3168
The Journal of Physical Chemistry, Vol. 83,
No. 24, 1979
dihydro free-base porphyrin obtained as an intermediate might participate in an electron-transfer reaction by accepting electrons from the unprotonated dianion, thus forming the dianion of the dihydro compound and the free-base porphyrin. This electron transfer and subsequent protonation may continue further, i.e. H2TPP2-,2Na++ 2CH30H
+ 2CH30-,Nae H4TPP2-,2Na"+ H2TPP
-
- +
H4TPP + HzTPP2-,2Na+
H4TPP
H4TPP2-,2Na++ 2CH30H
+ 2CH30-,Na+,etc.
or a disproportionation reaction might take place to form H2TPP and H8TPP, for example, H2TPP2-,2Na++ CH30H H3TPP-.,Na+ CH30-,Na+ --t
-
+
H4TPP + H2TPP2-,2Na+
-
H4TPP + HzTPP2-,2Na+ H4TPP2-,2Na+t CH,OH
T h e nature of t h e protonation products of H2TPP2-,2Na+ is completely different from that of ZnTPP2-,2Na+ reported by Closs and Clom2 They observed the formation of phlorin and a subsequent slow transformation to chlorin. The protonation experiment of ZnTYP2-,2Na+was repeated in our laboratory and the results were consistent with those reported by Closs. We cannot suggest any explanation for the difference in the behavior toward protonation between H2TPP2-,2Na+and ZnTPP2-,2Na a t this moment. However, we are planning to investigate it in the future. +
HsTPP
2H3TPP-.,Na+
Marcoux, van Swaay, and Setser
Acknowledgment. The support of this study by the National Science Foundation is gratefully acknowledged. Also, we thank Pr. H. Wang for his valuable suggestions during the experimental phase of this research. References and Notes K. M. Smith, Ed., "Porphyrins and Metalloporphyrins", Elsevier, Amsterdam, 1975. G. L. Closs and L. E. Closs, J . Am. Chem. Soc., 85, 818 (1963). J. W. Dodd and N. S. Hush, J . Chem. Soc., 4607 (1964). R. H. Feiton and H. Linschitz, J. Am. Chem. SOC.,88, 1113 (1966). M. Szwarc and G. Levin, J . Photochem., 5, 119 (1976). M. Szwarc and G. Levin in "Protons and Ions Involved in Fast Dynamic Phenomena", Elsevier, Amsterdam, 1978. G. Ramme, M. Fisher, S. Claesson, and M. Szwarc, Proc. R . SOC. London, Ser. A , 327, 467 (1972). G. Levin, J . Phys. Chem., 82, 1584 (1978). L. Pekkarinen and H. Linschitz, J. Am. C h m . Soc., 82, 2407 (1960). G. Levin, E. E. Hoiloway, and M. Szwarc, J . Am. Chem. SOC.,98, 5706 (1976). E. D. Lillie, D. Van Ooteghem, G. Levin, and M. Szwarc, Chem. Phys. Lett., 41, 216 (1976). Y. Harel, Thesis, submitted to the Scientific Council of the Weizmann Institute of Science, Rehovot, Israel, July 1978. G. Levin, J. Jagur Grodzinski, and M. Szwarc, J . Am. Chem. Soc., 92, 2269 (1970). N. H. Vetthorst, Doctoral Thesis, Free University of Amsterdam, 1963.
+
H4TPP2-,2Na+ HzTPP
H5TPP--,Na++ CH30-,Na+
2H5TPP-.,Nat -* H8TPP
+ H21'PP, etc.
Protonation of the dianion derived from an aromatic hydrocarbon followed by subsequent electron transfer or partial protonation followed by disproportionation was previously reported by Szwarc et al.I3 and Ve1th0rst.l~ Analysis of the protonation products in conjunction with the calculated ones using charge balance required that the reaction products include 662/3% of H2TPP and 331/3% of H'TPP. Actually, 70% of' H2TPP was found which is in good agreement with the expected percentage.
Vibrational Relaxation of CO+(A*n,), CS(A'II), and C2(A311,) in Helium P. J. Marcoux,+ M. van Swaay, and D. W. Setser* Department of Chemistry, Kansas State University, Manhattan, Kansas 66506 (Received May 7, 1979) Publication costs assisted by the Department of Defense
Nonequilibrium vibrational distributions of CO+(A2n,u'=0-6),CS(A1rI,u'=&5),and Cz(A3TI,u'=M)were prepared by collisional processes in a 300-I< helium flowing-afterglow apparatus. The vibrational band intensities of the electronic emission systems were used to obtain the steady-state vibrational distributions from 0.8 to 15 torr. Extensive vibrational relaxation by collisions with He was observed for CO"(A) and CS(A), but not for C,(A), over this pressure range, Electronic quenching of CS(A)probably is competitive with vibrational relaxation, even in helium. The data were fitted to relaxation models based upon Au = 1 collisional transitions by using the steady-state master equation formulation. The Au = 1 relaxation cross sections for CO+(A)and CS(A) with He are in the range of 0.01 of the gas kinetic values. The upper limit to the 4 u = -1 relaxation cross section for C,(A) is 5 X of the gas kinetic value. Studies of the relaxation of CS(A'n) in Ar were attempted, but electronic quenching appeared to dominate over vibrational relaxation. These results are compared to vibrational-translational relaxation of other electronically excited states.
