J. Phys. Chem. 1995, 99, 1686-1699
1686
Rydberg State Reactions of Atomic and Molecular Hydrogen
P. M. Dehmer" Argonne National Laboratory, Argonne, Illinois 60439
W. A. Chupka Sterling Chemistry Laboratory, Yale University, 225 Prospect Street, New Haven, Connecticut 0651 I Received: September 7, 1994; In Final Form: December 1, 1994@
-
-
Various aspects of the atomic and molecular Rydberg state reactions that result in H3+ formation by associative ionization [H*(n = 2) HZ H3+ e] and by chemiionization [H2* H2 H3+ H e] are presented. For associative ionization, the n = 2 Rydberg state of atomic hydrogen was prepared both by direct photodissociation of H2 and D2 into the continuum above the first dissociation limit and by predissociation of H2 Rydberg states. The most dramatic result of the associative ionization study was the observation of oscillations in the ionization cross section for the reaction involving atoms formed by direct photodissociation. These oscillations arise as a result of a quantum interference effect between two dissociation paths leading to the same final state. The experimental data are presented here with new calculations of this effect by M. Glass-Maujean. For chemiionization, the npa and npn Rydberg states of molecular hydrogen were prepared by photoabsorption of a liquid-nitrogen-temperature sample of -90-95% pure para-Hz; these sample conditions enabled the study of the ion yield of the chemiionization reaction for principal quantum numbers in the range 3-17. The ion yield for n = 3 was zero; the yields for n 2 4 increased by many orders of magnitude approximately as n6 over a rather small range of n and quickly approached that for the analogous ionmolecule reaction. Both the n dependence of the ion yield and the value of n for which the ion yield becomes constant are qualitatively explained by a two-step mechanism for chemiionization involving an ion-molecule reaction of the Rydberg state core (with the Rydberg electron acting as a spectator) followed by autoionization of H3* to form H3+. At least three factors combine to determine the onset of the high-n regime. These are (1) the relative rates of radiative decay of H2* and collision of H2*, (2) shielding of the H2+ ion core by the Rydberg electron at low principal quantum numbers, and (3) the value of the principal quantum number at which rapid decay of the H3* intermediate by rotational autoionization becomes energetically allowed.
+
+
I. Introduction
Because a highly excited Rydberg electron moves in an orbit that is far removed from the ion core, collisions between high Rydberg atoms or molecules (A*) and neutral molecules (B) have been interpreted by using formalisms appropriate to one of two quite different types of collision phenomena. Those collisions that involve only the Rydberg electron and the neutral molecule (eA-B) are well described by electron-molecule scattering theory, while those that involve only the ion core and the neutral molecule (A+-B) are more appropriately described by ion-molecule scattering theory. That eA and A+ can be considered separate scatterers was first suggested by Fermi' more than a half century ago; this concept has since been used successfully to explain a variety of collision phenomena involving highly excited Rydberg states. A number of excellent reviews describing experimental and theoretical approaches to the investigation of Rydberg state properties and collision dynamics have been collected in ref 2. A more complex problem arises for collisions of Rydberg states having low to intermediate n; in such cases, both the Rydberg electron and the ion core can play important roles in the collision. This transition region between the low-n and the high-n regimes has been difficult to study experimentally and to model theoretically. Here we present new results for collisions of Rydberg states of atomic and molecular hydrogen that address this issue and others relating to the spectroscopy and dynamics of H2. These data, taken during the period 1972@Abstractpublished in Advance ACS Abstracts, January 15, 1995.
0022-365419512099-1686$09.00/0
+
+ +
1975 and presented here for the first time, focus on atomic and molecular Rydberg state reactions of the following two types that result in H3+ formation
+ H, -H,' + H + e chemiionization (1) H*(n = 2) + H, - H3+ + e associative ionization (2) H2*
The energetics of these Rydberg state reactions are reviewed in Figure 1, which was constructed by using recent values of the ionization energy of H (109 678.758 ~ m - ' ) ,the ~ ionization energy of H2 (124 417.507 ~ m - ' ) ,the ~ dissociation energy of HZ (36 118.11 ~ m - ' ) ,the ~ threshold for dissociation of HZ (1 18 377.06): the dissociation energy of H2+ (21 379.37 cm-')? the ionization energy of H3 (29 562.6 cm-'),6 the dissociation energy of H3+ [35 270(170) ~ m - ' ] ,and ~ the calculated energy levels for the symmetric stretch ( V I ) and the bending ( ~ 2 modes ) of H3+.* The threshold for the chemiionization reaction is 110 527( 170) cm-'; thus, the reaction is energetically allowed for HZ(n 2 3) and for high-lying vibrational levels of H2 (n = 2). The threshold for the associative ionization reaction is the threshold for dissociation of HZ (118 377.06 ~ m - ' ) . ~In the present work, we examine these reactions in the energy region from the first dissociation threshold of H2 to just above the first ionization threshold of H2. There is considerable exothermicity (-1.0-1.7 eV) in this energy region, and both theoretical9 and experimentallo results indicate that, at the collision energies relevant to the present experiments, approximately two-thirds of the exothermicity will appear as intemal energy of the H3+ product.
0 1995 American Chemical Society
Rydberg State Reactions of Hydrogen
J. Phys. Chem., Vol. 99, No. 6, 1995 1687 applied electric field. The present results, which were taken on a fine energy mesh (-3 cm-I) throughout the region from the first dissociation threshold to the first ionization threshold for both H2 and D2, present a more complete picture of this interference effect. They are presented here with new calculations by Glass-Maujean.I4 In the remainder of this paper, we first describe the experiment in more detail (section II). We then provide a brief review of the Rydberg state spectroscopy and decay dynamics for H2 (section III.A), followed by discussions of the results for associative ionization (section II1.B) and chemiionization (section III.C). Throughout the discussion, we occasionally speculate on possible new experiments that are suggested by these data and that are now feasible with the new generation of high intensity vacuum ultraviolet light sources.
H 2 + H +H++e‘
h
145ooo
.-
.. ‘E Y
>
8w
125000
H~+H;+~-
z w 12oooo
t ... .. ... _. ... _. ... ._. .. ..
._....
