J. Phys. Chem. 1988, 92, 1813-1816 Finally, it should be noted that the same relaxation mechanism applies for diphenyloctatetraene vapor and that the absence of the 1'B, fluorescence from diphenylhexatriene and diphenyloctatetraene is just a consequence of the larger energy separation between 2'A, and l'B,. Conclusion
At low pressure diphenylbutadiene vapor fluoresces from unrelaxed levels of both the 2IA, and l'B, states: the relative contribution of 1'B, increases with increasing excitation energy. At high total pressure the emission mostly consists of lIB, fluorescence from a thermally equilibrated set of levels. This is because of the much higher radiative rate for fluorescence from 1'B, versus fluorescence from 2'A,. In a supersonic jet the 1'B, state is not thermally populated, therefore fluorescence originates primarily from the 2'A, state. The small amount of llB, fluorescence that can be seen at low pressure comes from unrelaxed levels in the 1'B,-2IA, mixed state. As pressure is increased, collisional deactivation competes with nonradiative processes from the mixed state so that the l'B, fluorescence intensity increases with increasing pressure.
1813
Fluorescence from diphenylhexatriene and diphenyloctatetraene vapors comes primarily from the 2'A, state. The fluorescence origin for diphenyloctatetraene vapor at 378 K is at 22020 f 23 cm-I. Fluorescence intensity increases with increasing pressure and decreases slightly with increasing excitation energy. The rate of nonradiative decay from the 2'A, state increases with increasing excitation energy. As pressure is increased, collision redistribution of population from unrelaxed 2IA, levels to a thermal distribution between the 2]A, and 1'A, states competes with nonradiative decay from 2'A, so that the fluorescence quantum yield increases with pressure. The absence of the l'B, fluorescence from diphenylhexatriene and diphenyloctatetraene vapors is due to the large 2'A,-1 'B, energy separation.
Acknowledgment. We are indebted to Dr. James Honvitz (now at the Naval Research Laboratory, Washington, DC) for his interest in and help with the experiments. This work was supported in part by grants from the National Science Foundation (CHE8514873) and the National Institutes of Health (EY-06466). Registry No. Diphenyibutadiene, 886-65-7; diphenylhexatriene, 1720-32-7;diphenyloctatetraene,3029-40-I ; perfluorohexane, 355-42-0.
Photodissociation Dynamics of C4H,+ Ions from 1,3-Butadiene Thomas L. Bunn and Michael T. Bowers* Department of Chemistry, University of California, Santa Barbara, California 931 06 (Received: September 25, 1987)
The photodissociationdynamics have been obtained for C4H6+ions derived from 1,3-butadiene. The reactant ions were formed primarily by charge exchange from NO+ and thus had insufficient energy to decompose via metastable reactions. The ions were mass selected and then photodissociated with the 514- and 488-nm lines from an argon ion laser. The photoproducts were mass and energy analyzed by using a high-resolutionenergy analyzer. Asymmetry parameters were obtained by measuring the product laboratory peak shapes for different laser polarization angles. The results indicate that the photoexcited state accessed is bound and the system survives many rotations before dissociating. Two photoproducts are observed: C3H3+/CH3 and C4H5+/H. The kinetic energy distribution of the C4H5+/Hproducts peaks at relatively high energy (-0.25 eV), indicating a reverse activation barrier is present. The C3H3+/CH3channel, however, peaks at very low energy (-0.01 eV) and falls off in a near-exponential manner. The latter data are well fit by use of statistical phase space theory, indicating there is no barrier to the reverse reaction and that vibrational predissociation from the ground state is the mechanism. Our results are in good agreement with the recent data of Bunn and Baer but disagree with earlier data of Preuninger and Farrar.
Introduction The study of the detailed kinetics and dynamics of gas-phase ions has become an area of increasing activity in recent years.' Of particular importance has been the development of photoion-photoelectron coincidence techniques2 and of the numerous methods developed to study photoinduced c h e m i ~ t r y . In ~ many emerging areas of chemistry particular molecules or systems take on added importance as "prototype" systems to study. They do so because they are usually convenient to study yet provide a useful foil for demonstration of the various facets of the technique being developed. In gas-phase ion chemistry the C4H6+ion has emerged as one of these prototype systems. The C4H6+ion was one of the first studied by coincidence methods4v5and it was a system used in the early development and application of QET/RRKM6 and phase space theory' to reactions of complex gas-phase ions.