Introduction Vibrational to translational energy transfer in the ground electronic state has been extensively and is reasonably well understood, There is much less information about V-T energy transfer in electronically excited states, but much of the available dat~5-15suggest that V-T relax-
'Hewlett-Packard Laboratories, Palo Alto, CA
94304.
0022-3654/79/2083-3168$01 .OO/O
ation can be much faster for excited electronic states than for the ground state, even for molecules with large energy spacings between vibrational levels. In orle case, Li,(B), vibrational relaxation even competed successfully with rotational relaxation.' 111 the Present work the m&astable rare gas atom flowing-afterglow technique was utilized to produce CO+(A211),CS(A'II), and Cz(A311) in nonequilibrium vibrational levels and vibrational refaxation was ob0 1979 American Chemical Society
Vibrational Relaxation
of CO’(A211,), CS(A’n), and C2(A311,)
served from 0.8 to 10 torr. In addition to providing data on vibrational relaxation in electronically excited states, the present work is of general interest to visible and ultraviolet laser systems pumped by electrical discharges in rare gases, In some instances interactions between excited states of rare gases and added molecules can efficiently produce excited states.1625 Electronic quenching and vibrational relaxation rates of the excited states, as well as other factors, are of importance for evaluation of potential laser performance. The experiments consist of recording the electronic emission intensities from C2(A311g), CS(A’II), and CO+(A211)as a function of helium pressure. These electronic states are produced from the reactions of He(23S) with C2H2,CS2,and CO, respectively. These vibrational band intensities were converted to relative vibrational populations and thus the pressure dependence of the steady-state vibrational distributions is obtained. These results are compared with model calculations by using the steady-state master equation to extract rate constants for V-T energy transfer. The CO+(A211)and CS(AIII) molecules are found to relax readily in He, even at a few torr pressure. However, no relaxation could be observed for C2(A311g)or for CO(a311);the latter has been reported ~eparate1y.l~ We also found that electronic quenching of CS(A’II) may occur in He. Results from preliminary experiments in which CS(AlI1) was generatedz1by collisions of Ar(2P2)with CS2 suggest that electronic quenching is even more severe in Ar. These studies required the handling of a large amount of data. Therefore, a laboratory computer was interfaced to the monochromator for acquisition of the spectra on magnetic tape, and the band areas of the spectra subsequently were reduced to relative vibrational distributions with the computer. The interface to the computer is described in the supplementary material (see paragraph at end of text regarding supplementary material). Experimental Section The experiments were performed in a metastable atom flow reactor which generated He(2%) by the usual hollowcathode discharge technique used in our 1aboratory.l6-l9 Typical operating parameters for the discharge were 400 V and 5 mA. The flow tube was pumped by a 1000 L/min mechanical pump. The total pressure varied from 0.8 to 15 torr; this range corresponds to flow rates of 800 to 6000 pmol/s of helium (measured by a Fischer and Porter triflat flow meter). Reagent flow rates were 1-3 pmol/s. Several flow reactors were used in this study because of difficulty in covering a large pressure range. The reactors varied in the diameter of the helium inlet tube and in the separation between the reagent mixing zone and the observation window. Generally, the reactors which had large (12-mm i.d.) helium inlet tubes worked well at high pressure but failed to sustain a good discharge at low pressure (55 torr). The smaller helium inlet tubes (8-mm i.d.) functional well at low pressure but “streaming” was a serious problem at high pressure (28 torr). For all reactors the reagent was added to the He flow through a second concentric tube to create a diffusion flame. As the pressure is increased, the concentration of other energy carriers increase in the He flowing-afterg10w.l~ In the present work He+ (identified by the N2+(C-X) emission) was not a problem. However, at pressures above -6 torr the He2+concentration became significant. This will not be of importance for C2(A) or CS(A) but could be of possible importance for CO+(A). The N2,COP,and H 2 0 impurities were removed by passing the He flow through activated molecular sieve (Linde-5A) traps at liquid nitrogen temperature. The reagent gases
The Journal of Physical Chemistry, Vol. 83,No. 24, 1979 3169