I
0
--I
--3
Hs+H
Figure 1. Energetics of the H2
+
Hz system. In reaction 1, npa and npn Rydberg states of molecular hydrogen were prepared by photoabsorption of a liquid-nitrogentemperature sample of -90-95% pure para-H2; these sample conditions enabled the study of the ion yield of reaction 1 for principal quantum numbers in the range 3-17. The ion yield for n = 3 was zero; the yields for n 2 4 increased by many orders of magnitude over a rather small range of n and quickly approached that for the analogous ion-molecular reaction. Thus, the data span the entire transition region described above. In reaction 2, the n = 2 Rydberg state of atomic hydrogen was prepared both by direct photodissociation of H2 and D2 into the continuum above the first dissociation limit and by predissociation of H2 Rydberg states. This reaction is of importance in understanding both collisional deactivation of H(W and the reverse reaction of dissociative recombination. However, perhaps the most dramatic result of the present study was the observation of oscillations in the ionization cross section for the reaction involving atoms formed by direct photodissociation. Since the present experimental conditions dictate that reaction 2 proceeds via H(2s) [since the H(2p) atoms radiate before they collide], we speculated as early at 1975 that the observed oscillations might be due to structure in the partial photodissociation cross section for H(2s) formation.’ However, at that time, there was no theoretical basis for such a hypothesis. It was not until 1987 that our still-unpublished results were explained by the elegant calculations of Beswick and GlassMaujean,’* which showed that the energy dependence of both the H(2s) and the H(2p) partial cross sections does indeed show pronounced oscillations as a result of a quantum interference effect between two dissociation paths leading to the same final state. In 1988, Glass-Maujean et al.I3 published an observation of this effect. They determined the ratio of the partial cross sections for H(2p) and H(2s) formation at about a half dozen energies by using the technique of extrapolating the Lya fluorescence intensity to zero pressure with and without an
11. Experimental Apparatus and Results Spectra were taken by using a high-intensity photoionization mass spectrometer, which has been described in detail previo ~ s l y . ’Briefly, ~ the apparatus consisted of a 3-m near-normal incidence monochromator that dispersed and then refocused the selected light into a gold-plated copper ionization chamber that was attached to a liquid nitrogen Dewar, a set of ion extraction and focusing lenses, and a quadrupole mass spectrometer for ion detection. Mass-selected ions and photons that were transmitted through the ionization cell were monitored simultaneously by using nude, 20-stage, Cu-Be Venetian-blind multipliers whose outputs were monitored using standard techniques. Spectra of transmitted light were corrected for the wavelength-dependent response of the detector by using the known photoionization cross sections of the rare gas atomse8 The 3-m monochromator employed a 1200 line/”, MgF2coated aluminum grating blazed for 1300 8, in first order. The highest wavelength resolution obtained with this apparatus was 0.016 (fwhm) with 10-pm entrance and exit slits in third order; the hi hest wavelength resolution used in the present work was 0.025 , obtained with 25-pm entrance and exit slits in third order. Para-H2 of approximately 90-95% purity was obtained directly from the boiloff of a 15-Ldewar of “aged” liquid hydrogen. Ordinary D2 (66.7% ortho; 33.3% para) of purity 99.5% was used directly from commercial cylinders without further purification. The sample-gas pressure in the ionization region was typically 0.01 Torr. Figure 2 shows the spectra of H3+ formation and transmitted light for para-Hz in the energy region from the first dissociation threshold to just above the first ionization threshold, taken at a wavelength resolution of 0.025 A. These spectra, each containing more than 11 000 points, were taken in a continuous scan lasting nearly 70 h. Two features of the spectra should be noted. First, the ordinate (relative H3+ production) changes between parts c and d and again between parts e and f. Second, there is a very small step in the H3+ ion production at the dissociation threshold. This step appears on a much more intense background that is due primarily to ionization of H2 by scattered light to form H2+, followed by a rapid ion-molecule reaction with H2 to form H3+. The ordinate is offset by a constant amount on all frames of the figure. Ion yields for many of the transitions shown in the figure are given in Table 1. Figure 3 shows the relative cross sections for H3+ and D3+ production (the ratio of ionization to transmitted light) in the region near the fiist dissociation threshold, taken at a wavelength resolution of 0.077 A. The ordinate for these spectra has been greatly expanded to highlight the oscillations in the continuum. These lower resolution scans were taken by using light from the first order of the grating, and the ratio of true signal to the background signal is much more favorable than that of the high-
K
Dehmer and Chupka
1688 J. Phys. Chem., Vol. 99, No. 6, 1995
, 119600
119400
119200
119000
118800
118600
118400
118200
118000
TRANSmON ENERGY (cm-l)
Figure 2. Spectra of transmitted light and H3+ formation in the region of transition energy 118 000 to 119 600 cm-' taken at a wavelength resolution of 0.025 A, a pressure of 0.010 Torr, and a temperature of 77 K for a sample that was 90-95% para-H2.
resolution data shown in Figure 2. For H3+, the continuum intensity was approximately equal to the background intensity; for D3+ the continuum intensity was approximately 30% of the background intensity. The difference in the intensity of the scattered light background in these two scans probably results because the spectra were taken at rather different times in the life of the grating. In Figure 3, we have attempted to subtract the background due to scattered light; however, some uncertainty in the relative intensities remains, particularly for the H3+ spectrum. The spectra shown in Figure 2 were energy calibrated by interpolating between approximately 100 calibration points, which were chosen to be emission lines in the helium continuum light source or "sharp" absorption lines, Le., absorption lines that are not broadened by predissociation. The lower resolution spectra shown in Figure 3 were energy calibrated in a similar manner but with fewer calibration points. The assignments of the transitions shown in Figure 2 were judiciously selected from assignments reported previously by a number of workers. I 7-25 111. Discussion A. Spectroscopic Background. The photoabsorption spectrum of molecular hydrogen from the ground electronic state is now well understood, owing to a combination of experimental measurements of the high-resolution absorption2' and photoionization26spectra of para-H2 at low temperature (which greatly simplify the spectra and thereby permit the observation of transitions to high principal quantum numbers) and multichannel quantum defect theory analyses (which have provided an understanding of channel i n t e r a c t i o n ~ , ~ ' ,rotational ~ ~ - ~ ~ and vibrational a ~ t o i o n i z a t i o n , ~and ~ - ~p~r e d i s s ~ c i a t i o n ~ ~ -At ~~). low principal quantum numbers, members of the observed Rydberg series correspond to npa '&+and npn 'nuseries of
states. However, as n increases, there is a transition from Hund's case b coupling, in which the orbital angular momentum Lof the electron is strongly coupled to the intemuclear axis, to Hund's case d coupling, in which the orbital angular momentum Lof the electron is strongly coupled to the axis of nuclear rotation N+.39 For large n, the separation into npu '%+ and npn In, states is no longer observed, but rather the rotational levels of the Rydberg states are ordered solely on the basis of the rotational level of the ion core to which they converge. The spectrum of para-H2 at 77 K is particularly simple, since it consists almost entirely of transitions from J" = 0 (that is, of R(0) transitions). At low n, two series are observed, corresponding to the R(0) transitions to the npa and npn 'nu states; at high n, one of these series (npO) converges to the N+ = 0 level of the ion, while the other (np2) converges to the N+ = 2 level of the ion. At high n, the Rydberg states are usually labeled by using quantum numbers appropriate to case d coupling (e.g. npN+). The transition from Hund's case b to Hund's case d coupling occurs at about n = 8 for H2, and the spectra shown in Figure 2 are labeled accordingly. Because the sample used for these experiments contained 5-10% orthoH2, many transitions from J = 1 are also observed, particularly the more intense transitions (Le., those to excited states of low principal quantum numbers); all of the prominent ortho-HZ transitions are labeled in Figure 2. Note that the P(l) and the Q(l) transitions are to pure u and n states, respectively, even at very high principal quantum numbers;2' in accordance with tradition,21the a and n notation has been retained for these series at high principal quantum numbers. The spectra presented here span the region from the first dissociation limit of Hz to just above the first ionization limit of H2 and show transitions to the direct dissociation and
Rydberg State Reactions of Hydrogen
J. Phys. Chem., Vol. 99, No. 6,1995 1689
p&+
3px,v=4
I
I I\
-7
- 6
- 5
0
1
1
121200
121000
120800
120600
120400
120200
120000
119800
119600
TRANSmON ENERGY (cm-')
Figure 3. Same as in Figure 2 for transition energies from 119 600 to 121 200 cm-I.
