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Vibration-vibration energy transfer in CH3Br-HCN mixtures
VIBRATION-VIBRATION
-11 March 1983
CHEMICAL PHYSICS LETTERS
Volume 95, number 4.5
ENERGY TRANSFER
IN CH3Br-IitiN
MIXTURES
Andrew OUDERKIRK and Eric WEITZ * Department of Chemistry. Northwestern
University. Evanston. Illinois 60201. USA
Received 2 December 1982; in f&al form 3 January 1983
The pathways for energy transfer between CH$r and HCN have been determined along with their relative importance. The rate of vibrational energy transfer from CHsBr&) to HCN&) has been determined to be 75 f 25 rns-’ Torr-I. The factors which determine the relative importance of intermolecular vibrational energy transfer pathways will be discuswd.
1, Intr~uction Highly specific energy transfer pathways have been shown to exist in a variety of molecular systems. Understanding what leads to this specificity is crucial in determining why some molecules possess vibrational states which are metastable with respect to energy transfer and relaxation processes. These metastable states are ~po~ant in the develop~~ent and optimization of molecular laser systems and may be of use in laser-induced chemicai reactions. For example, two well-known lasing gases, CO, and N20 exhibit metastable asymmetric stretching modes [ 1,2], the upper laser level for laser action in the 10 pm region in both systems. There have also been some studies of mixtures exhibiting mode specific intermolecular energy transfer_ Recent examples are CH3F-SO? f3] and CH3FN,O [4] _ In the latter system it was observed that energy transfer between the v3 and v6 states of CH3F and the N,O symmetric stretch (10’0) was faster than transfer to the overtone of the N20 bending mode (020) despite the overtone of the N,O bending mode bein closer in energy to the initially excited CH3F mode than the N,O symmetric stretch. Results of a similar nature were found in the CH,F-SO, study. In both systems it could not be definitively determined whether preferential transfer to a stretching mode was due to the multiple quantum number
Cf+$r(qj) f HWO) %
CH, Br(0) + HCN(r$,
k_
1
PLE = 240 cm-l,
(1) k_
CH3Br(y3)
+ HCN(0)z
LIE= -101
CH3Br(0) + HCN(+),
cm-‘_
(2)
It has then been possible to draw some conclusions about the specificity of energy transfer in this and related systems.
2. Experimental The experimental apparatus has been described previously [5] _Briefly, the experiment consisted of
* Alfred P. Sloan Fellow.
0 CO9-2614/83/0000-0000/$03.00
change involved in transfer to the overtone of the bending mode or due to the difference in the nature of the motion associated with the CH,F states and the bending mode overtones in N20 and SO,. It was felt that a study of a system such as CH3BrHCN might shed light on this and related questions. In this system two primary pathways of energy transfer are available from excited CH3Br to HCN. An analysis of energy transfer rates into and out of the v3 mode of CH3Br and the V~ mode of HCN has allowed the determination of the relative rates for these channels, which are indicated in the equations
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monitoring rhe infrared emission from v3 of CH3Br and 18, of HCN following excitation by a Q-switched CO2 laser. The CO, Iaser provided a 2.0 mJ pulse with a temporal width of 1 .O petsfwhm at 200 Hz. Single-line operation on R( 14) of the 9.6 bun branch was confirmed by an Optical Engineering spectrum anaiyLer_ Ct Ij Br( r!; ) and t ICS(LJ,) fluorescence were detectcd h>, a liquid-helium cooled Cu : Ge detector containing a cooled 13.5 pn long pass (LP) interference filter. Tht response time of the detector and the associated electronics WJS measured to be 61 ps. The sip reals \vere digitized by a Biomation 6 10B and averaged by a hard wired signal avrraper. The data were then transt‘crrcd 10 3 CDC 7hOO computer for signal analysis and d13Ia reduction. The 14. i pm radiation from tlCN was isolated front thr rch ivci)- strong 16.4 pm C’f1,Br radiation by t rsnsntit 1inf t iic fluorescence through a 1 cm NaCi \x$rtJo\v ;~nd 3 30 cm cold gas filter (CCF) filled with IOU. 200 Torr of Ct I;Br. in separate experiments for each WI of cspcrimental conditions it was determined that this range of CH,Br in the CGF was sufficient 10 complrtely absorb emission from pure CH3Br in the sample cell. CI i3 Br( ~2~) emission was observed by blocking 1ICN emission with a 14.5 pm LP filter. The CI 1.; t3r obtained from hlatheson (99.5% pure) was subjected to several freeze--pump-tIla\\, cycles using 3 dr>‘-ice -acetone bath to remove CO2 impurities. The t iCX obtained from Fumaso Inc. was purified by muitiplz fieezr--puInp-tliaw cycles using an IIpcn131ie slusl~ to remove the large amount of CO pres~111. The purified I K’N UTISstored at -7S”C to retard i~~~l?.i1lr‘1jjr3tioIl. t\rgorl (W.W5!T pure) was obtained from Markson and ~vas used without further purificsIicui. \~h!n Inisrures of gases were prepared they were aII~~\vcd to niis in the fluorescence cell for 25 min. Longer times were used for higher pressures. The ahuuinium cell and monel gas handling system had 311 outpasjleak rate of =.6 p/h and was maintained 31 21 ? 1°C.
