J. Phys. Chem. 1983, 87,429-441
of the vibrational frequencies of the reactants and the transition state. The VP can be analyzed in the same way that we have done for the EXC and ZPE terms. The results are shown in Table VII. In both cases the VP term is determined by the contributions of the new modes. Analysis of the different contributions shows that, as for the vibrational term, the leading contributions are associated with modes 3 and 2 in the first case and with 1, 4, and 5 in the second case. We can evaluate now the contribution of the three groups of frequencies to the total isotope effect, as shown in the last column of Table VII. It can be seen that the importance of the new modes is greatly tempered. In the first case, the contribution of the new modes is exactly balanced by the contribution of the ethylene modes, which comes mainly from the bagcontribution to the VP term. In the second case, the contribution of the new modes is the leading one but the contribution of the methyl modes cannot be neglected. Shortly, the absence of kinetic effect in CH3 + CD2=CD2/CH2=CH2 is the result of the cancellation of the contributions from the new modes (through both the EXC X ZPE and VP terms) and those from ethylene (through the VP term only); the kinetic effect for CD3/CH3 + CH2=CH2 is the result of the cooperative contributions of the new modes (through the EXC X ZPE and VP terms) and those of the methyl radical (through the EXC X ZPE term only). The contribution of the new modes will probably become dominant for higher values of HRR but it is not possible to conclude that they are the principal contributors to the kinetic isotope effect, as was
429
proposed previo~sly,8~~ without a careful examination. Coming back to eq 1 and its thermodynamical implications, we can conclude that the isotopic substitution at the ethylene has a differential effect on the rotational and translational activation entropies, favoring the unsubstituted reaction, which is balanced by the differential effect in the vibrational activation enthalpy and entropy, favoring the deuterated reaction. Isotopic substitution at the methyl radical has a larger differential effect on both the vibrational actbation enthalpy and entropy than the rotational and translational activation entropies and, consequently, the deuterated reaction is favored. Needless to say, the above results should not be extended to other free-radical addition reactions without some caution. A theoretical analysis of the effect of substituents in olefins and radicals other than methyl as well as a comparison of intermolecular and intramolecular additions is now under way.25 Acknowledgment. The calculations reported here have been carried out on the UNIVAC 1108 computer of the Ministerio de Educacidn y Ciencia through the terminal in the Centre de Ciilcul de la Universitat Politgcnica de Barcelona. Registry No. CH,., 2229-07-4; CHz=CHz,74-85-1;deuterium, 7782-39-0. (25) J. M. Poblet, E. Canadell, and S. Olivella, to be submitted for publication. Reactions with stronger modifications in the transition state, as the radical abstractions, have also been studied.
Infrared Laser-Induced Isomerization and Decomposition of Volatile Uranyl Complexes R. G. Bray,' D. M. Cox,' R. 8. Hall, J. A. Horsley, A. Kaldor, G. M. Kramer, M. R. Levy,+ and E. B. Priestley Corporate Research-Science Laboratories, Exxon Research and Engineering Company, Linden, New Jersey 07036 (Received: June 23, 1982; I n Final Form: October 12, 1982)
Molecular beam mass spectrometric, laser-induced fluorescence, and IR-IR double resonance measurements have been applied to the investigation of the IR laser chemistry of bis(1,1,1,5,5,5-hexafluoropentane-2,4dionato)dioxouranium(VI) trimethylphosphate [UOz(hfacac)zTMP].The results have been correlated with energy deposition and FT IR absorption data, yielding a more complete understanding of the dissociation mechanism than obtained in previous studies of an analogous molecule, UOz(hfacac)zTHF. IR dissociation appears to be slower, and more complicated, than previously deduced. Disappearance of laser-induced fluorescence or parent molecular ion upon COz laser irradiation is attributable to rapid isomerization (>lo79-l) of parent molecules to a species with a red-shifteduranyl absorption feature. The latter molecules have sufficient excitation to subsequently decompose by loss of TMP. For the TMP complex, formation of the isomer requires AH 10 kcal/mol and A S 20 eu, which is consistent with ring opening (via U-0 bond) of the bidentate hfacac ligand, compared to AH 36 kcal/mol and AS = 55 eu for dissociation of TMP. For excitation of either uranyl or TMP vibrational modes with 450-11s fwhm COzlaser pulses, the dissociation yield depends only on the energy deposited and the decomposition rate is consistent with RRK predictions.
-
-
Introduction
In a series of preceding publicationsl-7 from this laboratory, several aspects of the infrared laser-induced chemistry of volatile uranyl complexes have been reported. Compounds which have been investigated may be represented by the common formula, UOZLzB,where L is an 'Present Address: John Howard Upper School, Biddenham Turn, Biddenham, Bedford, MK 404AZ, United Kingdom.
0022-3654/83/2087-0429$0 1.50/0
anionic ligand, most frequently the monoanion of 1,1,1,5,5,5-hexafluoropentane-2,4-dione (hexafluoro(1) A. Kaldor, R. B. Hall, D. M. Cox, J. A. Horsley, P. Rabinowitz, and G. M. Kramer, J. Am. Chem. Soc., 101, 4465 (1979). (2) D. M. Cox, R. B. Hall, J. A. Horsley, G. M. Kramer, P. Rabinowitz, and A. Kaldor, Science, 205, 390 (1979). (3) D. M. Cox and J. A. Horsley, J . Chem. Phys., 72, 864 (1980). (4) D. M. Cox and E. T. Maas, Jr., Chem. Phys. Lett., 71, 330 (1980). (5) J. A. Horsley, D. M. Cox, R. B. Hall, A. Kaldor, E. T. Maas, Jr., E. B. Priestley, and G. M. Kramer, J . Chem. Phys. 73, 3660 (1980).