were stored in reservoirs and metered to the mixing zone. The emission intensities were observed at low resolution with a 0.75-m Jarrell-Ash Czerny-Turner monochromator. The detection train consisted of a cooled EM1 95586 photomultiplier (S-20 response), Solid State Radiation 1100 series photon counter, and a strip chart recorder. The monochromator drive system and the photon counter were interfaced to a Digital Equipment PDP-8/E minicomputer (see Appendix). The relative quantum efficiency of the monochromator and detection train was calibrated between 200 and 850 nm. The 300-850-nm region was calibrated against a NBS standard quartz-iodine lamp (Electro Optics Associates Inc. type LlOl lamp). Care was taken to remove secondorder effects and the same number and type of quartz windows as actually used in an experiment were placed between the lamp and monochromator. The response function was determined from 200 to 380 nm by using the molecular branching ratio method.20 The NO(A,u’=OXu”), NO(B,u’=O-Xu”), CO+(B,u’=O,l-Xu’’), and CO(a, u’=O.l-Xu”) band systems were used. The molecular branching ratio method requires accurate Frank-Condon factors and knowledge of the variation (if any) of the electronic transition moment. The FC factors for the NO y and p bands, CO+(B-X) bands, and the CO(a-X) bands were taken from ref 26-28, respectively. The variation of the electronic transition moment given by Jain and SahniZ6 was used for NO(A-X). For the other molecular band systems the electronic moments were assumed to be con~ t a n t After . ~ ~ this work was completed, the monochromator was recalibratedz2 in the 200-350-nm region with a standard D2 lamp. The new calibration curve agreed with the one used in this work. Experimental Results CO+(A211i)in N e . The He(23S) Penning ionization of CO produces CO+ in the X2Zf, A2111,,and B2Z+electronic state^.^^^^^ The CO+(B) channel is not suitable for vibration relaxation studies because mainly u’ = 0 is produced. However, CO+(A)is produced in a broad distribution with a maximum for u’ = 2 and relaxation of this distribution can be studied. The COS(A) u ” = 0 progression is strong and bands originating in u’ = 0-6 and terminating in u” = 0, plus the 0-1 and 1-1 band were studied from 0.5 to 15 torr. Under all conditions studied here, the 21131z/2n112 relative populations for u’ = 0-6 were 300 K Boltzmann and the areas of both spin multiplets were combined for a given u’level, The band areas, obtained by integration with the minicomputer, were corrected for monochromator response by using the wavelength corresponding to the midpoint of the multiplet subbands. The intensity of a particular band in the r-centroid approximation is given by
Ib,”,, = D N , ~ v , ~ , ~ ~ ~ R , ( F , ~ , ~ ~ (1) )~~~~,~~ where Iutu,fis the integrated band intensity in units of photons/s, D is a constant, N , is the population of the upper state u’, it,,ufJis the energy of the transition (cm-l), is the FC factor, and Re(F,/,,3is the electronic transition moment. The FC factors used were those of Albritton et al. The electronic transition moment was assumed constant based on the data presented by Holland and Maier30 and Judge and Lee.31 The relative vibrational populations were calculated from the experimentally measured band areas, eq I, and the normalization condition C,,N,, = 1.0. The CO+(A)steady-state vibration distributions are shown in Figure 1;extensive relaxation occurs over this relatively small pressure range. As the pressure is increased, the He2+concentration becomes more important and CO+(A) qLldJ
3170
The Journal of Physical Chemisfry, Vol. 83,No. 24, 7979
Marcoux, van Swaay, and Setser
TABLE I: Initial Relative Distributions and Radiative Lifetimes vibrational distributions molecule
T,p
CO+(AZri)
- 3a
CS(A'11)
-0.3b
CS(A'n ) CS(A'11) C?(A3nn )
-0.3b 0.1ZC
u' = 0
collision process
s
He* Penning ionization (this work) Penning ionization (electron spectroscopyd) He*/CS, electron recombination with CS,+(X) Ar*/CS, dissociative excitation photodissociation, h = 123.9 nm h = 92.3 n m He*/C,H, dissociative excitation
1
2
3
4
5
6
0.15 0.12 0.20
0.20 0.19 0.31
0.24 0.24 0.19
0.17 0.20 0.13
0.11 0.13 0.12
0.08 0.08 0.05
0.05 0.04
0.23 0.15 0.16
0.31 0.30 0.30
0.20 0.10 0.10 0.25 0.15 0.12 0.23 0.17 0.14 see Table I1
0.06
a Reference 30b. The lifetimes for u = 0-6 are 3.85, 3.41, 3.09, 2.84, 2.66, 2.35, and 2.39 p s . Reference 37. The lifeReference 38. Reference 33. times for u' = 0-4 are 255, 339, 292, 292, and 292 ns. We assumed T , also was 292 ns.
0.3
,ob v
Y
=3
OQ
w
>
Y
0.0 0 ~
Figure 1. Variation of the CO+(A) vibrational distribution with helium pressure: ( 0 )v = 0; ( 0 )v = 1; ( 0 )v = 2;(E)v = 3; (A)v = 4; (X) v = 5. The dashed curves are the best fit calculated results, see text.