Furthermore, both bimolecular and unimolecular reactions on the C4H6+surface have been thoroughly modeled and their mechanisms determined by use of the transition-state-switching form of statistical rate theory.* Photoelectron spectroscopyg has identified the C4H6+excited states accessible from the C4H6 neutral ground state; photodissociation cross sections of C4H6+ at selected wavelengths have been obtained;I0J' and multiphoton methods'* have been used to create and subsequently excite and dissociate C4H6+ions. One of the principal methods for discerning the mechanism for dissociation of excited ions is to measure the kinetic energy distribution of the products. Metastable peak shapes in mass spectrometry have been used for many years to determine if reverse activation barriers existed in ionic dissociation^;'^ broad peaks indicate a reverse activation barrier and narrow peaks no activation
( 1 ) See, for example: Gas Phase Ion Chemistry; Bowers, M. T., Ed.; Academic: Orlando, FL, 1979; Vol. 1 and 2; 1984; Vol. 3. (2) For a review see: Baer, T. In Gas Phase Ion Chemistry; Bowers, M . T., Ed.; Academic: Orlando, FL, 1979; Vol. 1, pp 153-197. ( 3 ) See Vol. 3 in ref 1. (4) Werner, A. S.; Baer, T. J . Chem. Phys. 1975, 62, 2900. See also: Dannacher, J.; Flamime, J.; Stadelmann, J.; Vogt, J. Chem. Phys. 1980,51, 189. ( 5 ) Klots, C. E.; Mintz, D.; Baer, T. J . Chem. Phys. 1979, 66, 5100. (6) Buttrill, S. E. J . Chem. Phys. 1970, 52, 6174. (7) Chesnavich, W. J.; Bowers, M. T. J . Am. Chem. SOC.1977, 99, 1705.
(8) Jarrold, M. F.; Bass, L. M.; van Koppen, P. A. M.; Bowers, M. T. J . Chem. Phys. 1983, 78, 3756. (9) See, for example: Kimura, K.; Katsumota, S.; Achiba, Y.; Yamazaki, T.; Iwata, S . Handbook of He I Photoelectron Spectra of Fundamental Organic Molecules; Halsted: New York, 198 1. (IO) Dunbar, R. C. Chem. Phys. Lett. 1975, 32, 508. (11) Preuninger, F. N.; Farrar, J. M. J . Chem. Phys. 1982, 77, 263. (12) Woodward, A. M.; Chupka, W. A.; Colson, S . D. J . Phys. Chem. 1984, 88, 4561. (13) Cooks, R. G.; Beynon, J. H.; Caprioli, R. M.; Lester, G. R. Mefastable Ions; Elsevier: Amsterdam, Netherlands, 1973.
