The Journal of Physical Chemistry, Vol. 83,
Localized Resonances in CHBF
It should be emphasized that the type of reaction under consideration in this work is really a balance between the two conditions set forth as the important parameters for the reaction. Thus, in the case of the alcohol^^^^ it has been observed that reaction 3 can occur even for cases where the alcohol has a higher proton affinity than the ester. In these cases, it is believed that the very favorable formation of a stable carbonium ion in the collision complex can compete appreciably with proton transfer in cases where the exothermicity of the latter is very small. The behavior of reaction 7 is in principle unexpected, and does not correlate with the rules advanced in this paper. This case is not well understood a t present, and its interpretation is further obscured by the uncertainty in the value for the proton affinity of benzyl chloride. While the reactions reported in this work have no direct analogue in solution, and in fact they would not be suspected on the basis of our knowledge of solution chemistry,lg they provide further evidence of the principles which govern complex ionic reactions in the gas phase. Acknowledgment. The present work was made possible by the continuous suppqrt of the Conselho Nacional de Desenvolvimento Cientifico e Tecnol6gico do B r a d (CNPq). One of us (J.F.F.) thanks the FundaGBo de Amparo B Pesquisa do Estado de Silo Paulo (FAPESP) for a postdoctoral fellowship. References and Notes (1) (a) Universidadede Slo Paulo (b) Universidade Federal do Rio Grande do Norte, Natal, RN, Brazil. (c) Universidade Estadual de Campinas.
No. 11, 1979 1491
P. W. Tiedemann and J. M. Riveros, J. Am. Chem. Soc., 96, 185 (1974). J. L. Beauchamp in "Interactions between Ions and Molecules", P. Ausloos, Ed., Plenum Press, New York, 1975, pp 418-436. J. K. Pau, J. K. Kim, and M. C. Caserio, J . Am. Chem. SOC., 100, 3831 (1978). T. B. McMahon, Can. J . Chem., 56, 670 (1978). P. Kebarle, NATO Advanced Institute Study on "Kinetics of IonMolecule Reaction", La Baule, France, 1978. J. K. Pau, J. K. Kim, and M. C. Caserio, J . Chem. Soc., Chem. Commun., 120 (1974). J. F. G. Faigie, P. C. Isolani, and J. M. Riveros, J . Am. Chem. Soc., 98, 2049 (1976). S. M. Jose and J. M. Riveros, Nouv. J . Chim., 1, 113 (1977). K. Takashima and J. M. Riveros, J . Am. Chem. Soc., 100, 6128 (1978). T. B. McMahon and J. L. Beauchamp, Rev. Sci. Instrum., 43, 509 (1972). J. F. G. Faigle, Doctoral Thesis, University of Slo Paulo, 1977. P. C. Isolani, J. M. Riveros, and P. W. Tiedemann, J . Chem. Soc., Faraday Trans. 2, 69, 1023 (1973). J. L. Beauchamp, D. Holtz, S. D. Woodgate, and S.L. Patt, J . Am. Chem. Soc., 94, 2798 (1972). This estimate has been based on the proton affinity measured for methyl formate by J. F. Wolf, R. H. Staley, I. Koppel, M. Taagepera, R. T. McIver, Jr., J. L. Beauchamp, and R. W. Taft, J . Am. Chem. SOC.,99, 5417 (1977). Absolute values have been nevertheless increased by 5 kcal mol-' according to the recent measurements of J. L. Beauchamp (private communication). W. L. Jorgensen, J . Am. Chem. SOC., 100, 1057 (1978). B. S. Freiser, R. L. Woodin, and J. L. Beauchamp, J . Am. Chem. SOC.,97, 6893 (1975). J. H. Stewart, R. H. Shapiro, C. H. DePuy, and V. M. Bierbaum, J . Am. Chem. SOC.,99, 7650 (1977); C. H. DePuy, V. M. Bierbaum, G. K. King, and R. H. Shapiro, ibid., 100, 2921 (1978). For cases where the dialkoxycarboniumions can be considered as intermediatesin the transestertfication reaction,see R. A. McCleliand and M. Ahmad, J. Am. Chem. Soc., 99, 5356 (1977), and references therein.
Localized Resonances in CH3F and Their Influence on Vibrational Energy Transfer Georges Granert Laboratoire d'lnfrarouge, Laboratoire Associ.6 au CNRS, Universit.6 Paris XI, Bstiment 350, 9 1405 Orsay Cedex, France (Received October 14, 1978)
We report in this paper a part of the interpretation of the high resolution (0.005 cm-') spectrum of CH3F near 3000 cm-'. The KilK = 6-11 subbands of v4 show local resonances which are proved to be due to a Coriolis interaction with the very weak 3v3band. This fact explains why excitation of CHBFby a COz laser very quickly populates not only the u3 = 2 and u3 = 3 levels but also the u4 = 1 level and, through other interactions, all levels near 3000 cm-'.
