J . Phys. Chem. 1989, 93, 3062-3068
3062
would imply that the actual spin-orbit coupling effect is slightly larger than reported here. There is almost complete loss of vibrational structure in acetonitrile (Figure 5), as well as in the other polar matrices of DMABN that we examined: ammonia, HCl, and HBr. The fluorescence spectrum loses all vibrational structure, while the phosphorescence spectrum has an intense leading peak approximately I O nm wide, followed by one broader peak center at 338 nm in acetonitrile, 1600 cm-I from the frequency at half-height of the leading peak. This could be a vestige of the vibrational structure in the rare gas matrices, which consists of an intense leading peak, followed by structure building on a broad base, with the most intense and central band situated 1560 cm-I from the 0-0 band. Thus, we attribute the lack of structure in the polar matrices to inhomogeneous broadening. The "anomalousn fluorescence of polar, room-temperature solutions appears around 400-550 nm, depending on the solvent, and has a typical fluorescence lifetime of a few nanoseconds. We see no evidence of this fluorescence in the rare gas, or even in the highly polar 12 K acetonitrile, matrices. The triplet decays are single exponential and wavelength independent. These observations are in accordance with those of previous workers, who noted that the anomalous fluorescence present at room temperature is replaced by phosphorescence in 80 K matrices of both PVA' and EPA.~~ (21) Khalil, 0. S.; Hofeldt, R. H.; McGlynn, S . P.Chem. Phys. Lett. 1972, 17, 479.
Conclusions We have measured relative fluorescence and phosphorescence yields and singlet and triplet lifetimes of DMABN isolated in argon, krypton, and xenon matrices. The quantum yields and lifetimes are consistent with a much greater increase in k , than in either k,, or kiscin the presence of the external heavy atoms krypton or xenon. Lifetime measurements in mixed matrices of argon doped wtih krypton or xenon indicate that a single heavy atom neighbor significantly increases rates of spin-forbidden processes. The higher resolution emission spectra we present indicate that DMABN has an SI state which is more polar than either So or T I and involves some distortion of the aromatic ring. We saw no evidence of formation of a twisted intramolecular chargetransfer state in these 12 K matrices, in accordance with previous observations.
Acknowledgment. This work was supported by the Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the U S . Department of Energy, under Contract No. DE-AC03-76SF00098. We thank Drs. Kenneth Sauer and Hermann Keuper for assistance with the fluorescence lifetime measurements and Dr. Edward Orton for the IR spectra and purification of DMABN. Registry No. DMABN, 1197-19-9; Kr, 7439-90-9; Ar, 7440-37-1; Xe, 7440-63-3; CH,CN, 75-05-8.
Angular Distributions of Electrons Emitted by Collisional Ionization of Hydrogen Sulfide and Argon with Helium Metastable Atom Koichiro Mitsuke,* Kaoru Kusafuka, and Koichi Ohno Department of Chemistry, College of Arts and Sciences, The University of Tokyo, Komaba, Meguro- ku, Tokyo 153, Japan (Received: August 17, 1988; In Final Form: October 26, 1988)
The relative intensity of electrons emitted in Penning ionization of H2S and Ar with He*(2 3S) metastable atoms is measured as a function of the angle B with respect to the vector of the relative velocity. In the case of the He*(2 3S) + H2S system, the angular distribution is markedly dependent on the average relative kinetic energy &. At & = 59 meV, the distribution ascends with 6' between 40' and 90' and becomes flat beyond 90°, whereas that at = 141 meV shows an ascending tendency up to 8 = 120'. Theoretical distribution curves are obtained by numerically integrating an electron angular distribution in the molecular fixed frame (internal distribution) over classical collision trajectories. A parameter-fitting procedure to the experimental data shows that the continuum wave function of the emitted electron can be expanded in s, p, and d partial waves and that features of the distribution at & = 59 meV are found to be governed by the deflection of the trajectories by a long-range attractive potential. In contrast, the angular distribution for the He*(2 'S) + Ar system is independent of the collision energy and more asymmetric with respect to B = 90°, which can be explained by the kinematics of a "hard-sphere" collision.
