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to Hund's case d state. It was shown by Johns7 that in such a case only the transitions of A(N,R) = 0 are dominant.8 Figure 3 shows the MPI excitation spectra due to the transitions from the same rotational levels of J = 41/2 ( N = 4) belonging to the different vibrational states of u = 0, 1, and 2 in the A2Z+ state. Similar to the case of the transitions from the different rotational levels (Figure 21, the observed spectra resemble each other. However, the observed peaks were found to be uniformly shifted by 2.4 cm-' to higher frequency for the transition from u = 1 and by 3.6 cm-' for the transition from u = 2 to higher frequency when compared with the Rydberg peaks of the spectrum from u = 0. The remarkable resemblance of the spectra obtained from the different vibrational states indicates the highly selective vibrational selection rule Au = 0, which results from the similar potentials between the A2Z+ state and the high Rydberg states. The observed small shifts of the peaks represent a slight change of the (7)J. W. C. Johns, 'Molecular Spectroscopy", Vol. 2,The Chemical Society, London, 1974,p 513. (8)In Hund's case d, the core rotational quantum number R should be used instead of N . A(N,R) = 0 means that the rotational quantum number N defined for the A%+ state (Hund's case b) and R defined for the high Rydberg state (Hund's case d) are equal.
vibrational frequency in going from the A2Z+state to the high Rydberg states. The frequency change may be compared with the increase of the vibrational frequency of 1.8 cm-' in going from NO(A2Z+)to NO+(X'Z+). In summary, the high npa and npa Rydberg states were observed by two-color multiphoton spectroscopy using the A2Z+state (3sa) as an intermediate state. In this work we have explicitly demonstrated that the transitions from the A2Z+state to high Rydberg state are determined by the highly selective selection rules A(N,R) = 0 and Au = 0, as had been assumed by previous workersa3The ionization potential was accurately determined by direct observation of the ionization threshold for the isolated molecule in a supersonic jet and by the Rydberg series obtained for the gas a t room temperature. Addendum. After our initial manuscript was written and submitted, we were informed by a referee about the very closely related paper by Seaver et al.3 published in a recent issue of J. Phys. Chem. that arrived in Sendai after our manuscript had been submitted. After a careful examination of the paper by Seaver et al., we realized an essential difference in the content between the two works and resubmitted our manuscript after a slight revision. Registry No. NO, 10102-43-9.
Plcosecond Measurements of Time-Resolved Geminate Charge Recombination C. L. Braun' D6partment of Chemistry. Dartmouth College, Hanover, New Hampshlre 03755
and T. W. Scott Bell Laboratorles, Murray HI4 New Jersey 07974 (Received: July 25, 1983)
At 296 K, geminate cation-electron pairs in liquid hexane are found to recombine with an initial half-life of 9 ps or less. The first half-life increases to 70 f 20 ps at 214 K consistent with the known decrease in the drift mobility of electrons in hexane. The results support the view that coulomb-field-drivendiffusion of a localized electron and ita parent cation determines the lifetime of the geminate charge pairs.