Introduction The infrared spectrum of methyl fluoride in the 3000-cm-l region has been the subject of many Nevertheless, due to its very intricate structure, it can be safely stated that, even now, this spectrum is not well understood. We have recorded this spectrum on a third generation Fourier transform spectrometer which has been extensively de~cribed.~-'OTwo spectra were recorded. Spectrum A was run with a sample pressure of 0.03 torr and a path length of 80 m. The experimental limit of resolution of the spectrometer is 0.005 cm-' but, due to Doppler broadening (0.0064 cm-l a t 3000 cm-'), the recorded line width was about 0.008 cm-l. Spectrum B was run a t 1torr and 28 m. Most of the analysis between 2800 and 3100 cm-' were performed on spectrum A only since spectrum B was often saturated. Nevertheless in less dense regions, such as above 3100 cm-l, spectrum B was quite useful, specially for very high J and K values or, as is the case in 0022-3654/79/2083-1491$01 .OO/O
TABLE I: Ground-State Rotational Constants of CH,Fa A , = 5.182009 Bo = 0.85179425 DoJ = 2.0090 x D o J K= 14.660 X D o K= 70.33 x a F r o m ref
HoJ= 0 HoJK = 4.41 x lo-" H o K J = 8.10 x HaK= 0
13. All values in crn-l.
the present paper, for weak transitions. (Spectrum B was analyzed by other members of our group between 2000 and 2700 cm-l.ll~lq) The accuracy of the wavenumber measurements is about 1X cm-l but their relative precision is about 0.3 X cm-l. As usual, the line positions were automatically obtained by a computer program.
Localized Resonances in the v4 Band The spectrum between 2800 and 3160 cm-' involves the bands v4, vl, 2u2, 2u50, 2uj2, vq + u5, and 3v3 (not to mention 0 1979 American Chemical Society
1492
The Journal of Physical Chemistry, Vol. 83, No. 11, 1979
Georges Graner
4E
I.
rt
3P10.
+ R
Q9
t
+ + + +
1
Pt
3P05.
0.
I
I
400.
800.
I
1eoo.
J ( J + I )1) 1600.
Figure 1. Plot of the upper state energies of the transitions in the subband K”AK = 6. These energies have been corrected by the 1) - D,”J”(J’ 1)’. quantity B”J’(J’
+
+ + +
t t
+
+
J(J+l) I
0.
TE
400.
1eoo.
800.
-
1600.
= 9.
Figure 4. Same caption as Figure 1 except for K”AK
1
R
I‘
Q7
3P75.
+ +
+
I
R
J (J+I) I
400.
0.
-
- 1 -
Q10
I
1200.
800.
I6dO.
Figure 2. Same caption as Figure 1 except for K ” A K = 7 .
tE
0.
Q8
t
-+++++ti++++
++
+ + + + + + + + + + + t
J(J+I) 3.
I
800.
1
iPnn
-
Figure 5. Same caption as Figure 1 except for K”AK = 10.
R
3345.0
I
400.
400.
800.
1eoo.
1600.
Flgure 3. Same caption as Figure 1 except for K“AK = 8.
hot bands and I3CH3Fbands). Rovibrational transitions belonging to all these seven bands have been assigned, thanks to the extensive use of ground state combination differences (GSCD), as was explained in ref 13 where an
accurate set of ground state rotational constants was determined (Table I). A great number of long-range and local resonances, linking all the aforementioned vibrational levels in multiple ways, have been positively found. They make global treatment of all the levels involved extremely difficult and, although this treatment is our final objective, we choose to report here a small part of our findings concerning the interaction between v4 and 3v3. We feel justified in singling out 3u3 by the relation it bears to interesting problems with v3 and 2u3. The v4 band is now extensively known since we have been able to assign lines belonging to 33 different K subbands for K”AK = -15 to 17 (pP15to RR17). Among them, six subbands with K”AK = 6,7,8,9,10,and 11were found to show a small anomaly. For instance, the RR&J) lines have almost equal spacings until J = 24 where the spacings undergo a rapid decrease while the intensities decrease until the lines disappear for J = 31. Simultaneously a new series appears with an inverse behavior and can be followed up to J = 40. This phenomenon and similar one8 in other subbands are depicted in Figures 1-6 where we have plotted the upper energy level E’corrected by the quantity B”J’(J’ + 1) - DJ”JJn(J’ 1)’. In this
+
The Journal of Physical Chemistry, Vol. 83, No. 11, 1979
Localized Resonances in CH,F
TABLE 11: The K A K = 6 Subband of v q lower branch
upper branch
--
J’a
RR,-
R&,-
3065.8892 38067.584 8 31069.2 8 0 0 3070.9742 ZI 0 7 2.6 68 6 3 07 4.3 6 2 4 3076.0559 307 7.7 49 6 3079.4433 3 08 1,1368 3 08 2.8 3 0 6 3 0 84.5 2 4 2 3086,2176‘ 308 7.9 113 3 08 9.6 0 4 8 3091.2981 3 09 2.99 10 3 09 4.6 8 3 3 3 09 6.3 7 5 0 3098.0660 3099.7558 3 10 1.444 3 3103.1314 3 104.8 15 9 3 106.497 3 3 108.17 4 2 3 109.84 3 5 :3111.499 5g ,3113.1126 ,3114.5 5 05 3114.9829
7
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Rp,-
(3053.9742) (3053.9686) (3053.9630) (3053.9569) (3053.9514) (3053.9459) (3053.9406) (3053.9361) (3053.9324) (3053.9291) (3053.9270) (3053.9254) (3053.9243) (3053.9248) (3053.9259) (3053.9278) (3053.9304) (3053.9335) (3053.9371) (3053.9412) (3053.9454) (3053.9496) (3053.9537) (3053.9566) (3053.9579) (3053.9562) (3053.9484) (3053.9322) 3053.8694 3053.6342 3052.3971
1493
RR,
RQ6
+
+
3035.2387 3033.5338 3030.1266 3028.4246 3026.7240 3025.0249 3023.3 263e 3021.6317 3019.9378 3018. 2454d 3016.5550 3014.8667 3013.1802 3011.4953d 3 008.1 302e 3004.77 22d 3003.0942 3001.4166 2999.7412f
3117.047 7 3118.5038 3120.1160 3121.7622
3054.4612 3054.2483 (3054.1934) (3054.1747)
Frequencies between brackets are computed, usually from R R a The J ’ value refers to the upper state of the transition. lines by using GSCD, ‘ Weight 0.5. Weight 0.1. e Weight 0.01. f Weight 0.001. Weight 0.