Introduction When an electronica~~y excited atom A* collides with a ground-state molecule B, Penning ionization can occur A*
+B
-
A
+ B+ + e-
(1)
where the excitation energy of A* exceeds the first ionization potential of the target B. Several authors have investigated the angular distributions of the intensity of the electrons (Penning electrons) emitted in the collision of He*(2 'S) metastable atoms with Kr, Xe, co, N2,and Hg in the thermal energy range.l-4 ( I ) Ebding, T.; Niehaus, A. Z.Phys. 1974, 270, 43. (2) Niehaus, A. Adu. Chem. Phys. 1981, 45, 399. (3) Le Nadan, A,; Le Coz, G.; Tuffin, F.; Peresse, J. J . Phys. (Les Ulis, Fr.) 1982, 43, 1607.
0022-3654/89/2093-3062$0l.50/0
Ebding and Niehaus have measured the electron angular distribution Z(0) in the center-of-mass system as a function of the angle B with respect to the vector of the initial relative velocity of the colliding particles.' In almost all cases, angular distributions are anisotropic and asymmetric with respect to 0 = 90' except for the He(2-3S) + Hg system where I(B) & essentially flat. These results have been interpreted in terms of the angular-dependent transition rate W(R, y) called the internal angular distribution,l-7 Here, R and denote the intermolecular distance and the electron ejection angle with respect to the intermolecular axis vector BA*. --?)
(4) Tuffin, F.; Le Nadan, A,; Peresse, J. J . Phys. (Les Ulis, Fr.) 1985, 46, 181. (5) Morgner, H. J. Phys. B 1978, 11, 269. (6) Micha, D. A,; Nakamura, H. Phys. Reu. A 1975, 11, 1988. ( 7 ) Hoffmann, V.; Morgner, H. J . Phys. B 1979, 12, 2857.
0 1989 American Chemical Society
Collisional Ionization of H2S and Ar with He*(2 3S)
The Journal of Physical Chemistry, Vol. 93, No. 8, I989
3063
m k3
B
Figure 1. Schematic diagram of the apparatus: (B) beam exhausting chamber; (E) excitation chamber; (R) reaction chamber; (M) metastable atom detection chamber; (N) nozzle; (EB) electron bombarders; (Q) quench lamp; (D) deflector; (A) electron energy analyzer; (EM) channel electron multiplier; (PS) He I photon source.
The angular distribution I(6’) is determined by averaging W(R, y) over all possible intermolecular orientations during collision. Several studies on the Penning ionization process8-l0 and elastic scattering have proposed an exponentially decreasing function for W(R, y) with increasing R, so that the transition favorably occurs in the neighborhood of the turning point of the classical collision trajectory. Hence, a qualitative feature of I(6’) can be predicted by the well depth D eof the interaction potential for the entrance channel and the initial relative kinetic energy Ek.I When Ek is much larger than De, the so-called “hard-sphere” collision occurs and the orientation of BA* at the turning point is directed to the angle of 0 1 r / 2 . The measured anisotropic and asymmetric distribution with respect to 6’ leads to the conclusion that W ( R , y ) is also anisotropic and asymmetric with respect to y = 90’. Such behavior of W(R,y) suggests that, as a first approximation, a continuum wave function of the ejected electron can be expanded in s and p partial waves of u ~ y m m e t r y . ~ . ~ In the case of Ek5 De, the distribution becomes rather isotropic, because the attractive potential causes the deflection of collision trajectories, and the turning points are isotropically situated around the collision center. Actually, distributions weakly dependent on the angle have been obtained for systems with a strong attractive interaction such as Hg He*(2 3S) (0.i= 100 meV)’ and H 2 0 He*(2 3S) (D.= 0.4 eV).I4 The variation of the angular distribution with changing collision energy has been studied on the Ar + He*(2 3S) system. Niehaus has found that the behavior of the distribution curve is rather insensitive to Ek in the range 80-350 meV, probably because of a weak attractive interaction (D.i= 3.7 meV).2 In this paper, we present the angular distribution of Penning electrons emitted in the collision of H2Swith He*(2 3S)obtained by using a supersonic helium metastable beam. By controlling the stagnation temperature for the atomic beam, we can measure the angular distribution at the two energy regions characterized by the conditions Ek < D. and Ek > De. As expected by the above discussion, the two distribution curves are apparently different from each other. In order to explain the experimental curves, we present theoretical calculations with a trajectory analysis by assuming an appropriate interaction potential and an internal angular distribution.
