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A rapid “pump-and-probe” laser technique for determining state-resolved product distributions
Volume 59, number
1
CHEhfICAL
PHYSICS LETTERS
1 November 1978
A RAPID “PUMP-AND-PROBE” LASER TECHNIQUE FOR DETERMINING STAT?3=OLVED PRODUCT DISTRIB%KIONS* W-H- BRECKENRIDGE”, 0. KIM MALhlIN, W.L. NIKOLAI and D. OBA’ Department of Chemti~, University of Utah. Salt Lake City, Utah 84I12. USA Received24 July 1978 A new lasertechniqueis describedfor the determinationof statejesokxi product distriiutionsat relativelyhigh total pressures(==I torr). An activespeciesis usted by one laserpulse, and productsof its destructionare detected by laser-inducedfluorescencewithin 520 ns. For the E-to-V process, Cd(’ Pl) + N2 + W(3Pe,~,2) + N2, the initial 3Po:3P~:3P2 distriiution is 0.0.5:0.27:0.68_
1. introduction There is an increasing interest in the measurement of enew transfer and chemical reaction rates at the detailed “state-to-state” level. We describe here a new laser “pump-and-probe” technique which wiU allow us to determine initial quantum-state energy distriiutions of physical and chemical exit channels in the collisional quenching of electronically excited atoms under “bulb” rather than “beam” pressure conditions_ The basic idea is a simple one: to use a very fast observation technique rather rhan low particle densities to create “singl~Iiision” kinetic conditions_ The time resolution is achieved by producing excited atoms with one short laser pulse, then probe the products of collisions of the excited atoms with a molecular substrate (at total pressures on the order of one torr) with another laser pulse, all within a ==20 ns tine period- Very few of the excited atoms even collide with the substrate molecules during the delay period (mean collision times are =I00 ns at one torr) but neither do the products, thus in most cases preventing appreciable collisional relaxation of the initial product internal quantum-state distriiutions. The technique essentially depends on the analytical sensitivip of Supportedby the National ScienceFoundation, Grant ,XZ-E7707603. * Qmille and Henry Dreyfus FoundationTeacher-scholar; 1973-1978. * Universityof Utah GraduateResearchFellow. l
38
laser-tiduced fluorescence, as developed originally by Zare and co-workers [l] , for determining stateresolved product distributions at extremely low concentrations. Ln the first experiment, we have chose= to determine the initial electronic J-state distribution of the product Cd(3PJ) states in the process f2,3] : Cd(‘P1) f N2 + Cd(3PI) + N2.
(1)
which is known to occur with a very high cross section for a spin-forbidden urocess [3,4] _ The energies of the Cd(‘PI), Cd(3P2>, Cd(‘Pl) and CdcPo) excited levels above ground-state Cd(‘So) are 125.0,90.9, 87.6, and 86.0 k&/mole, respectiveiy.
2. Apparatus Cadmium vapor is entrained ~II a stream of nitrogen gas by means of an apparatus very similar to those developed for metal-vapor oxidation studies [5]. See fig. 1 for a schematic diagram of the flow system. The N2 is added through the “carrier gas” inlet. A Molectron UV4ClO nitrogen laser is used to pump two Molectron DL-200 dye laser heads simul‘Qneousiy. The output of one of the dye +sers is tied at the appropriate frequency and passed through a potassium pentaborate crystal to produce a =56 ns pulse of 2288 A light, which in turn excites Cd(lP1) atoms in ‘the cadmium/nitro~n stream via the 5s2 ‘So + 5sSp ‘PI transition. The other dye laser
Volume 59. number
1
CHEMlcAL
PHYSICS LETTERS
lNovem-&x1978
Fig. 1. A schemdic diagram of the metal vapor flow system.