R Qll
I 1
3082
J(J+l)
3 6 10 $1
8
0.
400.
800.
-
1eoo.
Flgure 6. Same caption as Figure 1 except for K”AK
= 11
representation, if a subband is unperturbed and its effective B’is equal to B” and Dj’= Dj”,then all the points are on an horizontal line. We have also shown in Figure 7 one characteristic Q branch of v4 with all individual transitions packed together except near the anomaly where they stick out clearly. All the wavenumbers of the relevant transitions are gathered in Tables 11-VII. The “local resonances” or “avoided crossings” depicted in Figures 1--6 have the following characteristics: (a) For each subband, the crossing occurs for a different J value as shown by the first line of Table VIII. This value decreases with increasing K. This explains why we have not observed this reijonance for other K values. For K“AK = 1 2 and above, the crossings take place for low values of J forbidden by the irule J 1 K. For K”AK < 6, they occur
3082.5
3083
crn-1
30815
Figure 7. Experimental spectrum of CH,F in the region of the branch of v4 Pressure, 0.03 torr; path length, 80 m. Outside the central region where all J values are superposed, J values have been given with and - denoting the upper and the lower branches, respectively (see Table VI).
+
for such a large value of J that the corresponding transitions are too weak to be seen. (b) The distance of minimum approach A in these local resonances is a decreasing function of K as shown by the second line of Table VIII. As this distance should be equal to or slightly largerz6than twice the effective interaction term We, between the interacting levels, it is clear that Weffis strongly K dependent. Therefore, one can rule out a t once the hypothesis that the interaction responsible for this phenomenon is a Fermi-type or anharmonic resonance. On the other hand, it appears very plausible that the interaction is of the Coriolis type, i.e.
Wef= f Wc[J’(Jf+ 1) - K1K’ + 1)11/’
(1)
1494
The Journal of Physical Chemistry, Vol. 83, No. 11, 1979
TABLE 111: The K A K = 7 Subband of
Georges Graner
uqa
lower branch J'a
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 a-g
RR;
upper branch
RQ,-
3074.9408 3076.6379 3078.3345 3080.0306 3081.7264 3083.4216 3085.1168 3086.81 1 3 3088.5058 3090.1999 3091.8938 3093.5873 3095.28 07 309 6.9 7 3 6 3098.6662 3100.3593 3102.0500 3103.7409 3105.4311 3107.1192 3108.8057 3110.4883 311 2.1642 3113.8251 3115.4399 3116.7985 3117.0272
RP,-
(3061.32771 i3061.3244j (3061.3210) (3061.3176 ) (3061.3144) (3061.311 2 ) ( 3061.3086) (3061.3061) (3061.3042) (3061.3027) (3061.3018) (3061.3014) (3061.3018) (3061.3027 ) (306 1.3043) (3061.3064) (3061.3092) (3061.3124) (3061.3161) (3061.3190) (3061.3215) (3061.3216) ( 306 1.3162) (3061.2974) 3061.2337 3060.9156 3059.4697
+
RQ7+
-
3039.2034d 3035.8035 3034.1042 3032.4067 3030.7106 3029.0158 3027.3227 3023.9406 3022.2522 302 0.5657 3018.88lod 3017.1975 3015.5166 3013.8348d 3012.1545 3010.4749 3007.09 18e 3005.3508g 3118.3427 3119.2757d 3120.8301 3122.4726e 3 124.1445"
3062.4598 3061.7214 3061.5997 3061.57 12
See the corresponding footnotes t o Table 11.
TABLE IV: The K A K = 8 Subband of
u4
lower branch 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
3083.9430 3085.6395 3087.3352 3089.0305 3090.7 254 3092.4196 3094.1134 3095.8067 3097.4994 3099.1914 3100.8830 31 02.57 39 31 04.2642 3105.9532 3107.6412 3109.3276 3111.0116 3112.6915 3114.3633 3116.0142 3117.5823 3118.5702
(3068.6334) (3068.6303 j (3068.627 0) (3068.6237) (3068.6207 ) (3068.6176) (3068.6147 ) (3068.612 1 ) (3068.6096) (3068.6073) (3068.6054) (3068.6037) (3068.6024) (3068.6008) (3068.5993) (3068.5973) (3068.5940) (3068.5878) (3068.5748) 3068.5421 3068.4282 3067.7356
upper branch
3049.9 225e 3048.2200 3044.8184 3043,1184" 3041.419 5" 3039.7204 3036.3295 3034.6350 3032.9400e 3031.2496 3029.5597d 3027.8696' 3026.1796 3024.4894 3019. 3883d
32
33 34 35 36 37 38 39 40 41 a-g
RR,
3046.01 29' 3044.3097 3042.6072
3119.5967' 3119.507gd 3119.9364 3121.3479 3122.9724 3124.6348 31 26.3095 3127.9875 3129.6690 3131.3508 3133.0332 3134.7157d 3136.398lC 3138.0797d
3070.5079 3069.1027f 3068.8337 3068.7853f 3068,7676" 3068.7676e (3068.77 14) 3068.78531 (3068.7937) 3068.8098d
3016.5868 3012.9127
See the corresponding footnotes to Table 11.
If we compute A/(2[J'(J'+ 1)- K ( K + 1)]1/2), as is done on the third line of Table VIII, it is apparent that this
quantity is roughly constant,'6 its lower limit being 21.9 x IO-3cm-l, a first approximation for W,.
