordinate cubic force constants and the (dP/dq,) values are known. The former are available in ref 4, and the latter are listed in Table 11. On the other hand, in order to estimate the second derivatives of dipole moment, an a b initio calculation was carried out by GAUSSIAN 80 program" using Pople's 4-31G* basis set, where d-orbitals were used as polarization functions for the C and F atoms.20s2' The dipole moment derivatives were calculated for the experimental normal coordinates22aat the experimental geometry: C H = 1.0837 A, C F = 1.3890 A, and LHCH = 110' 19'.22b The calculated values of the dipole moment for various displacements were fitted by a least-squares method to a power series expansion in the symmetry coordinates as in the case of force field c a l ~ u l a t i o n . The ~ ~ results for CH3F and CD3F will be shown later in column IV of Tables V and VI, respectively. The predicted band intensities have been obtained by using these values of P,*. They are listed as pred I1 in Tables 111 and IV; for the pred I values in these tables only the mechanical anharmonicity was taken into account. In the subsequent sections, the calculated band intensities will be used extensively to make assignments of the observed bands. C. Observed Spectra and Band intensities for CH3F. For C H 3 F molecule, the spectral region from 6300 to 800 cm-' has been investigated. Here the most intense bands are due to the fundamentals and two overtones the latter of which appear in the CH stretching region. As was mentioned before, these overtones are involved in very complicated resonances with u1 and others.8 It was noticed that the other observed bands were mostly due to the binary transitions. In many places in the spectrum these bands are badly overlapping with each other. In particular, the intensities (19) Binkley, J. S.; Whiteside, R. A.; Krishnan, R.; Seeger, R.; DeFrees, D. J.; Schlegel, H. B.; Topiol, S.; Kahn, L. R.; Pople, J. A. QCPE 1981, 1 3 , 406 (GAUSSIAN 80). (20) (a) Ditchfield, R.; Hehre, W. J.; Pople, J . A. J . Chem. Phys. 1971, 54, 724. (b) Hehre, W. J.; Lathan, W. A. J . Chem. Phys. 1972, 56, 5255. (21) Hariharan, P. C.; Pople, J. A. Theor. Chim.Acta 1973, 28, 213. (22) (a) Blom, C. E.; Muller, A. J . Mol. Spectrosc. 1978, 70. 449. (b) Eggers, D. F. J . Mol. Struct. 1976, 31, 367. (23) Kondo. S.;Koga, Y.; Nakanaga, T. J . Chem. Phys. 1984, 81, 1951
112
2U6? 2V6@
+
u, u6 2JJ3
? ? ? 4057.6' 3905.4" 2927.39g 2926.009 2922.239 2863.249 ? ?
I
1
-0.093e 1 '?
? ? ? ?
}2.81 (30) '
0.380 0.465 0.806 0.208 0.046 0.002 0.019 (0.000 0.007 0.001 0.020 0.000 0.020 0.002 1.629 23.698 0.017 15.216 1.038 0.040 1.773
[
1.66 (56)
{
1
i
? 1 0 . 6 9 (35) ? ? 0.0 (0.3) 0.084e 1.44 (30) 0.18 (4) 0.4909 ? 12.8 (1.5) -0.246g ? ?
? ? }0.54 (3) ? ? 2513.79h -0.245h o,049 (24) 2499.80* ? ? ? ? ? 2222.6' 0.27' 0.23 (3) 2081.42j 1.81 (9)
1
{
{
0.110 0.452 0.078 0.910
1.417 0.131 0.598 0.040 1.114 0.176 1.847 1.719 0.000 0.365 0.002 0.310 1.495 0.224 0.124 23.656 0.002 10.106 0.836 0.624 0.596 0.122 0.049 0.000 0.009 0.440 1.501
OBand center in cm-I. bEffective values of Coriolis zeta constant. 'Numbers in parentheses are uncertainties. dPred I considers only mechanical anharmonichy, and pred I1 considers both mechanical and electrical anharmonicities. 'Jones et al., ref 7. /This work. gChampion et al., ref 8. hBetrencourt, ref 9. 'Smith et al., ref 10. 'Pickworth et al., ref 1 I .