-
+
+
Experimental Section Figure 1 shows a schematic diagram of the apparatus. There exist four differentially pumped chambers: beam exhausting chamber, excitation chamber, reaction chamber, and metastable atom detection chamber. (8) Miller, W. H.; Slocomb, C. A,; Schaefer, H. F. J . Chem. Phys. 1972, 56. 1341.
(9) Illenberger, E.; Niehaus, A. Z . Phys. E : Condens. Matter Quanta 1975, 20, 33.
(10) Miller, W. H.; Morgner, H. J . Chem. Phys. 1977, 67, 4923. (1 1) Brutschy, B.; Haberland, H.; Schmidt, K. J . Phys. B 1976, 9, 2693. (12) Siska, P. E. Chem. Phys. Lett. 1979, 63, 25. (13) Gregor, R. W.; Siska, P. E. J . Chem. Phys. 1981, 7 4 , 1078. (14) Mitsuke, K.; Ohno, K., unpublished data.
\r/
Figure 2. Side view of electron bombarder A (EB,) and electron bombarder B (EBB). Numbered components: (1) grid of EB,; (2) filaments of EB,; (3) filament shield; (4) filaments of EBB; (5) grid of EBB; ( 6 ) electron repeller.
An atomic beam was produced by a supersonic nozzle expansion of helium (Tomoe, purity of 99.999%) with the stagnation pressure of 2000-3000 Torr. The nozzle was made of a platinum aperture, and the orifice diameter was 50 pm. A nozzle mounting block could be electrically heated to 630 K in order to increase the flow velocity of the beam and the collision energy. The beam source was pumped by a 6-in. oil diffusion pump and was in the 5 X 10-4-1 X Torr range. A central portion of the He beam was sampled by a conical skimmer with an entrance hole of 1 mm and was led into two electron bombarders mounted in series at the excitation chamber. The chamber was pumped by a liquid nitrogen (LN,) trapped 4-in. oil diffusion pump and had a pressure of 5 6 X 10” Torr. Here, helium metastable atoms, He*(2 3S,2 lS), were produced by electron impact at the electron energy of 100 eV. Each electron bombarder composed of four pieces of spiral filaments (thoriated tungsten, 0.1 5-mm 0.d.) and a spherically shaped stainless-steel grid separated with a minimum spacing of 2 mm from the filaments as shown in Figure 2. The atomic beam traversed a central hole of the grid and was excited by the impact of electrons that were accelerated to the direction of 135’ f 20’ (bombarder A) or 45’ f 20’ (bombarder B) with respect to the He beam axis. Under typical conditions, the electron emission current for each bombarder was -50 mA. After the excitation, the He beam was irradiated by the light of a spirally shaped helium gas discharge lamp (quench lamp) that quenched the metastable atoms in the singlet state, He*(2 ‘S). At most, 1% of the He*(2 ‘S) atoms remained in the beam under the condition that an electric current supplied to the lamp was 25 mA. Charged particles and highly excited Rydberg atoms were removed from the beam flow by applying a 1.0 kV cm-I transverse electric field to a parallel-plate deflecter downstream of the quench lamp. The atomic beam containing He*(2 3S) was collimated into a reaction chamber surrounded by p-metal shielding that reduces the geomagnetic field. The chamber was pumped by a LN2trapped 6-in. oil diffusion pump, and the background pressure was about 4 X Torr. When the beam was admitted, the pressure was found to increase to 3 X 10” Torr. Argon (Takachiho, purity of 99.99%) or H2S (Matheson, purity of 99.9574) was introduced in the effusive condition into a collision cell fitted to an electron energy analyzer system. The pressure of the target gas was controlled by a variable leak (Anelva Model 951-7170) and kept Torr with monitoring of the pressure constant to (2 =k 0.3) X of the reaction chamber by an ion gauge. Electrons produced by Penning ionization were sampled by a molybdenum slit of 1-mm diameter and focused by cylindrical electrostatic lenses onto the entrance hole of the electron energy analyzer. The analyzer was of a hemispherical electrostatic deflection type, and the mean radius of the electron orbit and the spacing between the two spherical surfaces were 30 and 10 mm, respectively. The best energy resolution of the analyzer was estimated from a full width at half-maximum of an Ar+(2P312)peak on a photoelectron