The Journal of Physical Chemistry, Vol. 83, No. 11, 1979
Localized Resonances in CH,F
TABLE V: Vie KAE: = 9 Subband of
u4
lower branch
J'"
RR,,-
10
3092.8928 3094.587 5 3 096.2 8 10 3097.9744 3099.6670 3101.3587 3103.01496 3104.7 397 3106.4285 3108.1163 3109.8026 3111.486F 311 3.1677 3 114.814 2 5 31 16.510 25 3118.1069 3119.2934 3119.4932
11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26 27 28 29 30 3 3. 32 33 34 35 36 37 38 39 40 41 42 "-g
1495
RQ9-
(3075.8886) (3075.8847) (3075.8802) (3075.8761) (3075.8719) (3075.8674) (3075.8629) (3075.8583) (3075.8532) (3075.8481) (307 5.84 23) (3075.8354) 3075.8266e 3075.8121d 3075.7839 307 5.7 012 3075.2030 307 3.7 159
upper branch
._
RP,-
RR9+
RQ9+
RP9+
3053.7814 3052.0815f 3050.3800 3048.6787a 3043.5845 3041.8871 3036.7954e 3033.3782 3031.6088e 3029.4280
3119.7678 3119.8970 3120.3774 3121.7803 3123.4088 3125.07 29 3126.7463 3128.4244 3130.1941 3131.7849 3133.4662 3135.1470 3136.8278 3138.509 2 3140.1898 3141.8687 3143.5482 3145.227 6d 3146.9037e
3080.5981d 3079.05 OOe 3076.2868 3076.0051 307 5.9505 3075.9291e
3033.4012d 3030.5124 3028.5469 3026.8102 3023.4265 3020.0750e 3018.4062e
See the corresplonding footnotes t o Table 11.
TABLE VI: The K A K = 10 Subband of u 4 lower branch
J'= 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
RRIO31 01.7 8 7 1 3103.47 87 31 05. I. 694 3106.8590 3108.5474 3 110.2 34 1 31 11.9185 3 113.599 6 3115.2737 3 116.92 8 1 3118.4706
RQN-
(3083.0904) (3083.0845) 3089.07 8 3 j (3083.0716) (3083.0644) (3083.0562) 3083.0464e 3083.0340d 3083.0159 3082.9788 3Q82.8306f 3081.9448
i
upper branch
RP,o-
RQIO+
RP,"t
3057.588ge 3055.8859' 3052.4808d 3050.77 65 3049.0661 3047.338ge 3045.5013 3042.9251d
31 19.ij274d
36
3118.9643 3120.5299 3122.1331 3123.7940 3125.4671 3127.1446 3128.8239 3130.5035 3132.1834 3133.8638 3135.5436 3137.2237 3138.9024 314 0.58 06 3142.2584
3085.0143 3083.7703 3083.2003 3083.1151 3083.0888e
3044.1826 3042.4097d 3 040.69 68
3143.9360
See the corresponding footnotes to Table 11.
(c) From the asymptotes in Figures 1 4 ,it is obvious that the two interacting levels have strongly different slopes, i.e., B'- B"va1ues. While the main level, v4, has a relatively small negative slope, the perturbing level has a huge slope of -0.030 to 0.035 crn-l which, by itself, strongly suggests that it is the u3 = 3 level.
This large difference in slopes explains why the resonance is so localized. The perturbing band (here 3v3)has a very small intensity by itself (at least for these J and K values) so that it appears only when a strong wave function mixing occurs with the other level. Moreover, for KAK = 6 and 7 , the crossings occur for relatively high J values,
The Journal of Physical Chemistry, Vol. 83, No. 11, 1979
1496
Georges Graner
TABLE VII: The K A K = 11 Subband of v 4 lower branch
a--g
J’a
RRl,-
12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
3110.6231 3112.3077 3113.9858 31 15.637 0 3116.9529 3117.6031
upper branch
Rp,,
RRII+
3064.7326 3062.993@
3115.7864d 3116.5190 3117.5186 3119.1164 3120.7856
RQli-
(3090.2362) (3090.2245) (3090.2069) 3090.1632 3089.7853
RPl-
RQII+
3 092.0092 309 1.9453 3090.3503 3090.2545 3090.2311”
3063.8732< 3061.4886 3059.7006 3057.9845 3056.2806 3054.5800 3052.8753“ 3051.177 lg
3124.1445 3125.8259 3127.5072 3129.1880 3 130.8686 3132.5486 3134.2282 3135.9069 3137.5858 3139.2625 3140.9393 3142.6151 3144.2892 3145.9642 3147.636gd 3149.3073“ 3150.9787e 3152.6470‘
See the corresponding footnotes t o Table 11.
TABLE VIII: Results Concerning the Local Resonances in u 4
-
-
K”AK value of J ’ nearest to the crossing A , cm-’ (distance of minimum approach) cm-I) A / ( 2 [ J ’ ( J ’t 1)- K(K i 1)]1’2) a
6
7
8
9
10
11
37 1.95a 26.4
33 1.5442 23.6
30 1.3662 23.3
26 1.0840 21.9
21 0.9397 25.0
16 0.5657 23.9
Not actually seen, but estimated from the curve.
where the transitions of v4 itself are becoming weaker. The most favorable case is KAK = 9 since, not only the J value is average but, for spin statistical reasons, the intensity of each transition is multiplied by two.
Numerical Treatment of the Resonances To obtain more information on these localized resonances and especially on the perturbing level, we treated each of them separately by the procedure used in ref 14. Let us suppose for the moment that only two subbands of two different bands are involved in this resonance. If we represent unperturbed upper state energies of each subband as
+ alJ’(J’+ 1) + azJn(J’+ 1)2 E2 = bo + b,J’(J’+ 1) + bzJn(J’+ 1)’
El = a.