also probably is produced17"by charge exchange with Hez+. The He(23S) and Hez+ reactions are thought to give the same CO+(A) vibrational distrib~tionsl~" and this additional source of CO+(A) should cause no difficulty. To obtain the relative populations of CO+(A)which arise solely form direct Penning ionization, the contribution from CO+(B-A) radiative cascade should be removed. Richardson and Setser16 found that CO+(A)and COYB) account for 55 and 45% of the total emission intensity. Only 9% of the CO+(B)emission radiates to CO+(A). The CO+(A, u=O-3) vibrational levels produced by radiative cascade have the following proportions: 0(0.51), 1(0.27), 2(0.16), and 3(0.06). These results were used to correct the data obtained below 5 torr and smooth extrapolations were made to obtain the zero pressure Penning ionization CO+(A) distribution of Table I. These relative populations differ only slightly from the zero pressure distributions obtained by extrapolation of the data (uncorrected for cascade) in Figure 1. The differences are within the experimental errors associated with the extrapolation. CS(AIII in H e ) . The reaction of He(23S) produces CS(A); the following is a simplified reaction scheme:19 He(23S) CS2 CS2+(B,A,X) He + e- (2a)
+
-
+
-
CS2+(B,a) CSz+(X)+ e-
CS+(A) + S + He
+ e-
(2b)
CS2+(X)+ hu
(3)
CS(A,a) + S(3Pi
(4)
-
2
4
6 8 1 0 1 2 1 4 PRESSURE ,TORR
Figure 2. Variation of the CS(A) vibrational distribution with helium pressure: (E) v = 0; ( 0 )v = 1; (9)v = 2; (V)v = 3; ( 0 )v = 4; (A) v'= 5. The dashed curves are the best fit calculated resuks, see text. The discrepancy between the calculated and experimental results for v = 0 at pressures >6 torr is attributed to electronic quenching, see text.
The main evidence that CS(A) is produced via an electron recombination reaction with CS2+(X)is that the addition of a small flow of SF6,which reduced the CS2+(A-X) intensity by a factor of 2, reduced the CS(A-X) intensity by a factor of -14. Also the variation of I(CS(A-X))/I(CS+(B-X)) with operating conditions generally supports this kinetic scheme,lgalthough other contributions to CS(A) formation cannot be excluded. The band areas for the Au = +2, +1, 0, -1, and -2 sequences were used to obtain relative populations. The sum of the band areas from a given u' were used to obtain relative populations, with the exception of the 4-6 band, which could not be used since it is overlapped by the CS2+(B-X) transitions. This procedure was used because the transition moment for the CS(A-X) system is not constant and individual bands from a given u'level must be used with care.lg The variation of the relative vibrational distributions with pressure is shown in Figure 2. The vibrational relaxation is not as extensive as for CO+(A),in part because of the shorter lifetime of CS(A). Nevertheless, there is a definite shift in the population distribution to lower u' levels as the pressure increases. Cz(A311g)in He. The reaction of He(23S)with acetylene produces a rich spectrum;z3the main emissions are CH(A2A-X211)and Cz(A311g-X311,). Although the emission
Vibrational Relaxation of CO+(A,n,), CS(A'n), and C2(A3n,)
TABLE 11: Pressure Dependence of the C, ( A 3 n g ) Vibrational Distribution pressure,b torr
0
1
2
3
4
1.6 3.8 8.5 13.1
0.231 0.218 0.205 0.198
0.177 0.168 0.177 0.185
0.271 0.276 0.288 0.285
0.123 0.125 0.135 0.138
0.198 0.211 0.194 0.198
re1 vibrational distributiona
a The estimates of the relative population in i i ' = 5 and 6 are < 5 and < l o % of the total population in u ' = 0-4, respectively. These are representative pressures selected from the available experiments (11)which covered the range from 1.6 to 1 3 torr.
is moderately intense, formation of Cz(A)comprises only 3-4% of the total quenching. The u' = 5 and 6 levels are weakly populated and vibrational populations were assigned only for u' = 0-4. The C2(A-X) spectra were recorded in the 500-600-nm region. However, only the Au = -1 sequence was used to obtain vibrational distributions since it offered the simplest analysis. The peak heights were corrected for monochromator response and converted into fractional populations with the FC factors of The data, which are presented in Table 11, show that the A state of C2 does not undergo vibrational relaxation up to 13 torr of He. However, the results can be used to set a lower limit to the relaxation rate constant and this is given in the next section. CS(AIII)in Ar. The formation of CS(A'II) constitutes about 17% of the total quenching of Ar(3P2)by CS2.21 Data initially were collected from 0.5 to 5 torr for the purpose of observing vibrational relaxation. Over this pressure range some levels appeared to undergo vibrational relaxation but others did not. Data obtained at higher pressure showed that the CS(AIII-XIB+) emission intensity declined relative to that of other exit channels from the quenching. This strongly suggested that the CS(A'II) state was being electronically quenched. Therefore, no further effort was made to study the vibrational relaxation of CS(A'n) in Ar. The initial vibrational distribution from Ar(3P2)+ CS2 is given in Table I. Discussion