0 1983 American Chemical Society
430
The Journal of Physical Chemistty, Vol. 87,No. 3, 1983
acetylacetonate, hfacac) and B is a neutral Lewis base, whose bond to the uranyl moiety is fairly weak (23-40 kcal mol-’). The first two papers1e2reported that irradiation of the asymmetric stretch of the UO?+ moiety of U02(hfa~ac)~TH led F to apparent high yields of tetrahydrofuran (THF)dissociation product at very low fluences (e.g., 100% yields a t 0.1 J cm-2). The decomposition reaction U02(hfacac)2THF U02(hfacac), + THF (1)
-
was estimated to have an activation energy.(assumed equal to the enthalpy of reaction) of about 30 kcal mol-l.lp2 More recently, in thermal decomposition studies of U02(hfacac),THF the enthalpy of reaction AH has been measured’ to be 33 f 3 kcal mol-’ in good agreement with earlier estimates. In ref 1 the extent of the reaction was monitored by a laser-induced fluorescence depletion (LIFD) technique in which the temporal loss of fluorescence from the starting reactant8 was measured. It was assumed that the time dependence of the dissociation process was accurately monitored by the fluorescence depletion and it was concluded that dissociation was more rapid than would be predicted by RRK theory. However, it was stateda that “the fluorescence depletion may monitor a sequence of reactions culminating in dissociation”. Real time pumpprobe measurements reported here show that indeed an “intermediate” is formed very rapidly which subsequently decays more slowly into the reaction products. The time evolution of the reactant loss and of the formation of the “intermediate” is identical and extremely rapid (rate Ilo7 s-’) within our limited time resolution of -70 ns. With actual dissociation rates much slower than initially believed, a previously developed general statistical model has been applied to this case and accurately predicts dissociation yields? temperature dependence^,^ and isotopic sele~tivities.~ The model is valid for large molecules in general and in particular for molecules of the generic species U02(hfacac),B, where B is any one of a series of neutral Lewis bases such as THF, TMP, Me,SO, H20, acetone, etc. Previously we had reported results of a systematic study of several U02L2Bmolecules in the gas phase6 and in solution.’o In this paper we report experiments performed in a static cell and in a molecular beam on UOz(hfaca&TMP, where TMP is the trimethylphosphate neutral base ligand. The static cell gas-phase experiments consisted of (a) accurate IR absorption cross sections and line widths as a function of frequency and temperature; (b) COP laser energy deposition measurements as a function of laser fluence and frequency; (c) time-resolved depletion of visible laser induced fluorescence (LIFD) as a function of pulsed CO, laser fluence and frequency; (d) time-resolved (-70-ns resolution) infrared-infrared double resonance (IRDR) measurements, whereby a low-power CW C02laser probes the disappearance of parent IR absorption, as well as appearance of product absorption due to decomposition induced by a pulsed C 0 2 laser. The molecular beam experiments measured the fluence, frequency, and time dependence of (i) the disappearance of parent and most abundant fragment ions (e.g., U02L2B+and U02LB+),and (6) R. B. Hall, A. Kaldor, D. M. Cox, J. A. Horsley, P. Rabinowitz, G. M. Kramer, R. G . Bray, and E. T. Maas, Jr., “Advances in Chemical Physics”, J. Jortner, Ed., Wiley, New York, 1981. (7) R. L. Woodin, D. M. Cox, R. B. Hall, and A. Kaldor, J . Phys. Chem., 85, 2898 (1981). (8) Thermal chemistry experiments show that the dissociation products U02(hfacac)z, THF, and T M P do not fluoresce under the experimental conditions employed in the LIF depletion measurements. (9) See footnote 23, ref 1. (10) G. M. Kramer, E. T. Maas, Jr., and M. B. Dines, Inorg. Chem., 20, 1415 (1981).
Bray et al.
(ii) the appearance of product ions (e.g., U02L2+). Although there are some differences between U02(hfacac)2TMPand U02(hfacac)2THFsuch as vapor pressure, thermal stability, small signal IR absorption cross sections, and yield obtainable at a particular fluence both molecules exhibit qualitatively similar behavior. U02(hfacac)2TMP has been used in the present study primarily for two reasons: (1) The bond strength of UO,(hfacac),TMP is - 3 kcal/mol larger than that for U0,(hfaca~)~THF which leads to greater thermal stability at elevated temperatures (>100 ” C). (2) U02(hfacac)2TMPhas a second IR absorption feature accessible to C02laser transitions but associated with the CO stretches of the TMP moiety. This made it possible to compare the effect of IR laser energy deposited into the molecule via the two distinct absorption features which at least initially energize two different moieties.
Experimental Section The samples of Uo,(hfa~ac)~TMP, synthesized in our laboratory, were purified by vacuum sublimation and characterized by standard analytical techniques. The IR spectrum, differential scanning calorimetry, X-ray diffraction patterns, and molecular structure were reported recently.”J3 U02(hfacac)2TMPis volatile a t moderate temperatures (27 Pa a t 100 0C).11J2 Infrared Absorption Cross Sections. The infrared absorption cross sections14 were obtained with a Digilab Fourier transform spectrometer (FTS-20) a t a nominal resolution of either 0.5 or 1.0 cm-’. The absorption cell (10 cm path length, ZnSe windows), sample reservoir, and connecting vacuum manifold (including a 1333 Pa MKS Baratron head) were contained within a uniformly heated transite box equipped with KCI windows. Temperature uniformity throughout the box was maintained by a constant flow of preheated N2 gas; a separate independently adjustable N2 gas flow was used to control the sample reservoir temperature in order to maintain it at a slightly lower temperature (usually 5-10 “C) than the manifold and absorption cell. Copper-constantan thermocouples attached to various points within the box provided an accurate temperature monitor. Since UOz(hfacac),TMP exhibits slow thermal decomposition at elevated temperatures,13 the sample reservoir was pumped for several minutes prior to distillation into the absorption cell. This was done in order to remove more highly volatile components (e.g., free base, U(hfacac),, and sometimes Hhfacac). Infrared spectra were then taken with repetitive cell fillings until consistent data were obtained, and the results converted to frequency dependent cross sections. Contributions from vestigial small quantities of Hhfacac and TMP were subtracted out. The spectrometer calibration was checked by using accurately known C02 and NH, gas-phase absorption lines. Energy Deposition. Energy deposition16 in gas-phase U0,(hfacac)2TMP was determined from the attenuation of a (Lumonics 801A) pulsed C02 laser through a 30 cm long, 2.5 cm diameter, Pyrex sample cell fitted with ZnSe windows. The laser beam was collimated so the field in(11)J. H. Levy and A. B. Waugh, J . Chem. Soc., Dalton Trans., 1628 (1977). (12) J. C. Taylor and A. B. Waugh, J . Chem. SOC.,Dalton Trans., 1630 (1977). (13) A. Ekstrom, H. J. Hurst, C. H. Randall, and H. Loeh, J . Phys. Chem., 84, 2626 (1980). (14) R. G. Bray, Spectrochim. Acta., submitted for publication. (15) C. F. Meyer, R. L. Woodin, and A. Kaldor, Chem. Phys. Lett., 83, 26 (1981). (16) A. V. Nowack and D. 0. Ham, Opt. Lett., 6, 185 (1981).