TABLE I V Binary Overtone and Combination Band Intensities for CD3F (in kcal/mol) band U? (,b obsd' pred Id pred IId
"i
+
u4
ZU,
u2
+ u4
+ (uq + Us)O U, + u4 + u2 u ,I + , (u4 + U 6 ) 2 (uq + + vj + u6 (u4
ill
J
J
~
V6)0
is1
UI
2u2 u2
+ us
2V62
2U60
0.183' 0.089e
7 0.185'
-0.292e ? ?
3078.9 ? ?
?
?
? ?
/
O'O (o'6)
0.17 ( 2 ) 0.0 (0.1) ? ? ? 4.36 (69) ?
1'5
?
?
? ?
?
?
?
?
? 1977.24e
?
+ + u2 + U 6 ( u s + U6)2 + U6)0 2u3 + u6 Y,
0.1221
0,
2u50
(Vi
?
0.35 (1 1) 0.19 (10) 0.27 (3) 0.24 (24) 0.69 (7) 0.52 (1 1) 0.0 (0.1 I ) 0.26 (6) 0.29 (6) 0.31 (7) , ,
-0.345e
? 2151.0' ?
2u52 u: u,
4498.24' 4469.6' 4306.771 ? 3394.10e 3320.49e ? 3248.87/ 3206.6 3146.89' ?
1898.971 0 . 2 3 6 ? ? ?
1
?
2.01 (30) 0.052 (27) 0.0 (0.05) 0.0 (0.05)
0.217 0.204 0.466 0.087 0.012 0.021 0.003 0.000 0.026 0.005 0.009 0.015 0.001 0.002 2.325 0.172 0.952 269.095 3.081 0.005 1.580 0.211 0.154 0.434 0.012 0.099 0.175
{
0.846 0.075 0.327 0.01 1 1.466 1.054 0.066 0.175 0. I39 0.824 0.043 0.001 0.095 0.029 3.701 0.095 0.122 264.149 2.597 0.073 1.185 0.199 0.466 0.948 0.038 0.028 0.002
"Band center in cm". bEffective values of Coriolis zeta constant. 'Numbers in parentheses are uncertainties. dPred I considers only mechanical anharmonicity, and pred I1 considers both mechanical and electrical anharmonicities. 'Jones et al., ref 7. JThis work.
of those which are related with v 2 and v 5 were never obtained separately except for the fundamentals, because they are in extremely strong Coriolis resonance with each Nevertheless, the assignments have extensively been made for the bunch of bands falling in the CH stretching region by
Binary Overtone and Combination Band of Methyl Fluoride Champion et ah8 Also the majority of the two qkantum transitions which are not much degraded by overlapping bands have been assigned in the In the present study, these assignments have been confirmed by using the predicted band intensities listed in Table 111. Eventually the prediction has been found to be very helpful to determine the assignments of the bands. In fact, most of the predicted intensities of those which are free from strong resonances have been found to fall within a factor of 2 or so of the observed values. The whole spectral feature will be described in the following. In the 6200-5600-cm-' region, 2v4, (vl + v4), and 2vl bands are expected. The perpendicular component of the 2v4 band is clearly observed at 6000.78 ~ m - ' . However, ~ any of the other bands in this region were not definitely identified because of the noise level. Therefore, the sum is given of their intensities in Table 111. A broad absorbing area begins at around 4550 cm-' and continues all the way down to 3800 cm-', where Jones et al. have found ( v 3 v4) at 4057.6 ~ m - ' . Besides ~ this we expect ( u 4 4. (u2 ( V I + v6), and ( V I + v3) in + v4), (vl + v d , ( u l + v d , (v4 + this order from higher to lower frequencies. The absorption band intensities for the upper half of this region are given in two bunches. On the other hand, the intensities of the ( v 3 v4) and (vI v3) bands are given separately. The ( v l + 4,) band, which is expected to exist about the same place as the ( v3 + v4) band, was given a null intensity because we did not find any peaks to be assigned to this band among relatively strong absorption by
