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Cross section for the production of H+ (D+) ions from He+ + H2(D2) encounters below 7.2 eV
Volume 8 1, number 2
CHEMICAL PHYSICS LETTERS
15 July 1981
CROSS SECTION FOR THE PRODUCTION OF II+ (D+) IONS FROlK He+ -t H2 (D2) ENCOUNTERS BELOW 7.2 eV Darrel G. HOPPER and Richard L.C. WU Brehm Laborarmy.
Wrghr Srate Universiy.
Received
1981;
6 January
Dayton
OIiio 45435
USA
in fiial form 16 April 1981
A small cross section for H+ (D+) production from He+ + Hz (Dz) reactions has been detected in ion beam collisioncell experiments. Below 7 eV (c m.) this cross section exhibits a positive energy dependence down to =l eV (c-m.). An inverse dependence is observed over the range 0.1-l eV (c-m.). Possible mechamsms are discussed.
I_ Introduction We are engaged in a series of studies of state-tostate processes involving the reactions of helium ions Het(X *S) with hydrogen H2(X ’ xi, u = 0) yielding p, Hz, He*, H*(lzZ), HeH*(j”A). Kf(j’A), and other products [l-6] _In a theoretical paper Hopper [2] proposed a collisional radiative charge transfer (RCT) mechanism for the production of Hz at thermal collision energies. It was suggested that this mechanism accounted for most of the thermal rate for He* disappearance in Hz, as measured by Iohnsen and coworkers 17.81. Wu and Hopper [5] have recently performed and reported measurements of the absolute cross sections and rates for l$ production which confirm the importance of the RCT mechanism proposed by Hopper. 3ohnsen and Biondi (9 J have recently challenged Hopper’s RCT mechanism, restating their previous contention [7,8] that the branching of H’ is the dominant thermal channel. Hopper [lo] has pointed out that the very nature of the experiments of Johnson and co-workers [7,8], which follow He+ ion disappearance, precludes any statement whatsoever on the basis of those experiments regarding the relative importance of the four thermodynamically accessible product channels. These four exothermic channels are He(X’S) + l-$(X’Zi, u’), He(XlS) + H(X2S) + H+, Hel-I+(X’Z+,u’) + H(X*S), and HEl$(X*Z+, v; , u;, u’;)In order to elucidate the thermal mechanism(s) yielding H+, we have undertaken a series of experi230
ments in our laboratory_ In this paper we present cross sections obtained in an ion beam collision-cell apparatus, in which we follow the @(Df) product ions produced from He+ + H3 (D2) encounters at relative energies from 0.1 to 5.2 eV (cm.). In brief, we have found that apparently two mechanisms are responsible for K” production in this energy range: proton tunnelling dissociative charge transfer (TDCT) dominates below 1.5 f 0.5 eV, and collisional dissociative charge transfer (CDCT) dominates at higher energies_ Both of these mechanisms represent variants of the same dissociative charge transfer (DCT) process: He+(X ‘S) f H2(X ‘Zi, (a) tunnelling (b) collisional
l
[He(X ’ S)-H$(B
u = 0)
[He(XlS)-G(B
2Zz)],
(1)
‘zi)]
+ He(X1 S) + H(X 2S) + H’ + K.E.
(2)
These variants differ in an important way regarding the dynamics of reactive collisions_ From its threshold of 1 .I4 eV, the collisional mechanism, CDCT. yields atomic products with a total relative translational energy of 7.6 eV or more. At its thermal “threshold” of 0 eV, the tunnelling mechanism, TDCT, produces products with 6.5 eV kinetic energy. The latter is a consequence of the passage of the system through, rather than over, the potential barrier separating the reagent triatomic state, 22_41(2A’), from the product triatomic state, 1 2B2(2A’). Furthermore, as the ener-
Volume 81, number 2
CHEMICAL
15 July 1981
PHYSICS LIXTERS
gy increases, the tunnelling mechanism becomes rapidly iess important_ The present data is consistent with an G/w branching ratio of 5 + l/l at thermal energies
only relative cross sections
for the range 0.1-7.2
eV
(cm.).
