J. Phys. Chem. 1989, 93, 7287-7289
The diffusion-controlled rate constant was determined by using the Brownian dynamics method described in the previous section. Five independent runs of 400 trajectories each were used to determine the rate constant (Table I). One set of 2000 trajectories had the interparticle forces set to zero (Le., no electrostatics) while the second set of 2000 trajectories included full electrostatics.
IV. Results and Discussion A summary of the combination probabilities and the diffusion-controlled rate constants calculated from the Brownian dynamics simulations is found in Table I. The rate constant determined from the five runs for the system with no electrostatic interactions is 0.306 X 1O1Of 0.1 14 M-' s-' and that for the system with such interactions is 1.48 X 1O'O f 0.13 M-' s-I; the error ranges correspond to the standard deviations of the five runs for each system. Both of these rate constants are higher than the experimental rate constant3 of 4.8 X 108 M-' s-I. The higher rates in the calculations are likely due in part to the neglect of the loop motion, which should "gate" the r e a c t i ~ n ; ' ~ -the ~ " ~generous ~ (30) McCammon. J. A,: Northruu. S.H.Nature 1981. 293. 316. (31) Northrup, S.'H.;Zarrin, F.; McCammon, J. A. J. Phys. Chem. 1982, 86, 23 14.
7287
conditions assumed for reaction, in terms of the substrate location and orientation; and the neglect of hydrodynamic interactions. More detailed simulations are planned to explore these effects. The present results make clear, however, that the electrostatic field of the enzyme tends to steer the diffusion of the GAP substrate toward the active sites. This is reminiscent of the steering effects observed in Brownian dynamics simulations of superoxide diffusion to the active sites of superoxide d i s m ~ t a s e . " - ~As ~ in the case of superoxide dismutase, it is likely that the effectiveness of the steering will decrease with increasing ionic strength, resulting in decreases in the computed rate constants. These effects, and the possibility that the electrostatic fields might lead to orientational as well as translational steering of the substrate, will also be explored in future simulations.
Acknowledgment. This work has been supported in part by the NIH, the Robert A. Welch Foundation, and the National Center for Supercomputing Applications. J.A.M. is the recipient of the George H. Hitchings Award from the Burroughs Wellcome Fund. (32) Szabo, A.; Shoup, D.; Northrup, S. H.; McCammon, J. A. J . Chem. Phys. 1982, 77, 4484.
Acetylene C-H Bond Dissociation Energy Using 193.3-nm Photolysis and Sub-Doppler Resolutlon H-Atom Spectroscopy: 127 f 1.5 kcal mol-' J. Segall, R. Lavi, Y. Wen, and C. Wittig* Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 (Received: August 30, 1989)
H atoms are produced by 193.3-nm CzH2photolysis and probed spectroscopically with sub-Doppler resolution at Lyman-a by using two-photon, two-frequency ionization, for both expansion-cooled and effusive samples. The maximum Doppler shifts are in agreement with Do(C2H-H) = 127 f 1.5 kcal mol-', assuming (i) that the fastest H atoms are produced concomitantly with unexcited C2H and (ii) that vibrationally excited C2H2parent is not the source of these fast H atoms. In the sense that higher detection sensitivity might allow observation of faster H atoms, 127 f 1.5 kcal mol-' is an upper limit.
Introduction Despite its paramount importance, the acetylene C-H bond dissociation energy to this day remains a subject of major controversy. Early literature values ranged from 107 to 135 kcal mol-', a remarkably broad range for this most elementary alkyne bond-fission reaction:' C2Hz -.+ C2H
+H
(1)
By the mid-l970s, experiment and theory had more or less converged, and Benson's estimate of 126 f 1 kcal mol-' was accepted by the majority of the kinetics, thermochemistry, and combustion communities.2 However, in 1979 and 1985, Brauman and coworkers3 and Lee and co-workers' reported values of 132 f 5 and 132 f 2 kcal mol-', respectively. These "high" values subsequently received further experimental s ~ p p o r tbut ~ * have ~ failed to gain (1) Wodtke, A. M.; Lee, Y. T. J . Phys. Chem. 1985,89,4744 and references cited therein. (2) Benson, S., private communication. (3) Janousek, B. K.; Brauman, J. I.; Simons, J. J . Chem. Phys. 1979, 71, 2057. (4) Shiromaru, H.; Achiba, Y.; Kimura, K.; Lee, Y. T. J . Phys. Chem. 1987, 91, 17. ( 5 ) Chen, Y . ;Jonas, D. M.; Hamilton, C. E.; Green, P. G.; Kinsey, J. L.; Field, R. W. Ber. Bunsen-Ges. Phys. Chem. 1988, 92, 329.