3. Results An energy level diagram of the HCN-CHIBr system is allowed in fig. l_ For the purpose of dejermining the rate constants X-t and k,. fluorescence from 370
11 March 1963
PHYSICS LETTERS
-
2u,
3v,
-
-
2Y,
“2
-2+
-
“6
-=z
--=a
CH,
Br
HCN
Fig. 1. A partial vibrational energy level diagram of methyl bromidr and hydrogen cyanide. ~6 of CHsBr was the pumpcd state and the kinetics were drtermincd by the temporal beiuvior of the fluorcscencc from CIisBr(+) and HCN(v,).
V? of HCN and p3 of CH;Br was observed from a 0.125 Torr HCN. 0.5 Torr CH,Br mhture as a function of pressure of added argon. A typical fluorescence signal is shown in fig. 2. The variation of the rise and fall rates of 11, and p3 as a function of argon pressure is shown in fig. 3.
4. Discussion Three features of the plot in fig_ 3 immediately stand out and are relevant to the determination of k, and kz_ First. at low argon pressure zj2 of HCN is populated faster than y3 of CH,Br. Second. the fall wte of both states are quite close to each other. Third. the rise and fall of v3 in CH3Br is quite close to that determined for pure CH,Br as a function of added argon [6]_ The implications of these observations will now be discussed with additional information about the system provided by computer modeling_
Volume 95, number 4,5
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11 March 1983
I
I
t
11
40
11
”
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rvpial fluorescence sknal from HCN(v,). The s@tal was obtained from a mixture cf 0.125 Torr HCN in 0.5 Torr CHsBr.
Fig. 2. A
The solid line is the result of a’non-linear
least-squares analysis.
160
I
The rapid population of v2 of HCN versus v3 of CH,Br implies that the pathway involving direct transfer from ZQ of CH,Br to r~? of HCN, eq_ (I), is a major pathway for energy transfer to u2_ Furthermore, the implication of the data is that the rate constant associated with eq. (1) is larger than the rate constant associated with eq. (2). This is verified by computer modeling of.the system and allows us to establish bounds on the ratio of the two rate constants, k, and &-
60
PI
OO
10 Argon
20
30
1
The qualitative features of the rise rates in fig. 3 are consistent with this picture. Intem~olecular V-V processes will not be accelerated by the addition of a rare gas as they require a donor-acceptor collision_ However, intramolecular V-V processes can be enhanced by rare-gas collisions [7,S] _Thus as rare gas is added to the system, the rate of population of v3 increases since the process primarily responsible for its population is
Pressure (torr)
Fig. 3. Rise and fall rate dependence
on azon for a mixture of 0.5 Torr CH3Br and 0.125 Torr HCN. Fluorescence of CHxBr(Q) and HCN(@ arc plotted as triangles and squares, respectively_ The rise rates are faster than the corresponding fall rates. The lines are linear least-squares fits to the data.
CH3Br(v6)
li+ f- MC
AE = 341 cm-l.
3
CH3Br(v3)
+ M.
(3) 371
vohlrr1e
95. nurnhcr
CHEMICAL PHYSICS LETTERS
4.5
where Xl is the relevant collision partner. This is a nonresonazlt intraznolecular energy transfer process and can be enhanced by the addition of rare gas. Addition of sufficient rare gas can cause the rate of population of this state to exceed that of v2 of HCN. Though population of v , occurs via rare-gas-indepen&XI steps [eqs. (I band72)]. Y’ is a state in a kinetic:dly coupled system. As such it is coupled to states 111~ are poptzlarcd or depopulated via rare-gas-dependezzt processes. A frsctiozz of the amplitude of these pr~c’sscs c‘~inappear in zhs rise of pZ which can product XI ;Ipparezzt rare-gas depezzdence of its rise rate. 1lowever modeling of the system indicates that this is 3 ~1311 effect relative to the process of eq. (3). \\liilc ~1~and I,~ are not in equilibrium on the time scale of t hc rise otl z~?. the similar fall times of both st:ztes imply that these states are in equilibrium on 1112time scale of the fall. This equilibrium is expected tu occ‘lzr via the process of eq. (I!)_ Equilibriuzn could consckzbly occur via the pathways shown in eqs. ( 1 ) md (3 ).even ifk, did zzot have a signiticant magnitude. ilowcver. it has been previously shown that ~~rrr01111tl the horn” type processes where ezicrgy ~nust be tz3nsfcrred from a low-lying state through 3 state with less population are inefficient [S]. The above picture is verified by our computer modeling and allo\vs us to pun approsimrlte bounds on k.,. Another possible pathway for escitingHCN ZT-, involves lhc praccss (‘I 1; lSr(zjb 1 + I K%(O) -+ Cl 1; Br(0) + HCK(,I!V2 ). 3:‘
=
-460
a11
-1
_
t-olluwcd by rcson;int transfer of energy from 2v,. to I’, _This is cspected to be incfficienl because it is :~lst~>n-‘around the horn process”. In addition, it inwives a mulriple quantum number change which
should decrease the probability of such a process. The rise and fall rates of uj as a function of argon :irc sinziltir to that obtained for pure CH,Br in an argozl mixture. implving that HCN is not an estreznely cl’liciczzt promote; of V -L T/R processes in CHJBr. n01 is it estrcniely efficient at promoting V-V-trimsfcr het\veen v6 and +_
This allows us to computer
model the system with rate cozlstants for the V + T/R kzcrivation of zli and zj6 of CH,Br and the V-V cquilihralion of these states that are very similar to that for pure Cl I, Br and CH, Br in argozl.