Introduction In most condensed-phase materials, photoionization generates transient ion-electron pairs which are strongly correlated by their mutual Coulombic attraction.'+ Each pair consists of a parent positive ion and its associated photoelectron. It is generally assumed that once the photoelectron loses its excess kinetic energy and comes into thermal equilibrium with the surrounding medium, its fate is then determined by mutual diffusion on the pair's Coulombic potential energy surface.' In materials with (1) R. H. Batt, C. L. Braun, and J. F. Homig, J.Chem. Phys., 49,1967 (1968);Appl. Opt. SuppZ.,3,20 (1969);R. R. Chance and C. L. Braun, J. Chem. Phys., 59, 2269 (1973);64,3573 (1976). (2)A. C. Albrecht, Acc. Chem. Res., 3,238 (1970). (3)R. A. Holroyd and R. L. Russell, J. Phys. Chem., 78,2128 (1974). (4)R. C.Jarnagin, Acc. Chem. Res., 4,420 (1971). (5)D.M.Pai and R. C. Enck, Phys. Reu. B, 11, 5163 (1975). (6)D. S. Sethi, H. T. Choi, and C. L. Braun, Chem. Phys. Lett., 74, 223 (1980);H. T.Choi, D. S. Sethi, and C. L. Braun, J. Chem. Phys., 77, 6027 (1982). 0022-3654/83/2087-4776$01.50/0
low charge carrier mobilities, the separation probability is small, a n d most pairs suffer geminate recombination. This recombination process should be extremely fast8 unless deep electron traps2 are available. The fast time dependence of geminate cation-anion recombination, where the anion is formed by electron attachment, has recently been studied by pulsed electron beam excitation."" (7)L. Onsager, Phys. Reu., 54,554 (1938). (8)K. M. Hong and J. Noolandi, J. Chern. Phys., 68,5163 (1978). (9)M.C. Sauer, Jr., and C. D. Jonah, J.Phys. Chem., 84,2539(1980); C. D. Jonah, M. C. Sauer, R. Cooper, and A. D. Trifunac, Chern. Phys. Lett., 63,535(1979);J. P.Smith and A. D. Trifunac, J.Phys. Chem., 85, 1645 (1981). (10)C. A. M. van den Ende, L. H. Luthjens, J. M. Warman, and A. Hummel, Radiat. Phys. Chem., 19,455(1982);C. A. M.van den Ende, L. Nyikos, J. M. Warman, and A. Hummel, ibid., 15, 273 (1980). (11)S. Tagawa, Y. Tabata, H. Kobayashi, and M. Washio, Radiat. Phys. Chem., 19,193 (1982);Y.Katsumura, Y.Tabata, and S. Tagawa, ibid., 19,267(1982);S. Tagawa, M.Washio, Y. Tabata, and H. Kobayashi, ibid., 19,277 (1982);S. Tagawa, Y.Katsumura, and Y. Tabata, ibid., 19, 125 (1982).
0 1983 American Chemical Society
The Journal of Physical Chemistry, Vol. 87, No. 24, 1983
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We report here the first measurements of the recombination kinetics of geminate cation-electron pairs photogenerated by a picosecond laser.12 With pulsed electron beam excitation, evidence has recently been obtained13 that, in liquid hexane, the first half-life of such pairs is less than 100 ps. We find that photogenerated cation-electron pairs in liquid hexane have a first half-life of no more than 9 ps. In addition we observe geminate recombination kinetics which support the model of coulomb-driven charge pair annihilation.
Experimental Section Geminate charge pairs were formed in liquid n-hexane by resonant two-photon ionization of anthracene "impurities" introduced at a concentration of 4.5 X 1015 A .351-nm light pulse of 6-8-pa duration delivered ~m-~ 0.05 mJ of UV light over a 2-mm2 cross section of the sample. The UV pulses were obtained from the third harmonic of a mode-locked Nd3+ phosphate laser. We recorded ionic photocurrent transients lasting many milliseconds after irradiation of the solution with the picosecond pulse. The amplitude of the photocurrent we observed is determined by the total number of charge pairs which escape geminate recombination. Time-resolved measurements of the recombination process itself were carried out by combining pulse-probe optical techniques with the millisecond photoconductivity measurements. These experiments were motivated in part by the timeunresolved measurements of Lukin, Tolmachev, and Yakovlev (LTY)14who reported that photon absorption by a geminate electron in hexane (cross section = 3 X 1O-l' cm2at 1053 n m 9 resulted in an increased probability for geminate pair separation. Thus, following the arrival of the UV pulse, a 0.5-mJ probe pulse at 1053 nm interrogated the ionized sample for a period of 8-10 ps. We found that the cooperative action of both a UV and an IR pulse, separated in time, generated a larger photocurrent than when a UV pulse acted alone. No photocurrent was observed when only the IR pulse was present or under any conditions when only purified hexane