pulse is delayed ~20 ns by means of a spatial optical dela line andis scanned in wavelength to detect Cd( r Po,J,~) by means of laser-induced fluorescence at 4679 A, 4801 A, and 5087 A, corresponding to the 5sSp 3P~ + 5~6s 3Sr transitions. Optical baffle tubes are used to reduce scattered light from the “pump" and the “probe” Izser pulses. See fig. 2 for a schematic diagram of the apparatus. The signal is collected in the standard manner using a bare photomultiplier tube (except for a W filter) and a box-car integrator, with a laser repetition rate of 10 Hz. Tbe probe laser intensity was reduced by neutral density filters until the ff uorescence intensity was linear with laser power. Because of the allowed nature of the atomic transitions, this sometimes required very large attenuation factors of lo4 to 105. Easer-induced fluores?ence signal intensity was normalized to relative laser intensity (irz photons/s) by using an energy meter and correcting for the different photon energies at the three wavelengths. Since the transition probabilities in absorption for the three 5s5p 3P~ * 5~6s 3S1 multiplet transitions
Fig_ 2. A schematic diagram of the laser “pump-znd-probe” apparatus. Wavy lines represent Light paths_
are equal, and the fluorescence originates from a co.mmon upper state, the laser-intensir’ycorrected fluorescence signals give the populations of Cd(3Po), Cd(3P,), and Cd(3 P2) directly. In certzin experiments, an interference filter with maximum transmittance at 5090 A was used in front of the photomultiplier instead of the W filter, and consistent results were obtained. Experimental measurements [6] of the lifetime of the upper (5~6s 3S1) level (some of which are susceptible to cascade error) range from 7 to 19 ns. The apparent lifetime of the (5~6s 3S1) state was always < 10 ns (i-e., less than our time resolution) when the pressAre of N2 was 3 torr or greate: in the apparatus. For pressures of N2 less than 3 torr, it was necessary to use a high-gain end-on photomultiplier tube for which the response time happened to be too slow for lifetime measurements in the lo-30 ns region. 39
Volume 59, number 1
CHZMICAL. PHYSICS LETTERS
of Cd(‘PI) under the optimal experimental conditions was -100 ns, considerab!y longer than the natural radiative lifetime [7] of l-7 ns due to radiation imprisonment at Cd vapor concentrations in the flow stream estimated to be ~10’~ atoms/cm3. The longer effective lifetime of The effective
lifetime
Cd(l PI) is importantz
because
100
1
gas flow observed
vapor
is apparently
at nonequiLibrium previoutiy
met22 vapor
entrained
[IS]
as
_
The results are shorvn in fig. 3. Although net deactivation* of Cd(3Po) and Cdi3P1) [and probably Cd(3P2)] to ground-state Cd(lSo) by Nz is slow and would have no effect on the initial Cd(3PJ) distribution during the time-scale of the experiment [8], collisional intramultiplet mixing of the Cd(3PJ) states by N2 is knocrn to be rapid [8,9] _ It is therefore important to confirm that Cd(3Pz):Cd(3P1): Cd(3Po) relative populations determined experimentally are not affected by partial relaxation towards equilibrium even during the short probe delay period of 20 ns. This was done by determining the Cd(3PJ) relative populatiors as a function of N2 pressure and extrapolating to zero pressure. As can be seen in fig. I, the extrapoIation leads to values of 3P2:3P1 :3P~ fractional populations in reaction (1) of0.68:0.27: 0.05. Note that there is very little correction necessary for the lowest N2 pressure attainable computer
even though
simulation
it can be estimated
from
of the data that intram&ipIet
deactivation of Cd(3P2) and Cd(3P ) by N2 have cross sections on the order of IO A 1 _ The solid lines in fig. 3 result from a two-parameter kinetic fit of the collisional relaxation, by increasing pressures of half-He of Cd<‘PI) is 2.3 JLS[Sl, the errorduer0radiativedecciyofCd(~Pr)duringthe21 r~deIay
*Since the sdidve timeislessthan 40
1%
0
25
50 NZ
PfEssLRE
75
100
12 5
hrrJ
3_ The fractional populations of Ca(3P.& Cdc3Pl), and GI(3Po) = 20 ns after the production of Ca(’ PI). plotted qainst N2 pressure(Le., “‘pump” and “‘probe” laserpulses were sepzated by 21 ns). Open da& points are pure Nz, Fig_
for this kind of
3. Results and discussion
experimentally,
Cdt+;,
0
in the czrrier
concentrations,
with other metals
ff ow system
A
there is little net
radiative decay of Cd(‘Pr) during the delay time of z20 I1s, thus improving the sensitivity. The temperature of the flow stream in the !aser inte_raction region was measured with 2 thermocouple to be =39G II. The vapor pressure of cadmium at this temperature would correspond to 22 x 10” atoms/cm3, so the cadmium
1 November 1978
darkeneddata points are experimentswith = 15 torr He also presentas carriergas. &tramultipIet deactivationof CX(3P~> by helium is known to be extremely inefficient [8,9 J .) Solid lines are computersimulationsSf the variationof fractional populationswith N2 pressure,usingthe following rate constantsfor coUisionalintramultipIetmixing_liter/mole s units: &I = 2.9 X lOLO,7~20= 0, k10 = 3.5 x 10”. Rate constant subscriptsrefer to inSSaland fmal J-states. Reverserate constantswere calculatedby assumingmicrosco ic reversibility and a tempemnue of 390 K- (T5e 3P2:3Pi : PPOdistribution at zero nitrogen pressureIAich gave the best simuIationof the data was 0.58:0.27:0.05.)