ionization continua and to discrete Rydberg states embedded in these continua. In order to interpret the Rydberg state reactions observed in the present study, it is necessary to understand the fundamentals of the Rydberg state decay processes and the competition among them. In the absence of collisions, radiative emission and predissociation compete to depopulate the Rydberg states below the first ionization potential; autoionization is an additional mechanism that competes to depopulate the Rydberg states above the first ionization potential. The following discussion concentrates on Rydberg states that lie below the first ionization threshold, since those states are of direct relevance to the present work. We have selected a few states that lie above the ionization threshold for use in the determination of the ion yield for the ionmolecule reaction H ~ + ( x*E;, v+ = 0) HZ ~ 3 + H; these Rydberg states are all known to decay by vibrational autoionization.26 There is significant variation in the predissociation rates of the Rydberg states. The rates can be very fast for states of low principal quantum number; in particular, the 3pn state [the upper levels of the P(J) and R(J) transitions] is rapidly predissociated by the continuum of the 3pa ~tate!O-~~ Predissociation rates for the higher npn Ill: states are expected to be several orders of magnitude slower than that of the 3pn Ill: state, since these states may predissociate only according to one of the following second-order amplitudes: (1) homogeneous npn 'll;-3pn Ill: interaction, followed by heterogeneous npn 'II;-3pa predissociation, or (2) heterogeneous npn Ill:-npo interaction, followed by homogeneous npa I c - 3 p a predissociation. Guyon et al.43 found that radiative decay and predissociation do indeed compete for npn states (n 2 4) that are below the first ionization threshold. However, it is expected, the high-
+
-
+
'Ill 'g
'g
'Ill
resolution experiments have recently c~nfirmed,'"'~~~ that such second-order or "accidental" predissociation processes will be most rapid for states that interact strongly with states that are themselves very strongly predissociated, that is, the 3pn I + llu, 4pa and 4pn Ill: states. The 3pn 'II, and higher npn Ill; states [the upper levels of the Q(J) transitions] decay by radiative emission. Since interaction of the npn Ill, states with the 3pa state is symmetry forbidden, the npn 'II; states do not undergo the rapid predissociation observed for the npn Ill: states; the npn 1 l7; states may be predissociated only through the very weak interaction with the continuum of the 2pn Ill; states.46 Molecular fluorescence is the primary decay path for these states below the first ionization t h r e ~ h o l d . ~ ~ - ~ ~ states are predissociated predominantly by the The npa 3p0 state. Dehmer and Chupka26 showed that the decay rate of the 5pa I&+, v = 4 and 5 levels is more than an order of magnitude less than that of the 4po v = 1 level; in comparison, the radiative decay rate of the 5pa state is only about a factor of 2 less than that of the 4pa state (see section 1II.C). This rapid decrease in the predissociation decay rate compared to the radiative decay rate is expected to continue for higher Rydberg states, and radiative emission will be the dominant mechanism for the high-n Rydberg states in the absence of accidental predissociations. Thus, although the low-n Rydberg states of H2 predissociate with very different rates, it appears that, in the absence of accidental predissociation, the decay rates of all of the high-n Rydberg states may be approximated by the rate of radiative emission. B. Reactions of the Atomic Rydberg States-Associative Ionization. I . Observation of Integerence Effects between
'c,
'g
IC,
Dehmer and Chupka
1690 J. Phys. Chem., Vol. 99, No. 6,1995 TABLE 1: Relative HJ+ Ion Yields" transition
energy (cm-')
wavelength (A)
3pn, v = 3 Q(3) 3pn, v = 3 P(2) 3pn, v = 3 Q(2) 3pn, v = 3 Q(l) 3pn, v = 3 R(0) 3pn, v = 4 P(2) 3pn, v = 4 Q(2) 3pn, v = 4 Q( 1) 3pn, v = 4 R(0) 3pn, v = 5 R(0)
118 758.40 118 863.70 118 961.19 119 097.39 119 217.94 120 708.80 120 801.30 120 942.60 121 062.40 122 787.40
842.046 841.300 840.6 10 839.649 838.800 828.440 827.806 826.839 826.020 814.416
4pu, v = 1 P(2) 4pa, v = 1 P(1) 4pa, v = 1 R(2) 4pa, v = 1 R( 1) 4pa, v = 1 R(0) 4pa, v = 2 P(2) 4pa, v = 2 P(1) 4pa, v = 2 R ( l ) 4pa, v = 2 R(0) 4pu, v = 3 P(2) 4pa, v = 3 R(0)
118 640.00 118 826.50 118 887.30 118 974.90 118 994.70 120 563.30 120 750.60 120 895.90 120 918.10 122 349.30 122 704.40
842.886 841.563 841.133 840.513 840.374 829.440 828.153 827.158 827.006 817.332 814.967
4pn, v = 1 P(2) 4pn, v = 1 Q(2) 4pn, v = 1 Q( 1) 4pn, v = 1 R(2) 4pn, v = 1 R(0) 4pn, v = 2 Q(2) 4pn, v = 2 Q ( l ) 4pn, v = 2 R( 1) 4pn, v = 2 R(0)
119 742.10 119 849.90 119 974.13 120 027.90 120 096.60 121 918.64 122 050.08 122 154.50 122 169.20
835.128 834.377 833.513 833.140 832.663 820.219 819.336 818.635 818.537
= 0 P(1) = 0 R(2) = 0 R(l)
119 613.40 119 655.90 119 750.30 119 777.70 121 745.30 121 792.70 121 886.20 121 910.20
836.027 835.730 835.071 834.880 821.387 821.067 820.437 820.276
120 113.10 120 241.30 122 308.80 122 433.90
832.549 831.661 817.603 816.767
121 213.60 121 248.50
824.990 824.752
121 392.90 121 527.50 123 584.50
823.771 822.859 809.163
2.2 0.0 1.7 1.5 2.1 0.0 0.0 5.6 3.0 5.2 0.0 3.9 2.9 0.0 3.1 3.7 2.9 14.3 10.4 19.3 22.3 14.6
= 0 R(2) = 0 P(1) = 0 R( 1) = 0 R(0) 7pn, v = 0 R(0) 8pa, v = 0 R(l) 8pn, v = 0 R(0)
121 978.60 121 995.80 122 088.10 122 135.50
819.816 819.700 819.081 818.763
4.2 13.5 35.7 20.8
122 320.60
817.524
32.8
122 635.70
815.423
25.0
122 839.90
814.068
50.7
9pa. v = 0 R(0) 9p1, v = 0 R(l) 9pn, v = 0 Q(l)
123 058.60 123 012.00 123 027.60 123 323.00 123 463.60 123 278.20
8 12.621 812.929 812.826 810.879 809.955 81 1.173 809.578 808.543 808.798 807.979 806.531 806.187
347.0 444.9 384.4
5pa, v 5pa, v 5pa, v 5pa, v 5pu, v 5pa, v 5pa, v 5pa, v
= 0 R(0) = 1 P(1) = 1 R(2) = 1 R( 1) = 1 R(0) 5pn, v = 0 Q(l) 5pn, v = 0 R(0) 5pn, v = 1 Q ( l ) 5pn, v = 1 R(0) 6pa,v=OR(l) 6pa, v = 0 R(0) 6pn, v = 0 Q( 1) 6pn, v = 0 R(0) 6pn, v = 1 Q( 1) 7pa, v 7pa, v 7pa, v 7p0, v
10p0, v = 0 R(0) 10p2, v = 0 R(0) lOpx, v = 0 Q(l) 1lp0, v = 0 R(0) 1 lp2, v = 0 R(0)
123 521.20 123 679.20
12p0, v = 0 R(0) 13p0, v = 0 R(0)
123 640.30
16p0, v = 0 R(0)
123 987.80 124 040.70
17p0, v = 0 R(0)
123 765.60
ion yield
0.0 0.0 0.0 0.0 6.7 0.0 0.0 0.0 2.6 0.9 0.0 9.2 0.0 9.2 6.8 0.0 0.0 3.6 2.7 0.0 1.7
comments
& 4p0, v = 2 R(2)
0.0 0.0 0.0 0.0
639.1 127.3 136.6 591.4 492.3 328.0 75 1.O 806.2 650.8
& 4pn, v = 1 R ( l ) & 7pn, v = 0 Q(2)
& 7pn, v = 0 Q ( l )
& llpn,v=OQ(l)
J. Phys. Chem., Vol. 99, No. 6, I995 1691
Rydberg State Reactions of Hydrogen TABLE 1. (Continued) transition
wavelength (A)
energy (cm-I) H*+(X 'E:,
V+
= 0)
ion yield
+ H2 -.H3+ + H
comments
124 866.60 800.855 1846.4 Spu, v = 1 R(0) 125 243.00 798.448 1754.9 9pa, v = 1 R(0) 125 356.90 797.722 1906.7 9pn, v = 1 R(0) 125 514.00 796.724 1814.4 10pu, v = 1 R(0) 125 710.40 795.479 1942.4 1lp0, v = 1 R(0) 1715.1 13p0, v = 1 R(0) 125 953.80 793.942 1630.8 126 049.70 793.338 14p0, v = 1 R(0) 126 128.10 792.845 1732.5 15p0, v = 1 R(0) The ion yield, Y, is defined as the ratio of ionslsecond (g+) to absorbed photonslsecond (Io - Z), where I, is the photon intensity off resonance I,, and I from the spectra shown in Figure 2, only that part of the and I is the photon intensity on resonance. In determining the values of IH~+, ionization and absorption due to Rydberg states was considered; that is, contributions from the absorption and ionization continua were ignored. Photodissociation Continua in H2 and D2. The continuum above the first dissociation limit contains contributions from the B I%+, B' and C 'nustates. In the adiabatic approximation, the B' state correlates to the H(2s) f H( 1s) dissociation limit, and the B and C 'nu states correlate to the H(2p) f H(ls) dissociation limit.1235' On the basis of previous calculations of the cross sections for these dissociation continua,52this observation would indicate that the partial cross sections for H(2s) H(1s) and H(2p) f H(1s) would be smoothly varying functions of energy and would depend only on the magnitudes of the cross sections for the B' and the B C 'nucontinua. However, in 1987, Beswick and Glass-MaujeanI2 suggested that this is, in fact, not the case. By including the radial nonadiabatic couplings between the B and B' states at large intemuclear distances in their calculations, they predicted that the partial photodissociation cross sections would display pronounced oscillations as a function of energy. As expected, the sum of the two oscillating partial cross sections was equal to the sum of the previously calculated cross sections52that ignored the coupling between the B and B' channels. The same effect was predicted for D2, but the amplitude of the oscillations was smaller and the frequency was higher because of the increased reduced mass. In 1988, Glass-Maujean et a l . I 3 published an observation of this effect for Hz. They determined the ratio of the partial cross sections for H(2p) and H(2s) formation at about a half dozen energies by using the technique of extrapolating the Lya fluorescence intensity to zero pressure with and without an applied electric field. On the basis of their results, they deduced an experimental value of P, the nonadiabatic transition probability between the B and B' states during the halfcollision after the photon absorption, which was about a factor of 2 higher than the value from the quantum-chemistry calculation. The present experiments are a very sensitive probe of the predictions of Beswick and Glass-Maujean.I2 If H(2p) atoms fluoresce before they collide,53then reaction 2 proceeds solely via the reaction of H(2s) atoms, and the observed cross section should reflect the oscillations in the appropriate partial photodissociation cross section. Figure 3 shows the relative cross sections for H3+ and D3+ production in the region from the first dissociation threshold to about 4000 cm-' above this threshold. Also shown are new calculations of Glass-Maujean for the partial photodissociation cross sections for H(2s) H(1s) and D(2s) D(ls).I4 For H2, the calculations are for para-Hz at 77 K (s'= 0 only) with an experimentally determined value of P = 0.43;13 for D2, the calculations are for the equilibrium ortho-para mixture at 77 K with a value of P = 0.30. The calculations did not include the effects of the discrete states and should be compared to the structure in the continuum only. The experimental data were approximately normalized to the