Formation Mechanism. The initial vibrational distributions reflect the nature of the collision processes yielding the particular electronic state. Since the radiative lifetimes and the initial vibration distributions will be needed for the analysis of vibrational relaxation, both are included in Table I. The excitation of CO+(A)by Penning ionization has been thoroughly d i s c ~ s s e d . ' ~Within J ~ ~ ~ ~the experimental uncertainty involved in our extrapolation to zero pressure, the CO+(A)distribution deduced from Penning optical spectroscopy agrees with that deduced from Penning electron ~ p e c t r o s c o p yand ~ ~ there is little, if any, modification of the initial COt(A) vibrational distribution resulting from traversal of the exit channel. The vibrational and rotational distributions of C2(A3n,) frequently are abnormal.34 The distribution from dissociative excitation of C2H2is relatively flat out to u' = 4 and then drops rather abruptly; this seems to be another type of Cz(A) vibrational distribution. High resolution spectra of the C2(A-X) bands at 2 torr showed no indication of non-Boltzmann rotational distributions. We previously suggestedz3that Cz* is formed by consecutive C-H bond rupture from a CzH2*Rydberg state formed by the interaction with He(23S). The CS(A) vibrational distributions from electron recombination and dissociative excitation from interaction with Ar(3P2)are very similar. These distributions also can
-
The Journal of Physical Chemistry, Vol. 83,
No. 24, 7979 3171
be compared to recent photodissociation results35with CS2 at 92.3 and 123.9 nm, which are included in Table I. The similarity in the distributions is quite striking. Presumably this is because, in all three cases, the CS(A'II) molecules are formed by dissociation of excited states lying close to the ionization limit (10.1 eV) of CS2. Assignment of Vibrational Relaxation Rate Constants. Since the radiative lifetimes of CO+(A),CS(A), and C2(A) are relatively short, the excited states do not flow any appreciable distance and the vibrational distributions can be treated by steady-state analysis: dN,/dt = 0 = R, - T , - ~ N+&zC(P,,N, - P,NJ I
(5)
The steady-state master equation was utilized to calculate the relarive distribution from an assumed transition probability model. The steady-state population of the ith level is N,, z is the gas kinetic collision number, PI,is the probability per gas kinetic collision of transfer from level i to j , and R, is the relative rate of formation of the ith vibrational level. The relative rates of formation and the lifetimes of the levels, 7,,are given in Table I. The steadystate distributions, N,, were solved by using the method of Duewer et al.36 If electronic quenching of the ith level becomes significant, another term must be added to the above equation. Collision diameters of 2.55,3.60,4.22, and 3.91 A were used for He, COt(A), CS(A), and Cz(A),respectively, in the computation of z.39 We employed the simplest model for the transition probability matrix, Le., only Au = 1transitions were considered and PI, = 0 for i - j # 1. The elastic (diagonal) elements were calculated from the completeness condition, C,P, = 1.0. Up transitions were neglected since detailed balance indicates a very small ratio for up to down transitions at 300 K. Once the transition probability matrix was specified, the master equation was solved for N , over the range of experimental pressures. The P,,, i - j = 1, elements of the transition probability matrix were adjusted by trial and error until a satisfactory fit to the data was obtained. The calculated results are compared to the experimental data for CO+(A) in Figure 1. The best fit was with transition probabilities of Plo= 0.004, Pzl= 0.013, P32 = 0.025, and through P,, = 0.035. The ratio of P21/Plo in the main governs the behavior of levels u' = 0 and 1 and this ratio was carefully checked. For Pz1/Pl0 = 1,N1 was a monotonically decreasing function of pressure and P21/Plo and must be > L O in order to fit the data. The best fit was with Pz1/Pl0 3; a smaller ratio results in too rapid an increase in u' = 0 with a concurrent decrease in u' = 1; increasing the ratio to 5 underestimates the Nopopulation and overestimates the N1 population as the pressure increases. Actually the fit to the No and N1 at low pressure in Figure 1 still is not as good as could be desired. This may be a consequence of a contribution from Pzoor possibly an incorrect zero pressure population assignment. For the and higher terms, a variation of fO.O1 from the best value resulted in a significantly poorer fit to the pressure dependence of the level being simulated. The calculations in which the P,, values were varied indicate that the uncertainty in the assignments is f20% for the Au = 1model. The conclusions from this analysis are (i) a model with only Au = 1 transitions can give reasonable agreement with experiment, (ii) the initial increase followed by a decrease in N 2 arises because P21/Plo is > 1, and (iii) the Pu~,u!-l values increase with u'. For the above assignments of P,] and collision diameters, the inelastic cross sections are 0.12,0.38, and 0.74 A2 for u' = 1-3 and 1.0 for the higher u levels.