N2, of the initia.I 3P2:3P1:3Po distribution towards a Boltzmann distribution at 390 K. (0.01:0_29:0_70) during the 21 ns delay time. See caption of fig_ 3 for details. The initial distribution of J-states of Cd(3PJ) determined here for the E-to-V process represented by eq. (1) apparently cannot be rationalized by 2 simple mechanism. The Cd(3P2) state is formed preferentially. with very little CdcPo) produced at all. In table f , the experimental J-state initial distribution is compared to other possible distributions. First of all, no “temperature” can be associated with the resuhs, since the data cannot be made to fit a Rokzrnann distribution at any temperature. Shown in table 1 are Roitzrna~ distributions at the temperature of the experiment, 390 K, and at ten times that temperature, 3900 K Also shown in table 1 is the “prior” distribution of LevineXknstein surprisal theory, i-e., the distribution which wodd result if all
Volume
59, number 1
CHEMICAL
PHYSICS LETTERS
T&e 1 The experimental fractional population of Cii(j PJ) product states in the process other possible distributions. See text Product state
+ N2 as compared to
Boltzmann distribution at 390 K
Boltzmann distribution at 3900 rc
“Prior” distribution (surprisal theory)
Distribution from electronic dq,eneracies of cd$P~) states
0.68 5~0.03
0.01
0.44
0.49
0.56
0.27 to.02
0.29
0.40
0.37
0.33
0.05 +0.01
0.70
0.16
O-14
0.11
-Es Pl
Cd(’ Pt ) + N2 +Cd(3PJ)
Experimental rest&.
accessible quantum-state energy distributions were populated statistically. The Nz molecule was approximated as a rigid rotor, harmonic oscillator [lo] I Prob. =q.r(E,
1 November 1978
)=, PJ
where 4~ is the electronic degeneracy of the 3P~ level (5,3, or l), and the quantity taken to the 3 power is the term difference between Cd(‘PI) and the Cd(3PJ) state of interest (i.e., the amount of energy to be shared into the available density of translational, rotational, and vibrational product states). Initial translational, vibrational, and rotational energy makes a negligible contribution to the calculation because of the Iarge ‘PI ‘PJ term differences. As can be seen, the “surprising” aspect of the experimental distribution in terms of information theory is that Cd 3Pz) is formed preferentially over Cd(3PI) and Cd( 4 PO), with the Cd(3Po) relative population almost three times less than statistical. An oversimplified approach might be to consider the number of CdNz molecular states which correlate with Cd(3PJ) + Nz, since there must be net surface crossings from the CdNz states which correlate with Cd(’ PI) + Nz to those which correlate with Cd(3 PJ) + N2. Such naive reasoning would predict an initial distribution of 3P2:3PI:3Po levels of 5:3:1. It can be seen in table 1 that this fractional population distribution (0.56:0.33:0.11) also predicts too little CdCP2) and too much Cd(3Po), but the agreement is better. If one goes a step further and describes the CdN2 electronic states in the least-restrictive C, symmetry (it may be inferred from the high cross section [3,4] for eq_ (1) that the geometry for singlet-to-triplet curve crossing cannot be very restrictive), then there
t
are three states (2A’ + A”) which correlate with Cd(‘Pr) + N2, five with Cd(3P2) + Nz (2A’ + 3A”), three with Cd(3PI) + N2 (2A’ + A”), and one with Cd(3Po) + Nz (A”). Elementary considerations of the number of possible curve-crossing combinations between the states yields no better agreement with the experimental results. It has been suggested [3] that CdfNz states could be involved in the quenching of Cd(I PI) by N-J, and that the presence of these charge-transfer surfaces might facilitate the spin-forbidden production of Cd(3PJ) states with such a high cross section. Smith and Zare [l l] have rationalized the large cross section for another