The Journal of Physical Chemistry, Vol. 87, No. 3, 1983 431
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-- 0 J
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I i' +I+ LASER
A co-propagating, line tunable, low power, CW C02 probe laser beam (Sylvania Model 950) monitored pump laser-induced changes in the absorption spectrum. The laser beams, horizontally and vertically plane polarized, respectively, were combined and separated with Ge flats mounted at Brewster's angle. A Spex DoubleMate monochromator provided additional filtering of pulsed C02 laser radiation except when both lasers were tuned to exactly the same transition. In the latter case some leakage of pulsed laser radiation through the quadruple Brewster angle separator was always observed preventing accurate measurements at times less than 3 ps at the pump laser frequency. Transient absorption changes were detected with a fast, Cu-doped Ge detector (Santa Barbara Research Center Model 9145), amplified with a 5-MHz amplifier (Perry Amplifier Model 070/40), and recorded with a Biomation 8100 waveform recorder; typically 1000 scans were averaged. The Biomation was interfaced to a PDP 11/34 laboratory minicomputer configured for signal averaging. Spatial profiles of the pulsed and cw laser beams were taken by pinhole scans across the beam. Least-squares Gaussian fits to the data at 10P8 yielded w1 = 4.1 mm for the pulsed laser and w z = 1.9 mm for the CW laser. No attempt was made to eliminate mode beating in the pulsed laser output. The pulsed laser energy was measured by Gen-Tec Model ED 500 surface absorbing energy meter; CW laser power was measured with a Scientek power meter. Both the CW laser power and pulsed laser energy were controlled by propylene filled attenuator cells. Changes in the absorption spectrum were measured as a function of pulsed laser peak fluence. Since the CW laser beam diameter was about one-half the beam diameter of the pulsed laser, the CW laser probed the effect of a range of fluences not simply the peak fluence as in the LIF experiments. The consequences of this are also discussed in Appendix A. Molecular Beam Mass Spectrometry. The molecular beam mass spectrometry technique has also been described previously.24 An effusive beam of U02(hfacac)2TMPwas irradiated by a Lumonics 801A pulsed C 0 2 laser. Typically about 25% of the total pulsed energy was in the -2-pus nitrogen tail and 75% in the 450-11s sharper first spike. The spatial profile was measured by scanning a pinhole across the beam for the various laser transitions used. The beam diameter ( 2 4 was 10-13 mm at the intersection of the laser beam with the molecular beam. A quadrupole mass spectrometer detected the parent ion, UOzL2B+,the most abundant fragment ion, UO2LB+,and the product ion, UO2L2+.C 0 2 laser irradiation was performed 2 cm downstream of the oven orifice, and 10 cm from the mass spectrometer ionizer. In this case production of the dissociation product UOzLzcould not be detected. In some experiments irradiation was performed only 1cm upstream of the ionizer or, through ZnSe windows, in the oven itself1 where production of U02L2+could be observed. The depletion (production) appeared as a transient loss (increase) in the ion signal level and was measured as a function of peak fluence. Appendix B describes the procedure used to estimate absolute depletion fractions for these measurements.
TEA LASER
Flgure 1. The schematic diagram for the Infrared-infrared double resonance experiments is shown.
tensity along the absorption path was nearly constant. The pulsed laser spatial profile, after passage through the empty cell, was measured with a multielement pyroelectric array and each element of the array (0.1 mm wide by 1mm high) then correlated with a particular fluence. An element by element comparison between beam profiles through empty and filled cells allowed mapping of the energy deposition as a function of fluence over roughly an order of magnitude in fluence with only two laser pulses. (Note that the element area is too large to see the effects of mode beating of the laser longitudinal modes so that the observed pulse to pulse profiles were highly reproducible.) The complete fluence curve was obtained by varying the pulsed laser energy. So that measurable attenuation could be obtained, the sample pressure was kept between 7 and 30 Pa. At these pressures no laser beam distortion could be detected as has been observed in SF+15J6 Laser-Induced Fluorescence. The essentials of the laser-induced fluorescence (LIF) technique have already been described.2 Briefly, counterpropagating pulsed C02 and visible dye laser beams were passed through a heated sample cell, arranged as above, and the time-resolved fluorescence from parent UOz(hfacac)2TMPwas detected at right angles to the beams. Typically the sample pressure was 2.7 Pa and the cell temperature was 90 OC. The COz laser beam was collimated through the sample cell, with radius w1 = 4.25 mm. Pulse energy was measured with a Gen-Tec ED 500 energy meter. The nitrogen-pumped dye laser was operated at 450 nm, had a beam diameter w2 1.0 mm, and was passed collinearly through the center of the C02 laser beam, thus sampling the peak intensity region of the COi laser pulse (see Appendix A). The delay between the two laser pulses was typically varied from 0.5 ps to 5 ms. Infrared-Infrared Double Resonance. Infrared-infrared double resonance measurements were made with the experimental apparatus shown schematicallyin Figure 1. A brief description is given below but a more detailed description will be published elsewhere." The sample cell was arranged and housed in a heated transite box as described above. Typical operating conditions were T -385 K, p 26 Pa. The pulsed C 0 2 laser (Lumonics Model 801-A) was operated nearly nitrogen free so as to minimize the amount of energy in the nitrogen tail. The pulse width in this case was about 450 ns.
-
-
(17) M. R. Levy, R. 0. Brickman, and A. Kaldor, to be published.
Results Single-photon absorption cross sections, u, for a series of C 0 2 laser transitions are listed in Table I and the infrared absorption spectrum is shown in Figure 2.18 For (18)The infrared absorption spectra for a large number of uranyl compounds is reported and discussed in ref 14.
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The Journal of Physical Chemistry, Vol. 87, NO. 3, 1983
Bray et ai.
TABLE I: Absolute Absorption Cross Sections (lo-'' c m z molecule-') for UO,(hfacac),TMP at CO, Laser Transition Frequencies
9.4-pm band
10.6-pm band trans
freq, cm-I
u
trans
freq, cm-'
u
P(40) P(38) P(36) P(34) P(32) P(30) P(28) P(26) P(24) P(22) P(20) P(18) P(16) P(14) P(12)
925.06 927.08 929.07 931.05 933.00 934.92 936.83 938.71 940.56 942.40 944.21 945.99 947.75 949.49 951.20 952.89 954.56 956.20 957.81 959.40 963.27 964.78 966.26 967.72 969.15 970.56 971.94 973.30 974.63 975.94 977.23 978.49 979.73 980.94 982.13 983.29 984.43 985.55 986.64 987.71
0.08 0.00 0.08 0.09 0.06 0.07 0.08 0.02 0.15 0.18 0.19 0.38 0.60 1.01 2.13 3.36 4.77 3.06 1.76 0.69 0.22 0.19 0.21 0.10 0.07 0.06 0.04 0.05 0.03 0.06 0.00 0.11 0.05 0.04 0.08 0.06 0.03 0.07 0.06 0.06
P(40) P(38) P(36) P(34) P(32) P(30) P(28) P(26) P(24) P(22) P(20) P(18) P(16) P(14) P(12) P(10) P(8) P(6) P(4) P(2) R(2) R(4) R(6) R(8) R(10) R(12) R(14) R(16) R(18) R(20) R(22) R(24) R(26) R(28) R(30) R(32) R(34) R(36) R(38) R(40)
1027.36 1029.43 1031.46 1033.48 1035.46 1037.43 1039.36 1041.27 1043.16 1045.02 1046.85 1048.66 1050.44 1052.19 1053.92 1055.62 1057.30 1058.94 1060.57 1062.16 1066.03 1067.53 1069.01 1070.46 1071.88 1073.27 1074.64 1075.98 1077.30 1078.58 1079.85 1081.08 1082.29 1083.47 1084.62 1085.75 1086.86 1087.93 1088.98 1090.01
0.21 0.18 0.29 0.32 0.38 0.44 0.48 0.63 0.69 0.83 1.02 1.20 1.48 1.76 2.00 2.30 2.68 2.99 3.30 3.69 4.21 4.28 4.15 3.88 3.57 3.18 2.83 2.57 2.37 2.12 1.94 1.76 1.59 1.49 1.42 1.30 1.28 1.25 1.19 1.18
P(10) P(8) P(6) P(4) P(2) R(2) R(4) R(6) R(8) R(10) R(12) R(14) R(16) R(18) R(20) R(22) R(24) R(26) R(28) R(30) R(32) R(34) R(36) R(38) R(40)
5
t z 3
0
900 925
1
950
975 1000 1025 1050 1075 1100
WAVE NUMBERS (CM')
Figure 2. The infrared absorption spectrum for UOdhfacac),TMP (solM line) is compared with the shape of the depletion spectrum obtained from pulsed CO, laser irradiation of a molecular beam of UO,(hfacac),TMP (solid circles). Selected laser transitions, referred to in the text, have been labeled. The depletion spectrum was normalized to the absorption spectrum at the 10P6 laser transition.