filled the cell. By varying the time delay between the UV ionization pulse and the IR probe pulse, we studied the time evolution of the cooperative photocarrier generation process. Results and Discussion A schematic illustration of the process of IR-enhanced photogeneration is presented in Figure 1. As Figure 1 indicates, we assume as did LTY that absorption of IR photons by geminate electrons is responsible for the IRenhanced photocurrent. Figure 2 shows how the cooperative ionization process depends on the relative timing of the UV and IR optical pulses. Note that the IR enhancement is zero when the IR pulse arrives before the UV pulse, and then rises steeply as the two pulses overlap in time. The cooperative ionization gradually decreases as the IR pulse is further delayed. The full width at halfmaximum in Figure 2a is 21 ps with a half-width of 6 ps (12)Very recently two Letters have appeared which report subpicosecond photoinduced optical transients in polyacetylene [see 2. Vardeny, J. Strait, D. Moses, T.-C. Chung, and A. J. Heeger, Phys. Rev. Lett., 49, 1657 (1982);C. V. Shank, R. Yen, R. L. Fork, J. Orenstein, and G. L. Baker, ibid., 49,1660 (1982)]. It is not yet clear whether the observed excited-state species are charged and whether geminate recombination of oppositely charged species is the principal relaxation route. (13)C. D.Jonah, Radiat. Phys. Chem., 21, 53 (1983). (14)L. V. Lukin, A. V. Tolmachev, and B. S. Yakovlev, Chem. Phys. Lett.., 81. 595 (1981). . ,... ~ ~
(15)J. H. Baxendale and E. J. Raaburn, J. Chem. SOC.,Faraday Trans. 1, 70, 705 (1974).
i
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SO
Flgure 1. Schematic illustration of infrared photodissociation of geminate cation-electron pairs. Two 353-nm photons produce a 7-eV singlet state of anthracene, S,,which ionizes to form a geminate pair. The geminate electron thermalizes and then either recombines or escapes to infinity. The small escape probability of the electron (ca. can be increased by photoexcitation of the electron with a 1053-nrn probe photon which thus samples the population of surviving geminate pairs.
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0
100 TIME D E L A Y ( p s e c )
200
Flgure 2. Increase in photocurrent arising from the infrared photcdissociation of geminate cation-electron pairs: (a) 296 K. (b) 214 K. The geminate pairs are formed by a UV pulse at time zero. At various time delays shown above, an I R pulse probes the population of surviving geminate pairs. The dissociation signal (arbitrary units) is the photocurrent measured when both UV and I R pulses are incident less the photocurrent from the UV pulse alone. Typically the I R pulse doubled the photocurrent at 296 K and raised it by a factor of five at 214 K. The dissociation signals are normalized for shot-to-shot variations in laser intensity-each point represents an average of 25 repetitions. Photocarriers were collected by a field of 6.7 X lo5 V/m.
on the rising edge and 15 ps on the falling edge. The distinct asymmetry indicates that the initial population
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probed by the IR pulse has a first half-life of no more than 9 ps at room temperature. We also find that the decay is highly nonexponential. For example, the second and third half-lives are 28 and 125 ps, respectively. Repeating these experiments at lower temperature illustrates two additional facts: reduced temperatures dramatically extend the first half-life as well as increase the magnitude of the IR enhancement. Figure 2b shows that a t 214 K the first half-life is 70 f 20 ps and the enhancement has increased fourfold. It will be shown below that the observed temperature effects have their principal origin in the temperature-dependent mobility of an electron in n-hexane.16 This strongly supports the interpretation of LTY14 that geminate charge pairs are the principal intermediates responsible for the infrared enhanced photocurrents. The nonexponential decay curves in Figure 2 bear a close resemblance to the geminate charge pair decay functions predicted by Hong and Noolandi? A neutral excited-state intermediate, by contrast, would be expected to decay exponentially in time. A characteristic time, 7,for geminate recombination can be obtained for coulomb-driven recombination in the absence of diffusion. The time 7 equals 4 m ro3/(3pe) ~ ~ where E is the dielectric constant, eo the permittivity of vacuum, ro the initial radius of the