+
TABLE V Second Derivatives of Dipole Moment with respect to Normal Coordinates in CHtF (in lo-' D)
a.,
Nff)
p,"
obsd"
mechb 107 16 -8 1288 40 -370 104 -1 0 -18 -22 -23 1 -20 -14 -53 111 71 -6 20 -20 3 1134 -210 -35 125 174 61
+
+
+
(v3
The Journal of Physical Chemistry, Vol. 90, No. 8, 1986 1523
+ .4h7
In the 3000-cm-' region, several overtone and combination bands are underlying the strong fundamentals.8 Unfortunately, however, we were not able to obtain any detailed information about their intensities. The (v2 v6) and ( v 5 v6) bands are very heavily overlapping with each other, and their intensities are not given separately. The situation is the same for (u2 + v3) and (v3 + vJS9 The spectrum v g ) was reported by Smith and Millslo and 2v3 was of (v3 observed by Pickworth and Thompson." Both of these bands are well isolated from other bands and the intensities were obtained by simply integrating the respective absorption areas. In the 2v6 band region, we did not observe any absorption and a null intensity was assigned to both 2v: and 2vg2. The observed absorption intensities for CH3F are summarized in Table 111. D. Observed Spectra and Band Intensities for CD3F. For CD3F molecule, the spectral region from 4800 to 800 cm-' has been investigated. Many absorption bands in the spectrum have already been assigned by Jones et aL7 For the remaining ones, the assignments have been done aided by a combination of the predicted intensities in Table IV and the approximate band centers simply estimated from the fundamental frequencies in Table I. Fortunately, in this molecule the v2 and v5 bands are located at a certain distance from each other. The perpendicular component of the 2u4 band is located at 4498.24 cm-l? and the parallel one at 4469.6 cm-l. The individual intensities of these bands were roughly estimated by simply integrating the areas of 4700-4480 and 4480-4380 cm-' for the former and the latter, respectively. On the other hand, we could not identify even the central Q branch of 2vl. But a weak absorption area observed from 4240 to 4060 cm-' was tentatively assigned to this band. A perpendicular band located at 4306.77 cm-' was assigned to ( u 3 v4 v5) in the 1iteratu1-e.~This band is conspicuous in its intensity in this region and apparently looks independent of other bands. Therefore, it is hard to ascribe it to a ternary band. Rather, comparison of the observed intensity with the prediction leads to its assignment to the (vl v4) band. The integrated area from 4 3 8 0 to 4240 cm-' was given to this band. There is a large bunch of absorption bands observed from 3 5 0 0 to 2900 cm-'. From the higher to the lower frequencies the bands of ( v 2 + v4), (v4 + v5), ( v 3 + u4), ( v I + v 2 ) , ( v I + v5), and ( v l + v 3 ) have been observed. The individual band intensities were obtained by integrating appropriate frequency regions. The ab-
+
+
+
+ +
+
obsd'
calcdd
92 (-76) -1 17 (-2459) -152 (892) 0
186 (-146) -37 (143)
-60 -13 103 -238 15 -105 -194 -176 78 200 15 97 191 76 -7 2 -170 -208 -5 1 -120 25 56 -1 152 -102 -13 -1 50 -63
"Numbers in parentheses are uncertainties. bContribution of mechanical anharmonicity to R,,". 'The numbers in parentheses are for the alternative signs of a,*". d A b initio values. See text.