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unanimous acceptance by the community.6 In addition, recent spectroscopic measurements by Field and co-workers,' in which Stark-induced line broadening was used to infer predissociation, gives an upper limit of 126.6 kcal mol-', in sharp contrast to the 132 kcal mol-' value, thereby sustaining the present controversy. In the experiments reported here, sub-Doppler resolution vacuum-UV spectroscopy has been used to measure the maximum kinetic energy of nascent H atoms that derive from 193.3-nm acetylene photolysis. As long as the H atoms that possess this maximum kinetic energy are produced concomitantly with unexcited CzH, this method can straightforwardly provide a value for Do(H-C2H). The approach directly interrogates a photolysis product and is thus complementary, and in some ways more direct, than measurements that rely on interpretations of line broadenings or that combine several processes in a thermochemical cycle.
Experimental Section The general experimental approach has been described in detail elsewhere.* Briefly, C2H2,either neat or entrained in an inert (6) Kolln, W.; Shin, K. S.;Gardiner, W. C. Jr. Prog. Astromur. Aeromur. submitted for publication. (7) Green, P. G.; Kinsey, J. L.; Field, R. W. J . Chem. Phys., submitted for publication. (8) Xu,2.;Koplitz, B.; Wittig, C. J . Chem. Phys. 1989, 90, 2692.
0 1989 American Chemical Society
7288 The Journal of Physical Chemistry, Vol. 93, No. 21, 1989
Letters
carrier, was expanded from a pulsed nozzle into the acceleration region of a time-of-flight (TOF) mass spectrometer. Care was taken to ensure that collisions with the mesh grids did not affect any of the results. The nozzle effluent was crossed at 90' by counterpropagating photolysis and probe laser beams. C2H2 photolysis was carried out using -1 mJ of 193-nm radiation collimated to a 5-mm2 area, and the resulting H atoms were detected by using two-photon, two-frequency photoionization via Lyman-a: H( 12S) hv( 121.6 nm) H(22P), followed by H(22P) hv(364.7 nm) H+ e-. Tunable, sub-Doppler resolution vacuum-UV radiation was generated by frequency tripling, in rare gas,9 the output from a pulsed, btalon-tuned dye laser operating near 364.7 nm. The tripling cell was connected directly to the main chamber and the third harmonic and fundamental probe beams were focused by using a LiF lens located at the exit of the tripling cell, so that the photolysis and probe beams overlapped in the ion extraction region, as described previously.8 By tuning the frequency of the Lyman-a radiation, with the 364.7-nm radiation effecting efficient photoionization, sub-Doppler resolution spectra were obtained that reflected the different H-atom velocity components along the probe direction, bk. Relative and absolute wavelengths were calibrated by observing Lyman-a for both hydrogen and deuterium. Because of the 2:l Lyman-a doublet intensity ratio, spectra are not symmetric about line center, and this is taken into account when calculating Do.
-+
+
+
-
-6.0
(9) Zacharias, H.; Rottke, H.; Danon, J.; Welge, K. H. Opt. Commun. 1981, 37, 15.