convenience we denote COz laser transitions by the vibrational band wavelength (10 or 9 pm), followed by the rotational branch (P or R), and rotational quantum number, e.g., lOP4,9R22. The value of u reported here for the peak absorption of the uranyl stretch agrees reasonably
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Flgure 3. The uranyl absorption line width (fwhm) is plotted as a function of temperature for UO,(hfacac),TMP and UO,(hfacac),THF. 24
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1 a 200 FLUENCE imJicm')
Flgure 4. The average number of 10P8 CO, laser photons absorbed per irradiated molecule is plotted as a function of laser fluence.
well with that reported in ref 13. As noted from a study of the IR absorption spectrum, the COz laser energy can be absorbed not only by the uranyl asymmetric stretch centered near 954 cm-' but also by another broader feature near 1068 cm-l which is assigned to the C-0 stretches associated with TMP. Figure 3 shows the effect of temperature on line width for both UOz(hfacac)zTMPand UOz(hfacac)zTHF.Although the line width narrows as the temperature is lowered for UOz(hfacac),TMP, the peak absorption frequency of the uranyl stretch is constant (within f0.5 cm-') over the temperature ranges investigated. For UOz(hfacac)zTHFno appreciable narrowing of the line width can be observed, but again the position of the peak absorption remains unchanged. Energy deposition measurements in U02(hfacac),TMP for the lOP8 COz laser transition are shown in Figure 4, in which the average number of photons absorbed per molecule is plotted vs. laser fluence. The values are obtained by measuring the fraction of the C 0 2 laser pulse transmitted through a 30-cm gas cell. The analysis of the data is similar to that used earlier6 except that use of a multielement pyroelectric array allowed different laser fluence regions of nearly uniform field to be sampled at each array element. In the case of strong absorption (e.g., 1OP8 at peak of the uranyl absorption feature) a dramatic shift from linearity (constant absorption cross section) is observed, whereas on weaker absorption features (e.g., 9P8, 9R22, 10P10, 10P12, 10P14, data not shown) little or no
The Journal of Physical Chemism, Vol. 87, No. 3, 1983 433
I R Laser Chemistry of Volatile Uranyl Complexes
t
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Figure 5. The time evolutlon for spectral transients from IRDR measurements is shown. Positive amplitudes indicate induced transparency and negative amplitudes indicate induced absorption. The pump laser was tuned to the 10P8 transition at the peak of the uranyl absorption. The curve labeled parent depletion was obtalned with the probe cw CO, laser tuned to the 10P6 transition, the one labeled intermediate was obtained with the 10P14 transitlon, and the one labeled U0,(hfacac), was obtained with the 10P8 transition. The integral of the laser pulse is the other curve shown.
shift from linearity is observed. For the IRDR measurements the pump COz laser was tuned to the 10P8 (954.56 cm-’) transition at the peak of the uranyl absorption feature in U 0 & f a c a ~ ) ~ T M The P. CW COz laser was tuned to probe the spectral region both to the red and to the blue of the pump laser transition. The typical time dependence for the laser-induced opacity/transparency is shown in Figure 5, where the results have been normalized to unity at their maximum amplitudes. The laser fluence was 155 mJ/cm2 and the UOz(hfaca&TMP pressure in the cell was 26 Pa. With the CW laser tuned to the 10P6 (956.20 cm-l), one laser transition to the blue of the pump frequency, very rapid disappearance of absorption (induced transparency) was observed. When the probe CW laser was tuned to the red of the pump frequency (e.g., 10P14 at 949.49 cm-’), a very rapid induced absorption (opacity) was observed followed by the slower decay of this induced absorption. When the probe laser was tuned further to the blue (e.g., 10R8 at 967.22 cm-’), a second induced absorption was observed to grow at a slower rate but identical with the rate of decay of the rapidly formed red-shifted absorption. The time dependence of 10P6 induced transparency and the initial rapid rise of induced absorption to the red (i.e., 10P14 probe) of the pump frequency are identical within experimental uncertainty and occur so rapidly that they follow the time-integrated laser intensity. Thus we see that transient absorption to the red (10P14) is produced as rapidly as parent molecule absorption is reduced (10P6). Neither of these transient features can be resolved within the instrumental time resolution of 70 ns. The spectral changes induced by the pump laser are further elucidated by examination of the frequency dependence of the induced transients shown for two fixed delay times in Figure 6. In Figure 6a, the frequency dependence obtained 0.5 FS following the laser pump pulse is shown. The induced absorption to the blue which forms more slowly is nearly undetectable under these conditions. The data in Figure 6a have been deconvolutedZ0by as(19) See,e.g., W. C. Danen and J. s. Jang in ‘Laser-Induced Chemical Processes”,J. I. Steinfeld, Ed., Plenum, New York, 1981, for a discussion of “large” vs. “small”molecules.
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Figure 6. (a) The transient spectrum obtained at 0.5 p s after the laser pulse is shown as solM circles connected by a solid line. The deconvoluted spectral features are shown as smaller solid circles. (b) The spectral profiles of the deconvoluted transient species are compared with the Infrared absorption spectrum. The dashed curve labeled “intermediate” was that obtained 0.5 ~s after the pump laser pulse. The dotdash curve labeled “UO,L,” was that obtained 3.5 FS after the pump pulse. The solld curve is the infrared absorption spectrum.
suming Lorentzian profiles for all transient spectra. Subtraction of the parent absorption feature reveals an induced opacity with bandwidth similar to that of the parent, but peaking at 950 cm-’, about 4 cm-’ to the red of the parent absorption. The transient spectrum obtained 3.5 FS after the C02 pump pulse yields an absorption spectrum peaking near 966 cm-’, shifted about 12 cm-’ to the blue of the unexcited U02(hfacac)zTMPabsorption feature. The parent absorption spectrum and the two transient spectra are com(20) The details of the deconvolution using a least-squares fitting routine for two Lorentzians is described in detail in ref 17.