'g
+
'g
'2+
'g
'g
'g
'g
'c
+
+
theoretical calculations by matching the intensity of the spectra at the position of the maximum in the first oscillation. Figure 3 shows that the agreement between experiment and theory is quite striking. The calculated positions of the oscillations are in excellent agreement with experiment for both H2 and D2. (Note that the Beutler-Fano profiles associated with predissociation of the discrete transitions can have a significant effect on the shape of the oscillations.12) The calculated intensities of the oscillations agree less well with experiment, particularly for H2; however, this is as expected for two reasons. First, the cross section for reaction 2 is known to decrease with increasing velocity (see section III.B.2). For a given energy region (such as that shown in Figure 3), this velocity dependence will be more pronounced for H2 than for DZ because of the difference in reduced masses. Second, for the H3+ spectrum, the large background signal appeared to decrease slightly as a function of increasing energy, thus introducing greater uncertainty into the background correction. These experiments show that associative ionization is a very sensitive probe of the partial photodissociation cross sections. It would be of interest to use this technique to probe the partial cross sections for predissociating states and, in particular, to examine the variation of the ratio of the partial cross sections across predissociation profiles. Beswick and Glass-Maujean12 have calculated this ratio for several rotational transitions of the 3pn ill,,, v' = 3 X ' E:, v" = 0 electronic transition. A comparison with theory would require measurements similar to those presented here, taken at a number of pressures, to optimize the amount of absorption for each rotational transition to be studied. 2. Comments on the Velocity Dependence and the Magnitude of the Associative Ionization Cross Section. Reaction 2 was fiist reported in the late 1960s by Chupka et al.54and by Comes and Both groups studied the velocity dependence of the cross section by using velocity-selected H atoms that were prepared by predissociation of the 3pn state in vibrational levels ranging from 3 to 10. Ion yields were found to decrease as v W m ; however, there was considerable ambiguity in m, which ranged from a low of -154 to a high of 2-3.56 In the time since those first experiments, this reaction has attracted a great deal of interest because of the role that it plays in collisional quenching of H(24 atoms by H2. However, despite the many experimental and theoretical studies of the collision quenching r e a ~ t i o n , ~ ~neither - ~ O the velocity dependence nor the magnitude of the associative ionization reaction has been well characterized. Indeed, associative ionization was often ignored when considering the possible mechanisms for collisional quenching of metastable hydrogen atoms. Although the present experiments are not sufficiently comprehensive to provide definitive answers to these questions, we can make some comments on both the velocity dependence and the magnitude of this reaction.
-
1692 J. Phys. Chem., Vol. 99, No. 6, 1995
Dehmer and Chupka
TABLE 2: Relative H3+ Ion Yields for Associative Ionization energy (cm-’)
VHa
VXib
state
(lo5c d s )
(lo5 cm/s)
ion yield
3pz, v = 3 R(0) 3pn, v = 4 R(0) 3pn, v = 5 R(0)
119 217.94 121 062.40 122 787.40
3.172 5.668 7.264
3.298 5.739 7.319
6.68 2.63 0.86
4pa, v = 1 P(1) 4p0, v = 1 R ( l ) 4pa, v = 1 R(0) 4p0, v = 2 R ( l ) 4p0, v = 2 R(0) 4p0, v = 3 R(0)
118 826.50 118 974.90 118 994.70 120 895.90 120 918.10 122 704.40
2.607 2.927 2.718 5.617 5.513 7.195
2.758 3.063 2.864 5.689 5.587 7.251
9.25 9.18 6.81 3.60 2.75 1.69
The velocity of atomic hydrogen is given by VH = ( 2 E ~ / m ) ”where ~, EH = ( E - &)/2 and m is the mass of atomic hydrogen. Here E is the energy of the state above X ’2+,v = 0, J = 0, and DO is the dissociation energy of H:, (1 18 379.06 ~ m - ’ ) . ~The relative velocity of H and HZis vrel = ( V H ~ VH;)”~. Here V H ~= ( 8 k T / ~ m ) ”where ~, T is the temperature and m is the mass of Hz. At T = 77 K, VH> = 9.029 x 104 cm/s.
+
Rydberg states that predissociate completely provide an opportunity to study associative ionization without interference from chemiionization. As discussed in section III.A, the upper levels of the Q(J) transitions do not predissociate but rather decay by molecular fluorescence. Hence, we use these transitions to monitor the onset of chemiionization as a function of principal quantum number. States of low principal quantum number show no chemiionization, and therefore, they are good candidates for the study of associative ionization. In particular, Table I shows that the ion yield for all of the 3pn In,, v, Q(J) transitions is zero. A very small amount of ionization is observed for the 4pn In,,,v = 2, Q( 1) transition; although this transition is blended with the 7pn, v = 0, Q(2) transition (which is expected to produce chemiionization), we have chosen not to consider the 4pn ‘nu state in our analysis of associative ionization. We do, however, include the 4p0 state, because this state is known to decay very rapidly by predissociationSz6Table 2 and Figure 4 summarize the ion yields as a function of relative collision velocity for a number of R(J) and P(J) rotational transitions of the 3pn and 4p0 states. Only transitions having nonzero ion yields are included in Table 2. A fit of all of the data to a function of the form v - yields ~ a value of m = 1.9; a fit of only the 3pn ‘n: data yields m = 2.4, and a fit of only the 4po data yields m = 1.6. These results are consistent with the previous direct determinations of the velocity dependence of the associative ionization indicating that associative ionization is more strongly velocity dependent than collisional q~enching.~~-’O The maximum ion yield for associative ionization is quite small-more than 2 orders of magnitude smaller than the ion yield for the Hz+(X v+ = 0) H2 H3+ H ion-molecule reaction (see Table 1). By comparing the ion yields for associative ionization and for the ion-molecule reaction and by making a number of assumptions, we can estimate the associative ionization cross section to within a factor of perhaps 5. These assumptions are that (1) 70% of the absorption in the predissociating 3pn I ll: and 4p0 states results in H(2s) atom f ~ r m a t i o n ; ’ * , ~ *(2) , ~a~ ll-of~ ~the absorption above the first ionization threshold results in H3+ ion formation (Le., competing processes such as charge transfer (or no reaction at all) are negligible); and (3) the cross section for the H2+(X 2 + Eg, v+ = 0 ) HZ.- H3+ H ion-molecule reaction under the conditions of the present experiment is 300 A2 (assuming that the relative collision energy is 8.4 meV, as determined in section III.C, and that the contribution to the collision energy from the repeller voltage is zero). The cross section for
‘c
‘g
2Zl,
+
-
associative ionization at 3 x lo5 c d s is then approximately [(9.3/0.70)/1800]300 A2 x 2 A2. This is in agreement with the estimate of Chupka et al.54and with the most recent indirect determination of this cross section by Terazawa et aL70 who predicted that this cross section is on the order of 10 A2. For a more rigorous determination of the velocity dependence and the magnitude of the associative ionization cross section, several additional factors must be taken into account. First, the partial photodissociation branching ratio must be known for each predissociating transition under study; this branching ratio is expected to be a function of both the electronic and the rotational transitions. Second, the analysis of the ion yield data for associative ionization must include processes that compete to deplete H(2s), the most important of which is collisional s-p mixing. This process, which appears to have a significantly larger cross section than associative ionization, is now well understood and can be included in an exact way. The study of Terazawa et al.?O published within the past year, includes a detailed analysis of the kinetics of the deexcitation process and summarizes much of the previous work in this area. Third, if the ion yield for associative ionization is to be compared to the ion yield for the ion-molecule reaction (as we have done here), the analysis must include processes that compete to deplete Hz+, such as charge exchange. Obviously, an accurate estimate of the ion-molecule reaction cross section at the collision energy of interest here is also necessary. Fourth, even though associative ionization is independent of pressure for the reaction of H(2s), ion yield data should be taken as a function of sample pressure to ensure that reaction of H(2p) is negligible. C. Reactions of the Molecular Rydberg StatesChemiionization. Pratt et al?4 recently examined reactions of the (X*E;)np, v = 0 Rydberg states with n = 30-70 by using double-resonance excitation via the E,F ‘E;, v = 0, J = 1 level and by detecting the product ions or electrons. That study showed that, for n = 30-70, the dominant Rydberg state reaction proceeds via the molecular Rydberg state reaction (reaction 1) and not via the H* atom reaction (reaction 2). The reaction appeared to be independent of the Rydberg electron and thus reflected the ion-molecule reaction of the core. Here, we present new data for reaction 1 for Rydberg states with n = 3-17. Taken together with the work of Pratt et al.,74these data now provide a more complete picture of the chemiionization process. Because reaction 1 proceeds via a Rydberg state that may radiatively decay, the kinetics of this reaction are more complex than those of reaction 2, and it is helpful to review the processes involved in the formation and destruction of Hz*. Most simply, these processes can be written as follows.