(2)
(3)
then the perturbed energies are given by E* = (El + E , ) / 2
f
[ ( E ,- E2)’/4
+ Weff2]”z (4)
in which We, is given by eq 1when we deal with a Coriolis interaction. The experimental frequencies are converted into upper state energies by using the ground state rotational constants of ref 13. Then these energies are fitted by least squares according to eq 4. This fitting of each perturbed subband of v4 was quite easy for K h K = 9, 10, and 11 and yielded standard decm-l. Slight but real viations slightly larger than l X improvements giving standard deviations of less than 5 X cm-l wete obtained by adding to formula 2, which
relates to v4, an extra term a3J5(J’+l)3.This means that the assumption that only two bands are interacting is only approximately valid. There are indeed other interactions with v4, which are reflected in the necessity of including the fourth term in the expansion of the so-called “unperturbed energy”. The same reason explains why we had more problems satisfactorily fitting the KAK = 6, 7 , and 8 subbands. Of course, the fact that we had very little information on the quasi-vertical part of the curves on Figures 1-3 was a serious handicap. However the main reason is the existence of a stronger Coriolis resonance of v4 with a band that we have identified as 2vS2. This interaction is governed by a W, term (see eq 1) of -0.110 cm-l. Actual avoided crossings were observed in the KAK = 3 and 4 subbands of v4. There is no actual crossing in subbands 6,7, and 8 but this third perturbing level is not far off. For instance, it was found that for J’ = 20, this third level is about 25 cm-’ above the corresponding level of RR6v4. We, for J’= 20 is then about 2 cm-l. This interaction by itself pushes down the u4 = 1 level by roughly Weft/A = 0.160 cm-’ which is by no means negligible as compared to the effect of the resonance with 3v3. This spurious effect is strongly J dependent and spoils our efforts to fit our data according to a simple model. Therefore, the results of our fits, which are given in Table IX, are to be taken with a grain of salt for KAK = 6-8 while they can be reasonably trusted for KAK = 9-11. The terms al and bl are effective B’ values for the corresponding subband. If they are actually completely deperturbed, they should be equal to B’- DJK’K‘, which explains why they decrease regularly for increasing K
The Journal of Physical Chemistry, Vol. 83, No. 11, 7979
Localized Resonances in CH,F
1497
TABLE IX: Results 09 the Fits of the K Subbands of CH,F by Eq 1-4'
K AK
8 Band v 4 Parameters a0 3209.7767(16) 3273.3509(3) 3345.4915(14) a, 0.8510001(96) 0.8508750(23) 0.8506882(19) 106a, 1.589(1 4 ) 1.655(4) 1.761(3) 101la, - 13.4(59) -9.35(21) -4.87(11) Band 3v3 Parameters bo 3254.3465(22) 3310.6267(120) 3375.5485(112) b, 0.8183434b 0.8180941(104) 0.8177807(124) 106b, 1.732b 1.732b 1.732b 22.372(8) 22.036(8) coupling term 1O3WC 22.378(41) std dev of fit 1030 3.423 0.570 0.582 a
6
7
9
10
11
3426.1934(5) 0.8504155(28) 1.798(4) -3.50( 1 7 )
3515.4388(3) 0.8500794(16) 1.792(3) -3.83( 1 2 )
3613.2081(4) 0.8497030(27) 1.768(5) -5.45(24)
3449.0671(21) 0.8174408(31) 1.732b 21.773(6) 0.481
3531.1991(15) 0.8170439(55) 1.732b 21.661(6) 0.271
3621.9341(9) 0.8165720(37) 1.732b 22.750(12) 0 299
All results are in crn-'. The errors quoted are standard deviations in units of the last significant figure.
TABLE X: Summary of Molecular Parameters of '*CH3F u , = 1 (ref 1 6 ) u , = 2 (ref 1 6 )
u, = 2 (ref 15)
--
E, A, - A, Bu - Bo DJ - DjO LIJ, - DJK' DK - L)KO
1048.61077 -9.81 x 10-3 -11.294 X l o - , -0.15 X 4 x 10-6 -5 x
2081.3803 -19.45 X -22.200 x 10-3 -0.15 X 4 x 10-6b - 5 x 10-6b
2081.383 -19.47 x -22.162 X -0.1 x 4.5 x 10-6 -5 x 10-6
Fixed.
u, = 3 (ref 15)a
3098.441 -32.73 x -0.3 x
a The parameters of the u , = 3 state are obtained from those of the 3v,-v3 band by adding those of the u, = 1 state. authors af ref 1 6 have assumed that the distortion parameters in the u, = 2 state are equal to those in the u, = 1state.
values. In the same way, a2 and b2 should be close to -DJ; this is reasonably verified for a2 while we had to constrain b2 to -Dj'.