11 hlarch 1983
The above iznplications were confinned and additional information about the systezn obtained via coznputer modeling of CH3Br-HCN system. The computer model consisted of the ground state of CH;Br and HCN as well as zig and v6 of CH,Br and y of HCN. The model involved a numerical integation of the rate equations shown in eqs. (l)-(3) as well as equations for the V + T/R deactivation of v3 and v6 of CH,Br and LJ?of HCN. Rate equations for processes induced by CH3Br, HCN and Ar collisions were included for all V -+ T/R and intramoleczzlar V-V processes. The details of computer znodeling are described in ref. [7]_ Rate constants for V + T/R deactivation of v3 and vs of CH,Br by CH3Br and argon were taken from ref. [6] as were the rate constants for the process of eq. (3)_ V + T/R deactivation of_yCN was taken to be equal to the value of 54 111s Torr-’ given in ref. [9] for the deactivation of zlZ of HCN. The deactivation of HCN by argon is insignificant in deterznining k, and kz as long as it. as expected, is of a smaller magnitude than the self deactivation of HCN. The remaining unknown rate constants sre the V -+ T/R deactivation of CH3Br by HCN, the V + T/R deactivation of HCN by CH,Br and the process of eq. (3) for Xl = HCN. It was found that sohztiozzs to the model consistent with experimental data could be generated over a range of reasoluble rate constants for these processes_ Furthermore. the priznary behavior of the data that are being duplicated involve the argon dependence of the rise times of vj and Y? and the above unknown rate constants do not significantly enter into these dependences, they have little effect on our conclusions. Values which should not be taken as actual values for these rate constants but which do provide good fits with experimental data are SO,30 and 20 ms-’ Torr-’ respectively for the above processes. With these parazneters it is possible to find acceptable values for the rate constants ,k 1 and k, _ It is found that k, must always exceed k2 and% must exceed k _? which is the more relevant quantity for coznparison since it, like k 1, is an exothermic rate constant. Typically X-t must be between 2 and 3 times X-_? _ For reasonable
variations of the rate con-
stants disccssed in the preceding paragraph, a value of 75 + 25 IIIS-~ Torr-’ can be established for kl. With argon-dependent rates based upon refs. [6,10] the znodel very well duplicates the behavior of fig_ 3
CHEMICAL
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PHYSICS LETTERS
both qualitatively and quantitatively_ It is now reasonable to consider what this ratio and the maetudes of the rate constants tells us
I1 March 1983
and 020 are -103 and IS cm-‘, for v6 it is 34 and 166 cm-‘? respectively [3]_ These are sufficiently close that near-resonant energy transfer should be
V + T/R processes, especially for systems consisting of hydrides, these calculations often produce very good relative values of rate constants and surprisingly accurate V-V rate constants *_ For the HCNCH,Br system, SSH calculations predict a value of
important in the transfer process [ 14]_ If so, the magnitude of the transition probability will be proportional to the square of the dipole moment derivative matrix element for the transition occilrring in each molecule_ It is then clear that transfer from u3 or v6 to the 100 state is preferred over transfer to the overtone of the bending mode. The overtone transition in both these systems is weali ]I 51 and therefore trnasfer to the 100 state will dominate the near-resonant energy transfer probability. Of course SSH type transfer processes can also occur, but here there is
=l .S for k,/k_,. The major difference in the underlying nature of the energy transfer process to vZ from v3 and v6 is the difference in the + versus u6 normal mode motions: “a being characterized as a C-F stretching motion and v6 as a methyl group wagging motion. Despite these motions being very different in character and the transfer of vibrational energy going to a bending mode which is certainly different in mechanical character than a C-F stretclr-
also a bias against a transition to the overtone_ The magnitude of the transition probability for an overtone is reduced by a factor of -10 over a transition to a fundamental (with everything else being equal) [ 16]_ Though the energy gap and perhaps the breathing-sphere parameter will bias the probability of transfer toward the overtone. this is unlikely to be enough to make up for the reduction in probability relative to 100 due to the multiple quantum number
ing motion, the SSH calculations predict reasonably well the ratio of rate constants. The only parameter that differentiates these states as far as the SSH calculation is concerned is the breathing sphere param-
change_ This is particularly true when it is realized that both “near-resonant” and “hard-core” energy transfer processes will likely be acting in concert in
about the nature of the energy transfer process in this and related systems. Along these lines an SSH calculation of rate constants was performed for energy transfer from + and v&of CH,Br of HCN [ 1 1]_ Though SSH rate constants often predict absolute values of
rate constants
that are significantly
in error for
eter [ 121. This would imply that the mecllanical nature of a mode motion is not that important in V-V energy transfer or at least is adequately accounted for via a breathing-sphere parameter treatment [ 13]_ If so. what implication does this have for the
Cll;F-N,O and CH,F-SO, systems? The fact that simple SW calculations adequately indicate the relative rates fork, and li -2 in the CH3Br-HCN system when very different mechanical motions couple to a common state implies that perhaps the explanation for the behavior in the CH,F-N,O and SO, systems lies elsewhere_ For these systems the energy gap between the donor and acceptor mode is substantially smaller than in the CH, Br-HCN system_ For CHa FN, 0 the energy gaps between y3 and 100.02°0 and O??O are 237, -119 and -137 cm-’ respectively_ For v6 it is even closer; -90,
29 and 11 crnM1 respec-
tively. For SO2 the energy gaps between
* See ref. 171 and references therein.