3. Results 2. Experimental method The measurements were made with an in-line tandem mass spectrometer_ The instrument has been described previously [4,11,12]. Helium ions produced in an electron-impact source are extracted and formed into a mass-selected (m/e = 4) and energy-resolved primary ion beam over the accessible range from 0.3 to 180 eV (lab). The beam spread is 0.15 eV halfwidth at half-maximum_ Due to the favorable laboratory to center-of-mass conversion factors for He”/H2 and He+/D2 _ relative energies down to 0.1 and 0.15 eV, respectively, may be reached with this instrument. The primary beam is focused on a collision cell which is 3.2 mm in length. The transit time of 0.3 eV (lab) helium ions through this collision cell is 0.84 ps. The hydrogen pressure was 40 mTorr, and the temperature of the gas in the collision cell was maintained at 473 K. As noted above, the product p (D+) ions from He+/H? (Dz) collisions are produced with =6.5--7.6 eV (cm.) distributed over the three relative translational degrees of freedom for the products from reaction (2). Accordingly, in the current experiments we have not attempted to calibrate the observed cross section against the thermal reaction of methane ions with methane_ The reason is that we had expected there to be an unknown discrimination factor against translationally hot product ions in our instrument, whose extraction field was originally designed with the assumption that product ions would have low kinetic energy. However, because of the success we have had previously in following product ions I? (D*) with 13.6 eV (cm.) or more product translational energy [4], resulting from He+/H, (D2) rllisions above 7.1 eV (cm.), and for other reasons , we have confidence that at least the relative cross section obtained for H’ (D+) production below 7.1 eV (cm-) is reliable- Accordingly, we report here
For footnote see next column
The observed apparent cross sections for K’ production from He+/H2 collisions are presented in fig. 1. The results of two separate runs are displayed. Both indicate that the cross section for K’ production exhibits a linear rise from el-2 eV (c-m.) to 5 eV (c-m.). In one run the helium ion energy was followed down to 0.3 eV (lab), which corresponds to 0 1 eV
COLLISION
ENERGY
(eV)
Fig. 1. Relative cross section for H+ production from He*(X2S) -I- Ha(Xrz+ u = 0) over the helium ion energy range 0.3-21.6 eV (A). This energy range corresponds to a relative energy range of 0.1-7.2 eV (cm.). The left ordinate scale applies to the data. The computed cross section for the tunneIling mechanism from ref. 1141 is included as solid lure for comparison (right ordinate scale applies).
* In previous studies of proton transfer reactions having exothermicities up to 3 eV, it has been found that the cross sections o(Et) measured in OUTtandem apparatus were not seriously distorted by collection efficiency variations as a function of Et (set ref. [ 131). As noted in section 5, many of the mechanisms which are thermodynamically possible for H+
231
CHEMICAL
Volume 81, number 2 He-(X%,
* O,CX’X; .v=ol
D*dl(nf) lHelX'S)
-
.
y Cl-J =
l
.
.
.,
.
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PHYSICS
.
02-
Q O 00
1 I I2345
t
2
I 3 6
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I
a
7
:
3
I 5 IO
, II
I 6 12
1 13
I 7 14
CM LAB
COLLISION ENERGY (eV) Fig. 2. Relative cross section for DC production from He+(X*S) + Dz(XlC+, u = 0) over the hehum 10x1range 0.5-14.5 eV (lab). T&s energy range corresponds to a relative ener,T range of 0.25-7.25 eV (c-m.). (c.m_) for He+/HZ encounters.
From 0.1 to ~1.2 eV decreases. Only above -1.2 eV (cm.) does the direct energy behavior dominate the total observed cross section. The data from this run also indicate that a relative minimum may occur at =S_S eV (cm_)_ The linear behavior above ~2 eV (cm.) was verified by repeating the experiment with deuterium in the place of hydrogen_ The observed apparent cross section for D+ production from He+/D, collisions is presented in fig. 2. Here, three runs were made and the results are all included in fig. 2. All three sets of data indicate a linear dependence of the cross section with the reIative collision energy below 7.1 eV (c.m.), and beginning at or below 2 eV (c_m_). Data below 2 eV (cm.) was taken in one of these deuterium runs, and the results indicate the same inverse behavior found for p from He*/H, collisions below -1.2 eV (cm_)_ Again, there is some indication of a relative minimum near 6 eV (cm_)_ (c.m_) the cross section for H’ production
4. Discussion 4.1. Collision energies below I.14 eV(c.m.) The present results imply that there are two distinct mechanisms for Hf production below 7.1 eV (cm_)_ One mechanism accounts for the cross section 232