spin-forbidden process (Ba f SO2 + BaC(’ X+) + SO(3C-)) by the presence of singlet and triplet charge-transfer surfaces (Ba%Oz) which enable net curve crossings to occur. Unfortunately, at least in C, symmetry, the presence of such states does not provide any simple correlation argument to explain the preference of Cd(3Pz) over Cd(3Po), since Cd”(2Sl,2) + NF(2111,~ 3/2) correIates wirh an equal number of A’ and A”surfaces in C, symmetry (lA’, ‘A”, 3A’, 3A”)_ As might have been expected, the deactivation of Cd(‘PI) to CdcPJ) by N2 appears, therefore, to be a complicated process involving multiple curve crossings of neutral and ionic surfaces, the net result of which is preferential production of Cd(3P2) over Cd(3Po)_ Such factors as the number and the shape of potential surfaces of weakly bourrd versus totally repulsive neutral CdN2 surfaces [3,12,13] would obviously affect the Cd(3PI) product distribution. One final point, however, should be mentioned. Spin-orbit coupling in Cd is rather large, and a Russell-Saunders coupling scheme cannot be rigorously correct. At very high spin-orbit coupling for 41
Vokme
59, nnmber 1
CHEMICAL
PHYSICS
the sp configuration,the ‘PI and 3P2 terms become multiplets of the same electronic state for i,i coupling, so that the preferencefor deactivationof Cd(lP1) to Cd(3P2) might be explained by a scheme somewhat intermediatebetween (Ls) and Q,j) coupling. Experiments in progresswith other molecular quenchersmay provide fintber information about efficient spinforbidden Cd(‘Pl) to Cdf3PJ) energy disposal processes. The faser “p~~~d-probe” technique described here should be of generaiimportance to modern molecular dynamics. For example, determination of initial vibrationatand rotational q~t~-stats distributions of &atomic or triatomic products of excited atom reactiveor inelastic quenchingshould be possible in the very near f%ture_The technique can also he applied to detection of quantum-state distributionsin photodissociation processes and, with some modification, wi.U
facilitate detailed time-re&lved studies of
the collisional deactivation of vibrationallyand rotationaliy excited species, e.g.. simpIe diatomic metal hydrides-
A&nowfe&ement We wish to acknowledge helpful discussions with F&rry Dewey, Joel Hati, Professor RN. Zare and his researchgroup, and severalmembers of the Quantum Institute, University of California, Santa Barbara-We would also hke to thank Dr- RI Donovan for many stimulating discussionswinch were facilitated by a
42
LETTERS
1 November
1978
NATO Research Grant for support of collaborative researchon fluorescence tech.niques.
Refemnces [l ] A. Schultz, H.W. Cuse and RN. Zare, 3. aem.
Days. 57 (197211354: and IhgdigEan, science185 <1974) 739. W.IL 3reckenridge and A.B. CdIear, Trans. Faraday Sot. 67 (1971) 2009. 1V.H.Breckenridge and A.M. Renlund, J. phys. (Them. 82 (1978) 1474. W.H. Breckenridge, R-I. Donovan and 0. I&r Xalmin, to be submitted for publication. J.B. West, R% Bradford Jr_, J.D. Eversole and CR_ Jones. Rev. ScL Instr. 46 (1975) 164. AR Schafer, J. Quant- Spectry. Radiative Transfer ll(l971) 197. A. Lurio and R. No&k, Pbys. Rev. A 134 f1964) 608. W-H_ Brackenridge, T-W. Broadbent and D.S. Moore, 3. Phys. Chem- 79 (1975) 123% S_ Yamamoto, ht Takoaka, S. Tsunashima and S. !&to, Bull. Cbem. Sot. rapan 48 (1975) 130. RD. Levine and A. Ben-Shaul, Thermodynamics of molecular disequihirium, in: Chemical and biochemical . apphcattons of Iasen, VoL 2, ed_ CB. More (Academic Press, New York, 1977) p. 165. 1111 G.. Smith and RN_ Zare, 3. Am. Cbem. Sot. 97 (1975) 1985. 1121 A-B. Cal&r and J. M&u&, J. (hem. Soc_ Faraday II 69 (1973) 97. 1131 G. Karl, P. Kruus and J-C Manyi, 3. Chem. Phys. 46 (1967) 224. 1141 G_ Her&erg, Atomic spectra and atomic structure (Van Nostrand, Princeton, 1944) pp. 173-17-I.