v3 and 1OC
this system which will then virtually certainly bias the overall energy transfer probability significantly toward the 100 state.
5. Conclusions By examining
the rates of energy transfer into and
out of the v3 mode of CH3Br and the 11~mode of HCN in CH,Br-HCN-Ar mixtures we have determined the relative rate constants of energy transfer from v6 and v3 of CH,Br to HCN. We have also set bounds on these rate constants_ We find that SSH calculations predict reasonably well the relative rate constants in this system_ The implications of these results for other systems which exhibit specific energy transfer pathways are examined. We conclude that a multiple quantum change is more important in determining rates of energy transfer than is the mechanical motion of the modes exchanging energy_ This conclusion is in accord with vibrational energy transfer propensity rules previously put forth [17,1S]_ 373
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Ackttcwledgentent We would like fo thank the National Science l%w~dation for support of this work under grants CITE 79-OS501 and CIfE SZ-06976.
References L.O. ilockcr, M.A. Kovacs. C.K. Rhodes, G.W. Flynn and A. Javan. Phys. Rev. Letters 17 (1966) 233; C.B. hloorc. R.E. \\‘ood. B.L. Hu and J.T. Yardley. J. Chcm. Phys. 16 ( 1967) 4222. RD. Batrs Jr.. C.\\‘. Flynn and A.M. Ronn, J. Chcm. I’hys. 49 ( 1966) I ‘lx!: J.T_ Sardlcy. J. Chcm. Phys. 49 (1968) 2816. KC. Shtcr and G.\\‘. Flynn. J. Chem. Phys. 65 (1976) 4’5. RX;. Ituddkston and E. \\‘eitz. J. Chum. Phys. 7-1 (1981) 2879. G.T. Fujimoto and E. \\‘citz. Chcm. Phys. 27 (1978) 65. A.J. Oudcrkirk. \‘.A. Apkarirtn and E. Weitz. Chcm. Phys.’ 62 (1981) 387. Xl. Mo.ux. \‘.A. Atkuhn 2nd 1:. U’&tr. J. Chcm. Phys. 5-t (1981j 342.
LETTERS
11 March
1983
[S] V.A. Apkarian and E. Weitz. J. Chem. Phys. 71 (1979) 4349. [Y] J-A. hlcGarwy,Jr., N-E. Friedman and T.A. Cool, J. Chem. Phys. 66 (1977) 3189. [lo] A. Hariri, A.B. Peterson and C. Wittig, J. Chem. Phys. 65 (1976) 1872. [ 111 R.N. Schwartz, Z-1. Slawsky and K.F. Herzfeld. J. Chem. Phys. 20 (1952) 1591. [ 121 B-L. Earl and A.hl. Ronn. Chem. Phys. 12 (1976) 113. [ 131 J-L. Stretton. Transfer and storage of eneqy by molecules, Vol. 2. Vibrational enemy (Wiley-Interscience, New York, 1969). [ 141 R-D. Sharma and CA. Brau, J. Chem. Phys. 50 (1969) 924. 1151 G. Herzbeq, Xlolecular spectra and molecular structure, Vol. 2 (Van Nostrand, Princeton, 1945). 1161 J-T_ Yardlcy and C.B. hloore. J. Chem. Phys. 49 (1968) 1111. 1171 E. Wcitz and G-W. Flynn, Photoselective chemistry. Part 2. Vol. 47. Advances in chemical physics (Wiley, New York. 1981): Ann. Rev. Phys. Chem. X.(1974) 275. ] 161 G.W. Flynn, Accounts Chem. Res. 14 (1981) 334; A.C.S. Symposium State-to-State Chemistry, A.C.S. Symposium Series, eds. P.R. Brooks and E.F. llaycs (1977)
-11 March 1983
CHEMICAL PHYSICS LETTERS
Volume 95, number 4.5
ENERGY TRANSFER
IN CH3Br-IitiN
MIXTURES
Andrew OUDERKIRK and Eric WEITZ * Department of Chemistry. Northwestern
University. Evanston. Illinois 60201. USA
Received 2 December 1982; in f&al form 3 January 1983
The pathways for energy transfer between CH$r and HCN have been determined along with their relative importance. The rate of vibrational energy transfer from CHsBr&) to HCN&) has been determined to be 75 f 25 rns-’ Torr-I. The factors which determine the relative importance of intermolecular vibrational energy transfer pathways will be discuswd.