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1814 The Journal of Physical Chemistry, Vol. 92, No. 7, 1988
barrier. These peaks contain information on the product kinetic energy distributions and eventually techniques were developed for extracting this i n f ~ r m a t i o n . ' ~ -The ~ ~ first application of these techniques was to CH, loss from C4H6+which theoretical modeling indicated was a statistical process with no reverse activation It appeared that the C4H6+system was well understood. The coincidence experiment^^,^ indicated that the quasi-equilibrium hypothesis was operative (Le., electronic excited states rapidly internally converted to the ground state followed by statistical vibrational predissociation) and both bimolecular and unimolecular reactions have been modeled using a single set of physical parameters over wide ranges of internal energy and angular momentum. Preuninger and Farrar" then reported results of photodissociation experiments at complete variance with all other data in the literature. They formed C4H6+ions in an ion source by electron impact, mass selected the beam, crossed it with the 514 nm (2.41 eV) line of an argon ion laser, and mass and energy analyzed the products using an electric sector. There are two energetic products possible within 2.41 eV of the C4H6+ground state:
C4H6+
+
hu
,
\
C4Hs*
+H
(lb)
Due to the low resolution of their ESA they could detect only the C3H,+ channel. They used seven different neutral isomers to form C4H6+with five of them photodissociating via reaction l a . The surprising result was the product kinetic energy distributions were very much broader than predicted by statistical theory, peaking between 100 and 150 meV while theory peaked near 20 meV. Preuninger and Farrar interpreted these results to indicate a repulsive state was being accessed by the photon from C&+ that somehow could not be accessed from the C4H6neutral precursors used in the coincidence studies. Recently Bunn and BaerI7 have reexamined the C4H6+system using a sophisticated extention of the PIPECO method. Energy-selected C4H6+ions were generated in their electronic ground state by standard coincidence techniques. The resultant C4H6+ ion was then exposed to the output of an excimer pumped dye laser. Bunn and Baer" sampled total energies of the same magnitude as Preuninger and Farrar." Their experimental kinetic energy distributions were in good agreement with statistical theory calculations and in substantial disagreement with the Preuninger and Farrar results. Bunn and Baer suggested that the results of Preuninger and Farrar may be due to experimental difficulties since they were trying to observe a very small photodissociation signal in the presence of a very large metastable signal that tended to saturate either the detector or the detection electronics. Hence, even though phase-sensitive detection was employed an invalid result might have been obtained. We have initiated a program in recent years aimed at studying the photodissociation dynamics and energy disposal in photoinduced reactions of gas-phase ions. Our set up is, in principle, similar to that of Preuninger and Farrar although we have substantially better product mass and energy resolution and much lower background pressure in the laser/ion beam interaction region (and hence a much lower collision-induced background signal). We have applied our technique primarily to the photodissociation of small cluster ions,'* but we have analyzed the photodissociation dynamics of one hydro~arbon,'~ C6H6+. One particularly im(14) Terwilliger, D. T.; Cooks, R. G.; Beynon, J. H. In?.J . Mass Specrrom. Ion Phys. 1975, 18, 43. (15) Holmes, J. L.; Osborne, A. D. Int. J . Mass Spectrom. Ion Phys. 1977. 23, 189. (16) Jarrold, M. F.; Illies, A. J.; Bowers, M. T. Chem. Phys. 1982, 65, 19. (17) Bum, T. L.; Baer, T. J. Chem. Phys. 1987, 85, 6361. (1 8) See, for example: Jarrold, M. F.; Illies, A. J.; Bowers, M. T. J . Chem. Phys. 1983, 79, 6086. Ibid. 1984, 81, 214. Ibid. 1984,81, 222. Ibid. 1985, 82, 1832. Jarrold, M. F.; Misev, L.; Bowers, M. T. Ibid. 1984.81, 4369. Kim, H. S.; Bowers, M. T. Ibid. 1986, 85, 2718.
Bunn and Bowers MIRRORS ARGON ION LASER
SHUTTER
LASER
POLARIZATION ROTATOR
ANALYSER
COMPUTER
PULSE COUNTING EQUIPMENT
Figure 1. Schematic representation of the ion beam machine used in these studies.
portant feature of our experiment is that we can measure the asymmetry for the photodissociation event. Determination of this parameter sets unambiguous limits on the lifetime of the photoexcited state and hence unambiguously indicates whether it is bound or repulsive. In this paper we will report product peak shapes for reactions l a and l b for photodissociation of C4H6+from 1,3-butadiene at 5 14 and 488 nm and present product kinetic energy distributions for these reactions. These distributions will be compared with those of Bunn and Baer17 and Preuninger and Farrar" and with the predictions of a statistical phase space theory model. Asymmetry parameters for both reactions will also be presented and conclusions will be drawn about the mechanism of the photodissociation reaction.