LETTERS
I5 July 1981
observed at collision energies below 1.14 eV (c.m.). As noted in section 1, thermodynamics requires that this reactivity results from a quantum-mechanical process in which proton tunnehing (RHJJ goes from ~0.74 to 1.16 A) takes the system from the 22A1(2A’) triatomic state, through the 1.4 eV barrier, to the fully dissociative 1 2B2(2A’) triatomic state. This mechanism is expected to have an inverse dependence on the collision energy, which IS inversely related to the lifetime of the collision event: turmelling cannot occur if the collision complex does not exist. Preston et al. [ 141 have computed the rate for this tunnelling process and report that the cross section decreases exponentially with the relative energy, from 21 .O pm2 at 0.01 eV (cm.) to 5.2 pm’ at 0.28 eV (cm.). Accordingly, we may interpret the weak inverse energy dependence of the cross section, which we report in this paper, with the proton tunnelling mechanism. These results apparently represent the first experimental observation of protons produced via the tunnelling mechanism_ The computed cross section from Preston et al. [ 141 has been included for comparison in fig. 1. The observed cross section for H+ production falls off somewhat more slowly in the 0.1-0.3 eV (cm_) range than does the theoretical cross section. Apparently, the gaussian distribution of the ion beam about the nominal value, and perhaps too the Doppler motion of the target molecules, causes low-energy collisions below 0.1 eV, where the tunnelling cross section is the highest, to contnbute significantly to the observed cross section just above 0.1 eV (cm_)_ The theoretical cross section cut-off at 0.28 eV (cm.) precluded integration over these distributions to provide a more direct comparison with experiment _ Previous works have reported inverse temperature dependencies for both the thermal disappearance rate of helium ions in hydrogen [7,8] and for the appearance rate of H$ ions from He*/H encounters [5] _ The rate coefficient of 1.5 X lo- 13 cm3 s-l reported by Wu and Hopper [S] for H$ production fully accounts, to within experimental error. for the helium ion disappearance rate coefficient of 1.1 X 10-13 cm3 s-l reported by Johnsen and co-workers [7,8] _The thermal rate coefficient for H+ production, via the tunnelling mechanism , is computed by Preston et al. [14] to be 2.5 X lo-l4 cm3 s-l _ Only the trmnelling mechanism is possible for @ production at thermal collision energies_ Apparently, the @ channel is 4-6
CHEMICAL
Volume 81, number 2
PHYSICS LETTERS
times less important than the s channel under thermal conditions_ In other words, the rate coefficients imply a q/II+ branching ratio of between 4/l and 6/l. This l-l$/l-l+ branching ratio is expressible, too, in terms of the cross sections at a He+/H* relative energy of 0.1 eV. Wu and Hopper [5] have reported a calibrated experimental cross section of 42 + 4 pm’ for H$ production. Preston et al. [14] report a quantum-mechanical calculated cross section of 7.6 pm’ for ~YI+production (see fig. 1). From these results the l-@H+ branching ratio is computed to be between 5/ 1 and 6/l. 4.2. Collision energies in the range I. I4- 7.2 e V (cm.) For He+/H2 (D2) encounters at relative energies above 1.14 eV the energy necessary to reach the avoided crossing seam for the 2 ‘AI(2A’) and 1 “B2(‘A’) He% states is available by a classical T + V energy transfer mechanism_ We term this mechanism collisional dissociative charge transfer (CDCT) to distinguish it from the tunnelling dissociative charge transfer (TDCT) mechanism discussed above. The steady rise in the observed cross section for H+ (D+) production is obviously c;onsistent with a classical barrier mechanism_ The present data for H’ (D”) in the relative range l-14-7.2 eV may be interpreted primarily in terms of the CDCT mechanism_ The TDCT mechanism is apparently of little consequence above 1 .I4 eV. At relative energies greater than 3.7 eV (cm.) the endothermic charge transfer channels He+(X 2S) + H2(X ‘Zp’, u =
* He(X
0)
‘S) + H*(nl) + I-l+
(3)
become thermodynamically accessible. At 3.7 eV (c_m_) the n = 2 channel opens up, followed at 5.1 eV (cm.) by the n = 3 channel, and so forth. These II+ channels proceed by way of bound Rydberg states of H$ (D$) produced in dissociated vibrational levels_ The advent of these channels is not discernible in all of the presently reported cross sections for II? from He+/H2 (D2) collisions. However, further experiments with more product ion counting time at each energy, and with a greater density of data in the vicinity of 3.7 and 5.1 eV (cm.), may make it possible to distinguish the slight increases in the slope of the cross section above that attributable to reaction (lb).