1, Intr~uction Highly specific energy transfer pathways have been shown to exist in a variety of molecular systems. Understanding what leads to this specificity is crucial in determining why some molecules possess vibrational states which are metastable with respect to energy transfer and relaxation processes. These metastable states are ~po~ant in the develop~~ent and optimization of molecular laser systems and may be of use in laser-induced chemicai reactions. For example, two well-known lasing gases, CO, and N20 exhibit metastable asymmetric stretching modes [ 1,2], the upper laser level for laser action in the 10 pm region in both systems. There have also been some studies of mixtures exhibiting mode specific intermolecular energy transfer_ Recent examples are CH3F-SO? f3] and CH3FN,O [4] _ In the latter system it was observed that energy transfer between the v3 and v6 states of CH3F and the N,O symmetric stretch (10’0) was faster than transfer to the overtone of the N20 bending mode (020) despite the overtone of the N,O bending mode bein closer in energy to the initially excited CH3F mode than the N,O symmetric stretch. Results of a similar nature were found in the CH,F-SO, study. In both systems it could not be definitively determined whether preferential transfer to a stretching mode was due to the multiple quantum number
Cf+$r(qj) f HWO) %
CH, Br(0) + HCN(r$,
k_
1
PLE = 240 cm-l,
(1) k_
CH3Br(y3)
+ HCN(0)z
LIE= -101
CH3Br(0) + HCN(+),
cm-‘_
(2)
It has then been possible to draw some conclusions about the specificity of energy transfer in this and related systems.
2. Experimental The experimental apparatus has been described previously [5] _Briefly, the experiment consisted of
* Alfred P. Sloan Fellow.
0 CO9-2614/83/0000-0000/$03.00
change involved in transfer to the overtone of the bending mode or due to the difference in the nature of the motion associated with the CH,F states and the bending mode overtones in N20 and SO,. It was felt that a study of a system such as CH3BrHCN might shed light on this and related questions. In this system two primary pathways of energy transfer are available from excited CH3Br to HCN. An analysis of energy transfer rates into and out of the v3 mode of CH3Br and the V~ mode of HCN has allowed the determination of the relative rates for these channels, which are indicated in the equations
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monitoring rhe infrared emission from v3 of CH3Br and 18, of HCN following excitation by a Q-switched CO2 laser. The CO, Iaser provided a 2.0 mJ pulse with a temporal width of 1 .O petsfwhm at 200 Hz. Single-line operation on R( 14) of the 9.6 bun branch was confirmed by an Optical Engineering spectrum anaiyLer_ Ct Ij Br( r!; ) and t ICS(LJ,) fluorescence were detectcd h>, a liquid-helium cooled Cu : Ge detector containing a cooled 13.5 pn long pass (LP) interference filter. Tht response time of the detector and the associated electronics WJS measured to be 61 ps. The sip reals \vere digitized by a Biomation 6 10B and averaged by a hard wired signal avrraper. The data were then transt‘crrcd 10 3 CDC 7hOO computer for signal analysis and d13Ia reduction. The 14. i pm radiation from tlCN was isolated front thr rch ivci)- strong 16.4 pm C’f1,Br radiation by t rsnsntit 1inf t iic fluorescence through a 1 cm NaCi \x$rtJo\v ;~nd 3 30 cm cold gas filter (CCF) filled with IOU. 200 Torr of Ct I;Br. in separate experiments for each WI of cspcrimental conditions it was determined that this range of CH,Br in the CGF was sufficient 10 complrtely absorb emission from pure CH3Br in the sample cell. CI i3 Br( ~2~) emission was observed by blocking 1ICN emission with a 14.5 pm LP filter. The CI 1.; t3r obtained from hlatheson (99.5% pure) was subjected to several freeze--pump-tIla\\, cycles using 3 dr>‘-ice -acetone bath to remove CO2 impurities. The t iCX obtained from Fumaso Inc. was purified by muitiplz fieezr--puInp-tliaw cycles using an IIpcn131ie slusl~ to remove the large amount of CO pres~111. The purified I K’N UTISstored at -7S”C to retard i~~~l?.i1lr‘1jjr3tioIl. t\rgorl (W.W5!T pure) was obtained from Markson and ~vas used without further purificsIicui. \~h!n Inisrures of gases were prepared they were aII~~\vcd to niis in the fluorescence cell for 25 min. Longer times were used for higher pressures. The ahuuinium cell and monel gas handling system had 311 outpasjleak rate of =.6 p/h and was maintained 31 21 ? 1°C.