+
H2 H2*
+ hv -H2* k2
+
+
H,*
+ H,
photon absorption
+ H, -H3+ + H + e
‘g
H2*
kl
k4
k3
+
H,’
chemiionization
+ hv’ radiative decay
-
(3) (4)
(5)
+
H2* H, H2+ 4- H, e all collisional deactivation processes, including, for high n, collisional ionization (6)
Assuming that, in the steady state, the rate of formation and destruction of H2* are equal, then75
Rydberg State Reactions of Hydrogen
b
'
122800
"
, " ' 122600
J. Phys. Chem., Vol. 99, No. 6,1995 1693
, " ' 122400
, . . . , . . . , . . . ( . . . 122200
122000
121800
121600
I
.
121400
'
.
(
121200
TRANS~ON ENERGY (cm-1)
Figure 4. Same as in Figure 2 for transition energies from 121 200 to 122 800 cm-'.
k4[H2l[HZ*I = 0 (7) Following Huffman and Katayama,76the rate of reaction 3 in excited molecules per second is equal to (Z, - I),where Zo and I are the photon intensities in photons per second off and on resonance, respectively, the rate of reaction 4 is equal to the ion current, IH,+,in ions formed per second, and k3 = l/z, where z is the lifetime for radiative decay of H2* to the X ' Z l ground state. (Radiative decay of these states involves little or no cascading via the E,F 'Zistate.77) The ion yield, Y, is then defined as ZH,+/I~- I). Rearranging equation 7 and making appropriate substitutions gives
-1= I + - - + - 1 1 Y rk2 [H21
k4 k2
Since z can be rather accurately estimated for these states, a determination of Y as a function of H2 number density would permit both k2 and k4 to be determined as a function of principal quantum number. However, because the spectra reported here were taken at only a single pressure and with detectors that were not calibrated for absolute photon or ion counting rates, it is not possible to determine individual values of k2 and k4 as a function of n. Nevertheless, the present data do provide insight on the n dependence of the relative chemiionizationcross section in the transition region from low n to high n. We have used the present data to obtain relative chemiionization ion yields in the following way. For low n, we used the Q(J) transitions to obtain the relative ion yield; since the upper levels of these transitions decay only by radiative emission, there will be no interference from associative ioniza-
tion. For high n, the Q(J) transitions are too weak to provide accurate determinations of the relative chemiionization ion yield. Instead, we used the R(0) transitions. As discussed in section IILA, in the absence of accidental predissociation, the high-n ( n k 7) Rydberg states will decay by radiative emission not by predissociation. Figure 5 shows a plot of the chemiionization ion yield for the Q(J)lines for n = 4-6 and the R(0) lines for n = 7-17. Also shown is the ion yield for the H2+ H2 H3+ H ion-molecule reaction, taken at a number of wavelengths corresponding to autoionizing Rydberg states that converge to H2+, v+ = 1 (see Figure 2f). These states, which have principal quantum numbers in the range 8-15, decay by vibrational autoionization to produce H2+(X *2:,v+ = 0). As expected, the ion yield for the ion-molecule reaction shows no dependence on principal quantum number. The relative chemiionization ion yield for n = 3 is zero; the yields for n 2 4 increase by several orders of magnitude over a rather small range of n and become relatively constant at about n = 10-12. That the ion yield for chemiionization for n L 12 is within a factor of 2 of that for the analogous ion-molecule reaction is quite remarkable, since, under the present experimental conditions, the high-n limit of the ion yield for the chemiionization reaction is not necessarily expected to be that for the analogous ion molecule reaction for several reasons. For example, the ion-molecule reaction is a rather sensitive function of collision energy, having an E-1i2 energy dependence in the Langevin-Gioumousis-Stevenson78~79limit. At high collision energies, charge exchange will compete with the ion-molecule reaction.*O In the present experiments, the collision energy for the chemiionization reaction is determined by the sample temperature; however, the collision energy for the ion-molecule reaction will also depend on the voltage used to repel ions out of the ionization chamber and into the stack of ion-focusing
+
+
-
1694 J. Phys. Chem., Vol. 99, No. 6, 1995
Dehmer and Chupka
6 p x , v=l
.
.HI
V=O
9
12
13
12
11 12
I
i:
50
40
30
.-
s E $’-
v)
2
P 20 +f
L
10
123400
123800
123600
123200
123000
122800
TRANSITION ENERGY (“1)
Figure 5. Same as in Figure 2 for transition energies from 122 800 to 123 800 cm-l.
elements. Under the present experimental conditions, the ion yields for the two processes have nearly the same limiting value, because the ion repeller voltage was set to near zero to optimize H3+ formation for the ion-molecule reaction. Had we used a higher repeller voltage (to optimize H2+ formation), the ion yield for the ion-molecule reaction might actually have been lower than that for the high-n limit of chemiionization. A second factor that might contribute to the observed discrepancy between the ion yields for the high-n limit of chemiionization and the ion-molecule reaction is accidental predissociation of the R(0) Rydberg states below the ionization threshold. Such predissociation processes would decrease the ion yield for chemiionization. The straight line through the data points for n = 4-12 in Figure 5 is a fit to the function Y = cnx, where x = 6 f 0.5. We now ask if we can use eq 8 and our knowledge of the basic properties of Rydberg states to understand, at least qualitatively, both the n dependence of the chemiionization ion yield at intermediate n and the lowest value of n for which the relative chemiionization ion yield approximates that of the analogous ion-molecule reaction. In what follows, we examine two effects that will decrease the chemiionization ion yield at low n. The fist of these is the radiative emission rate of the Rydberg states; at low n, the emission rate will be greater than the H2*H2 collision rate and, therefore, the Rydberg states will radiatively decay before collision and chemiionization can occur.