3064
The Journal of Physical Chemistry, Vol. 93, No. 8. 1989
Mitsuke et al. 1.1
a. Ar t He* ( 2 % )
1.3 1.2
*
Observed
1.1 1.0
+ +
0.9
2 5 =
0.8 0.1
+ + +
0.6
c)
0.5
+
*
s
0.4
b. H z S t He* (2%)
e,
0
200 He'(Z3S)
400
600
800
.-
1000
c1
IL
1
Figure 3. Measured time-of-flight spectra of He*(2 3S) for different nozzle temperatures TN. The most probable velocity calculated from the spectral peak was 1720 m s-I at TN = 298 K with electron bombarder A (panel a) and 2720 m s-' at TN = 630 K with electron bombarder B (panel b).
(15) Brutschy, B.; Haberland, H. J . Phys. E 1977, 10, 90
+ +
Observed
e,
Time O f F l i g h t / jis
spectrum measured by the use of a dc-discharge He I photon source and was found to be 45 meV at a pass energy of 1.46 eV. In the case of the measurement of the angular distribution for the He*(2 'S) + H2Ssystem, the energy resolution was lowered to 110 meV at a pass energy of 3.65 eV so as to increase the transmission efficiency. A Penning ionization electron spectrum (PIES) was obtained by applying a sawtooth potential to the entrance hole of the analyzer with respect to the grounded collision cell. The output signal from a channel electron multiplier (Murata Model EMS-608 1B) placed at the exit hole of the analyzer was processed by a conventional pulse-counting system and accumulated in a homemade multichannel scaler whose channel advance is synchronized with the sawtooth waveform. The analyzer system was mounted on a turntable in the reaction chamber and was rotatable around the ionization region. We measured PIES every IOo in the range 40° I: OL I 120° to calculate the integrated intensity of the peak corresponding to the final ionic state of interest. Here, the angle OL is defined as the angle between the direction of the incoming He metastable atom and the outgoing Penning electron. The obtained intensity was multiplied by sin OL for correction of the ionization volume and was transformed to a relative value with respect to the intensity at OL = 90". The angular distribution I(OL)was then obtained by plotting the relative intensity against OL. The diameter of the molybdenum slit was so small that the effective angular resolution was determined only by the geometry of the collision volume to be about f 2 O . The velocity distribution of the He*(2 'S) was obtained by pulsing the formation of metastable atoms in the electron bombarder and measuring the time of flight from the bombarder to a metastable atom detector. A 100-V positive pulse with a duration of 1.5 1.1s and a typical repetition rate of 200 Hz was applied to the grid in the bombarder. The detector was a channel electron multiplier (Murata Model EMF-2061B) and was located at 98 cm downstream of the bombarder B. The metastable atom detection chamber was pumped by a turbo molecular pump and had a pressure of 5 1 X Torr when the sample gas was introduced in the collision cell. The time-of-flight (TOF) spectrum was accumulated in a transient recorder with I + resolution (Kawasaki Electronica Model TM-1410). The time resolution of the T O F measurement was estimated to be 2-4% at the nozzle temperature of 298 K from the pulse width and the length of the excitation region in the electron bombarders. Figure 3 shows typical T O F spectra for different nozzle temperatures TN. The velocity distribution of He* is rather degraded as compared with that of a ground-state beam, which is ascribed to that when He atoms are excited in collision with 100-eV electrons the final velocity of the He* with nearly the same scattering angle in the laboratory system ranges wide because of a large range of the scattering angle in the center-of-mass system.15
1.1
0.9 0.8
0.1
30
SO
40
10
60
BO
90
1W
110
120
130
Electron E j e c t i o n Angle / d e g
.,
Figure 4. Observed angular distributions of Penning electrons emitted from Ar (panel a) and H2S (panel b) in collision with He*(2 %). The curves are normalized at 90' to unity. Average relative kinetic energies:
59 meV; 0, 59 meV; 0 , 141 meV.