15 July 1981
5. Conclusions Relative cross sections are reported for the production of I?I+(D’) ions from He+ + H, (D2) reactions at relative energies in the range 0.1-7.2 eV (c-m.). From co mparisons made in section 4 with the theoretical results of Preston et al. [14], it is apparent that the presently reported l-l+ cross section below =1.14 eV (c.m.) may be attributed to a tunnelling mechanism. The linear rise in the presently reported cross section above el.5 + 0.5 eV (cm.) may be attributed to a classical T + V energy transfer mechamsm, accompanied by a concomitant charge transfer. The reactivity presently reported below 7.2 eV (cm.) is considerably less than found above 7.2 eV in our previous studies at higher collision energies up to 160 eV (lab) [4]. In those studies, Jones et al_ [4] reported a vev strong threshold at 7.1 + 0.2 eV (cm.) in the p (D*) relative cross section from He+/H, (D2) collisions_ Hopper [ 151 has suggested that the dynamics of the collision changes at 7.1 ri:0 2 eV (c.m.) due to the movement of the “avoided” crossing seam for the potential energy surfaces of the 2 ‘AI(2A’) and 1 “B2C2A’) triatomic states to RIIII values less than the outer vibrational turning point, Rfi”z = 0.74 + 6, for H2(X lx+ u = 0). The energy transfer mechanism then becom&‘that of a barrier reaction in which motion in the He-H, coordinate alone is sufficient to take the system to the top of the adiabatic barrier separating reactants from products_ In the range 1.14-7.1 eV (cm_), however, the translational energy must be first transferred to hydrogen so as to extend the motion in the RHH coordinate. Asymptotically, R,, must stretch from R& = 0.74 AtoRbH= 1.15 A. Here, R& refers to the isolated Hz equilibrium bond length, and R& to the value ofRHH at the crossing locus in the Hep2 system. As RHe_-H2 decreases, R& decreases very slowly as the energy at the intersection rises several eV above the level of the reactants, He+(X 2S) + H,(X ‘Zd, u = 0) [15] _OXIXI~fen does R& decrease to values less -R& + 6. The need for the energy to than RRB be filtered through the RHH coordinate is apparently the reason for the much slower reactivity found here below 72 eV (cm.), relative to that found previously [4] above 7.1 f 0.2 eV (cm.). Comparisons made in section 4 lead us to conclude that the branching ratio q/l? from the He+ + Hz reaction is *S f l/ 1 under thermal conditions_ This 233
Volume 8 1, number 2
conclusion is in direct contradiction
CHEMICAL PHYSICS LETTERS
with the inter[7-91 of their drift tube data for the rate of helium ion disappearance in hydrogen_ However, as Hopper [2,10] has previously shown, it is impossible to make any conclusions regarding the branching ratio on the basis of the He+ disappearance data of Johnsen and co-workers_ Wu and Hopper [S] have presented calibrated cross sections for H$ production from the He+ + H2 reaction. Preston et al. [ 141 have presented excellent quantummechanical calculations for the tunnelling mechanism yielding H’ (see aho fig. 1). The data of Johnsen and co-workers, the data of Wu and Hopper, the quantum tunnehing calculations of Preston et al., and the data of the present work are all consistent with a g/H+ thermal branching ratio of between 4/ 1 and 6/l _This result is of considerable consequence in astrochemistry, and in the chemistry of planetary atmospheres. It is of interest to note that many of the mechanism discussed here for H+ (D+) formation from He+/H, (Dz) collisions below 7.1 eV (cm.) may tend to favor collinear coilisions. The turmelling mechanism is allowed in Cmv, but forbidden in C, collisions, by spatial symmetry constraints on the total system wavefunction. Several of reactions (3) are similarly constrained by symmetry considerations. Reaction (1 b) involves a T + V energy transfer during the colli-
pretation by Johnsen and co-workers
234
15 July 1981
sion event and may favor C,, encounters for dynamical as weil as symmetry reasons, since the barrier to reaction (1 b) is in the RHH coordinate.
References [I] [2] [3] [4]
D.G. Hopper, intern. J. Quantum Chem. S12 (1978) 305. D.G. Hopper, J. Chem. Phys. 73 (1980) 3289. D-G. Hopper, J. Chem. Phys. 73 (1980) 4528. E.G. Jones, R.L.C. Wu, B.M. Hughes, T-0. Tiernan and D-G. Hopper, J. Chem. Phys. 73 (1980) 5631. [S] R-L-C. Wu and D-G. Hopper, Chem. Phys. 57 (1981) 385. [6] D.G. Hopper, unpublished_ [7] R. Johnsen and M.A. Biondi, J. Chem. Phys. 61 (1974) 2112. 181 R. Johnsen, A. Chen and M.A. Biondi, J. Chem. Phys 72 (1980) 3085. PI R. Johnsen and A. Biondi, J. Chem. Phys. 74 (1981), to be published. llO1 D.G. Hopper, J. Chem. Phys. 74 (1981), to be published. WI J.H. FutreU and CD. Miller, Rev. Sci. Instr. 37 (1966) 1521. 1121 B.M. Hughes and T-0. TieAnan, J. Chem. Phys. 55 (1971) 3419. 1131 C. Lifshitz, R.L.C. Wu and T-0. Tieman, J. Am. Chem. Sot. 100 (1978) 2040. 1141 R.K. Preston, D.L. Thompson and D.R. McLaughlin, J. Chem. Phys. 68 (1978) 13. 1151 D-G. Hopper, to be published.