RN.zare li
1
CHEhfICAL
PHYSICS LETTERS
1 November 1978
A RAPID “PUMP-AND-PROBE” LASER TECHNIQUE FOR DETERMINING STAT?3=OLVED PRODUCT DISTRIB%KIONS* W-H- BRECKENRIDGE”, 0. KIM MALhlIN, W.L. NIKOLAI and D. OBA’ Department of Chemti~, University of Utah. Salt Lake City, Utah 84I12. USA Received24 July 1978 A new lasertechniqueis describedfor the determinationof statejesokxi product distriiutionsat relativelyhigh total pressures(==I torr). An activespeciesis usted by one laserpulse, and productsof its destructionare detected by laser-inducedfluorescencewithin 520 ns. For the E-to-V process, Cd(’ Pl) + N2 + W(3Pe,~,2) + N2, the initial 3Po:3P~:3P2 distriiution is 0.0.5:0.27:0.68_
1. introduction There is an increasing interest in the measurement of enew transfer and chemical reaction rates at the detailed “state-to-state” level. We describe here a new laser “pump-and-probe” technique which wiU allow us to determine initial quantum-state energy distriiutions of physical and chemical exit channels in the collisional quenching of electronically excited atoms under “bulb” rather than “beam” pressure conditions_ The basic idea is a simple one: to use a very fast observation technique rather rhan low particle densities to create “singl~Iiision” kinetic conditions_ The time resolution is achieved by producing excited atoms with one short laser pulse, then probe the products of collisions of the excited atoms with a molecular substrate (at total pressures on the order of one torr) with another laser pulse, all within a ==20 ns tine period- Very few of the excited atoms even collide with the substrate molecules during the delay period (mean collision times are =I00 ns at one torr) but neither do the products, thus in most cases preventing appreciable collisional relaxation of the initial product internal quantum-state distriiutions. The technique essentially depends on the analytical sensitivip of Supportedby the National ScienceFoundation, Grant ,XZ-E7707603. * Qmille and Henry Dreyfus FoundationTeacher-scholar; 1973-1978. * Universityof Utah GraduateResearchFellow. l
38
laser-tiduced fluorescence, as developed originally by Zare and co-workers [l] , for determining stateresolved product distributions at extremely low concentrations. Ln the first experiment, we have chose= to determine the initial electronic J-state distribution of the product Cd(3PJ) states in the process f2,3] : Cd(‘P1) f N2 + Cd(3PI) + N2.
(1)
which is known to occur with a very high cross section for a spin-forbidden urocess [3,4] _ The energies of the Cd(‘PI), Cd(3P2>, Cd(‘Pl) and CdcPo) excited levels above ground-state Cd(‘So) are 125.0,90.9, 87.6, and 86.0 k&/mole, respectiveiy.
2. Apparatus Cadmium vapor is entrained ~II a stream of nitrogen gas by means of an apparatus very similar to those developed for metal-vapor oxidation studies [5]. See fig. 1 for a schematic diagram of the flow system. The N2 is added through the “carrier gas” inlet. A Molectron UV4ClO nitrogen laser is used to pump two Molectron DL-200 dye laser heads simul‘Qneousiy. The output of one of the dye +sers is tied at the appropriate frequency and passed through a potassium pentaborate crystal to produce a =56 ns pulse of 2288 A light, which in turn excites Cd(lP1) atoms in ‘the cadmium/nitro~n stream via the 5s2 ‘So + 5sSp ‘PI transition. The other dye laser
Volume 59. number
1
CHEMlcAL
PHYSICS LETTERS
lNovem-&x1978
Fig. 1. A schemdic diagram of the metal vapor flow system.