thermalized electron, 1.1 the sum of the positive and negative carrier mobilities, and e the electronic charge. Comparison of this expression with the detailed theory of Hong and NoolandisJ7 indicates that the initial half-life for geminate pair decay is approximately 1.27. Using the experimentally determined initial pair separation of ro = 4.5 nm14 and known values for the electron mobility18and dielectric constantlg of n-hexane, we find 1.27 equals 6.4 ps at 296 K and 94 ps at 214 K. These values are in close agreement with the initial half-life estimates of no more than 9 and 70 f 20 ps made from Figure 2. The magnitude of the infrared enhancement was superlinear in infrared intensity with an intensity dependence exponent of 1.4 f 0.2. Given the IR intensity of approximately 1 X photons/(cm2.s) and an electron cm2,the probability for IR photon cross section of 3 x absorption by an electron which survives 1 ps is 0.3. Longer-lived electrons have a very high probability of absorbing one IR photon from the 8-ps pulse and a significant probability of absorbing two or more. Thus the (16) R. M. Minday, L. D. Schmidt, and H. T.Davis, J. Chem. Phys., 54,3112 (1971); A. 0. Allen, T.E. Gangwer, and R. A. Holroyd, J.Phys. Chem., 79, 25 (1975). (17) K. M. Hong and J. Noolandi, J. Chem. Phys., 69, 5026 (1978). (18) H. T.Davis and R. G. Brown, ’Advances in Chemical Physics”, Vol. 31, I. Prigogine and S.A. Rice, Ed., Wiley, New York, 1975, p 356.
The mobility of the anthracene cation is at least of the electron and will be ignored. (19) L. M. Heil, Phys. Rev., 39, 666 (1932).
1OX
smaller than that
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observed superlinear intensity dependence is expected and was also observed by LTY.14 As depicted in Figure 1, excitation of the geminate electron at 1053 nm raises its total energy well above the coulomb potential. The excess energy is rapidly dissipated as the electron returns to thermal equilibrium. This rethermalization process will in general lead to a new pair separation. A computer simulation of the change in escape probability following spherically symmetric rethermalization about the initial position of the electron predicts an increase in free carrier generation for all finite values of the initial pair separation.20 For an initial pair separation of 4.5 nm, secondary thermalization lengths of 3 nm can account for the magnitude of the IR enhancement seen in Figure 2. Unfortunately under these conditions the measurement technique is itself time dependent. The magnitude of the enhancement depends on the instantaneous pair separation probed by the IR pulse as well as the total number of charge pairs present in the sample. Time-resolved measurements of geminate pair recombination kinetics can be expected to answer a number of questions: (a) Is the diffusion equation approachsVz1an adequate description of the time evolution of geminate pairs? (b) Are there any quantum mechanical states, either “Rydberg-like”22or WannierZ3which are intermediates in the recombination process? (c) What is the appropriate distribution function of geminate pair separations?6 Semiquantitatively as examined above and qualitatively with respect to the long tail in Figure 2a, the observed decay kinetics are consistent with the time-dependent diffusion theory of Hong and Noolandi.8J7 No evidence of any intermediate states is evident in the present results. Given the adequacy of the diffusion theory, the distribution function of thermalization lengths will be recovered from recombination kinetics of adequate time resolution. A start has already been made.1° Whether it is worthwhile to press the present experiments to that end will depend on the sensitivity20of the IR enhancement to initial geminate pair radius. Acknowledgment. We acknowledge the help and encouragement provided by Professor Robin Hochstrasser and the staff at the NSF Regional Laser Laboratory, University of Pennsylvania. The assistance of Fuad Doany and Ted Heilweil in these experiments is gratefully acknowledged. Contract No. DE-AC02-83ER13102 of the Department of Energy provided partial support for this work. ~
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(20) T. W. Scott and C. L. Braun, unpublished. (21) A. Mozumder, J. Chem. Phys., 48, 1659 (1968). (22) K.-C. Wu and S. Lipsky, J. Chem. Phys., 66,5614 (1977); K. Lee and S. Lipsky, J. Phys. Chem., 86, 1895 (1982). (23) I. Messing, B. Raz, and J. Jortner, Chem. Phys., 23, 23 (1977).