CHEMICAL PHYSICS LETTERS
15 July 1981
CROSS SECTION FOR THE PRODUCTION OF II+ (D+) IONS FROlK He+ -t H2 (D2) ENCOUNTERS BELOW 7.2 eV Darrel G. HOPPER and Richard L.C. WU Brehm Laborarmy.
Wrghr Srate Universiy.
Received
1981;
6 January
Dayton
OIiio 45435
USA
in fiial form 16 April 1981
A small cross section for H+ (D+) production from He+ + Hz (Dz) reactions has been detected in ion beam collisioncell experiments. Below 7 eV (c m.) this cross section exhibits a positive energy dependence down to =l eV (c-m.). An inverse dependence is observed over the range 0.1-l eV (c-m.). Possible mechamsms are discussed.
I_ Introduction We are engaged in a series of studies of state-tostate processes involving the reactions of helium ions Het(X *S) with hydrogen H2(X ’ xi, u = 0) yielding p, Hz, He*, H*(lzZ), HeH*(j”A). Kf(j’A), and other products [l-6] _In a theoretical paper Hopper [2] proposed a collisional radiative charge transfer (RCT) mechanism for the production of Hz at thermal collision energies. It was suggested that this mechanism accounted for most of the thermal rate for He* disappearance in Hz, as measured by Iohnsen and coworkers 17.81. Wu and Hopper [5] have recently performed and reported measurements of the absolute cross sections and rates for l$ production which confirm the importance of the RCT mechanism proposed by Hopper. 3ohnsen and Biondi (9 J have recently challenged Hopper’s RCT mechanism, restating their previous contention [7,8] that the branching of H’ is the dominant thermal channel. Hopper [lo] has pointed out that the very nature of the experiments of Johnson and co-workers [7,8], which follow He+ ion disappearance, precludes any statement whatsoever on the basis of those experiments regarding the relative importance of the four thermodynamically accessible product channels. These four exothermic channels are He(X’S) + l-$(X’Zi, u’), He(XlS) + H(X2S) + H+, Hel-I+(X’Z+,u’) + H(X*S), and HEl$(X*Z+, v; , u;, u’;)In order to elucidate the thermal mechanism(s) yielding H+, we have undertaken a series of experi230
ments in our laboratory_ In this paper we present cross sections obtained in an ion beam collision-cell apparatus, in which we follow the @(Df) product ions produced from He+ + H3 (D2) encounters at relative energies from 0.1 to 5.2 eV (cm.). In brief, we have found that apparently two mechanisms are responsible for K” production in this energy range: proton tunnelling dissociative charge transfer (TDCT) dominates below 1.5 f 0.5 eV, and collisional dissociative charge transfer (CDCT) dominates at higher energies_ Both of these mechanisms represent variants of the same dissociative charge transfer (DCT) process: He+(X ‘S) f H2(X ‘Zi, (a) tunnelling (b) collisional
l
[He(X ’ S)-H$(B
u = 0)
[He(XlS)-G(B
2Zz)],
(1)
‘zi)]
+ He(X1 S) + H(X 2S) + H’ + K.E.
(2)
These variants differ in an important way regarding the dynamics of reactive collisions_ From its threshold of 1 .I4 eV, the collisional mechanism, CDCT. yields atomic products with a total relative translational energy of 7.6 eV or more. At its thermal “threshold” of 0 eV, the tunnelling mechanism, TDCT, produces products with 6.5 eV kinetic energy. The latter is a consequence of the passage of the system through, rather than over, the potential barrier separating the reagent triatomic state, 22_41(2A’), from the product triatomic state, 1 2B2(2A’). Furthermore, as the ener-
Volume 81, number 2
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PHYSICS LIXTERS
gy increases, the tunnelling mechanism becomes rapidly iess important_ The present data is consistent with an G/w branching ratio of 5 + l/l at thermal energies
only relative cross sections
for the range 0.1-7.2
eV
(cm.).