-
3172
The Journal of Physical Chemistry, Vol. 83, No. 24, 1979
The study of vibrational relaxation in CO(A111)6~7 and Liz(B1II.J8 identified Au = 2 processes. Two calculations were performed with CO+(A) to test for the role of Au = 2 processes in our data: (i) the inelastic cross sections determined above were partitioned 90% to Au = 1 and 10% to Au = 2 and (ii) 50% to Au = 1 and 50% to Av = 2. For (i) the u’ 1 1 populations were less than those for the PIJ,i - j = 1, model and the u’ = 0 population was larger. These differences increase with increasing pressure. The model with 50% of the transition probability in the Au = 2 process follow the same general trend; however, the magnitude of the effects are larger. Our data certainly could be fitted by introducing contributions from Au = 2 processes, reassignment of the Au = 1 probabilities, and reducing the total inelastic cross sections. Our assignment for the V-T cross section for CO+(u’= 1)can be compared to a recent laser-induced fluorescence report.& Miller and Bondybey selectively excited CO+(A,u = 1) with a dye laser and observed fluorescence from u = 1 and u = 0 as a function of pressure. They estimated a u’ = 1 relaxation cross section of 0.02 A2; adjustment of this result to the radiative lifetime used in our analysis gives -0.03 A2. In subsequent more extensive work, these authors40bhave observed the time-resolved kinetics of the CO+(A,u’=1,2,3)levels following selective laser excitation. A three-level scheme was required to interpret the data: CO+(a,u?
+ He
CO+(X, high u’?
-
CO+(X, high u’?
+ He
-
+ He
(6a)
CO+(A,u’-l) .t He (6b)
The effective cross sections for vibration relaxation were evaluated and the new results are 0.11,0.27, and 20.6 A2 for u’ = 1, 2 , and 3, respectively. These are in gratifying agreement with the results of our study. Without doubt, CO+(A) undergoes vibrational relaxation and the cross section increases with u’. The time-resolved data40b strongly suggest that relaxation occurs via a mixed electronic-vibration relaxation mechanism. Calculations were done for CS(A) by using only Au = 1 elements in the transition probability matrix. The calculated results are compared with the experimental data in Figure 2. The reasonably good fit shows that relaxation can be reproduced with only Au = 1 transitions; the best fit was obtained with PI, = 0.01, P,, = 0,015, P3, = 0.045, P45= 0.04, and PM= 0.03. However, this fit is not unique and Au = 2 events could be introduced into the model. In order to maintain a pressure-independent Nl distribution, the P2,/Ploratio can be only slightly larger than unity. Any increase in this ratio results in a more rapid decrease of the N 2 population with a concomitant increase in N1. A larger ratio also results in an increase in the population of No as a consequence of the increased v’= 1 population. The broad maximum in the u’ = 2 population is similiar to that for u t = 1 of CO+(A) and requires that P21/P32 < 1.0, For u t > - 4 the values of Plidecline with increasing v’. Within the constraints of the Au = k1 model, this effect is real because increasing values of PIJfor u’ = 4 and 5 to 0.045 results in N4and N5 populations which declined too rapidly with increasing pressure. The main reason for the weaker pressure dependence of the CS(A) vibrational distribution, relative to CO+(A),is the shorter lifetime of CS(A) because the PIJvalues are rather similar. Electronic quenching also may be occurring; this would only affect our assignment of the Pi., if the electronic quenching cross sections vary with u’. In Figure 2 the calculated fractional population for u’ = 0 appears to be higher than the experimental values. This difference, as well as the declining values assigned to P43and Pb4,may be a consequence of u’ level dependent electronic quenching. Comes and Fink6
Marcoux, van Swaay, and Setser
TABLE 111: Vibration Transition Probabilitiesa for Some Electronicallv Excited Diatomic Molecules __
molecule
~,(133r1,,~’=1) N, ( A3x U t ,u’= 1 ) NO( A’ c ,u’= 1) +
OH( A 2 ~ + , u ’ = 1 ) CO( A ’ n ,u’=l) CO( A ’ n , u ’ = 2 ) HD(B’cU+,v’=3) Li,(B’r1,,u’=2) Na,( E’ n u ,u’=6) CN(A2n,u’=3-9) S2(B3X;,u’=4)
collision partner
P,,“-,
ref
N2 N? Ar Ar N2 He Ar He Ar He Ne Ar He Ne Ar He Ne He Ar Ar Ar He Ar
5.5 ( 2) 3.5 (-2) 2.4 (--2) 4.9 ( - 9 ) 1.4 ( - 7 ) 3.5 (-5) 3.6 (-4) 5 . 2 (-3) 1.2 (-2) 1 . 5 (-2) 2.0 ( - 2 ) 3.0 (-1) 1.1( - 2 ) 1 . 2 (-2) 2.1 (-1) 3.3 (-2) 3.2 ( 2 ) 1 . 5 (-1) 2.0 (-1) 5 . 2 (--2) 0.7-5.0 (-3) 1 . 2 (-1) 1 . 4 (-1)
14 14 43 5 10 10 11 11
7 7 7 7 7 7 12 12 8 8 9 44 45 45
a Defined as the ratio of the observed deactivation rate constant divided by the gas kinetic collision number.