In our experimental conditions, the minimum value of the most probable velocity of He*(2 3S)was found to be 1720 m s-l at TN = 298 K with electron bombarder A (low-energy condition). The maximum value of 2720 m s-l was obtained at TN = 630 K with electron bombarder B (high-energy condition). The average kinetic energy of He*(2 3S) calculated from its most probable velocity was 61 meV under the low-energy condition and 153 meV under the high-energy condition. Assuming a Maxwellian velocity distribution for HIS molecules, the average relative kinetic energy Ek for the He*(2 'S) H2S system was 59 meV under the low-energy condition and 141 meV under the high-energy condition.
+
Results Figure 4a shows the angular distribution I(OL)of Penning electrons produced by the process He*(2 'S)
+ Ar
-
He
+ Ar+(2P312)+ e-
at = 59 meV. As mentioned in the Experimental Section, the relative intensity is normalized to unity at OL = 90". Almost the same distribution is obtained at = 143 meV. The error bars shown are statistical errors ( 2 0 ) derived from five independent measurements. The angular distribution is anisotropic and asymmetric with respect to OL = 90°, which is in accordance with I(@,) in the literature.]-' Figure 4b shows the angular distributions of Penning electrons produced by the process
-
+ H2Sf(2Bl)+ e(3) = 59 meV (open circle) and at 6= 141 meV (full circle). He*(2 3S) + H2S
He
at Both distributions are quite different from that for the He*(2 'S) + Ar system. At OL I 90°, the data points obtained at the two conditions agree with each other within experimental uncertainty and the relative intensities increase less rapidly with OL than that for the He*(2 'S) Ar system. Beyond 90°, the relative intensity at = 59 meV becomes a constant value around 1.01 0.01, = 141 meV shows an increasing tendency up whereas that at to or = 120O.
+
Model Calculation In this section, the angular distribution I(O) of the center-of-mass system is theoretically determined from the internal angular distribution W(R,y) according to the following outlined procedure:
Collisional Ionization of H2S and Ar with He*(2 )S)
The Journal of Physical Chemistry, Vol. 93, No. 8, 1989 3065
(A) The position of the classical turning point on a collision trajectory is found for a certain impact parameter b and a certain relative kinetic energy Ek,assuming a model potential V * ( R ) between He*(2 )S) and the target molecule. (B) At the turning point, W ( R , y) is calculated for the electron emission in the direction of the detector. (C) The transition rate is integrated numerically over b to obtain I ( 0 ) and then is compared with the experimental angular distribution IL(0).16317 The model potential of the Morse type proposed by Brutschy et al. is used for the He*(2 )S) Ar system:"
+
a
1.7
a. Ar t He* (23S]
1.5
a
v
I
.
60 70 EO 90 100 I10 120 130 E l e c t r o n E j e c t i o n Angle / deg
140
s t p (GOmeV) .