The second of these is the mechanism of formati f H3+ and the factors that combine to reduce the rate of formation (Le., k2) at low n. Since the H2*-H2 collision rate plays an important role in these discussions, we first estimate this rate by using the approximation of hard spheres in a homogeneous Maxwellian gas. The collision rate is given by
where (T is the cross section for the analogous ion-molecule reaction (a = d , where d is the collision diameter), N is the number density, and vrel is the relative collision velocity [vrel = (2)II2F = (2)1’2(8kT/mn)1/2= 1.277 x lo5 cm/s at 77 K]. The average collision energy in the center-of-mass system is E,, = l/@vr,? = ’/2mF2;Ecm = 8.4 meV at 77 K. Recent theoretical and experimental determinations of a for the reaction H ~ + ( v= 0) f H2 + H3+ H have been summarized by Ng;sohowever, there have been no experimental measurements of the cross section at the low collision energy of interest here. We have estimated the cross section at this energy by extrapolating the experimental results of Shao and Ng8’ to 8.4 meV; this process yields a value for a of 300 A2. The calculated value of kcollision is then 4.804 x lo6 SKI.This extrapolation and the subsequent calculation of kcollisionare quite approximate, because there is significant variation in the values of the ion-molecule reaction
+
Rydberg State Reactions of Hydrogen
J. Phys. Chem., Vol. 99, No. 6,1995 1695
v=o
5pn, v=2 Q(1)
32
25
I
-
. 124800
124600
124400
123200
124000
123800
TRANSITION ENERGY (cm-1)
Figure 6. Same as in Figure 2 for transition energies from 123 800 to 124 800 cm-l.
cross section obtained by extrapolating the various theoretical and experimental results.80 We now return to a consideration of eq 8. The term (l/zQ)(1/[H2]) is expected to have the largest n dependence and is further expected to have the greatest influence on the total ion yield. (This is because the ratio k4/k2 is expected to be small, since the cross section for processes such as n-changing collisions and collisional ionization will be small compared to the cross section for chemiionization when the scatterer is a quadrupolar molecule like H2.82,83)We consider separately the n dependence of the two factors z and k2 in this term. It is well-known that, for a fixed value of 4 the lifetime z of the Rydberg state varies as n3.82 We can estimate the actual lifetimes of the Rydberg states under investigation by using the radiative emission rate A,+ for either the 2pn 'nu state (A,=o = 1.180 x lo9 s-') calculated by Allison and Dalgarnog4 or the 3pn Ill, state (AY=o= 0.346 x lo9 s-l) calculated by GlassM a ~ j e a n .These ~ ~ values agree to within a few percent with the simple n3 scaling law. Since the A, values for the npa and npn transitions rapidly approach one another for equal values of n, the lifetime of the Rydberg states under investigation may be approximated by
for Rydberg states in the range n = 2-100. It is seen that the lifetime of the Rydberg state is much shorter than the collision time for small n. The values of krad and kcollision become equal at about n = 12. It is more difficult to quantify the dependence of k2 on n . However, we can be confident that it will increase with n for the following reasons. The reaction may be thought of as occurring in two steps. In the first step, the core reacts to produce H3* H; as in the free ion-molecule reaction, we expect that the H3* will retain perhaps two-thirds of the exothermicity of the reaction. In the second step, the excited H3* autoionizes to produce H3+ e. As discussed below, the rates of both steps are expected to increase with n.
+
+
In the first step, the Rydberg electron can be considered a spectator only for high values of n. At the very least, the Rydberg electron probability density in the region of the core ( ~ n - will ~ ) partially shield the Coulomb field of the core for low values of n. Other deactivation modes of interaction can also occur. For example, the relatively high average kinetic energy of the electron ( ~ n - can ~ ) lead to some rotationally inelastic p-wave scattering with a decrease in n to form more short-lived states ( J = 0 J = 2, AE = 365 cm-I). We very crudely estimate the n dependence of these effects by considering the number of electron orbits made during the H2*-H2
-.
1696 J. Phys. Chem., Vol. 99, No. 6, 1995
Dehmer and Chupka
T v= 1
300
:
l l
.-
250 3
t. E
200
'3 9
150
5
v)
+m I
100
50
A
I
126200
126000
125800
125600
125400
125200
125000
124800
TRANSITION ENERGY (cm-1)
Figure 7. Same as in Figure 2 for transition energies from 124 800 to 126 200 cm-'.
collision. The orbit frequency is given bya2
where Ry is the Rydberg constant, which for H2 is 109 707.42 cm-l. Using this very simple argument, k2 will be inversely proportional to korbit and will therefore vary as n3, at least for that range of n for which the Rydberg electron makes many orbits during the time of the collision. The duration of the H2*s) can be estimated from the H2 collision (-7.832 x collision diameter (- 10 A) and the relative (thermal) velocity of the heavy particles (1.277 x IO5 c d s ) . (Note that this estimate is almost certainly an upper limit to the duration of the collision; since one-third of the excess energy of the reaction goes into translational energy of the products, the relative velocity of the heavy particles will be faster than the thermal velocity as the particles separate.) Table 3 summarizes the values of korbit and the number of orbits during an H2*-H2 collision for Rydberg states in the range n = 2-100. The number of electron orbits during an H?*-H2 collision falls to 3 for n = 12 and to 1 for n = 17. At higher values of n, where s-wave electron scattering dominates and shielding becomes negligible, the Fermi model of the Rydberg state and, therefore, the two-step model of the chemiionization reaction become very good. If all of the product H3* autoionizes, then we can equate k2 to the rate of the
corresponding ion-molecule reaction. The argument for this being approximately the case is strong. Helm and co-workers86 have extensively investigated the predissociation and vibrational and rotational autoionization of s, p, and d Rydberg states of H3 in the (O,O), (l,O), and (0,l) vibrational levels. Their studies have shown that vibrational autoionization via Av = -1 is generally faster than predissociation, but both are about 2 orders of magnitude slower than rotational autoionization when the latter is allowed by energy and angular momentum selection rules. The rotational autoionization studies were specifically on np states, which is applicable to the present case, since (within the Fermi model) Gas well as n will tend to be preserved for the reacting np states. Recent trajectory calculations have helped quantify the degree of vibrational and rotational excitation in the H3+ product following ion-molecule reaction.8 At the lowest translational energy of the calculation (0.11 eV), -50% of the exothennicity appears as vibrational energy; nearly all of this energy is in the asymmetric stretch mode, which is nearly as efficient as the symmetric stretch mode in vibrational autoionization (and probably much more efficient in predissociation). About 20% of the exothermicity appears as rotational energy with the most probable values of J 12 and K = 0. (Here, we ignore the effects of nuclear statistics, which are of little importance in this approximation.) At the translational energy of the present experiment, we expect that -15% of the
Rydberg State Reactions of Hydrogen
J. Phys. Chem., Vol. 99, No. 6, 1995 1697
5 1J
I 5
z
0 W
f
D(2s) + D2+ D:
U
+e
r'
5F
c
v)
8
-5
H(2s) + H2+ H i + e
- 4
- 3
- 2
- 1
0
118000
119000
120000
121000
122000
123000
TRANSITION ENERGY (cm-1)
+
+
Figure 8. Relative photoionization cross section for H3' and D3+ formation from the reactions H(2s) H2 and D(2s) D2 for atoms formed by direct photodissociation of H2 and D2, respectively. The more intense sharp structure corresponds to H3+ (D3') formation from chemiionization (reaction 1) and from associative ionization (reaction 2) with H(2s) atoms formed by predissociation. The solid curves theoretical calculations of the H2 H(2s) H(1s) and D2 D(2s) D(1s) partial photodissociation cross sections from M. Glass Maujean.I4
-
-
+
-I
I
2
3
I
4
Relative Velocity
+
1
1
I
1
5
6
7
8
(lo5 c d s e c )
I
+
Figure 9. Relative H3+ ion yield for the reaction H(2s) H2 versus relative collision energy. The H(2s) atoms were formed by predissostates. The solid line is ciation of HZin the 3pn 'll: and the 4pa a fit of all of the data points to a function of the form v,;". The two data dashed lines are separate fits of the 3pn 'll: and the 4pa points.