Experiment The instrument used in these studies has been previously described. A schematic is given in Figure l . Ions are formed by electron impact in a high-pressure ion source. We use a mixture of 1 part 1,3-butadiene to 30 parts NO. Under these conditions the primary source of C4H6+ions is via reaction 2. Since reaction NO+ 4- C4H6
-+
C4H.5'
NO
(2)
2 is exoergic by only 0.17 eV the product C4H6+ions do not have enough energy to dissociate (the appearance potentials for formation of C3H3+/CH3and C4H5+/H require C4H6+to be internally excited by 2.31 and 2.48 eV, respectively). consequently the metastable formation of C3H3+/CH3and C4H5+/Hare greatly reduced and provide less of a problem for detection of photoinduced products than in the experiment of Preuninger and Farrar. Once the ions diffuse from the source, they are mass selected and brought to a spatial focus where they are crossed with the polarized laser beam at 514 or 488 nm. The photofragments are then mass and energy analyzed by use of a high-resolution electrostatic analyzer and detected by single ion counting. The laser is turned on and off with a shutter and up/down counting is done to remove contributions from background processes (primarily residual metastable reactions). Experiments are done at three different laser polarization angles with respect to the ion beam direction, Oo, 90°, and the "magic angle" 54.7O, for reasons that will become apparent later.
Results The laboratory peak shapes at 514 nm for C3H3+/CH3and C4H,+/H products are given in Figures 2a and 3a, respectively. These data were taken with a laser polarization set at the magic angle of 54.7'. At this angle the laboratory peak mimics the isotropic photodissociation and contains information on the kinetic energy distribution of the products only.18 A simple transformation'* yields the center of mass product kinetic energy distribution. These are given for the two reaction channels in Figures 2b and 3b. (19) Krailer, R. K.; Russell, D. H.; Jarrold, M. F.; Bowers, M. T. J . Am. Chem. SOC.1985, 107, 2346. (20) Zare, R. N . Mol. Phorochem. 1972, 4, 1. (21) Busch, G. E.; Wilson, K. R. J . Chem. Phys. 1972, 56, 3638.
Photodissociation Dynamics of C4H6+
The Journal of Physical Chemistry, Vol. 92, No. 7, 1988 1815
10
I
I
C H,; ((1) %
c 2 2
t hv
CH ,:
0.6
i = 514 nm
0.4
6 =0009
+ CH3
(01
02
0.4
a
a
PRODUCT c m K I N E T I C ENERGY, eV
2u
0 O 5685 1
om
-0.4
5735 5785 5835 L A B O R A T O R Y ENERGY, eV I
I
-
I
C4HZ t bv
I
5885
0.81
I
~
CSH:
C4H6+ t bv
4
C4Hl+ H
(b)
I
0.6
A = 514 nm
tCH3
A = 514 nm E, = 152 +- i 0 meV
m
2l
4
a 0 2
Figure 4. Asymmetry parameter, fi, as a function of product kinetic energy for (a) C3H3' + CHI and (b) for C4HS++ H at 514 nm. An asymmetry parameter of zero denotes isotropic dissociation of photoexcited C4H6+in the center of mass.
0 0
0.4
02 0.3 0.4 0.5 0.6 CENTER OF MASS K I N E T I C ENERGY, eV
0.7
Figure 2. (a) Laboratory kinetic energy peak for the C3H3++ CH3 product channel at 514 nm. The C4H6+main beam energy is 8 kV. (b)
Center of mass kinetic energy distribution for C3H3' + CH3 products derived from the laboratory peak given in (a). i o
I
I
I
I
I
(a) 0 8 -
'
A
>
2 a
= 514 nm
06-
m
r
O0 7762
2 7812 7862 7918 L A B O R A T O R Y ENERGY, eV C,HG+
io,
t hv
/-Y
-.-c
'
CH ,: I
1 7962
t H I
I
I
I
08
0i 9
A = 514
-
>
5-
E, = 346 i 5 meV
0 6
\
a 0.41
n 00
direction. This information can be condensed into a single parameter, called the asymmetry parameter, @.20,z1 We have developed methodsI8 for extracting this parameter as a function of product kinetic energy using the 0" and 90' peak shapes. In the case of C4H6+photodissociation, identical peak shapes were obtained for Oo, 54.7O, and 90" laser polarization angles for both product channels at both 514 and 488 nm. The asymmetry parameter is plotted in Figure 4, a and b, for the two reaction channels at 514 nm. As expected the average value of the @ parameter is very near zero indicating the dissociation is completely isotropic in both channels.