A
1.3 A
B "
1.1
0
00.0 C
-
0.7 0.5
(4)
.-+F -a
b. Ar t He* ( Z 3 S )
1.6 1.1
(2:
1.2
Three parameters, the well depth De, the minimum distance Rmin, and the shape parameter @, are taken from the values determined from differential elastic scattering data:"J8 D. = 3.7 meV; R,, = 10.7~10;/3 = 3.77. Here, a. is the symbol of the atomic unit of length (Bohr radius). On the other hand, a Lennard-Jones 6,12-type potential is used for the He*(2 )S) H2S system:
+
The well depth D. is estimated from the peak position of the H2S+(2BI)band on the Penning ionization electron spectrum. Namely, the electron kinetic energy E, at ,44% of the peak maximum on the low-energy electron side can be related to the well depth asI9 De
V*(m)- V+(m)- E , = Eo - E,
(6)
Here V,(m) and V+(m)are the asymptotic potential energies of the entrance and exit channels, respectively; their difference, Eo, was calculated from the excitation energy of He*(2 )S) and the vertical ionization energy I, of HIS with respect to the .transition to the H2S+(2BI)state. The resultant value of D, is 100 f 10 meV. It is probable that the entrance potential of He*(2 )S) H2S has such a deep since both species are highly polarizable and H2S possesses a considerable dipole moment (- 1 .O D). Moreover, the diffuse He* 2s orbital may change into a so Rydberg-type orbital enveloping He+-H2S as R that the charge-dipole interaction characterizes V.(R) at sufficiently small R . There exist no available data for the minimum distance Rmin. For the following reasons, Rminis taken from a calculated bond distance 5 . 2 6 of ~ ~the Li-H2S molecular complex.22 In scattering
+
~
1.0 0.e
0.6 n r ".-
30
40
50
Figure 5. Calculated angular distributions of Penning electrons emitted from Ar in collision with He*(2 '9. The internal angular distributions involving s- and p-wave contributions are used. The relative kinetic energy is 60 meV. The free parameters are the pwave relative amplitude f I and the cosine of the p-wave relative phase shift cos 6,. Panel a shows a El dependence of the distribution curves with a fixed value of cos a,, while panel b shows a cos 6, dependence with a fixed value of f , . Sets of parameters: 0,[I = 1.0, cos 6, = 0.6; V, = 0.82, cos 6, = 0.6; A, [I = 0.62, COS 6, = 0.6; a, [I = 0.42, COS 6, = 0.6; f i = 0.62, COS 6, = 1.0; 0 , (1 = 0.62, COS 6, = 0.8; V, [I = 0.62, COS 61 = 0.4.
.,
experiments, a lithium atom is known to behave like He*, which implies that the interaction potential of Li + H2S is essentially the same as that of He*(2 )S) + H2S at the intermediate separation where a long-range attractive force and a short-range repulsive force keep their balance.12,21The reported minimum energy structure of Li-H2S has the geometry with an angle of 78' between the dipole axis of HIS and the intermolecular axis;22 Le., Li is located above the molecular plane of H2S. This geometry probably corresponds to a favorable configuration of He*(2 %)-H2S resulting in the transition to H2S+(2BI)by process 3. It should also be noted that the dissociation energy of the Li-H2S complexZ2is reported to be about 80 meV, which is nearly equal to the value of De for the He*(2 )S) + H2S system as estimated above by eq 6 . The internal angular distribution is given by the form of a partial-wave expansion, as indicated by Miller et al.:8
W ( R , y) = 2?r~ICY,,(r)i-'e'"'Z,,l~ fm
(1 6) The approximation that the transition occurs only at the turning point
does not practically affect the shape of the angular distribution curve. This statement was examined for the He*(2 'S) Ar system by calculating W(R, y) at all positions in the range of R 5 2700 on each trajectory and integrating them over 6 in the range 0.0001ao-26.75ao. Here, the time interval was set for 1.2 fs. The obtained distribution curve was found to be in accordance with I ( 8 ) in Figure Sb (FI = 0.62, 6, = 0) within 3% at 50' 5 8 5 150'. (17) The angular distribution I(0,) in the laboratory system is a convolution of the distribution I(8) in the center-of-mass system over the velocity vector of H2S. Since the most probable velocity of He*(2 ' S ) is 4 times as large as that of HIS at Ek = 60 meV, the maximal difference between the laboratory angle BL and the center-of-mass angle 8 is 14", when the laboratory velocity vectors of the two particles intersect at 90' (the worst case). Hence, I(8,) is considered to be almost identical with I(8). (18) Siska et al. proposed a realistic optical potential for He'(2 ' S ) + Ar that is constructed by mixing two functions: one for describing the alkali-rare gas like interaction of Ar with the He* 2s electron and the other for describing the He*-Ar The trajectory analysis using their potential gives a similar angular distribution to that determined by the potential of Brutschy et al. (Figure S ) . ' O (19) Miller, W. H. J . Chem. Phys. 1970, 52, 3563. (20) Cermik, V.; Yencha, A. J. J . Elecfron Spectrosc. Relat. Phenom. 1977, 11, 67. (21) Martin, D. W.; Gregor, R. W.; Jordan, R. M.; Siska, P. E. J . Chem. Phys. 1978, 69, 2833. (22) Trenary, M.; Schaefer, H. F.; Kollman, P. J . Am. Chem. SOC.1977, 99, 3885.