'q
'g
exothermicity will appear as rotational energy with J I!8. Since rotational autoionization proceeds via hRr+ = -2, -4, ..., the
energy separation between N+ = 8 and W = 6 will approximate the binding energy for the onset of rotational autoionization. This energy difference is about 1300 cm-I (BO= 43.23 c ~ - I ) , * ~ so that Rydberg states with n* > 9.2 may rotationally autoionize. We expect that most states of H3* with larger values of n* will decay pedominately by rotational autoionization, which is much faster than predissociation. However, the calculations show that both the vibrational and rotational product distributions are broad, and therefore, some fraction (probably small) of the H3* will predissociate. Such predissociation would be found primarily for states with low rotational energy and (probably) high vibrational energy in the asymmetric stretch mode. The calculations show that less than 1% of the product H3+ is formed with no intemal energy and, therefore, only a very small fraction of the corresponding H3* would be incapable of autoionization. Finally, we note that, for H3* molecules formed with n > 21, even the minimum amount of intemal (rotational) energy will enable the molecule to decay by rotational autoionization; however, for H3* molecules formed with n < 7, autoionization must proceed via IAvl < 1, which will tend to favor predissociation. We thus expect that, for n < 7, the ion yield for chemiionization will be significantly less than the high-n limit, while for n =- 21, the ion yield will be equal to the high-n limit. In summary, it appears that chemiionization is now well
Dehmer and Chupka
1698 J. Phys. Chem., Vol. 99, No. 6, 1995
+
moo/
L
.
e
4
3
5 6 7 8 9 10 12 14 16 10 Principal Quantum Number
+
Figure 10. Relative H3+ ion yield for the reaction H2* H2 versus principal quantum number. The solid line is a fit of the data for n = 4-12 to a function of the form nx. Also shown in the ion yield for the H3+ H ion-molecule reaction taken at a number of H2+ H2 wavelengths corresponding to autoionizing Rydberg states that converge to H2+, v+ = 1 (See Figure 1). These states, which have principal quantum numbers in the range 8-15, decay by vibrational autoion' :, y' = 0). As expected, the ion yield for ization to produce H2+(X E the ion-molecule reaction is independent of the principal quantum = 0). number of the autoionizing state used to produce H ~ + ( v +
+
-
+
TABLE 3: Properties of Rydberg States of Molecular Hydrogen n 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
kra# (s-l) 1.168 x 3.460 x 1.460 x 7.474 x 4.325 x 2.724 x 1.825 x 1.281 x 9.342 x 7.019 x 5.406 x 4.252 x 3.404 x 2.768 x 2.281 x 1.901 x 1.602 x 1.362 x 1.168 x
30 3.460 x 40 1.460 x 50 7.474 x 60 4.325 x 70 2.724 x 80 1.825 x 90 1.281 x 100 9.342 x
lo9 lo8 lo8 lo7
lo7 lo7 lo7 lo7 lo6 lo6 lo6 lo6 lo6 lo6 lo6 lo6 lo6 lo6 lo6 lo5 lo5 lo4 lo4 lo4 lo4 lo4 lo3
krad kcoilision
karbl; (s-I)
243.088 72.026 30.386 15.558 9.003 5.670 3.798 2.668 1.945 1.461 1.125 0.885 0.709 0.576 0.475 0.396 0.333 0.284 0.243
8.222 x 2.436 x 1.028 x 5.262 x 3.045 x 1.918 x 1.285 x 9.023 x 6.578 x 4.942 x 3.807 x 2.994 x 2.397 x 1.949 x 1.606 x 1.339 x 1.128 x 9.590 x 8.222 x
lOI4 loi4 loL4 lOI3 lOI3 lOI3 lOI3 10l2 10l2 10l2 10l2 10l2 loL2 10l2 loL2 10l2 loL2 10" 10"
0.072 0.030 0.016 0.009 0.006 0.004 0.003 0.002
2.436 x 1.028 x 5.262 x 3.045 x 1.918 x 1.285 x 9.023 x 6.578 x
10" 10" 1O'O 1O'O lolo 1O'O lo9 lo9
number of orbitsd during an H2-H2* collision 643.966 190.805 80.496 41.214 23.851 15.020 10.062 7.067 5.152 3.871 2.981 2.345 1.877 1.526 1.258 1.049 0.883 0.75 1 0.644 0.191 0.080 0.041 0.024 0.015 0.010 0.007 0.005
a From eq 10. From eq 9, kco~llslon (s-I) = uNvrel= 4.804 x lo6 s-l at T = 77 K and 0.010 Torr. From eq 11. From section IIIC, the duration of an H*-Hz* collision is -7.832 x s.
understood in terms of an ion-molecule reaction of the Rydberg state core, with the Rydberg electron acting as a spectator. Following the reaction of the Rydberg state core, the Rydberg electron is bound to the H3+ core and has a principal quantum number approximately equal to that of the H2* reactant. The H3* Rydberg state subsequently undergoes rapid decay by
autoionization to produce H3+ e. The ion yield for H3+ production increases rapidly from n = 3 to n = 12 as a result of two factors-( 1) the competition between radiative decay and reaction of the H2* reactant and (2) the rate constant for chemiionization. It is argued that, in the critical range from low-n behavior to high-n behavior, the ion yield has an nx dependence, where n may be as high as 6 if the term (llzk2)(l/[Hz]) is the dominant term in eq 8. Furthermore, on the basis of considerations of the principal quantum number for which the radiative decay rate is equal to the collision rate ( n x 12), the onset of significant electron shielding of the core ( n < 12), and the onset of energetically allowed rotational autoionization (n > 9), the high-n regime is predicted to begin at about n = 12, which is approximately where we observe that the ion yield has become constant.
Acknowledgment. This work was supported by the U S . Department of Energy, Office of Energy Research, Office of Health and Environmental Research, under Contract No. W-31109-ENG-38 and by the National Science Foundation under Contract CHE-9298203. We are grateful to Dr. Michele GlassMaujean, Laboratoire de Spectroscopie Hertzienne de 1'Ecole Normale SupCrieure, UniversitC Pierre et Marie Curie, Paris, France, for providing us with new calculations of the partial photodissociation cross sections for HZand D2. We would also like to thank Dr. Stephen Pratt for many helpful discussions during the course of the preparation of this manuscript and Mrs. Sandy Gotlund for recovering the spectra presented here by typing more than 45 000 data points into new computer files. References and Notes (1) Fermi, E. Nuovo Cimento 1934, 11, 157. (2) Rydberg States of Atoms and Molecules; Stebbings, R. F., Dunning, F. B., Eds.; Cambridge: New York, 1983. (3) Moore, C. E. Atomic Transition Probab es, Volume I. Hydrogen through Vanadium; NSRDS-NBS 35, 1971. (4) Gilligan, J. M.; Eyler, E. E. Phys. Rev. A 1992, 46, 3676. ( 5 ) Balakrishnan, A.; Smith, V.; Stoicheff, B. P. Phys. Rev. A 1994, 49, 2460. (6) Lembo, L. J.; Bordas, M. C.; Helm, H. Phys. Rev. A 1990, 42, 6660. (7) Cosby, P. C.; Helm, H. Chem. Phys. Lett. 1988, 152, 71. (8) Tennyson, J.; Henderson, J. R. J . Chem. Phys. 1989, 91, 3815. (9) Eaker, C. W.; Schatz, G. C. J . Phys. Chem. 1985, 89, 2612. (10) Douglass, C. H.; McClure, D. J.; Gentry, W. R. J . Chem. Phys. 1977, 67, 4931. (11) Chupka, W. A.; Dehmer, P. M. Bull. Am. Phys. SOC.1975, 20, 1454. (12) Beswick, J. A.; Glass-Maujean, M. Phys. Rev. A 1987, 35, 3339. (13) Glass-Maujean, M.; Frohlich, H.; Beswick, J. A. Phys. Rev. Lett. 1988, 61, 157. (14) Glass-Maujean, M. Private communication, 1994. (15) Chupka, W. A.; Dehmer, P. M.; Jivery, W. T. J . Chem. Phys. 1975, 63, 3929. (16) Samson, J. A. R. Adv. At. Mol. Phys. 1966, 2, 177. (17) Monfils, A. J . Mol. Spectrosc. 1965, 15, 265. (18) Namioka, T. J . Chem. Phys. 1964, 40, 3154. (19) Namioka, T. J . Chem. Phys. 1964, 41, 2141. (20) Takezawa, S. J . Chem. Phys. 1970, 52, 2575. (21) Herzberg, G.; Jungen, Ch. J . Mol. Spectrosc. 1972, 41, 425. (22) Dabrowski, I.; Herzberg, G. Can. J . Phys. 1974, 52, 1110. (23) Takezawa, S.; Tanaka, Y. J . Mol. Specrrosc. 1975, 54, 379. (24) Rothschild, M.; Egger, H.; Hawkins, R. T.; Bokor, J.; Pummer, H.; Rhodes, C. K. Phys. Rev. A 1981, 23, 206. (25) Roncin, J.-Y.; Launay, F.; Larzilliere, M. Can. J . Phys. 1984, 62, 1686. (26) Dehmer, P. M.; Chupka, W. A. J . Chem. Phys. 1976, 65, 2243. (27) Fano, U. Phys. Rev. A 1970, 2, 353. (28) Atabek, 0.;Dill, D.; Jungen, Ch. Phys. Rev. Lett. 1974, 33, 123. (29) Jungen, Ch.; Atabek, 0. J . Chem. Phys. 1977, 66, 5584. (30) Dill, D.; Jungen, Ch. J . Phys. Chem. 1980, 84, 2116. (31) Jungen, Ch.; Dill, D. J . Chem. Phys. 1980, 73, 3338. (32) Jungen, Ch.; Raoult, M. Faraday Discuss. Chem. SOC. 1981, 71, 253.