Discussion and Conclusions A number of unambiguous observations can be made from the data of Figures 2-4. First, the asymmetry parameters are es-
04-
a
PRODUCT c m K I N E T I C ENERGY, eV
-- O 0 4
01
0 2
03
0 42
0 5
06
07
CENTER OF MASS K I N E T I C ENERGY, eV
Figure 3. (a) Laboratory kinetic energy peak for the C4H5++ H product channel at 514 nm. The C4H6+main beam energy is 8 kV. (b) Center
of mass kinetic energy distribution for C4H5++ H products derived from the laboratory peak given in (a). At any laser polarization angle other than 54.7" the product laboratory peak shape contains information on the spatial asymmetry in the dissociation of C4H6+. This asymmetry is best detected by comparing the peak shapes obtained at the extreme laser polarization angles of Oo and 90° relative to the ion beam
sentially zero for both product channels. Consequently the photoexcited ions that lead to these products live very much longer than a rotational period and hence must be bound states and not repulsive states. Since there is insufficient energy available to dissociate to electronically excited products, the mechanism of dissociation must be photoexcitation to the 2A, excited state followed by internal conversion to the ground state and then vibrational predissociation. The kinetic energy distributions for the C3H3+/CH3and C4H5+/H products are substantially different; the C3H3+distribution peaks at very low energies (-0.01 eV) and has a long high-energy tail. On the other hand, the C4H5' distribution peaks near 0.25 eV and is more triangular in shape. This latter distribution is characteristic of a dissociation occurring with a reverse activation energy barrier along the reaction coordinate and is consistent with results obtained by Jarrold et a1.I6on the analogous metastable dissociation reaction. The C3H3+distribution suggests there is no barrier along the reaction coordinate and the dissociation proceeds statistically. We tested this hypothesis by performing statistical phase space theory calculationsZZon this reaction channel. The results are shown in Figure 5. Two theoretical distributions are presented. The lower energy curve assumed the C4H6+ion had 0.17 eV internal energy when it absorbed the photon (from the NO+ charge exchange reaction). The second assumed it had an additional 0.5 eV internal (22) The parameters we used for these calculations are the same as those used in ref 16.
J . Phys. Chem. 1988, 92, 1816-1821
1816
I
I
I
1
Experiment - This work
__-Preuninger
-
8 Farrar
Phase Space Theory
= 0 03 eV = 0 33eV
,,,,E, ,,,,E,
, \
\
1
I
I
0' 0
I
0.1
I
0.2 0.3 0.4 0.5 0.6 PRODUCT c m KINETIC ENERGY, eV
I
0.7
Figure 5. Comparison of C3H3+/CH3product kinetic energy distributions from various sources: (-) experimental results of this work; ( 0 , m) phase space theory results of this work: (---) experimental results of Preuninger and Farrar, ref 1 1.
energy. Neither theoretical curve fits the experimental distribution exactly, but both nicely mimic the location of the peak in the distribution and the shape of the falloff in the distribution to higher energy. It is, in fact, reasonable that these distributions do not fit exactly. Under our experimental conditions we have C4H6+ ions formed both by chemical ionization from NO+ (reaction 2) and from electron impact (as evidenced by the fact we still observe a small metastable signal). Hence the experimental photoinduced kinetic energy distribution corresponds to C4H6+ions with a variety
of internal energies. This fact probably accounts for the discrepancy between experiment and theory. Also shown in Figure 5 is the kinetic energy release distribution reported by Preuninger and Farrar." Their distribution should be very similar to ours since the experiments are so similar. Yet, their distribution peaks at much higher energy (>0.2 eV as compared to 0.01 eV) and has a much different shape. Since the same excited state is undoubtedly accessed in both experiments it appears clear that there must be instrumental reasons for the discrepancy. Our data are in very good agreement with those published by Bunn and Baer given the differences in the experimental techniques. In addition, we have now applied our method to more than 30 systems and have had no experimental difficulties. We maintain our count rates well within the ability of the electronics to cope with them and consequently do not suffer from potential saturation effects. We thus conclude, in agreement with Bunn and Baer, that the data of Preuninger and Farrar are most likely flawed, probably due to difficulties in accurately subtracting the huge metastable signal they had from the photoinduced plus metastable signal.