The Journal of Physical Chemlstty, Vol. 87,No. 3, 1983
434
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FLUENCE (mJ/cm*)
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60
80
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120
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LASER FLUENCE (mJ/cmz)
Figure 7. (a) The maximum yield for reactant depletion (soM squares), intermedlate productbn (solid circles) and UO&hfacac), production (solid triangles) Is shown as a function of laser fluence. (b) The time necessary for UO,(hfacac), production to grow to one-half of Its peak amplitude Is plotted vs. laser fluence for 0.1 torr of UO,(hfacac),TMP at 120 OC. The pump laser was tuned to the 1OP8 transition and the probe laser was tuned to the 10R8.
pared in Figure 6b. The shapes of different fluence curves, normalized at 10P6, are nearly identical suggesting that neither the transient red feature nor the transient blue feature exhibit a further frequency shift as the pump fluence is varied from 9 to 120 mJ/cm2; only the amplitude of the transient absorption increases. The amplitudes of these transient signals at fixed probe and pulsed laser frequency depend on the pulsed laser fluence. This dependence, plotted as log yield vs. log fluence, is shown in Figure 7a. Note that the shapes of the fluence dependence of reactant depletion and red feature formation are identical within experimental uncertainty. The individual curves were normalized to 100% yield at the maximum fluence used since only relative signal amplitudes were obtained in these IRDR measurements. The blue feature, on the other hand, shows a markedly different fluence dependence. Figure 7b displays the fluence dependence of T~ for the red to blue feature transformation where T ~ is /t i ~e half-life of the red feature decay (or the half-life of blue feature growth). The U02(hfacac)2TMPpressure was 27 Pa for the measurements in Figure 7a and 13.3 Pa for the lifetime measurements in Figure 7b. Under these conditions the mean time between hard sphere gas kinetic collisions is -0.5 and 1.0 ps, respectively. Since r l I 2varies from 0.1 to 10 ps, collisions may play an important role. This will be discussed in the next section. We are now performing experiments with shorter pump pulses (-50 ns) and at much lower pressures (-2.6 Pa) in order to further assess the influence
c
-
1
‘0
I
20
30
40
,
,
50
FLUENCEirJ
6c CT
70
,
ao
90
IOC
1
Figure 8. The depletion fraction obtained from irradiation of a U0,(hfacac),TMP molecular beam is plotted vs. laser fluence for the parent molecular ion, UO,(hfacac),TMP+ (circles), and the dissociative ionization fragment, UO&hfacac)TMP+(squares). The laser beam crossed the molecular beam 10 cm in front of the ionizer.
of collisions on the infrared excitation/dissociation process in these large molecules. Next we present results of the molecular beam depletion measurements. In Figure 8 the laser-induced depletions are shown for the parent molecular ion, U02(hfaC ~ C ) ~ T MatP + an, mle of 824, and the most abundant high mass fragment ion U02(hfacac)TMP+,at an mle of 617. The depletion on the parent ion is considerably higher than depletion on the fragment ion for fluences below 100 mJ/cm2. The depletion on both ions tends to approach 100% for sufficiently high laser fluence. Similar results obtain if the pump laser is tuned to the 9P8 transition which is resonant with the CO stretch of the TMP moiety. The molecular beam irradiations reported in Figure 8 were made 10 cm upstream from the ionizer. The time of flight (TOF) from this laser irradiation zone to the ionizer is s. Thus the yields obtained at least partially reflect the loss from the beam of molecules which dissociate with reaction lifetimes of s or shorter, i.e., the integral yield of all molecules with reaction lifetimes less than s. The laser-induced molecular beam depletion at constant fluence measured for a series of C 0 2 laser transitions is shown in Figure 2 and closely mimicks the infrared absorption spectrum. In attempts to detect dissociation products two other experimental arrangements which utilized mass spectrometric detection were used. First, COz laser irradiation (1OP8 transition) which crossed the molecular beam only 1 cm (instead of 10 cm) from the ionizer allowed the solid angle subtended by the ionizer relative to the irradiation zone to be increased by about two orders of magnitude but the integrated reaction time was reduced to about lo-* s from s. The net effect was to increase the fraction of the dissociation products which entered the ionizer by about a factor of 50. Second, as described previously,l “in-oven” irradiations allowed microsampling of the irradiated volume by the mass spectrometer. These results are shown in parts a and b of Figure 9, respectively. Comparison of Figures 8 and 9a shows that for a given fluence the depletion signal on the parent molecular ion U02(hfacac)2TMP+is fairly insensitive to distance, i.e., 10and 1-cm irradiations result in nearly identical depletion yields; whereas at low fluence the depletion on the fragment ion U02(hfacac)TMP+is considerably reduced at the shorter laser-ionizer distance. Irradiation, both “in-oven” and at the shorter laser-ionizer distance led to increased ion signals for m / e 684 assigned as the U02(hfacac)2monomer, Le., the dissociation product is detected. The fluence dependence of the U02(hfacac)2+production in molecular beam irradiations exhibits no fluence threshold
The Journal of Physical Chemistry, Vol. 87, No. 3, 1983 435
I R Laser Chemistry of Volatile Uranyl Complexes A
L
P
I
I
100
200
FLUENCE (mJlcm’) IU6
A
$5
0
10
20
30
40 50 60 FLUENCE (mJlcm’)
70
80
90
100
Figure 10. The comparison between LIF depletion (triangles), IRDR red feature yield (circles), molecular beam depletion (squares), and yield predicted from the equilibrium model for isomer production (soli line) is shown as a function of fluence.
L
0
52
i
-1.0
t
A
A A A
Flguro 9. (a) The relative depletion/productlon signals obtained from molecular beam irradiation 1 cm from the ionizer are plotted as a furctlon of laser fluence for the parent mdecular ion UOdhfacachTMP+ (circles) and for the parent ion of the monomer dissociation product UOdhfacac),+ (triangles). (b) Relative depletion/production signals obtained from “inoven” irradiation of UO,(hfacac),TMP with mass spectrometric sampling are plotted vs. fluence for the depletion on the parent moiecukr ion UO,(hfacac),TMP+ (circles) and production of the monomer ion UO,(hfacac),+ (triangles).