Identification of the Perturbing Level Positive identification of the perturbing level as 3v3 is not difficult, We have two reliable pieces of information on the nu3 levels. First Betrencourt15 reported a high resolution study of 2v3 and of 3v3-v3. Then Freund et a1.16 used laser Stark spectroscopy to study v3 and 2v3-v3. The results of their investigations are gathered in Table X, and enable us to predict reasonably well the 3u3 band. Moreover, it happenEi that the same spectrum B which is used here also contains the region of 2000-2100 cm-l. We have thus been able to look at a better resolved spectrum of 3v3-v3 on which we can see K fine structure that was not visible in ref '15. The application of the Ritz principle to transitions of 3v3-v3 and those of v3 yields the transitions of 3v3 We have thus been able to find, among the numerous lines present in this region, many low J and low K lines of 3v3. Most of these lines have been checked through the use of GSCD. It should be pointed out that this band 3v3 is very weak. T o give an example, one of the strongest lines QR3(S)has about the intensity of R&14(25)of v4 or one third of the intensity of RRv7(29).Therefore, we have no chance to see the lines near the region of the crossing with v4 except the very few lines which borrow intensity from v4 and which are listed in Tables 11-VII. We have fitted these lines of 3v3 to a classical model for a parallel band of a symmetric top, without any perturbation. The rlesults of this fit are given in Table XI and the fitted lines are given in Table XII. The results of Table XI call for two different comments. First, comparison of 'Tables X and XI shows convincingly that the 64 low J and K lines used here belong to 3v3 and that the u3 = 3 state is essentially unperturbed. The reader can also follow the variations of A,-A. and Bo-Bo in the sequence of states u3 = 1, 2, and 3 as well as the less obvious variations of the centrifugal distorsion constants. It is quite rare that such a "long" series of unperturbed bands can be obtained for a pentatomic molecule so that the trends obEierved are informative.
The
TABLE XI: Results of the Fit of 64 Transitions of 3 u 3 with an Unperturbed Modela VO
103(~'- A " ) 1 0 3 ( ~-' B " ) 106(Dj'- DJ") 1 0 6 ( D j ~-' DJK") 1 0 6 ( D ~- 'D K " ) std dev 1O3u
3098.4428(7) -29.170(49) -32.721(48) - 0.277(51) 5.60(29) - 11.13(46) 1.29
All values in cm-'. All ground state constants have been fixed to the values of Table I. The errors quoted are standard deviations in units of the last significant figure.
However our main purpose was to prove that the localized perturbations in v4 that we have analyzed earlier are actually due to 3v3. From Tables I and XI, we can easily compute the subband origins and subband effective B' for the u3 = 3 state. They are given by Esub
=
~0
+ (A'- B')P - DK'P
(5)
Bef/ = B ' - DjK'K2
(6) and should be equal to bo and bl of Table 1X respectively. The comparison is made in Table XIII. It shows unquestionably that our identification of the perturbing level as u3 = 3 is correct. Small differences between Be,,' and bl are probably not really significant. On the other hand, Esub is always slightly larger than bo by 0.02 or 0.03 wavenumbers, a difference which might point to a small imperfection in our model. To summarize, we have proved that the anomalies found in the K"AK = 6-11 subbands of v4 are due to a Coriolis interaction of the ~4 = 1 state with the K = 6-11 sublevels of u3 = 3.
Consequences The interest of the resonances we have identified between the u3 = 3 and u4 = l states of CH3F lies mainly in the relations between u3 = 3 and u3 = 1 and in the importance of the latter level. It has been noticed several years ago that several lines of the C 0 2laser at 9.5 pm are absorbed by the v3 band of CH3F. This fact has given rise to a wealth of scientific
1498
The Journal of Physical Chemistry, Vol. 83, No. 7 1, 1979
Georges Graner
TABLE XII: Transitions of 3u3 Used in the Fit of Table XIa line
obsd
obsd - calcd
line
3 097.819 5 - 0.0008 QR 3(12) QQ 3(4) 3097.8468 0.0005 QR 5 V 2 ) QQ 4(4) 3097.4932 0.0005 QR 6(12) QQ 3(5) 3097.5548 0.0019 QR 5 U 3 ) QQ 5(5) 3097.1007 0.0010 QR W 3 ) QQ 3(6) 3097.1599 0.001 1 QR 5(14) QQ 5(6) 3096.6405 - 0.0008 QR 6(14) QQ 3(7) 3096.702gb 0.0038 QP 3(5) QQ 5(7) 3096.7417 - 0.0005 QP 3(6) QQ 6(7) 3 096.79 37 QP 3(7) - 0.0029 QQ 7(7) 3096.1168 QP 4(7) - 0.0007 QQ 3(8) 3096.17 20b QP 5(7) -0.0019 QQ 5 ( 8 ) QQ 6(8) 3096.21 58 - 0.0002 QP 4(9) 3096. 3286c - 0.0067 QP 6(9) QQ 8(8) 3095.5831 - 0.0001 QP 3UO) QQ 5(9) 3 09 5.6 2 44 0.0002 QP 4~ QQ 6 ( 9 ) 309 5. 1452d -0.0123 QP 5(10) QQ 9(10) 3094.2442 0.0002 QP 6(10) QQ 6(11) QQ 8(11) 3094.3559 0.0020 QP 7 ~ 0 ) QQ 9(11) 3094.4291 - 0.0001 QP 2 ( 1 1 ) QQ 6(12) 3 09 3.4 548 - 0.0009 QP 3(11) QR 3(3) 3104.6313b -0.0018 QP 4(11) QR 3(5) -0.0011 QP 5(11) 31 07.3168 - 0.0005 QP 6(11) QR 3(7) 3109.7 394 3110.8528 0.0003 QP 3 U 2 ) QR 3(8) 311 0.8735 - 0.0004 QP 6(12) QR 4(8) QR 6 ( 8 ) 3110.9418 0.0007 QP 3(13) QR 3(9) - 0.0003 QP 4(13) 3111.8990 3111.9827 QR 6(9) - 0.0014 QP 5(13) 3112.8801 - 0.0003 QP 2 ~ 4 ) QR 3UO) QR 4(10) 3112.8985 -0.0013 QP 3 0 4 ) QR 3(11) 3113.7962 0.0003 QP 4(14) a Note that the lines corresponding to K = 0, 1, and 2 are overlapping so that they 0.1. Weight 0.01. Weight 0.001. TABLE XIII: Comparison of the Subbands Analyzed in Table IX with the Subbands of 3 u , bo Esub b, (Table IX) (eq 5) (Table IX) 3254.3465 3254.3816 (0.8183434)a 3310.6267 3310.6552 0.8180941 3375.5485 3375.5613 0.8177807 3449.0671 3449.0894 0.8174408 3531.1991 3531.2274 0.8170439 11 3621.9341 3621.9617 0.8165720
K 6 7 8 9 10 a
Beff’ (es 6 ) 0.8183434 0.8180800 0.8177761 0.8174317 0.8170468 0.8166213
Fixed t o B,ff’. All values in ern-’.