3. Results An energy level diagram of the HCN-CHIBr system is allowed in fig. l_ For the purpose of dejermining the rate constants X-t and k,. fluorescence from 370
11 March 1963
PHYSICS LETTERS
-
2u,
3v,
-
-
2Y,
“2
-2+
-
“6
-=z
--=a
CH,
Br
HCN
Fig. 1. A partial vibrational energy level diagram of methyl bromidr and hydrogen cyanide. ~6 of CHsBr was the pumpcd state and the kinetics were drtermincd by the temporal beiuvior of the fluorcscencc from CIisBr(+) and HCN(v,).
V? of HCN and p3 of CH;Br was observed from a 0.125 Torr HCN. 0.5 Torr CH,Br mhture as a function of pressure of added argon. A typical fluorescence signal is shown in fig. 2. The variation of the rise and fall rates of 11, and p3 as a function of argon pressure is shown in fig. 3.
4. Discussion Three features of the plot in fig_ 3 immediately stand out and are relevant to the determination of k, and kz_ First. at low argon pressure zj2 of HCN is populated faster than y3 of CH,Br. Second. the fall wte of both states are quite close to each other. Third. the rise and fall of v3 in CH3Br is quite close to that determined for pure CH,Br as a function of added argon [6]_ The implications of these observations will now be discussed with additional information about the system provided by computer modeling_
Volume 95, number 4,5
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11 March 1983
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I
t
11
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11
”
50
(psec)
rvpial fluorescence sknal from HCN(v,). The s@tal was obtained from a mixture cf 0.125 Torr HCN in 0.5 Torr CHsBr.
Fig. 2. A
The solid line is the result of a’non-linear
least-squares analysis.
160
I
The rapid population of v2 of HCN versus v3 of CH,Br implies that the pathway involving direct transfer from ZQ of CH,Br to r~? of HCN, eq_ (I), is a major pathway for energy transfer to u2_ Furthermore, the implication of the data is that the rate constant associated with eq. (1) is larger than the rate constant associated with eq. (2). This is verified by computer modeling of.the system and allows us to establish bounds on the ratio of the two rate constants, k, and &-
60
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10 Argon
20
30
1
The qualitative features of the rise rates in fig. 3 are consistent with this picture. Intem~olecular V-V processes will not be accelerated by the addition of a rare gas as they require a donor-acceptor collision_ However, intramolecular V-V processes can be enhanced by rare-gas collisions [7,S] _Thus as rare gas is added to the system, the rate of population of v3 increases since the process primarily responsible for its population is
Pressure (torr)
Fig. 3. Rise and fall rate dependence
on azon for a mixture of 0.5 Torr CH3Br and 0.125 Torr HCN. Fluorescence of CHxBr(Q) and HCN(@ arc plotted as triangles and squares, respectively_ The rise rates are faster than the corresponding fall rates. The lines are linear least-squares fits to the data.
CH3Br(v6)
li+ f- MC
AE = 341 cm-l.
3
CH3Br(v3)
+ M.
(3) 371
vohlrr1e
95. nurnhcr
CHEMICAL PHYSICS LETTERS
4.5
where Xl is the relevant collision partner. This is a nonresonazlt intraznolecular energy transfer process and can be enhanced by the addition of rare gas. Addition of sufficient rare gas can cause the rate of population of this state to exceed that of v2 of HCN. Though population of v , occurs via rare-gas-indepen&XI steps [eqs. (I band72)]. Y’ is a state in a kinetic:dly coupled system. As such it is coupled to states 111~ are poptzlarcd or depopulated via rare-gas-dependezzt processes. A frsctiozz of the amplitude of these pr~c’sscs c‘~inappear in zhs rise of pZ which can product XI ;Ipparezzt rare-gas depezzdence of its rise rate. 1lowever modeling of the system indicates that this is 3 ~1311 effect relative to the process of eq. (3). \\liilc ~1~and I,~ are not in equilibrium on the time scale of t hc rise otl z~?. the similar fall times of both st:ztes imply that these states are in equilibrium on 1112time scale of the fall. This equilibrium is expected tu occ‘lzr via the process of eq. (I!)_ Equilibriuzn could consckzbly occur via the pathways shown in eqs. ( 1 ) md (3 ).even ifk, did zzot have a signiticant magnitude. ilowcver. it has been previously shown that ~~rrr01111tl the horn” type processes where ezicrgy ~nust be tz3nsfcrred from a low-lying state through 3 state with less population are inefficient [S]. The above picture is verified by our computer modeling and allo\vs us to pun approsimrlte bounds on k.,. Another possible pathway for escitingHCN ZT-, involves lhc praccss (‘I 1; lSr(zjb 1 + I K%(O) -+ Cl 1; Br(0) + HCK(,I!V2 ). 3:‘
=
-460
a11
-1
_
t-olluwcd by rcson;int transfer of energy from 2v,. to I’, _This is cspected to be incfficienl because it is :~lst~>n-‘around the horn process”. In addition, it inwives a mulriple quantum number change which
should decrease the probability of such a process. The rise and fall rates of uj as a function of argon :irc sinziltir to that obtained for pure CH,Br in an argozl mixture. implving that HCN is not an estreznely cl’liciczzt promote; of V -L T/R processes in CHJBr. n01 is it estrcniely efficient at promoting V-V-trimsfcr het\veen v6 and +_
This allows us to computer
model the system with rate cozlstants for the V + T/R kzcrivation of zli and zj6 of CH,Br and the V-V cquilihralion of these states that are very similar to that for pure Cl I, Br and CH, Br in argozl.