TABLE VI: Second Derivatives of Dipole Moment with respect to Normal Coordinates in CD,F (in lo-' D) ~~~~
~~
~
a,,. rs(ff)
p,,.
obsd"
mechb
-133 (100) 118 (13) 92 (5)
81 36 -7 -570 -478 -262 -9 2 -12 8 17 78 -246 0 -14 23 85 62 9 -16 19 -1 1 -445 1 -187 -7 8 65 122 65
-566 (44) 69 (4) -87 (10)
0 (51) -126 (7) -79 (1 0) -46 (14) -81 (25) -17 (13)
0 (51) 78 (9) 0 (86) 0 (121) -566 (47)
0 (66) 0 (46)
obsde -214 (52) 82 (-154) 99 (-85) -304 (828) 161 (23) -75 (99) -8 -143 (109) -79 (79) -69 -166 -139 -9 94 -19 11 3885
-122 -65
(23) (-4) (15) (-62) (-5017)
calcdd -53 47 76 -149 39 -125 170 -132 20 -202 -20 33 -6 5 66 -62 -136 -1 84 31 128 -13 -1 3 41 120 -58 -2 -111 -30
"Numbers in parentheses are uncertainties. Contribution of mechanical anharmonicity to R,,". 'The numbers in parentheses are for the alternative signs of a,;. d A b initio values. See text.
+
sorption area from 3480 to 3360 cm-l was ascribed to (v2 v4), from 3360 to 3280 cm-' to ( u 4 4, from 3280 to 3225 cm-l to ( v 3 + v4), from 3225 to 3180 cm-' to (vl + v2), from 3180 to 3110 cm-' to (v, + v5), and from 3 1 10 to 3040 cm-' to ( v I u3). At the bottom of this region, an extra band was observed at 2976.2
+
+
J . Phys.
1524
C'httti.
cm-l, which was due to C H D 2 Fmolecule. It is concluded from its intensity that the concentration of this species does not exceed 1 %. Many of the binary transition bands fall into the C D stretching fundamental region. Very complicated interactions are expected among the bands just like the ones in CH,F molecule. The band intensities of 2v2, ( v 2 + v 5 ) , ( v 2 + v,), ( v 3 + us), and (v2 + v6) could not be determined because they are underlying the much stronger vl, vj, and 2v50,whereas the intensity of 2 1 was ~ ~ obtained by simply integrating the appropriate absorption area. We could not find (v5
+ v6).
The ( v 3 + v6) band was found at 1898.97 cm-I. A null absorption was given to both components of the 2v6 band. The observed band intensities for CD3Fare summarized in Table IV. E. Experimental Second Dericatices of Dipole Moment. The observed and predicted intensities are compared in Tables 111 and IV. If the observed intensities are compared with the pred I values, agreement is not good a t all. Definitely, contribution from the electrical anharmonicity is needed to explain the observed intensities. In fact, agreement with pred I1 values is much better than for pred I. For most bands, the pred 11intensities agree with the observed ones within a factor of 2 or so, indicating that the a b initio P," values are pretty reliable. Discrepancy is only noted for the 2uS0band; in order to explain the intensity of this band satisfactorily, the complicated interactions must indeed be taken into accoutit precisely as was done by Champion et al. to illustrate the rotational fine structure of the spectra.' Tables V and V I show the result of analysis of the transition dipole moments. In these tables, the column I shows the observed values of R,," as defined in eq 7-13. Their signs were chosen as follows; at first, the contribution of the mechanical anharmonicity
1986, 90, 1524-1528 to R,," was calculated as shown in column 11. Then, the values of P,,were obtained by subtracting the numbers listed in column 11 from those in column I, and are shown in column 111. The resulting values of P,, for the two possible signs of Rr," were compared with the a b initio result listed in column IV. The signs were so chosen that the P,, thus obtained may agree better with the a b initio value. If they are chosen in this way, agreement between the observed and calculated P,,is very good. The numbers in parentheses in column 111 are for the alternative signs of the transition moment. In a previous paper, we have analyzed the effective dipole moment in the excited vibrational state^.^ It was found that P3,H = -0.0148, P,jD = -0.0195, P5sD= 0.0043, and P6GD= -0.0101 D. These are to be compared with the present results, Le., -0.01 52, -0.0304, 0.3885, and -0.0122 D. Agreement between the two results is excellent for P,,Hand p(,GD,while it is not good for P,," and PS5D.Probably, the discrepancy for P,,D is due to an error involved in the 2v3 band intensity. It is possible that the ( u s v 6 ) bands are underlying 2u3 with certain intensities (e.g., see pred I1 in Table IV). As the value of PI33 is small (1.6 cm-I, ref 4), this band cannot be much affected by Fermi resonance with v , . On the other hand, the result for PssDis rather natural because we did not consider the effect of close resonances occurring in the 2u5 region in the present analysis. In conclusion, the agreement obtained for P33H and P66D in the above may indicate the degree of accuracy of P,," resulting from the analysis of the binary transition intensities and/or of the effective dipole moments by using the anharmonic force field employed here.