Acknowledgment. We gratefully acknowledge the support of the National Science Foundation under Grant CHE85-12711 and the Air Force Office of Scientific Research under Grant AFOSR86-0059. We also gratefully acknowledge advice and assistance from Ms. H-S. Kim and Dr. C-H. Kuo. Registry No. C4H6*,34488-62-5; C,H,, 21540-27-2; CH,, 2229-07-4; C4Hs+,64235-83-2; H, 12385-13-6.
Electronic Structure from Semiclassical Dimenslonal Expansions: Symmetry Breaking and Bound States of the Hydride Ion D. J. Dorent and D. R. Herschbach* Department of Chemistry, Harvard University, Cambridge, Massachusetts 021 38 (Received: September 28, 1987)
-
For a large spatial dimension D, semiclassical techniques become applicableto electronicstructure calculations. The zeroth-order term, corresponding to D m, can be evaluated exactly by finding the minimum of an effective electrostatic potential. This defines a rigid configuration of the electrons (the "Lewis structure"). The first-order term, proportional to 1/D, can likewise be calculated exactly and corresponds to harmonic vibrations of the electrons (the "Langmuir vibrations") about the fixed positions attained in the D m limit. For a two-electron atom with nuclear charge Z > 1.237, the effective potential has a single minimum with the electrons equidistant from the nucleus. For smaller Z, this symmetry is broken. When Z < 1.2279 a double minimum obtains, with one electron much closer to the nucleus than the other. For the short range of intermediate Z , a triple minimum occurs; at Z 1.2334 the symmetric and asymmetric electron configurations become isoenergetic. Convergence of the perturbation expansion in powers of 1 / D is improved by a resummation technique which removes contributions from first- and second-order poles that occur for the singular D 1 limit. The hydride ion, with Z = 1, provides an extreme test since it has only two weakly bound states; in the restricted Hartree-Fock approximation both are unbound. Dimensional perturbation has the virtue of including electron correlation at all orders. The very simple first-order resummed dimensional expansion (Lewis and pole terms only, evaluated at D = 3 and 5 ) gives both H- bound states in a single stroke. The accuracy obtained with optimal truncation is a few tenths of a percent for both states.
-
+
I. Introduction The most notorious failure of the old quantum theory was its inability to determine the spectrum of two-electron atoms.) This stems from the rarity of stable orbits in such systems. Before applying any quantization conditions, one must find families of orbits for which the electrons never collapse into the nucleus or undergo autoionization. Despite modern developments in semiclassical mechanics2 and a long history of attempt^,^ there are still no known quantizing trajectories for the helium atom ground state. Quantum mechanics avoided that issue, yet the early variational calculations posed in its stead the quandary of finding simple 'Present address: AT&T Bell Laboratories, Murray Hill, NJ 07971
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pictures to describe multielectron systems. This need was largely met by the Hartree-Fock theory of orbitals, but that fails as a zero-order model when electronic motions are highly correlated. Generally, such is the situation for open-shell systems, multiply (1) Born, M. Mechanics o f t h e Atom; Ungar: New York, 1960. (2) For excellent surveys of current semiclassical methods, see several papers in: J . Phys. Chem. 1986, 90, 3453-3862 (a special issue dedicated to
R . A. Marcus). (3) Van Vleck, J. H. Philos. Magn. 1922,44, 842. For recent semiclassical treatments of two-electron atoms, see: Leopold, J . G.; Percival, I. C. J . Phys. B 1980, 13, 1037. Coveney, P. V.; Child, M. S. Ibid. 1984, 17, 319. Wesenberg, G. E.; Noid, D. W.; Delos, J . B. Chem. Phys. Lett. 1985, 118, 72. Solov'ev, E. A. Sou. Phys.-JETP (Engl. Transl ) 1985, 62, 1148. Klar, H. Phys. Rea. Lett. 1986, 57, 66.
0 1988 American Chemical Society