pulse is delayed ~20 ns by means of a spatial optical dela line andis scanned in wavelength to detect Cd( r Po,J,~) by means of laser-induced fluorescence at 4679 A, 4801 A, and 5087 A, corresponding to the 5sSp 3P~ + 5~6s 3Sr transitions. Optical baffle tubes are used to reduce scattered light from the “pump" and the “probe” Izser pulses. See fig. 2 for a schematic diagram of the apparatus. The signal is collected in the standard manner using a bare photomultiplier tube (except for a W filter) and a box-car integrator, with a laser repetition rate of 10 Hz. Tbe probe laser intensity was reduced by neutral density filters until the ff uorescence intensity was linear with laser power. Because of the allowed nature of the atomic transitions, this sometimes required very large attenuation factors of lo4 to 105. Easer-induced fluores?ence signal intensity was normalized to relative laser intensity (irz photons/s) by using an energy meter and correcting for the different photon energies at the three wavelengths. Since the transition probabilities in absorption for the three 5s5p 3P~ * 5~6s 3S1 multiplet transitions
Fig_ 2. A schematic diagram of the laser “pump-znd-probe” apparatus. Wavy lines represent Light paths_
are equal, and the fluorescence originates from a co.mmon upper state, the laser-intensir’ycorrected fluorescence signals give the populations of Cd(3Po), Cd(3P,), and Cd(3 P2) directly. In certzin experiments, an interference filter with maximum transmittance at 5090 A was used in front of the photomultiplier instead of the W filter, and consistent results were obtained. Experimental measurements [6] of the lifetime of the upper (5~6s 3S1) level (some of which are susceptible to cascade error) range from 7 to 19 ns. The apparent lifetime of the (5~6s 3S1) state was always < 10 ns (i-e., less than our time resolution) when the pressAre of N2 was 3 torr or greate: in the apparatus. For pressures of N2 less than 3 torr, it was necessary to use a high-gain end-on photomultiplier tube for which the response time happened to be too slow for lifetime measurements in the lo-30 ns region. 39
Volume 59, number 1
CHZMICAL. PHYSICS LETTERS
of Cd(‘PI) under the optimal experimental conditions was -100 ns, considerab!y longer than the natural radiative lifetime [7] of l-7 ns due to radiation imprisonment at Cd vapor concentrations in the flow stream estimated to be ~10’~ atoms/cm3. The longer effective lifetime of The effective
lifetime
Cd(l PI) is importantz
because
100
1
gas flow observed
vapor
is apparently
at nonequiLibrium previoutiy
met22 vapor
entrained
[IS]
as
_
The results are shorvn in fig. 3. Although net deactivation* of Cd(3Po) and Cdi3P1) [and probably Cd(3P2)] to ground-state Cd(lSo) by Nz is slow and would have no effect on the initial Cd(3PJ) distribution during the time-scale of the experiment [8], collisional intramultiplet mixing of the Cd(3PJ) states by N2 is knocrn to be rapid [8,9] _ It is therefore important to confirm that Cd(3Pz):Cd(3P1): Cd(3Po) relative populations determined experimentally are not affected by partial relaxation towards equilibrium even during the short probe delay period of 20 ns. This was done by determining the Cd(3PJ) relative populatiors as a function of N2 pressure and extrapolating to zero pressure. As can be seen in fig. I, the extrapoIation leads to values of 3P2:3P1 :3P~ fractional populations in reaction (1) of0.68:0.27: 0.05. Note that there is very little correction necessary for the lowest N2 pressure attainable computer
even though
simulation
it can be estimated
from
of the data that intram&ipIet
deactivation of Cd(3P2) and Cd(3P ) by N2 have cross sections on the order of IO A 1 _ The solid lines in fig. 3 result from a two-parameter kinetic fit of the collisional relaxation, by increasing pressures of half-He of Cd<‘PI) is 2.3 JLS[Sl, the errorduer0radiativedecciyofCd(~Pr)duringthe21 r~deIay
*Since the sdidve timeislessthan 40
1%
0
25
50 NZ
PfEssLRE
75
100
12 5
hrrJ
3_ The fractional populations of Ca(3P.& Cdc3Pl), and GI(3Po) = 20 ns after the production of Ca(’ PI). plotted qainst N2 pressure(Le., “‘pump” and “‘probe” laserpulses were sepzated by 21 ns). Open da& points are pure Nz, Fig_
for this kind of
3. Results and discussion
experimentally,
Cdt+;,
0
in the czrrier
concentrations,
with other metals
ff ow system
A
there is little net
radiative decay of Cd(‘Pr) during the delay time of z20 I1s, thus improving the sensitivity. The temperature of the flow stream in the !aser inte_raction region was measured with 2 thermocouple to be =39G II. The vapor pressure of cadmium at this temperature would correspond to 22 x 10” atoms/cm3, so the cadmium
1 November 1978
darkeneddata points are experimentswith = 15 torr He also presentas carriergas. &tramultipIet deactivationof CX(3P~> by helium is known to be extremely inefficient [8,9 J .) Solid lines are computersimulationsSf the variationof fractional populationswith N2 pressure,usingthe following rate constantsfor coUisionalintramultipIetmixing_liter/mole s units: &I = 2.9 X lOLO,7~20= 0, k10 = 3.5 x 10”. Rate constant subscriptsrefer to inSSaland fmal J-states. Reverserate constantswere calculatedby assumingmicrosco ic reversibility and a tempemnue of 390 K- (T5e 3P2:3Pi : PPOdistribution at zero nitrogen pressureIAich gave the best simuIationof the data was 0.58:0.27:0.05.)