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Registry No. CH,F, 593-53-3; CD,F, 1 I 1 1-89-3
EPR Spectra of AI(CO)* in Hydrocarbon Matrices' J. H. B. Chenier, C. A. Hampson,* J. A. Howard,* B. Mile,* and R. Sutcliffe3 Division of Chemistry, National Research Council, Ottawa, Ontario, Canada K l A OR9 (Received: July 31, 1985; In Final Form: October 9, 1985)
AI(C0)2 has been prepared in inert hydrocarbon matrices from AI atoms and CO and its EPR spectrum examined. Powder spectra in cyclohexane and adamantane indicate that Al(CO), is an almost axially symmetric species with the magnetic parameters Al,(AI)= 140 MHz, A,(Al) = 44.8 MHz, A,l(C)< 2.8 MHz, A , ( C ) = 25 MHz, gl,= g, = 2.0020. Isotropic spectra in adamantane at 2.50 K give A(AI) = 72.6 MHz, A(C) = -15.4 MHz, A(0) = -12.2 MHz. These data are consistent with a bent planar r radical of C, symmetry having the unpaired electron in a molecular orbital perpendicular to the molecular plane and constructed from the aluminum 3p, and carbon monoxide 2r,* orbitals while the aluminum "lone-pair" electrons reside in a sp2 orbital directed along the C2 axis.
Introduction Kasai and Jones4 have recently published the powder EPR spectrum of aluminum dicarbonyl produced by co-condensing AI atoms and CO in solid argon at 4 K. This spectrum provided evidence that AI atoms and CO reacted under these conditions to give a paramagnetic carbonyl containing one aluminum atom and two carbon monoxide ligands, Le., Al(CO),. Although there was no doubt from the powder spectrum that the aluminum carbonyl did contain one aluminum nucleus the number of carbon monoxide ligands had to be determined by a comparison of ex-
perimental and simulated spectra of AI/l3CO codeposits. A further difficulty with analysis of the powder spectrum involved determining the signs of the anisotropic aluminum hyperfine interactions. We have recently demonstrated5-' that metal atom carbonyls can be prepared in a rotating cryostat by sequential deposition of metal atoms and carbon monoxide in inert hydrocarbon matrices. An important advantage of hydrocarbon over rare-gas matrices is that they can be warmed to much higher temperatures without loss of the paramagnetic transient. This together with the larger size of the substitutional cavity (5-6 A) results in
( 1 ) Issued as NRCC No. 25378.
(2) Department of Chemistry and Biochemistry, Liverpool Polytechnic, Liverpool, England L3 3AF. (3) NRCC Research Associate 1979-1 984. Present address: Biotechnology and Chemistry Department, Forintek Canada Corp., 800 Montreal Road, Ottawa, Canada. (4) Kasai, P. H.: Jones, P. M. J . A m . Chem. SOC.1984, 106, 8018-8020.
0022-36S4/86/2090- I S24$0 1.50/0
(5) Howard, J. A.; Mile, B.; Morton, J. R.; Preston, K. F.; Sutcliffe, R. Chem. Phys. Lett. 1985, I 1 7, 1 1 5-1 17. (6) Howard, J. A.; Mile, B.; Morton, J . R.; Preston, K. F.; Sutcliffe, R. J . Phys. Chem. 1985, 90, 1033-1036. (7) Hampson, C. A,; Howard, J. A,; Mile, B. J . Chem. SOC.,Chem. Commun. 1985, 966-967.
Published 1986 American Chemical Society