and tends to saturate at high fluence. Finally the “in-oven” irradiation does indicate a threshold which is similar to that found in the blue feature production (Figure 7a) in the IRDR experiments. This effect appears to be consistent with a conclusion that uin-oven”measurements also are affected by collisional processes. The fluence dependence of LIFD is shown in Figure 10 for U02(hfacac)2TMPpumped with the 1OP8 COOlaser transition. Since only the parent molecular species are known to fluorescence under the experimental conditions used, the depletion of the fluorescence monitors the parent molecular concentration. From Figure 10, we observe that LIFD increases nearly linearly at low fluences and saturates a t 95% depletion for fluences greater than 100 mJ/cm2. The functional dependence mimicks that for the molecular beam depletion and for the IRDR “red feature” production shown in this figure. Although dependent on absorption cross section, this general behavior of linearly increasing depletion as a function of fluence at low fluences followed by nearly 100% depletion at high fluences is observed for all COz laser pump transitions. Discussion In our fist publication1 on U02(hfacac)2THF,we stated that LIFD measurements showed that the fluorescence disappeared at a rate > lo7 s-l. In addition, the fluence dependence of LIFD was found to agree well with the fluence dependence of the molecular beam depletion of
U02(hfacac)zTHF+parent molecular ion and reasonably well for depletion of the U02(hfacac)THF+fragment ion.2 This was taken as further evidence that LIF depletion did indeed measure dissociation yield. However, so that dissociation rates > lo7 s-l could be achieved for such a large molecule (44 atoms, 126 normal modes) in the framework of RRK or RRKM calculations, it was necessary to postulate’ that only a limited number of “active” modes participated in the energy absorption and energy redistribution, implying energy localization into a subgroup of modes. Subsequently, the dependence of the molecular beam depletion on temperature was m e a ~ u r e dand ~ . ~this result was satisfactorily explained by a model which assumed complete energy delocalization. Both UOz(hfaca&THF and U02(hfacac)2TMPdissociation rates and yields are found to depend on the energy fluence and can be accurately predicted by using the previously developed model.3 With the real time IRDR measurements presented here, we now recognize that both LIFD and parent molecular beam depletion are not direct measurements of dissociation but actually monitor those parent molecules which have not undergone reaction. The initial rapid loss of LIF is now interpreted to be due to the rapid formation of an “intermediate” species (red feature) formed prior to the subsequent slower dissociation into products U02(hfacac)2 (blue feature) and T M P (not detected in IRDR but detected from “in oven” experiments with TOF mass spectrometric detection). In this paper we extend the previous modeP5 by including the rapid low-energy formation of a reaction “intermediate”. It is postulated that the “intermediate” is produced by a rapid temperature jump due to infrared laser energy deposition. This rapid heating of the molecular ensemble displaces the initial thermal equilibrium between the “intermediate”and the starting reactant toward the “intermediate”and sets up a new equilibrium on a time scale faster than the 450-ns laser pulse duration. We attribute the rapid rate of LIFD as due to the formation of the “intermediate” which does not fluoresce. Dissociation of sufficiently energetic “intermediate” molecules occurs on a slower time scale. In addition, it should be noted that, within the time frame of COPlaser excitation rates used here and previously,’+ we detect no evidence indicative of vibrational energy localization in either the laser-induced “intermediate” formation or subsequent decomposition of these large molecules. In the remainder of this section, we will discuss the interpretation of the IRDR experimental results followed by presentation of a model for the IR decomposition processes occurring in these large molecules. Next we will
430
The Journal of Physical Chemistry, Vol. 87, No. 3, 1983
discuss the interpretation of the experimental measurments in the context of this model and finally we will conclude with some speculation concerning the physical structure of this “intermediate”. Interpretation of Infrared-Infrared Double Resonance Experiments. The infrared double resonance measurements show rapid removal of the parent molecular concentration accompanied by rapid formation of a red-shifted absorption feature which slowly decays into a blue-shifted absorption feature. Of these two, the blue-shifted feature is certainly the monomeric UOz(hfacac)z. IR absorption measurements13J4 have shown the peak of the monomer to occur a t 967 cm-’, identical with the peak of the blueshifted absorption feature. This transient spectrum is independent” of which parent uranyl molecule is dissociated, e.g., UOz(hfacac)zTHF or UOz(hfacac)2TMP, strongly suggesting that the blue feature does not contain the neutral Lewis base. Secondly, a feature centered a t 967.3 f 0.5 cm-’ is observed in the F T IR absorption of U0&1facac)~THFat 180 OC,14a temperature at which this complex is known’ to undergo substantial thermal dissociation. Thirdly, the IR depletion spectrum from molecular beam depletion measurements of UOz(hfacac)2 is identical with the IR absorption spectrum for this same monomeric species. Finally, the initial primary photoproducts of the IR multiple photon dissociation of all UOz(hfacac)zB complexes studied to date have been UOz(hfacac)zand B. The red feature, on the other hand, is more difficult to identify. It is produced as rapidly as the parent molecule is depleted, with the initial temporal evolution of these features following the integrated laser pulse temporal profile. At longer times the decay of the red feature is exactly mimicked by the growth of the absorption by the product U02(hfacac)z.Thus the red feature clearly represents some intermediate species, rapidly formed, but more slowly decaying into the dissociation products. The evidence which supports the identification of this feature as a truely distinct isomeric species rather than a vibrationally hot parent molecule is as follows: 1. The peak of the v3 asymmetric stretch for the parent molecule does not shift with temperature although the band does broaden with increasing temperature (see Figure 3)* 2. The induced red absorption does exist for several microseconds at lower pump laser excitation levels. This fact together with (4) below rules against the possibility of the induced red absorption being due to an excited molecule in the u = 1 level of the u3 mode; such a long lifetime for the u = 1 level would cause serious bottlenecking in the laser driven dissociation process-an effect not borne out by experiments. 3. The spectral deconvolution at a fixed time delay of the induced transparency/opacity shows that the resulting red feature is shifted from the parent absorption by -4 cm-’, independent of laser fluence between fluences of 9 and 120 mJ/cm2. This fluence range corresponds to an average absorption of between 2 and 15 C 0 2laser photons (see Figure 4) which is equivalent to an average temperature rise (if the deposited energy is statistically distributed in all the modes of the molecules) of between 42 and 375 K (see later discussion). 4. The disappearance of LIF due to C02laser pumping suggests a change in coordination in the uranyl complex. Over a temperature range from 70 to 120 “C, where the complex exhibits minimal thermal dissociation, the LIF signal is nearly constant indicating that temperature-dependent hot-band population changes have only a minimal
Bray et al.