results, of which we can quote only a small part. Passive Q switching of the C 0 2 laser by u3 of CH3F was obtained as early as 1969.17 Laser action on six rotational transitions near 500 pm was later observed in CH3F gads optically pumped by a pulsed C 0 2 laser. This led to the development of powerful lasers a t 496 pm. These lasers, on which many papers have been written, are apparently the most powerful available in the far-infrared. Reference 18 was also the pioneer work for the rapidly growing field of far-infrared lasers. Another interesting experiment was the observation of Doppler-free two-photon absorptionlg in the u3 band of CH3F. One COz laser line is close to the QR1(l)line of u3 while another one is close to the QR,(2) line of the hot band 2u3 u3 so that the two-photon absorption carries the molecule to the u3 = 2 state. This was apparently the first example of such two-photon absorption in the infrared. In addition to the obvious interest of Doppler-free absorptions, we should quote also the possibility of stimulated emission following two-photon excitation.20 However, it would be an oversimplification to assume that when CH3F absorbs photons from a COz laser, only the u3 = 1state is involved. As early as 1972, Weitz, Flynn,
-
obsd
obsd - calcd
3114.6455 3114.6884 3114.7168 3115.4681 3115.4945 3116.1833 3116.2107 3089.3039 3087.2751 3085.1792 3085.2077 3085.2424 3080.8168 3080.8996 3078.5033 3078.5274 3078.5629 3078.6070 3078.658gb 3076.1295‘ 3976.147 0‘ 3076.1742 3076.2076 3076.2494 3073.7274 3073.8288 307 1.2487 3071.2674 3071.3016b 3068.6783b 3068.69 5 0 3068.7184
- 0.0004 -0.0020 -0.0007 0.0004 -0.0023 - 0.0001 0.0004 - 0.0008 0.0006 0.0000 0.0020 0.0009 - 0.0024 0.0005 0.0001 -0.0011 0.0002 0.0001 -0.0037 -0.0017 - 0.0012 0.0013 0.0012 - 0.0003 - 0.0012 0.0013 0.0044 - 0.0003 0.0023 -0.0021 - 0.0008 0.0000
were not included in the fit.
Weight
and RonnZ1demonstrated that CH3F,when its v3 mode is pumped, exhibits fluorescence at 3000 cm-l, with a risetime of a few microseconds at 1 torr. Later the same authors and their collaborators have pursued the study of vibration-vibration equilibration in CH3F.22-25 I t appears from these studies that the absorption of energy from the laser is very quickly followed by “upthe-ladder’’ processes populating the u3 = 2 and u3 = 3 levels: C H ~ F ( U+~CHBF(v3) ) C H ~ F ( ~+UCH,F(GS) ~) (7) CHBF(u3) + C H ~ F ( B U+~ )C H ~ F ( ~+UCH,F(GS) ~) (8) where GS indicates the ground state. These processes are due to very efficient near resonant collisions. For instance, seven collisions are sufficient to activate the u3 = 2 ~ t a t e The . ~ succeeding ~ ~ ~ ~ steps, leading to fluorescence in the so-called u1 and u4 modes a t 3000 cm-l, have been also discussed by the same a ~ t h o r s ~but l-~~ not in an entirely satisfactory way. Quoting ref 23: “No pathway was found to have a probability large enough to account for the observed rapid filling of the u1 and v4 states”. The present author suggests that the process could be the following: (a) Filling the u3 = 3 state by the up-the-ladder process described by eq 7 and 8. (b) Fast redistribution of energy within the rotational substates of the u3 = 3 level. (c) Since the local resonances give a complete mixing of the wave functions, the energy is redistributed to u4 = 1. The privileged transfers take place near ( K = 6, J = 371, ( K = 7, J = 33), ( K = 8, J = 30), ( K = 9, J = 26), ( K = 10, J = 21), and ( K = 11, J = 16) (see Table VIII). (d) A new redistribution occurs within the rotational substates of u4 = 1. Since this state is itself coupled to 2u52,
The Journal of Physical Chemistry, Vol. 83,
Adiabatically Corrected Sudden Approximation
+
2~50,v2 v5, 2vz, and vl by numerous long-range and local resonances that we lhave positively identified, it is no wonder that all these [stateswill be populated shortly after us = 3 itself. This should explain why the risetime of the fluorescence a t 3000 cm-l is so short. These phenomena should of course also be introduced to explain all the processes where methyl fluoride absorbs energy from a C 0 2 laser such as Q switching, far-infrared lasers, and two-photon absorptions.