11 hlarch 1983
The above iznplications were confinned and additional information about the systezn obtained via coznputer modeling of CH3Br-HCN system. The computer model consisted of the ground state of CH;Br and HCN as well as zig and v6 of CH,Br and y of HCN. The model involved a numerical integation of the rate equations shown in eqs. (l)-(3) as well as equations for the V + T/R deactivation of v3 and v6 of CH,Br and LJ?of HCN. Rate equations for processes induced by CH3Br, HCN and Ar collisions were included for all V -+ T/R and intramoleczzlar V-V processes. The details of computer znodeling are described in ref. [7]_ Rate constants for V + T/R deactivation of v3 and vs of CH,Br by CH3Br and argon were taken from ref. [6] as were the rate constants for the process of eq. (3)_ V + T/R deactivation of_yCN was taken to be equal to the value of 54 111s Torr-’ given in ref. [9] for the deactivation of zlZ of HCN. The deactivation of HCN by argon is insignificant in deterznining k, and kz as long as it. as expected, is of a smaller magnitude than the self deactivation of HCN. The remaining unknown rate constants sre the V -+ T/R deactivation of CH3Br by HCN, the V + T/R deactivation of HCN by CH,Br and the process of eq. (3) for Xl = HCN. It was found that sohztiozzs to the model consistent with experimental data could be generated over a range of reasoluble rate constants for these processes_ Furthermore. the priznary behavior of the data that are being duplicated involve the argon dependence of the rise times of vj and Y? and the above unknown rate constants do not significantly enter into these dependences, they have little effect on our conclusions. Values which should not be taken as actual values for these rate constants but which do provide good fits with experimental data are SO,30 and 20 ms-’ Torr-’ respectively for the above processes. With these parazneters it is possible to find acceptable values for the rate constants ,k 1 and k, _ It is found that k, must always exceed k2 and% must exceed k _? which is the more relevant quantity for coznparison since it, like k 1, is an exothermic rate constant. Typically X-t must be between 2 and 3 times X-_? _ For reasonable
variations of the rate con-
stants disccssed in the preceding paragraph, a value of 75 + 25 IIIS-~ Torr-’ can be established for kl. With argon-dependent rates based upon refs. [6,10] the znodel very well duplicates the behavior of fig_ 3
CHEMICAL
Volume 95, number 4.5
PHYSICS LETTERS
both qualitatively and quantitatively_ It is now reasonable to consider what this ratio and the maetudes of the rate constants tells us
I1 March 1983
and 020 are -103 and IS cm-‘, for v6 it is 34 and 166 cm-‘? respectively [3]_ These are sufficiently close that near-resonant energy transfer should be
V + T/R processes, especially for systems consisting of hydrides, these calculations often produce very good relative values of rate constants and surprisingly accurate V-V rate constants *_ For the HCNCH,Br system, SSH calculations predict a value of
important in the transfer process [ 14]_ If so, the magnitude of the transition probability will be proportional to the square of the dipole moment derivative matrix element for the transition occilrring in each molecule_ It is then clear that transfer from u3 or v6 to the 100 state is preferred over transfer to the overtone of the bending mode. The overtone transition in both these systems is weali ]I 51 and therefore trnasfer to the 100 state will dominate the near-resonant energy transfer probability. Of course SSH type transfer processes can also occur, but here there is
=l .S for k,/k_,. The major difference in the underlying nature of the energy transfer process to vZ from v3 and v6 is the difference in the + versus u6 normal mode motions: “a being characterized as a C-F stretching motion and v6 as a methyl group wagging motion. Despite these motions being very different in character and the transfer of vibrational energy going to a bending mode which is certainly different in mechanical character than a C-F stretclr-
also a bias against a transition to the overtone_ The magnitude of the transition probability for an overtone is reduced by a factor of -10 over a transition to a fundamental (with everything else being equal) [ 16]_ Though the energy gap and perhaps the breathing-sphere parameter will bias the probability of transfer toward the overtone. this is unlikely to be enough to make up for the reduction in probability relative to 100 due to the multiple quantum number
ing motion, the SSH calculations predict reasonably well the ratio of rate constants. The only parameter that differentiates these states as far as the SSH calculation is concerned is the breathing sphere param-
change_ This is particularly true when it is realized that both “near-resonant” and “hard-core” energy transfer processes will likely be acting in concert in
about the nature of the energy transfer process in this and related systems. Along these lines an SSH calculation of rate constants was performed for energy transfer from + and v&of CH,Br of HCN [ 1 1]_ Though SSH rate constants often predict absolute values of
rate constants
that are significantly
in error for
eter [ 121. This would imply that the mecllanical nature of a mode motion is not that important in V-V energy transfer or at least is adequately accounted for via a breathing-sphere parameter treatment [ 13]_ If so. what implication does this have for the
Cll;F-N,O and CH,F-SO, systems? The fact that simple SW calculations adequately indicate the relative rates fork, and li -2 in the CH3Br-HCN system when very different mechanical motions couple to a common state implies that perhaps the explanation for the behavior in the CH,F-N,O and SO, systems lies elsewhere_ For these systems the energy gap between the donor and acceptor mode is substantially smaller than in the CH, Br-HCN system_ For CHa FN, 0 the energy gaps between y3 and 100.02°0 and O??O are 237, -119 and -137 cm-’ respectively_ For v6 it is even closer; -90,
29 and 11 crnM1 respec-
tively. For SO2 the energy gaps between
* See ref. 171 and references therein.