3. Results 2. Experimental method The measurements were made with an in-line tandem mass spectrometer_ The instrument has been described previously [4,11,12]. Helium ions produced in an electron-impact source are extracted and formed into a mass-selected (m/e = 4) and energy-resolved primary ion beam over the accessible range from 0.3 to 180 eV (lab). The beam spread is 0.15 eV halfwidth at half-maximum_ Due to the favorable laboratory to center-of-mass conversion factors for He”/H2 and He+/D2 _ relative energies down to 0.1 and 0.15 eV, respectively, may be reached with this instrument. The primary beam is focused on a collision cell which is 3.2 mm in length. The transit time of 0.3 eV (lab) helium ions through this collision cell is 0.84 ps. The hydrogen pressure was 40 mTorr, and the temperature of the gas in the collision cell was maintained at 473 K. As noted above, the product p (D+) ions from He+/H? (Dz) collisions are produced with =6.5--7.6 eV (cm.) distributed over the three relative translational degrees of freedom for the products from reaction (2). Accordingly, in the current experiments we have not attempted to calibrate the observed cross section against the thermal reaction of methane ions with methane_ The reason is that we had expected there to be an unknown discrimination factor against translationally hot product ions in our instrument, whose extraction field was originally designed with the assumption that product ions would have low kinetic energy. However, because of the success we have had previously in following product ions I? (D*) with 13.6 eV (cm.) or more product translational energy [4], resulting from He+/H, (D2) rllisions above 7.1 eV (cm.), and for other reasons , we have confidence that at least the relative cross section obtained for H’ (D+) production below 7.1 eV (cm-) is reliable- Accordingly, we report here
For footnote see next column
The observed apparent cross sections for K’ production from He+/H2 collisions are presented in fig. 1. The results of two separate runs are displayed. Both indicate that the cross section for K’ production exhibits a linear rise from el-2 eV (c-m.) to 5 eV (c-m.). In one run the helium ion energy was followed down to 0.3 eV (lab), which corresponds to 0 1 eV
COLLISION
ENERGY
(eV)
Fig. 1. Relative cross section for H+ production from He*(X2S) -I- Ha(Xrz+ u = 0) over the helium ion energy range 0.3-21.6 eV (A). This energy range corresponds to a relative energy range of 0.1-7.2 eV (cm.). The left ordinate scale applies to the data. The computed cross section for the tunneIling mechanism from ref. 1141 is included as solid lure for comparison (right ordinate scale applies).
* In previous studies of proton transfer reactions having exothermicities up to 3 eV, it has been found that the cross sections o(Et) measured in OUTtandem apparatus were not seriously distorted by collection efficiency variations as a function of Et (set ref. [ 131). As noted in section 5, many of the mechanisms which are thermodynamically possible for H+
231
CHEMICAL
Volume 81, number 2 He-(X%,
* O,CX’X; .v=ol
D*dl(nf) lHelX'S)
-
.
y Cl-J =
l
.
.
.,
.
I
04-
PHYSICS
.
02-
Q O 00
1 I I2345
t
2
I 3 6
t
I
a
7
:
3
I 5 IO
, II
I 6 12
1 13
I 7 14
CM LAB
COLLISION ENERGY (eV) Fig. 2. Relative cross section for DC production from He+(X*S) + Dz(XlC+, u = 0) over the hehum 10x1range 0.5-14.5 eV (lab). T&s energy range corresponds to a relative ener,T range of 0.25-7.25 eV (c-m.). (c.m_) for He+/HZ encounters.
From 0.1 to ~1.2 eV decreases. Only above -1.2 eV (cm.) does the direct energy behavior dominate the total observed cross section. The data from this run also indicate that a relative minimum may occur at =S_S eV (cm_)_ The linear behavior above ~2 eV (cm.) was verified by repeating the experiment with deuterium in the place of hydrogen_ The observed apparent cross section for D+ production from He+/D, collisions is presented in fig. 2. Here, three runs were made and the results are all included in fig. 2. All three sets of data indicate a linear dependence of the cross section with the reIative collision energy below 7.1 eV (c.m.), and beginning at or below 2 eV (c_m_). Data below 2 eV (cm.) was taken in one of these deuterium runs, and the results indicate the same inverse behavior found for p from He*/H, collisions below -1.2 eV (cm_)_ Again, there is some indication of a relative minimum near 6 eV (cm_)_ (c.m_) the cross section for H’ production
4. Discussion 4.1. Collision energies below I.14 eV(c.m.) The present results imply that there are two distinct mechanisms for Hf production below 7.1 eV (cm_)_ One mechanism accounts for the cross section 232
LETTERS
I5 July 1981