effect on the fluorescence quantum efficiency (51%). 5. A red-shifted absorption which shifts further to the red as a function of laser fluence is readily observed in small molecule^,'^ but is noticeably absent in these large molecules and is absent even in the transient spectrum under the present experimental conditions. In addition, the deviation from Beer’s law behavior of the energy deposition as a function of laser fluence shown in Figure 4 can now be explained. The molecules do not remain in resonance with the pump laser frequency due to the rapid shift (during the laser pulse) of the uranyl absorption band -4 cm-’ to the red. The new transient absorption is attributed to the rapid formation of the spectrally shifted “intermediate”. During the laser pulse (the energy deposition time) dissociation will be negligible for the fluence levels investigated in this study. The Beer’s law behavior for energy deposition using the 10P14 transition is attributed primarily to lower energy deposition for a given fluence due to its reduced absorption cross section compared to 10P8 (see Table I), which offsets induced absorption by the transient “intermediate”. As stated earlier, the 9-pm absorption of U02(hfacac)2TMP is attributed to the CO stretches of TMP. The near-Beer’s law behavior associated with the 9-wm absorption is fortuitous and occurs because the bound and free TMP have nearly identical absorption cross sections. Even if intermediate formation or dissociation does occur the total absorption in the 9-km band will change little, since the number and cross section of TMP absorbers does not change appreciably. Dissociation half-lifes obtained from IRDR measurement of blue feature formation vary from to lo* s (dependent on laser fluence). These are relatively slow dissociation rates when compared to red feature formation and are a direct consequence of the large number of modes, despite the relatively low dissociation barrier (- 33 kcal/mol). Obviously at higher average excitation energies, the dissociation lifetimes are expected to become shorter since the dissociation rate increases with increasing energy. This means that for large molecules with a large number of low frequency modes a broad distribution of dissociation lifetimes results. Thus upon absorption of photons those molecules initially in the high energy tail of the thermal distribution will be the most excited molecules and thus will exhibit the shortest dissociation lifetimes. The dissociation rate will increase until it becomes comparable to the laser up-pumping rate. Because of the unusual behavior of the IRDR signal we are pursuing experiments using shorter laser pulses to obtain better time resolution. Model for the “Intermediate”. Now we will explain these results in the context of a single model. It is assumed that the reaction barrier for formation of the intermediate is low compared to the dissociation threshold energy. Since the rate of intermediate formation is much faster than the dissociation rate (see Figure 5 ) and since the rate of decay of red feature is the same as the rate of production of blue feature, the red feature is assumed to be a direct precursor to blue feature formation. The postulate of a low barrier immediatley raises several important questions. First, if the reaction barrier is low, then why has not all or nearly all the original material reacted to form the intermediate at 100 “C? Secondly, an explanation is needed to account for the observation that the formation of the red-shifted feature appears to cut off sharply as soon as the laser pulse is over. One would normally expect a range of reaction rates, corresponding to the variation in the internal energy of the molecules in the ensemble, with some reaction occurring after the laser
IR Laser Chemistry of Volatile Uranyl Complexes
The Journal of Physical Chemistry, Vol. 87,No. 3, 1983 437
pulse is over. These questions can be answered if it is assumed that there is a rapid dynamic equilibrium between the starting material and the intermediate which can be the case if the intermediate is an isomer of the starting material. The reaction mechanism would then be k
5UOZLzB* isomer
UOzLzB
(2)
kb
fast
U02LB2* ‘slow U02Lz
+B
(3)
The rates of the forward and backward reactions, kf and kb,are not known, but if kb is much faster than kf, the equilibriumconcentration of isomer will be small compared to the concentration of the parent molecule at 400 K. When the equilibrium is perturbed by a rapid rise in temperature, for example, a new equilibrium concentration would be achieved very rapidly. If kb is taken to be k106 s-l at 400 K then the formation of the red shifted feature at 210’ s-l upon laser excitation can be explained. Further, the energy deposited by the laser can be considered to be simply causing a rapid shift in the equilibrium position, the shift “following” the integrated laser pulse if the laser pulse rise time is slower than the sum of the forward and back reaction rates (see Appendix D). As soon as the energy deposition stops, the shift in the equilibrium terminates (in the absence of collisions), and there is no subsequent formation of the intermediate, in agreement with the observations. There are, however, two other major difficulties with the proposed model. First, if the intermediate is indeed in equilibrium with the UOZLzB,then why is the intermediate only observed upon laser irradiation, and not under thermal equilibrium conditions? The explanation lies in the fact that under thermal equilibrium conditions two additional equilibria must be considered: the equilibrium7922between UOzLz“monomer” and dimer 2UOZLZ == (UO2Lz)z (4) and the equilibrium7J3between dissociated and undissociated UOZLz.B UOzLzB + UOZLZ
+B
(5) If known thermodynamic data are used, the thermal equilibrium concentration of intermediate is calculated to be relatively small at all temperatures and thus not readily observable in thermal equilibrium measurements. Laser irradiation creates a metastable situation in which the equilibrium between the isomers (2) is rapidly shifted, but the other equilibria (4) and (5) are collisional, and are achieved only on a much longer time scale. A second difficulty is caused by the observation that the loss of intermediate due to dissociation is not compensated by further formation of intermediate from UOzLzBin order to reestablish the equilibrium. However, in the absence of collisions there is no reason to expect that the equilibrium will be reestablished. Consider the equilibrium for those molecules having a given energy E. An equilibrium constant K ( E ) can be defined for these molecules as the ratio of the forward and back reaction rates at energy E . The overall equilibrium constant is the integral over the whole ensemble of all the K ( E ) . Unless the overall equilibrium has been displaced completely to the intermediate, the K ( E ) for the high-energy tail of the Boltzmann dis(21) D. M. Cox, J. A. Horsley, A. Kaldor, R. B. Hall, G. M. Kramer, E. T. Maas, Jr., and E. B. Priestley, Proceedings of the Technical Program, ElectroOptics/Laser 79, Oct 23-25, Anaheim, CA, 1979. (22) A. Ekstrom and C. H. Randall, J.Phys. Chem., 82, 2180 (1978).