also found that the vibrational transition probabilities for CO(AlII) in He declined for u’ > 3. As mentioned in the Results section, attempts to study vibrational relaxation of CS(A) in Ar gave data strongly suggestive of electronic quenching. Since the low u levels of CS(AIII) are strongly perturbed by high vibrational levels of the CS triplet transfer to the triplet manifold may readily occur. Collisions with heavier collisions partners may facilitate the interconversion process and this may be why quenching is more important for Ar than He. For pressures as high as 13 torr, no relaxation of Cz(A3&) was observed. A 10-15% increase in the N 3 / N 4 ratio could have been experimentally detected. Using 120 ns as the C2(A)lifetime36and assuming that P4-3= P3-2, we can establish a limit of C0.005 for P4.3. Comparison with Other Electronically Excited Molecules. This work and related studies give V-T relaxation results for CO(a), CS(a), C2(A),CS(A), and CO+ in He. The relaxation of CO(a311) is very slow and resembles ground state molecules of a comparable vibrational frequency.15 The CS(a311)data42are only qualitative but P,o is in the 10-4-10-5 range. In contrast both CS(A) and CO+(A) relax readily and Plox 0.004-0.01; only an upper limit can be set for C2(a311)and P32 .C 0.005. These results can be compared to some vibrational relaxation data from the literature. The summary in Table 111, which is not meant to be comprehensive, illustrates that a wide range of V-T transition probabilities has been found for other diatomic excited states, as well as for the molecules studied in this work. The recent44CN(A) study employed timeresolved laser fluorescence. The relaxation mechanism is complicated and involves high u levels of CN(X) in a mechanism resembling that of CO+(A), see eq 6. For at least two cases, CN(A) and CO+(A),the fast vibrational relaxation, in fact, proceeds via collisional cascade through nearly high vibrational levels of the ground state. The CO(A) and CS(A) states are known to be highly perturbed by close-lying triplet states, and, by implication, a cascade mechanism with the triplet levels playing the same role as the ground state for CN and CO+ appears quite reasonable, especially so, since electronic quenching already is
Vibrational Relaxation
of CO+(A2n,), CS(A'II), and C2(A3n,)
suspected for CO(A) and CS(A). Is collisional cascade through high u levels of a lower electronic state a general explanation of fast vibrational relaxation of electronically excited diatomic states? One of the most thoroughly studied cases with large vibrational relaxation cross sections is Li2(B'n,). In this case the second state presumably would be Li2(A'Z,+), which has an allowed radiative transition, T = 18 ns,46 to X(IZg+). Even though Li2(A-X) emission is ob~erved,~' indicating a competition between Li,(B) vibrational relaxation and electronic quenching to Li2(A),the short A state lifetime precludes the cascade mechanism as the explanation of the large vibrational relaxation cross sections, since collisional transfer from B(u? to A(high u ) and then from A(high u ) back to B(u'-1) would be impossible. On the basis of this argument, the cascade mechanism does not explain all examples of fast vibrational relaxation of electronically excited diatomic molecules. Other mechanisms, such as the nonadiabatic process suggested by Nikitin,'@may provide alternative possibilities for some molecules. For some Qi cases it also may be necessary to explicity include the two spin-orbit states in the relaxation mechanism.49
Conclusions Vibrational to translational energy transfer of four electronically excited diatomic states, CO+(A),CS(A), C,(A), and CO(a), with helium has been studied. For CO+(A)the relaxation mechanism40 is collisional induced crossing toand-from the CO+(X) high vibrational levels. A similar mechanism, but with the CS* triplet states as the second state, probably explains the fast relaxation in CS(A). This type of V-T relaxation mechanism may be fairly common for excited states and helps to explain the analomously fast V-T relaxation that has been observed. However, this mechanism does not seem to explain the fast relaxation observed for alkali metal dimers in the B('II,) state. Acknowledgment. This work was supported, in part, by the Advanced Research Projects Agency of the Department of Defense and monitored by ONR under Contract N00014-76-C-0380. We thank Dr. T. Miller, Bell Labs, for discussion of their work on CO+(A) relaxation. Supplementary Material Auailable: A description of the computer interface developed for the Jarrell Ash monochromator (5 pages). Ordering information is available on any current masthead page.
References and Notes E. Weitz and G. Flynn, Annu. Rev. Phys. Chem., 25, 275 (1974). D. Secrest, Annu. Rev. Phys. Chem., 24, 379 (1973). R. C. Amme, Adv. Chem. Phys., 26, 171 (1975). (4) I. W. M. Smith, Acc. Chem. Res., 9, 161 (1976). (5) D. Levron and A. V. Phelps, J . Chem. Phys., 69, 2260 (1978). (6) F. J. Comes and E. H. Fink, Chem. Phys. Lett., 14, 433 (1972).