observed at collision energies below 1.14 eV (c.m.). As noted in section 1, thermodynamics requires that this reactivity results from a quantum-mechanical process in which proton tunnehing (RHJJ goes from ~0.74 to 1.16 A) takes the system from the 22A1(2A’) triatomic state, through the 1.4 eV barrier, to the fully dissociative 1 2B2(2A’) triatomic state. This mechanism is expected to have an inverse dependence on the collision energy, which IS inversely related to the lifetime of the collision event: turmelling cannot occur if the collision complex does not exist. Preston et al. [ 141 have computed the rate for this tunnelling process and report that the cross section decreases exponentially with the relative energy, from 21 .O pm2 at 0.01 eV (cm.) to 5.2 pm’ at 0.28 eV (cm.). Accordingly, we may interpret the weak inverse energy dependence of the cross section, which we report in this paper, with the proton tunnelling mechanism. These results apparently represent the first experimental observation of protons produced via the tunnelling mechanism_ The computed cross section from Preston et al. [ 141 has been included for comparison in fig. 1. The observed cross section for H+ production falls off somewhat more slowly in the 0.1-0.3 eV (cm_) range than does the theoretical cross section. Apparently, the gaussian distribution of the ion beam about the nominal value, and perhaps too the Doppler motion of the target molecules, causes low-energy collisions below 0.1 eV, where the tunnelling cross section is the highest, to contnbute significantly to the observed cross section just above 0.1 eV (cm_)_ The theoretical cross section cut-off at 0.28 eV (cm.) precluded integration over these distributions to provide a more direct comparison with experiment _ Previous works have reported inverse temperature dependencies for both the thermal disappearance rate of helium ions in hydrogen [7,8] and for the appearance rate of H$ ions from He*/H encounters [5] _ The rate coefficient of 1.5 X lo- 13 cm3 s-l reported by Wu and Hopper [S] for H$ production fully accounts, to within experimental error. for the helium ion disappearance rate coefficient of 1.1 X 10-13 cm3 s-l reported by Johnsen and co-workers [7,8] _The thermal rate coefficient for H+ production, via the tunnelling mechanism , is computed by Preston et al. [14] to be 2.5 X lo-l4 cm3 s-l _ Only the trmnelling mechanism is possible for @ production at thermal collision energies_ Apparently, the @ channel is 4-6
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PHYSICS LETTERS
times less important than the s channel under thermal conditions_ In other words, the rate coefficients imply a q/II+ branching ratio of between 4/l and 6/l. This l-l$/l-l+ branching ratio is expressible, too, in terms of the cross sections at a He+/H* relative energy of 0.1 eV. Wu and Hopper [5] have reported a calibrated experimental cross section of 42 + 4 pm’ for H$ production. Preston et al. [14] report a quantum-mechanical calculated cross section of 7.6 pm’ for ~YI+production (see fig. 1). From these results the l-@H+ branching ratio is computed to be between 5/ 1 and 6/l. 4.2. Collision energies in the range I. I4- 7.2 e V (cm.) For He+/H2 (D2) encounters at relative energies above 1.14 eV the energy necessary to reach the avoided crossing seam for the 2 ‘AI(2A’) and 1 “B2(‘A’) He% states is available by a classical T + V energy transfer mechanism_ We term this mechanism collisional dissociative charge transfer (CDCT) to distinguish it from the tunnelling dissociative charge transfer (TDCT) mechanism discussed above. The steady rise in the observed cross section for H+ (D+) production is obviously c;onsistent with a classical barrier mechanism_ The present data for H’ (D”) in the relative range l-14-7.2 eV may be interpreted primarily in terms of the CDCT mechanism_ The TDCT mechanism is apparently of little consequence above 1 .I4 eV. At relative energies greater than 3.7 eV (cm.) the endothermic charge transfer channels He+(X 2S) + H2(X ‘Zp’, u =
* He(X
0)
‘S) + H*(nl) + I-l+
(3)
become thermodynamically accessible. At 3.7 eV (c_m_) the n = 2 channel opens up, followed at 5.1 eV (cm.) by the n = 3 channel, and so forth. These II+ channels proceed by way of bound Rydberg states of H$ (D$) produced in dissociated vibrational levels_ The advent of these channels is not discernible in all of the presently reported cross sections for II? from He+/H2 (D2) collisions. However, further experiments with more product ion counting time at each energy, and with a greater density of data in the vicinity of 3.7 and 5.1 eV (cm.), may make it possible to distinguish the slight increases in the slope of the cross section above that attributable to reaction (lb).