Rydberg State Reactions of Hydrogen (33) Comaggia, C.; Giusti-Suzor, A.; Jungen, Ch. J . Chem. Phys. 1987, 87, 3934. (34) Raoult,-M.; Jungen, Ch.; Dill, D. J . Chim. Phys. 1980, 77, 599. (35) Raoult, M.; Jungen, Ch. J. Chem. Phys. 1981, 74, 3388. (36) Jungen, Ch. In Electronic and Atomic Collisions; Datz, S., Ed.; North-Holland: Amsterdam, 1982; p 455. (37) Jungen, Ch. J . Chim. Phys. 1980, 77, 27. (38) Jungen, Ch. Phys. Rev. Lett. 1984, 53, 2394. (39) Herzberg, G. In Spectra of Diatomic Molecules; Van Nostrand: Princeton, NJ, 1950. (40) Julienne, P. S. Chem. Phys. Lett. 1971, 8, 27. (41) Fiquet-Fayard, F.; Gallais, 0. Mol. Phys. 1971, 20, 527. (42) Fiauet-Favard. F.; Gallais. 0. Chem. Phvs. Lett. 1972. 16. 18. (43) Guyon, P: M.; Breton, J.; Glass-MaujeA, M. Chem. Phys. Lett. 1979, 68, 314. (44) Glab, W. L.; Hessler, J. P. Phys. Rev. A 1987, 35, 2102. (45) Glab, W. L.; Hessler, J. P. Phys. Rev. A 1990, 42, 5486. (46) Guyon, P. M.; Breton, J.; Glass-Maujean, M. Chem. Phys. Lett. 1979, 68, 314. (47) Breton, J.; Guyon, P. M.; Glass-Maujean, M. Phys. Rev. A 1980, 21, 1909. (48) Roncin, J. Y.; Damany, H.; Jungen, Ch. In VUVRadiation Physics; Koch, E. E., Haensel, R., Kunz, C., Eds.; Pergamon-Vieweg: Braunschweig, 1974; p 52. (49) Larzilliere, M.; Launay, F.; Roncin, J. Y . J. Phys. Paris 1980, 41, 1431. (50) Roncin, J. Y . ;Launay, F.; Larzilliere, M. Can. J . Phys. 1984, 62, 1686. (51) Mulliken, R. S . J. Am. Chem. SOC. 1966, 88, 1849. (52) Glass-Maujean, M. Phys. Rev. A 1986, 33, 342 and references therein. (53) The radiative decay rate of hydrogen atoms in the 2p state is 6.265 x lo8 s-I (Wiese, W. L.; Smith, M. W.; Glennon, B. M. Atomic Transition Probabilities, Volume I. Hydrogen through Neon; NSRDS-NBS 4, 1966). From eq 9, the collision rate for H(W atoms with Hz is kcollision (s-l) = uNv,i. Assuming vrel = 10 x lo5 cm/s (which, from Table 2, is higher than any relative collision velocity in the present experiment) and s = 100 A2 (which is 1-2 orders of magnitude higher than many estimates for associative ionization), then kcollision = 1.254 x lo7 s-I. This is a factor of 50 less than the radiative decay rate of H(2p); thus, in the present work, we ignore reactions of H(2p) with H2. (54) Chupka, W. A.; Russell, M. E.; Refaey, K. J . Chem. Phys. 1968, 48, 1518. ( 5 5 ) Comes, F. J.; Wenning, U. 2. Naturforsch. 1969, 24a, 587. (56) Comes, F. J.; Wenning, U.2. Naturforsch. 1969, 2 4 , 1227. (57) Gersten, I. J. J. Chem. Phys. 1969, 51, 637. (58) Mentall, J. E.; Gentieu, E. P. J . Chem. Phys. 1970, 52, 5641. (59) Braun, W.; Carlone, C.; Carrington, T.; van Volkenburgh, G.; Young, R. A. J . Chem. Phys. 1970, 53, 4244.
J. Phys. Chem., Vol. 99, No. 6, 1995 1699 (60) van Volkenburgh, G.; Carrington, T.; Young, R. A. J . Chem. Phys. 1973, 59, 6035. (61) Dose, V.; Semini, C. Helv. Phys. Acta 1974, 47, 623. (62) Dose, V.; Hett, W. J. Phys. B 1974, 7, L79. (63) Dose, V.; Hett, W. J . Phys. B 1974, 7, L454. (64) Dose, V. Comments At. Mol. Phys. 1976, 5, 151. (65) Ryan, S . R.; Czuchlewski, S. J.; McCusker, M. V. Phys. Rev. A 1977, 16, 1892. (66) Dose, V.; Richard, A. J . Phys. B 1981, 14, 63. (67) Weissmann, H.; Hartmann, W.; Burch, D. S. Z. Phys. D 1987, 7, 119. (68) Glass-Maujean, M. Phys. Rev. Lett. 1989, 62, 144. (69) Vassilev, G.; Perales, F.; Miniatura, Ch.; Robert, J.; Reinhardt, J.; Vecchiocattivi, F.;Gaudon, J. J. Phys. D 1990, 17, 101. (70) Terazawa, N.; Ukai, M.; Kouchi, N.; Kameta, K.; Hatano, Y.; Tanaka, K. J. Chem. Phys. 1993, 99, 1637. (71) Mentall, J. E.; Guyon, P. M. J. Chem. Phys. 1977, 67, 3845. (72) Borondo, F.; Eguiagaray, L. R.; Riera, A. J. Phys. B 1982, 15, 899. (73) Mrugala, F. Mol. Phys. 1988, 65, 377. (74) Pratt, S. T.; Dehmer, J. L.; Dehmer, P. M.; Chupka, W. A. J. Chem. Phys. 1994, 101, 882. (75) See, for example: Weston, R. E., Jr.; Schwarz, H. A. Chemical Kinetics; Prentice-Hall: Engelwood Cliffs, NJ, 1972. (76) Huffman, R. E.; Katayama, D. H. J. Chem. Phys. 1966, 45, 138. (77) Glass-Maujean, M.; Breton, J.; Thieblemont, B.; Ito, K. Physique 1984, 45, 1107. (78) Langevin, P. Ann. Chim. Phys. 1905, 5, 245. (79) Gioumousis, G.; Stevenson, D. P. J. Chem. Phys. 1958, 29, 294. (80) For a comprehensive review of the charge exchange and ionmolecule reactions of Hz', see: Ng, C.-Y. Adv. Chem. Phys. 1992, 82, 401. (81) Shao, J. D.; Ng, C. Y. J . Chem. Phys. 1986, 84, 4317. (82) Matsuzawa, M. In Rydberg Stales of Atoms and Molecules; Stebbings, R. F., Dunning, F. B., Eds.; Cambridge: New York, 1983; p 267. (83) Matsuzawa, M. J. Electron Spectrosc. Relat. Phenom. 1974, 4, 1. In particular, see footnote 19, which summarizes unpublished results of W. A. Chupka giving relative collisional ionization cross sections for atoms, quadrupolar molecules, dipolar molecules, and electron-attaching molecules. (84) Allison, A. C.; Dalgamo, A. At. Data 1970, I , 289. (85) Glass-Maujean, M. At. Data Nucl. Data Tables 1984, 30, 301. (86) See: Bordas, M. C.; Lembo, L. J.; Helm, H. Phys. Rev. A 1991, 44, 1817 and references therein. (87) Dabrowski, I.; Herzberg, G. Can. J . Phys. 1980, 58, 1238.
JP942399H