tribution will be such that the equilibrium strongly favors the intermediate and the K(E) for the low-energy tail will strongly favor the original material. There will be a narrow energy region where neither is favored. The Boltzmann distribution can therefore be broken into two distributions, corresponding to the resultant distribution for the UOZLzB and the intermediate. Molecules in the high-energy tail of the distribution will also, of course, be the first to dissociate. From the arguments given above, these molecules will be almost entirely intermediate molecules. Initially, therefore, there will be loss of intermediate molecules, but no loss of starting material because there are essentially no UO2LZBmolecules in this energy region to replace the intermediate molecules that have been removed. The overall equilibrium cannot be reestablished without collisions which will repopulate the high-energy tail. Comparison and Interpretation of Experimental Results. The hypothesis of an intermediate in dynamic equilibrium with the starting compound is capable of meeting the principal objections that can be brought against it, at least qualitatively. We now apply this model to quantitatively reproduce the experimental observations. The pulse laser irradiation of the molecules can be thought of as analogous to a “T jump” experiment in which a shift in equilibrium is induced by a rapid temperature rise. The analogy is not exact, however. In a normal “T jump” experiment, a single temperature can be assigned to the whole system and both reactant and product are heated equally. This is not the case here because the product absorption band is shifted away from the laser line (assuming the laser line is on the peak of the product reactant absorption band) and so the “heating” of the product is less efficient than that of the starting compound. This means that the back-reaction rate is not influenced by the energy deposited by the laser nearly as much as the forward reaction rate. This would not matter if the reaction barrier for the back-reaction were very small or nonexistent, in which case the reaction rate would be nearly independent of temperature. In order to simplify the calculation, we assume that the back-reaction rate is indeed temperature independent, so that the “T jump” model is a good approximation. Assuming statistical behavior, we can estimate the magnitude of the temperature jump per absorbed photon as follows: The IR spectrum of UOz(hfaca&TMP indicates that about half the modes in the molecule have a frequency > 800 cm-’ (3KT at 400 K). These modes do not have a significant thermal population at 400-500 K. The modes with frequency Pt and Fo+> Fc;(b) Fc 1 P+ at all temperatures; (c) The ratio increases as the temperature increases which is a direct consequence of (a) and (b) above. Since Po+> P+ and [Bo] = 0, we can write a,[Aol > a,(l - X)[Aol + b,(X - Y)[A,I (C7) Rearranging eq C7 yields X / ( X - Y)
> b,/a,
(C8)
and since X / ( X - Y) > 1 at all X, Y values, together with the fact a > b, at X = 0 and at Y = X, it is concluded that for afi X a, > b,. Similarly since Po+> Fc,we also find that af > bf for all X,T. The depletion signals for the parent and fragment ions are written as follows:
D , = (Po+- Pt)/Po+ = [a,X - b,(X - Y)]/a,
((29)
or
D, = X
-
(b,/a,)(X - Y)
and the fragment depletion, Df, is given as Df = X - (bf/af)(X- Y) Since b,/a,
< 1 and bf/af < 1 and X
(ClO)
(ClU
1Y
X - Y 1 b,/a,(X - Y) thus D, 1 X - (X - Y) and D, 1 Y i.e., parent molecular ion depletion is larger than or equal to the dissociation fraction. By similar arguments D, IX i.e., parent molecular ion depletion is less than or equal to isomer fractional production. Similarly, Df L Y and Df IX so depletion of fragment ion is also greater than or equal to the dissociation fraction but less than or equal to isomer production. Appendix D Consider two isomer species A and B in equilibrium at temperature T A
k
~
B
k-l
Let [A,] and [Be]be the equilibrium concentrations of A and B, so that [BeI/[Ael = k ~ / k - ~ Now consider that the temperature Tis attained by a rapid jump from a lower temperature To so that the system is
J. Phys. Chem. 1983, 87, 441-446
momentarily no longer in equilibrium, but is approaching it. Let the instantaneous concentrations of A and B be [A] and [B] where [A] = [A,] + [AA], [B] = [Be] + [AB] d[A]/dt = -d[B]/dt = k-,[B] - k,[A] substituting for [A] and [B] d[AAl/dt = k-,([Bel
+ [ABI)-k-,([AeI + [AB])
however kl[AeI = k-1Pe1
so that d[AA]/dt = It-l[AB] - kl[AA] also [AB] = -[AA], hence
-d[AA]/dt = (It-'
44 1
+ ki)[AA] = rate of approach to equilibrium
Let the rate of photon deposition be Itphot. Then, if (It-'
+ Itl) >> Itphot, the system will approach equilibrium faster than the rate at which energy is deposited, so that the system essentially can be regarded as being at equilibrium throughout the laser pulse, although the position of the equilibrium is constantly shifting as the photons are deposited. When energy is no longer being deposited, then the system remains at the equilibrium position that was obtained at the end of the laser pulse. These arguments do not apply to very short intense laser pulses where it may be possible to observe some relaxation toward equilibrium once the pulse is terminated. Registry No. UOz(hfacac)2TMP, 64708-00-5.
Theoretical Studies of the Potential Surface for the Reaction C(3P)
+ H,
-
CH,('B,)
Lawrence 6. Hardlng Theoretical Chemistry Group, Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 (Received: June 7, 1982: I n Final Form: October 18, 1982)
Large basis set, RHF+1+2, Configuration interaction calculations on the reaction of C(3P)with Hz are reported. It is found that the reaction proceeds through a weakly avoided crossing of the 3Az and 3B1potential energy surfaces, in which the lowest energy path lies only slightly below the Czuconstrained crossing. The magnitude of the barrier is found to be very sensitive to the basis set with the best calculations (49,3p, 2d, lf/3s, 2p, Id), giving a barrier of -1 kcal/mol.
Introduction Atomic carbon is an important reactive component of most hydrocarbon flames. It is known that atomic carbon reacts with saturated substrates through two primary mechanisms: insertion and hydrogen abstraction. Recent experimental and theoretical studies on the reaction of atomic carbon with the simplest saturated substrate, Hz, have uncovered a number of interesting anomalies. Experimental studies by both Braun et al.' and Husain et al., have shown the reaction to be very fast, proceeding with a room temperature collision efficiency of between 0.1 and 1.0, implying both a high steric factor and a low activation energy. The first detailed theoretical study of this reaction was reported by Blint and N e w t ~ n . They ~ noted that, for a C,, approach, there are two surfaces relevant to this reaction, with symmetries 3Az and 3B1, see Figure 1. The 3Az surface was found to be lower in energy at large C-H2 separations while it is, of course, the 3B1surface that leads to the ground state of CHz. In non-Cz, approaches these two surfaces interact and the crossing of the two surfaces is avoided. Thus the energy of the lowest CZucrossing of the 3A2and 3B1surfaces represents an upper limit to the real barrier for the reaction. With minimum basis set (MBS), configuration interaction (CI) calculations Blint and Newton computed the lowest crossing of these two (1) W. Braun, A. M. Bass,D. D. Davis, and J. D. Simmons, Proc. R. SOC.London, Ser. A, 312,417 (1969). (2)(a) D. Husain and L. J. Kirsch, Trans. Faraday SOC., 67, 2025 Faraday Trans. (1971). (b) D. Husain and A. N. Young, J.Chem. SOC., 2, 71, 525 (1975). (3) R. J. Blint and M. D. Newton, Chem. Phys. Lett., 32, 178 (1975).
surfaces to be -50 kcal/mol above the reactants. They further noted that a preliminary search of non-C,, approaches uncovered no reaction paths involving barriers less than -45 kcal/mol. More recently Schaefer et al.4 have reexamined the CZu potential surfaces with a larger, polarized valence double-{ basis set. Using a Hartree-Fock plus all singles and doubles CI calculation (RHF+1+2) they find the energy of the lowest 3Az-3B1crossing to be only 9.1 kcal/mol above the reactants. While this is considerably below the MBS result it is still well above the near zero barrier implied by experiment. Schaefer et al.4 though did not consider non-Cz, pathways, leaving the possibility that relaxing the Czuconstraint leads to a further decrease in the magnitude of this barrier, thereby reconciling the theoretical and experimental results. An additional puzzling aspect of this reaction that has been noted3has to do with the relative reactivities of C(3P) with Hz and CH4. Most simple reactive species, for example, CHz(3Bl),CHz('A1),CH(,II), and C('D), have similar rates of disappearance in H, and CH4. For C(3P) this is apparently not the case. The reported, room temperatures collision efficiency for the CH4 reaction is compared with a value of >IO-' for reaction with H,. In both cases the only energetically allowed reaction is insertion, abstraction being 23 kcal/mol endothermic for both. Also for C(3P) + Hz the least motion insertion reaction is a Woodward-Hoffman forbidden process whereas for C(3P) + CHI insertion is allowed.
+
-
(4) M. E. Casida, M. M. L. Chen, R. D. MacGregor, and H. F. Schaefer 111, Zsr. J. Chem., 19, 127 (1980).
0022-365418312087-0441$0 1.50/0 0 1983
American Chemical Society