0.0
-1.2
-24
12
36
24
48
60
Wavenumbers from Line Center (Lyman-a)
vo= 82,259.1 cm-1
Results A typical H-atom Doppler profile is shown in Figure la. Were the value of Do(H-C2H) equal to 132 kcal mol-', and assuming no significant participation of vibrationally excited C2H2(hereafter referred to as C2HJ), and assuming that ground-state C2H is produced concomitantly with those H atoms having the largest velocities, the maximum Doppler shift would be approximately 3.3 cm-I, as shown by the vertical arrow. Note that the spectrum extends well beyond this point. Although the signal intensity in the wings is low, S/N is more than adequate for our measurements (see Figure 1, b and c, and these signals must be accounted for. It is the signal in the wings that results in our value of 127 f 1.5 kcal mol-', in contrast to the value of 132 f 2 kcal mol-' reported by Lee and co-workers.] Possible Hot-Band Contributions The photodissociation of vibrationally excited C2H2molecules can, in principle, yield H atoms whose maximum possible translational energy in the C2H2center-of-mass (c.m.) system is given by (25/26)(hv - Do+ EV(C2H2)),where EV(C2H2)is the vibrational energy of C2H2 prior to photodissociation. C2H2 rotation is neglected, since rotations are efficiently cooled in the expansion. Although room temperature samples may give results that include contributions from vibrationally excited C2H2[e.g., 9.0 and 5.2% of the molecules have one quantum of the 61 1 and 729 cm-I doubly degenerate bends, respectively, at 300 K], expansion cooling is expected to reduce markedly such contributions. Unfortunately, the absorption spectrum near 193 nm has not been analyzed, so we cannot identify the extent of hot-band participation. The data shown in Figure 1b indicate that there is very little, if any, change a t the edge of the Doppler profile as the expansion conditions are varied. Many spectra were obtained over a period of six months under a number of different conditions (e.g., room temperature bulk samples, as well as expansion-cooled samples of C2H2(neat), He:C2H2 (up to lO:l), Ar:C2H2 (up.to 20:1), Ar:SF6:C2H2,etc.) and in all cases the spectra were quite similar. The examples shown in Figure 1b are but a few of the many that display this same behavior. The average of several profiles is shown in Figure IC. Unless nature is truly perverse, freezing out the same (substantial) amounts of C2H2vibrational excitation under all conditions, data such as those shown in Figure 1b,c indicate that the edge of the Doppler profile cannot be assigned to C2H;. We have used pulsed nozzle expansions for
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1 I
I
I
1
1.0
-
0.8
1
0.6
-
I
I
125
I
I
I
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Do (kcal mol-')
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'
1
-3.60
'
I
-3.48
'
I
-3.36
Wavenumbers from Line Center(Lyman-a) Figure 1. (a) Typical H-atom Doppler profile following 193.3-nm C,H2 photolysis (expansion cooled, neat). The horizontal axis indicates the shift from Lyman-a line center. The Doppler shift associated with a value of Do = 132 kcal mol-' is indicated with an arrow. (b) Expanded view of the edge of the Doppler profile for different sample conditions. The spectra are offset for convenience; the lines are simply to connect points. (c) Average of the four spectra shown in (b). The horizontal axis labeled Doshows where the zero-signal intercept would lie for these values of Do.This axis takes into account shifts due to finite laser line width and the Lyman-a doublet (see text for details).
spectroscopic studies since 198 1 and have never encountered significant residual parent vibrational excitation due to incomplete cooling. Thus, it is expected that vibrational degrees of freedom, while not in equilibrium with rotations,I0will nevertheless be cooled (10) McClelland, G . M.; Saenger, K. L.; Valentini, J. J.; Herschbach, D.
R. J . Phys. Chem. 1979, 83, 947.
J. Phys. Chem. 1989, 93, 7289-7292
account in constructing the scale shown in Figure I C that depicts the Do values that correspond to different zero-signal intercepts. The effect of the Lyman-a doublet on the profile must also be considered. The splitting between the 2P3 2Sl/2and 2Pl 2S1 transitions is 0.366 cm-l,'' adding 6.183 cm-' to the halfwidth. This was taken into account in constructing the Do scale shown in Figure IC. In order to periodically check our system against a known standard, Doppler profiles were recorded for 193.3-nm HBr photodissociation. Here, the edge of the profile is sharp, because the Br atom has only one internal state. These profiles were consistent with the known values of Do(HBr),12 but more importantly ensured that there were no spurious wings in the vacuum-UV probe beam spectral distribution that could be misinterpreted as wings in the Doppler absorption line shapes.
-
Energy dependence of signal +3.3 cm-1 from line center 3 -
2 -
1 -
:b
@
0 OQ I
I
7289
I
Figure 2. A linear dependence of H-atom yield vs photolysis laser fluence indicates that C2H photolysis is unimportant. These data were taken at a Doppler shift corresponding to Do= 132 kcal mol-'.
significantly in the expansions.