N2, of the initia.I 3P2:3P1:3Po distribution towards a Boltzmann distribution at 390 K. (0.01:0_29:0_70) during the 21 ns delay time. See caption of fig_ 3 for details. The initial distribution of J-states of Cd(3PJ) determined here for the E-to-V process represented by eq. (1) apparently cannot be rationalized by 2 simple mechanism. The Cd(3P2) state is formed preferentially. with very little CdcPo) produced at all. In table f , the experimental J-state initial distribution is compared to other possible distributions. First of all, no “temperature” can be associated with the resuhs, since the data cannot be made to fit a Rokzrnann distribution at any temperature. Shown in table 1 are Roitzrna~ distributions at the temperature of the experiment, 390 K, and at ten times that temperature, 3900 K Also shown in table 1 is the “prior” distribution of LevineXknstein surprisal theory, i-e., the distribution which wodd result if all
Volume
59, number 1
CHEMICAL
PHYSICS LETTERS
T&e 1 The experimental fractional population of Cii(j PJ) product states in the process other possible distributions. See text Product state
+ N2 as compared to
Boltzmann distribution at 390 K
Boltzmann distribution at 3900 rc
“Prior” distribution (surprisal theory)
Distribution from electronic dq,eneracies of cd$P~) states
0.68 5~0.03
0.01
0.44
0.49
0.56
0.27 to.02
0.29
0.40
0.37
0.33
0.05 +0.01
0.70
0.16
O-14
0.11
-Es Pl
Cd(’ Pt ) + N2 +Cd(3PJ)
Experimental rest&.
accessible quantum-state energy distributions were populated statistically. The Nz molecule was approximated as a rigid rotor, harmonic oscillator [lo] I Prob. =q.r(E,
1 November 1978
)=, PJ
where 4~ is the electronic degeneracy of the 3P~ level (5,3, or l), and the quantity taken to the 3 power is the term difference between Cd(‘PI) and the Cd(3PJ) state of interest (i.e., the amount of energy to be shared into the available density of translational, rotational, and vibrational product states). Initial translational, vibrational, and rotational energy makes a negligible contribution to the calculation because of the Iarge ‘PI ‘PJ term differences. As can be seen, the “surprising” aspect of the experimental distribution in terms of information theory is that Cd 3Pz) is formed preferentially over Cd(3PI) and Cd( 4 PO), with the Cd(3Po) relative population almost three times less than statistical. An oversimplified approach might be to consider the number of CdNz molecular states which correlate with Cd(3PJ) + Nz, since there must be net surface crossings from the CdNz states which correlate with Cd(’ PI) + Nz to those which correlate with Cd(3 PJ) + N2. Such naive reasoning would predict an initial distribution of 3P2:3PI:3Po levels of 5:3:1. It can be seen in table 1 that this fractional population distribution (0.56:0.33:0.11) also predicts too little CdCP2) and too much Cd(3Po), but the agreement is better. If one goes a step further and describes the CdN2 electronic states in the least-restrictive C, symmetry (it may be inferred from the high cross section [3,4] for eq_ (1) that the geometry for singlet-to-triplet curve crossing cannot be very restrictive), then there
t
are three states (2A’ + A”) which correlate with Cd(‘Pr) + N2, five with Cd(3P2) + Nz (2A’ + 3A”), three with Cd(3PI) + N2 (2A’ + A”), and one with Cd(3Po) + Nz (A”). Elementary considerations of the number of possible curve-crossing combinations between the states yields no better agreement with the experimental results. It has been suggested [3] that CdfNz states could be involved in the quenching of Cd(I PI) by N-J, and that the presence of these charge-transfer surfaces might facilitate the spin-forbidden production of Cd(3PJ) states with such a high cross section. Smith and Zare [l l] have rationalized the large cross section for another spin-forbidden