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5. Conclusions Relative cross sections are reported for the production of I?I+(D’) ions from He+ + H, (D2) reactions at relative energies in the range 0.1-7.2 eV (c-m.). From co mparisons made in section 4 with the theoretical results of Preston et al. [14], it is apparent that the presently reported l-l+ cross section below =1.14 eV (c.m.) may be attributed to a tunnelling mechanism. The linear rise in the presently reported cross section above el.5 + 0.5 eV (cm.) may be attributed to a classical T + V energy transfer mechamsm, accompanied by a concomitant charge transfer. The reactivity presently reported below 7.2 eV (cm.) is considerably less than found above 7.2 eV in our previous studies at higher collision energies up to 160 eV (lab) [4]. In those studies, Jones et al_ [4] reported a vev strong threshold at 7.1 + 0.2 eV (cm.) in the p (D*) relative cross section from He+/H, (D2) collisions_ Hopper [ 151 has suggested that the dynamics of the collision changes at 7.1 ri:0 2 eV (c.m.) due to the movement of the “avoided” crossing seam for the potential energy surfaces of the 2 ‘AI(2A’) and 1 “B2C2A’) triatomic states to RIIII values less than the outer vibrational turning point, Rfi”z = 0.74 + 6, for H2(X lx+ u = 0). The energy transfer mechanism then becom&‘that of a barrier reaction in which motion in the He-H, coordinate alone is sufficient to take the system to the top of the adiabatic barrier separating reactants from products_ In the range 1.14-7.1 eV (cm_), however, the translational energy must be first transferred to hydrogen so as to extend the motion in the RHH coordinate. Asymptotically, R,, must stretch from R& = 0.74 AtoRbH= 1.15 A. Here, R& refers to the isolated Hz equilibrium bond length, and R& to the value ofRHH at the crossing locus in the Hep2 system. As RHe_-H2 decreases, R& decreases very slowly as the energy at the intersection rises several eV above the level of the reactants, He+(X 2S) + H,(X ‘Zd, u = 0) [15] _OXIXI~fen does R& decrease to values less -R& + 6. The need for the energy to than RRB be filtered through the RHH coordinate is apparently the reason for the much slower reactivity found here below 72 eV (cm.), relative to that found previously [4] above 7.1 f 0.2 eV (cm.). Comparisons made in section 4 lead us to conclude that the branching ratio q/l? from the He+ + Hz reaction is *S f l/ 1 under thermal conditions_ This 233
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conclusion is in direct contradiction
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with the inter[7-91 of their drift tube data for the rate of helium ion disappearance in hydrogen_ However, as Hopper [2,10] has previously shown, it is impossible to make any conclusions regarding the branching ratio on the basis of the He+ disappearance data of Johnsen and co-workers_ Wu and Hopper [S] have presented calibrated cross sections for H$ production from the He+ + H2 reaction. Preston et al. [ 141 have presented excellent quantummechanical calculations for the tunnelling mechanism yielding H’ (see aho fig. 1). The data of Johnsen and co-workers, the data of Wu and Hopper, the quantum tunnehing calculations of Preston et al., and the data of the present work are all consistent with a g/H+ thermal branching ratio of between 4/ 1 and 6/l _This result is of considerable consequence in astrochemistry, and in the chemistry of planetary atmospheres. It is of interest to note that many of the mechanism discussed here for H+ (D+) formation from He+/H, (Dz) collisions below 7.1 eV (cm.) may tend to favor collinear coilisions. The turmelling mechanism is allowed in Cmv, but forbidden in C, collisions, by spatial symmetry constraints on the total system wavefunction. Several of reactions (3) are similarly constrained by symmetry considerations. Reaction (1 b) involves a T + V energy transfer during the colli-
pretation by Johnsen and co-workers
234
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sion event and may favor C,, encounters for dynamical as weil as symmetry reasons, since the barrier to reaction (1 b) is in the RHH coordinate.
References [I] [2] [3] [4]
D.G. Hopper, intern. J. Quantum Chem. S12 (1978) 305. D.G. Hopper, J. Chem. Phys. 73 (1980) 3289. D-G. Hopper, J. Chem. Phys. 73 (1980) 4528. E.G. Jones, R.L.C. Wu, B.M. Hughes, T-0. Tiernan and D-G. Hopper, J. Chem. Phys. 73 (1980) 5631. [S] R-L-C. Wu and D-G. Hopper, Chem. Phys. 57 (1981) 385. [6] D.G. Hopper, unpublished_ [7] R. Johnsen and M.A. Biondi, J. Chem. Phys. 61 (1974) 2112. 181 R. Johnsen, A. Chen and M.A. Biondi, J. Chem. Phys 72 (1980) 3085. PI R. Johnsen and A. Biondi, J. Chem. Phys. 74 (1981), to be published. llO1 D.G. Hopper, J. Chem. Phys. 74 (1981), to be published. WI J.H. FutreU and CD. Miller, Rev. Sci. Instr. 37 (1966) 1521. 1121 B.M. Hughes and T-0. TieAnan, J. Chem. Phys. 55 (1971) 3419. 1131 C. Lifshitz, R.L.C. Wu and T-0. Tieman, J. Am. Chem. Sot. 100 (1978) 2040. 1141 R.K. Preston, D.L. Thompson and D.R. McLaughlin, J. Chem. Phys. 68 (1978) 13. 1151 D-G. Hopper, to be published.