No. 11, 1979 1499
(7) J. Connes, H. Delouis, P. Connes, G. Guelachvili, J. P. Maillard, and G. Michel, Nouv. Rev. Opt. Appl., 1, 3 (1970). (8) G. Guelachvili, Now. Rev. Opt. Appl., 3, 317 (1972). (9) G. Gueiachvili, T h k e d’Etat, Orsay, 1973. (10) G. Gueiachvili, Appl. Opt., 17, 1322 (1978). (1 1) M. Betrencourt and M. Morillon-Chapey, Mol. Phys., 33, 83-94 (1977). (12) M. Betrencourt and M. Morillon-Chapey, to be published. (13) G. Graner, Mol. Phys., 31, 1833-1843 (1976). (14) C. Betrencourt-Stirnemann,G. Graner, and G. Guelachvili, J~ Mol. Spectrosc., 51, 216-237 (1974). (15) M. Betrencourt, J. Mol. Spectrosc., 47, 275-285 (1973). (16) S. M. Freund, G. Duxbury, M. Romheld, J. T. Tiedje, and T. Oka, J. Mol. Spectrosc., 52, 38-57 (1974). (17) T. Y. Chang, C. H. Wang, and P. K. Cheo, Appl. Phys. Lett., 15, 157-159 (1969). (18) T. Y. Chang and T. J. Bridges, Opt. Commun., 1, 423-426 (1970). (19) W. K. Bischel, P. J. Kelly, and C. K. Rhodes, Phys. Rev. Lett., 34, 300-303 (1975). (20) D. Prosnitz, R. R. Jacobs, W. K. Bischel, and C. K. Rhodes, Appl. Phys. Lett., 32, 221-223 (1978). (21) E. Weitz, G. Flynn, and A. M. Ronn, J . Chem. Phys., 56, 6060-6067 (1972). (22) E. Weitz and G. W. Flynn, J . Chem. Phys., 58, 2781-2793 (1973). (23) F. R. Grabiner, G. W. Flynn, and A. M. Ronn, J . Chem. Phys., 59, 2330-2334 (1973). (24) B. L. Earl, P. C. Isolani, and A. M. Ronn, Chem. Phys. Lett., 39, 95-97 (1976). (25) J.M.PresesandG. W.Flynn, J. Chem. Phys.,66,3112-3116(1977). (26) The exact crossing of the unperturbed levels does not usually occur for an integer value of J’. I f this were the case, one would have exactly A = 2Wen and W , = A/(2[J’(J’+ 1) - K ( K l)]-’’*),
Acknowledgment. The author was a research fellow in Bright Wilson’si group during the academic year 1965-1966. He is pleased to be able to contribute to this Festchrift to testify how fruitful was his association with Bright Wilson. The author is indebted to Dr. G. Guelachvili who provided the spectrum of CH,F. References and Notes (1) K. P. Yates and H. ti. Nielsen, Phys. Rev., 71, 349 (1947). (2) J. Pickworth and H. VV. Thompson, Proc. R . SOC.London, Ser. A, 222, 443 (1954). (3) F. A. Andersen, B. Bak, and S.Brodersen, J . Chem. Phys., 24, 989 (1956). (4) T. L. Barnett, Ph.D. Dissertation, Michigan State University, 1967. (5) M. Betrencourt and 13. Graner, unpublished results. (6) J. Gguere and J. Overend, Spectrcchlm. Acta, PartA, 32, 241 (1976).
+
An Adiabatically Corrected Sudden Approximation for Rotationally Inelastic Collisions between Polar MoleculesS Miliarid H. Alexander * Department of Chemistry, University of Maryland, College Park, Maryland 20742
and Andrew E. DePristo Department of Chemistry, Princeton University, Princeton, New Jersey 08540 (Received October 25, 1978) Publication costs assisted by the National Science Foundation
The sudden approximation is applied to rotationally inelastic collisions between two polar molecules. The relative motion is assumed to be described by a straight-line classical path and only the dipole-dipole interaction is considered. The expression for the degeneracy averaged cross section for the j j b ja/jb’ transition can be factored into the product of angular coupling terms and j-independent dynamical factors. Introduction of an effective energy gap into the sudden action integral makes it possible to correct for the breakdown of the sudden approximation at large impact parameters, where the collision time is long compared to the rotational dephasing time. Within the resulting adiabatically corrected sudden (ACS) approximation the transition probabilities are related to the pure sudden values by a straightforward nonlinear mapping. Comparison with our earlier quantum close-coupling study of the HF-HF system indicates that the ACS method can provide accurate partial and integral cross sections for rotationally inelastic collisions at hyperthermal collisions with a reduction in computation time of at least three orders of magnitude over that required for comparable quantum or classical trajectory calculations.
-
I. Introduction Rotationally inelastic collisions between polar molecules, where the long-range dipolar interaction provides the necessary torque, have long provided the paradigm for rotational energy transfer in molecular co1lisions.l Spectral line broadening, which gave early indirect evidence for these processes, was interpreted within first-order perturbation t h e ~ r y The . ~ ~first ~ direct probe of the kinetics of rotational energy transfer was provided by microwave
* Research supported b y the National Sciance Foundation, Grant
NSF CHE78-08729; b y the General Research Board and the Computer Science Center, IJniversity of Maryland; and by the Office of Naval Research. 0022-3654/79/2083-1499$01 .OO/O
double resonance experiments, a technique pioneered a t Ottawa4 and a t Harvard in the research group of E. B. Wilson, Jra5In a landmark calculation Rabitz and Gordon6 used the first- and second-order Born approximations to determine rotationally inelastic cross sections and energy transfer rates for the HCN-HCN and ICN-ICN systems. Good agreement with the experimental double-resonance results was obtained. New experimental techniques7-12 now allow the measurement of state-resolved rotational energy transfer rates and cross sections in collisions between polar molecules. As an example, Wilcomb and Dagdigian, using electric quadrupole state selected beams of LiH in rotational state j = 1,l0have been able to determine relative cross sections 0 1979 American Chemical Society