The Edge of the Doppler Profile Figure IC shows that the edge of the Doppler profile terminates at a shift of 3.72 f 0.12 cm-I, corresponding to Do(H-C2H) = 127 f 1.5 kcal mol-'. Because the profile decays smoothly toward the base line, it is conceivable that the measured wing would extend even further with higher detection sensitivity. However, such a change would only lower Do. Three experimental factors lead to broadening of the observed Doppler profiles. One is the component of C2H2velocity along kprobersuch as that caused by the transverse spread of the nozzle e fluent, Le., movement of parent molecules perpendicular to the expansion axis. An estimate of this velocity component in our apparatus gives a maximum value of 104 cm s-', for C2H2dilute in He carrier. Furthermore, ( IvarriCr sin 01) is only -5 X lo3 cm s-l, for a nozzle-probe beam distance of 2.5 cm and a flight-tube opening in the TOF mass spectrometer of 1 cm. In contrast, the H atoms at the edge of the Doppler profile correspond to a velocity of 1.4 X 106 cm s-I. Since this effect does not appreciably broaden the observed profiles, it has been neglected in our analyses. Another consideration is that of the probe laser line width. The Lambda Physik 3002E dye laser, with an Etalon, has a typical line width of 0.04 cm-' near 365 nm. Deconvolution of the observed H-atom Doppler profiles using a vacuum UV Gaussian of 0.12 cm-' fwhm reduces the half-width of the profiles by -0.03 cm-I at the base. This is conservative; the vacuum-UV line width will probably be less than 0.12 cm-I. This shift is taken into
-
+ +
-
Secondary Photolysis: C2H bu Cz + H It is known that the C2H fragment can itself undergo 193.3-nm photodissociation to give C2 H, yielding high H-atom translational energies.' If neither photolysis step is saturated, H atoms that accrue from C2H photolysis will depend quadratically on photolysis laser fluence. Figure 2 shows the dependence of the H+ signals on photolysis laser fluence, with the vacuum-UV frequency +3.3 cm-' from line center (Le., 132 kcal mol-'). The observed linear dependence so far in the wing of the profile is strong evidence in support of primary C2H2photolysis with essentially no participation from secondary C2H photolysis. Summary In summary, analyses of the largest H-atom Doppler shifts following 193.3-nm C2H2photolysis are consistent with Do = 127 f 1.5 kcal mol-'. This disagrees with recent measurements of 132 f 2 and 135 f 5 kcal m01-1,1335 agrees with earlier v a l ~ e s , ' ~ J ~ and agrees with the upper bound of 126.6 kcal mol-' inferred from the line-broadening measurements of Field and co-workers.' It is possible that higher detection sensitivity would allow observation of faster H atoms, thus further lowering Do. Until structure corresponding to the internal states of the C2H fragment is observed and assigned in the H-atom kinetic energy spectrum, the present approach will be unable to measure Do with greater precision. Acknowledgment. This research was supported by the U S . Department of Energy, Office of Basic Energy Sciences. (1 1) Moore, C. E. Natl. Stand. Ref. Data Ser. (US., Natl. Bur. Stand. "Atomic Energy Levels"; NSRDS-NBS 35; US.GPO: Washington, DC, 1971; V O ~1-3. . (12) Danvent, B. de B. "Bond Dissociation Energies in Simple Molecules"; NSRDS-NBS, Washington, DC, 1970. (13) Frank, P.; Just, T. Combust. Flame 1980, 38, 23 1. (14) Okabe, H.; Dibeler, V. H.J . Chem. Phys. 1973, 59, 2430.
Bond Stretch Isomerism in Rhombic C2Si2 Pamidighantam V. Sudhakar, Osman F. Guner, and Koop Lammertsma* Department of Chemistry, University of Alabama at Birmingham, UAB Station 219 PBS, Birmingham, Alabama 35294 (Received: July 25, 1989) The differences in bonding and electronic properties between the MP/6-3 lG* optimized disilicon dicarbide structures 1 and 2 can be related to bond stretch isomerism, which occurs through a level-crossing mechanism. Their energy differences are calculated at the MP4 and GVB/6-31G* levels. Electron density analysis indicates concentration of charge in the center of rhombic structure 1 with some multiple bonding character between its transannular carbons. In contrast, the higher energy isomer 2 has a depletion of charge in the center relative to the circumference of the rhombic structure. Bond stretch isomerism is a form of geometrical isomerism that gives two distortion isomers by variation of one (or more) of the 0022-3654/89/2093-7289$01 .50/0
bond lengths. Jean et al.' eloquently illustrated the mechanisms of bond stretch isomerism in a detailed study on various or@ 1989 American Chemical Society