process (Ba f SO2 + BaC(’ X+) + SO(3C-)) by the presence of singlet and triplet charge-transfer surfaces (Ba%Oz) which enable net curve crossings to occur. Unfortunately, at least in C, symmetry, the presence of such states does not provide any simple correlation argument to explain the preference of Cd(3Pz) over Cd(3Po), since Cd”(2Sl,2) + NF(2111,~ 3/2) correIates wirh an equal number of A’ and A”surfaces in C, symmetry (lA’, ‘A”, 3A’, 3A”)_ As might have been expected, the deactivation of Cd(‘PI) to CdcPJ) by N2 appears, therefore, to be a complicated process involving multiple curve crossings of neutral and ionic surfaces, the net result of which is preferential production of Cd(3P2) over Cd(3Po)_ Such factors as the number and the shape of potential surfaces of weakly bourrd versus totally repulsive neutral CdN2 surfaces [3,12,13] would obviously affect the Cd(3PI) product distribution. One final point, however, should be mentioned. Spin-orbit coupling in Cd is rather large, and a Russell-Saunders coupling scheme cannot be rigorously correct. At very high spin-orbit coupling for 41
Vokme
59, nnmber 1
CHEMICAL
PHYSICS
the sp configuration,the ‘PI and 3P2 terms become multiplets of the same electronic state for i,i coupling, so that the preferencefor deactivationof Cd(lP1) to Cd(3P2) might be explained by a scheme somewhat intermediatebetween (Ls) and Q,j) coupling. Experiments in progresswith other molecular quenchersmay provide fintber information about efficient spinforbidden Cd(‘Pl) to Cdf3PJ) energy disposal processes. The faser “p~~~d-probe” technique described here should be of generaiimportance to modern molecular dynamics. For example, determination of initial vibrationatand rotational q~t~-stats distributions of &atomic or triatomic products of excited atom reactiveor inelastic quenchingshould be possible in the very near f%ture_The technique can also he applied to detection of quantum-state distributionsin photodissociation processes and, with some modification, wi.U
facilitate detailed time-re&lved studies of
the collisional deactivation of vibrationallyand rotationaliy excited species, e.g.. simpIe diatomic metal hydrides-
A&nowfe&ement We wish to acknowledge helpful discussions with F&rry Dewey, Joel Hati, Professor RN. Zare and his researchgroup, and severalmembers of the Quantum Institute, University of California, Santa Barbara-We would also hke to thank Dr- RI Donovan for many stimulating discussionswinch were facilitated by a
42
LETTERS
1 November
1978
NATO Research Grant for support of collaborative researchon fluorescence tech.niques.
Refemnces [l ] A. Schultz, H.W. Cuse and RN. Zare, 3. aem.
Days. 57 (197211354: and IhgdigEan, science185 <1974) 739. W.IL 3reckenridge and A.B. CdIear, Trans. Faraday Sot. 67 (1971) 2009. 1V.H.Breckenridge and A.M. Renlund, J. phys. (Them. 82 (1978) 1474. W.H. Breckenridge, R-I. Donovan and 0. I&r Xalmin, to be submitted for publication. J.B. West, R% Bradford Jr_, J.D. Eversole and CR_ Jones. Rev. ScL Instr. 46 (1975) 164. AR Schafer, J. Quant- Spectry. Radiative Transfer ll(l971) 197. A. Lurio and R. No&k, Pbys. Rev. A 134 f1964) 608. W-H_ Brackenridge, T-W. Broadbent and D.S. Moore, 3. Phys. Chem- 79 (1975) 123% S_ Yamamoto, ht Takoaka, S. Tsunashima and S. !&to, Bull. Cbem. Sot. rapan 48 (1975) 130. RD. Levine and A. Ben-Shaul, Thermodynamics of molecular disequihirium, in: Chemical and biochemical . apphcattons of Iasen, VoL 2, ed_ CB. More (Academic Press, New York, 1977) p. 165. 1111 G.. Smith and RN_ Zare, 3. Am. Cbem. Sot. 97 (1975) 1985. 1121 A-B. Cal&r and J. M&u&, J. (hem. Soc_ Faraday II 69 (1973) 97. 1131 G. Karl, P. Kruus and J-C Manyi, 3. Chem. Phys. 46 (1967) 224. 1141 G_ Her&erg, Atomic spectra and atomic structure (Van Nostrand, Princeton, 1944) pp. 173-17-I.
RN.zare li