v3 and 1OC
this system which will then virtually certainly bias the overall energy transfer probability significantly toward the 100 state.
5. Conclusions By examining
the rates of energy transfer into and
out of the v3 mode of CH3Br and the 11~mode of HCN in CH,Br-HCN-Ar mixtures we have determined the relative rate constants of energy transfer from v6 and v3 of CH,Br to HCN. We have also set bounds on these rate constants_ We find that SSH calculations predict reasonably well the relative rate constants in this system_ The implications of these results for other systems which exhibit specific energy transfer pathways are examined. We conclude that a multiple quantum change is more important in determining rates of energy transfer than is the mechanical motion of the modes exchanging energy_ This conclusion is in accord with vibrational energy transfer propensity rules previously put forth [17,1S]_ 373
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95. number
424
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PHYSICS
Ackttcwledgentent We would like fo thank the National Science l%w~dation for support of this work under grants CITE 79-OS501 and CIfE SZ-06976.
References L.O. ilockcr, M.A. Kovacs. C.K. Rhodes, G.W. Flynn and A. Javan. Phys. Rev. Letters 17 (1966) 233; C.B. hloorc. R.E. \\‘ood. B.L. Hu and J.T. Yardley. J. Chcm. Phys. 16 ( 1967) 4222. RD. Batrs Jr.. C.\\‘. Flynn and A.M. Ronn, J. Chcm. I’hys. 49 ( 1966) I ‘lx!: J.T_ Sardlcy. J. Chcm. Phys. 49 (1968) 2816. KC. Shtcr and G.\\‘. Flynn. J. Chem. Phys. 65 (1976) 4’5. RX;. Ituddkston and E. \\‘eitz. J. Chum. Phys. 7-1 (1981) 2879. G.T. Fujimoto and E. \\‘citz. Chcm. Phys. 27 (1978) 65. A.J. Oudcrkirk. \‘.A. Apkarirtn and E. Weitz. Chcm. Phys.’ 62 (1981) 387. Xl. Mo.ux. \‘.A. Atkuhn 2nd 1:. U’&tr. J. Chcm. Phys. 5-t (1981j 342.
LETTERS
11 March
1983
[S] V.A. Apkarian and E. Weitz. J. Chem. Phys. 71 (1979) 4349. [Y] J-A. hlcGarwy,Jr., N-E. Friedman and T.A. Cool, J. Chem. Phys. 66 (1977) 3189. [lo] A. Hariri, A.B. Peterson and C. Wittig, J. Chem. Phys. 65 (1976) 1872. [ 111 R.N. Schwartz, Z-1. Slawsky and K.F. Herzfeld. J. Chem. Phys. 20 (1952) 1591. [ 121 B-L. Earl and A.hl. Ronn. Chem. Phys. 12 (1976) 113. [ 131 J-L. Stretton. Transfer and storage of eneqy by molecules, Vol. 2. Vibrational enemy (Wiley-Interscience, New York, 1969). [ 141 R-D. Sharma and CA. Brau, J. Chem. Phys. 50 (1969) 924. 1151 G. Herzbeq, Xlolecular spectra and molecular structure, Vol. 2 (Van Nostrand, Princeton, 1945). 1161 J-T_ Yardlcy and C.B. hloore. J. Chem. Phys. 49 (1968) 1111. 1171 E. Wcitz and G-W. Flynn, Photoselective chemistry. Part 2. Vol. 47. Advances in chemical physics (Wiley, New York. 1981): Ann. Rev. Phys. Chem. X.(1974) 275. ] 161 G.W. Flynn, Accounts Chem. Res. 14 (1981) 334; A.C.S. Symposium State-to-State Chemistry, A.C.S. Symposium Series, eds. P.R. Brooks and E.F. llaycs (1977)