The Journal of Physical Chemistry, Vol. 83, No. 24, 1979 3173 E. H. Fink and F. J. Comes, Chem. Phys. Leff., 25, 190 (1974). G. Ennen and Ch. Ottinger, Chem. Phys., 3, 404 (1974). K. Bergmann and W. Demtroder, 2.Phys., 243, l ( 1 9 7 1 ) . H. P. Broida and T. Carrington, J . Chem. Phys., 36, 136 (1963). R. K. Lengel and D. R. Crosley, J. Chem. Phys., 56, 5303 (1978). E. H. Fink, D. L. Akins, and C. 6. Moore, J . Chern. Phys., 56, 900 (1972). M. Rubinson, B. Garetz, and J. I.Steinfekl, J. Chem. phys., 60, 3082 (1974). J. M. Calo and R. C. Axtman, J . Chem. Phys., 54, 1332 (1971). P. J. Marcoux, L. G. Piper, and D. W. Setser, J . Chem. Phys., 66, 351 11977) W.C. Richardson and D. W. Setser, J. Chem. Phys., 56, 1809 (1973). (a) L. G. Piper, L. A. Gundei, J. E. Vebzco, and D. W. Setser,J. Chem. phys., 62, 3883 (1975); (b) J. H. Koks and D. W. Setser in "Reactive Intermediates in the Gas Phase: Generation and Monitoring", Academic Press, New York, 1979. J. A. Coxon, M. A. A. Clyne, and D. W. Setser, Chem. Phys., 7, 255 (1975). J. A. Coxon, P. J. Marcoux, and D. W. Setser, Chem. Phys., 17, 403 (1976). L. A. Gundel, D. W. Setser, M. A. A. Clyne, J. A. Coxon, and W. Nip, J . Chem. Phys., 64, 4390 (1976), and references therein. J. H. Kolts, H. C. Brashears, and D. W. Setser, J. Chem. Phys., 67, 2831 (1977). J. E. Velazco, J. H. Kolts, and D. W. Setser, J. Chem. Phys., 65, 3468 11976). R. S. F. Chang, D. W. Setser, and G. W. Taylor, Chem. Phys., 25, 201 (1978). J. A. Coxon, W. H. Duewer, and D. W. Setser, J . Chem. Phys., 58, 2244 (1973). E. Zamir, A. Szoke, and R. Osgood, J. Chem. Phys., 65, 4885 (1976). D. C. Jain and R. C. Sahni, Trans. Faraday Soc., 64, 3169 (1968). D. L. Albritton, private communication. (a) P. H. Krupenie, "The Band Spectrum of Carbon Monoxide", US. Government Printing Office, Washington, D.C., 1966. (b) G. R. Mohlmann and F. J. DeHeer, Chem. Phys., 21, 119 (1977). H. Klemsdal, J . Quant. Spectrocs. Radiat. Transfer, 13, 417 (1973). (a) R. F. Holland and W. B. Maier, 11, J. Chem. Phys., 56, 5229 (1972); (b) W. B. Maier, 11, and R. F. Holland, J . Phys. B , 5, L418 (1972). D. L. Judge and L. E. Lee, J . Chem. Phys., 57, 455 (1972). D. C. Jain, J. Quanf. Spectrosc. Radiat. Transfer, 4, 427 (1964). (a) H. Hotop and A. Niehaus, Int. J . Mass Spectrom. Ion Phys., 5, 415 (1970); (b) D. S. C. Yee, W. 6. Stewart, C. A. McDoweil, and D. E. Brian, J . Electron Spectrosc. Relat. Phenom., 7, 93 (1975). K. S. Kini and M. I.Sovadatt, J . Phys. B , 10, 1139 (1977). L. C. Lee and D. L. Judge, J . Chem. Phys., 63, 2782 (1975). W. H. Duewer, J. A. Coxon, and D. W. Setser, J . Chem. Phys., 56, 4355 (1972). W. H. Smith, J . Quant. Spectrosc. Radiat. Transfer, 9, 119 (1969). T. Tatarczyk, E. H. Fink, and K. H. Becker, Chem. Phys. Lett., 40, 126 (1976). R. A. Svehla, NASA Tech. Rep., No. R-132 (1962). (a) T. A. Miller and V. E. Bondybey, Chem. Phys. Lett., 50, 275 (1977); (b) V. E. Bondybey and T. A. Miller, J. Chem. phys., 69, 3602 (1978). (a) D. Cossart and T. Bergeman, J. Chem. Phys., 65, 5462 (1976); (b) D. Cossart, M. Horani, and J. Rostas, J . Mol. Spectrosc., 67, 283 (1977). L. G. Piper, W. C. Richardson, G. W. Taylor, and D. W. Setser, Farac!ay Discuss., Chem. Soc., 53, 100 (1972). M. Touzeau and D. Pagnon, Chem. Phys. Lett., 53, 355 (1978). D. H. Katayama, T. A. Miller, and V. E. Bondybey, J. Chem. Phys., Iin press. T. A. Caughey and D. R. Crosley, J . Chem. Phys., 69, 3379 (1978). ID. H. Wine and L. A. Melton, Chem. Phys. Leff., 45, 509 (1977). Ch. Ottinger and G. Ennen, private communication. IE. E. Nikitin and S. Ya. Umanski, Faraday Discuss., Chem. Soc., 53, 7 (1972). S. A. Edelstein, D. L. Huestis, and J. Wyss, J . Chem. Phys., 70, 131 (1979). . I .
\
I
- I .