+
150
(7)
Here p , u,, and I/, represent the state density, the phase shift, and the matrix element of the transition, respectively. Assuming that the Penning ionization caused by the collision of He*(2 3S)follows the simple electron-exchange p r o c e ~ s , ' ~ ~I,,(R) ~ ' ~ ~can ' ~ be - ~re~ duced to a two-electron integral where and & are 1s and 2s orbitals, respectively, of He*, dMO is a molecular orbital from which the electron is derived, 4,, is an outgoing coulomb wave with an angular momentum quantum number I with respect to the center of mass and a projection quantum number m onto the intermolecular axis, and H is the total electronic Hamiltonian that couples the states. With the arguments given by Ebding and Niehaus' or Miller and Morgner,lo this exchange matrix element can be further approximated to the product of two terms:
(23) Hotop, H.; Niehaus, A. 2. Phys. 1969, 228, 68.
Mitsuke et al.
3066 The Journal of Physical Chemistry, Vol. 93, No. 8, 1989 1.4
1.10
I
I
l I. H z S
1.05 1.2 . 1.1
s t p (GOneV)
-
A
A i
8
"
4 "
1.0 .
:
t He* (2's)
s t p t d (GOmeV)
;
'?
I 0.95
B
0
01
0.90 0.85
i
A
0.1
:
:
:
:
:
:
:
:
:
0
1.00
0
:
:
B
0.80
.s
b. H z S t He* (Z3S) s t p t d (14OmeV)
1.1
v1
3
C -
t 1.0
'?
I
al 0.9
.-> 4
00 : 0.8 0.6
A
:
1.2
.
1.1
.
:
:
:
:
:
:
t He* ( Z 3 S )
HIS 1.3 .
:
:
B
B
B
B
0.7
:
.A
c. H z S t He* ( Z 3 S )
k
1.1
StP
s t p t d
f.0
1.0 .
0.9
0.9
0.8 0.1
P
06l
30
"
50
40
'
60
'
'
10
80
"
90
100
"
110
I20
"
130
140
'
0.1
150
E l e c t r o n E l e c t i o n Angle / d e g Figure 6. Calculated angular distributions of Penning electrons emitted from H2Sin collision with He*(2 3S). The internal angular distributions involving s- and p-wave contributions are used. The values of relative kinetic energy Ek are 60 mev (panel a) and 140 meV (panel b). Panel c shows a comparison of the distributions at different EL: -, 60 meV; 140 meV. Sets of parameters (see caption of Figure 5): A,ti = 1.4, COS 61 = 0.8; 0 , [I = 1.4, COS 6, = 0.6; 0,51 = 1.4, COS 61 = 0.4; 0,f l = 1.7, cos 6 , = 0.6; .,ti = 1.1, cos 6 , = 0.6. .e-.
The first factor is a charge-transfer matrix element coupled by H', an appropriate piece of H, and roughly determines the R dependence of W(R,y).'O The second factor vanishes except for o-symmetric partial waves ( m = O ) . ' * 5 Substituting eq 9 in eq 7 yields m
W R , 7)
a
1(4,SlH'l4M0)l2l1 + CPAcos y)e%I2 I= 1
(10)
Here PI(cos y) is the Legendre polynomial, [ I is the relative amplitude of each I partial wave, and 6, is the relative phase shift defined by
I 30
40
50
60
10
80
90
100
110
120
130
140
150
Electron Ejection Angle / deg Figure 7. Calculated angular distributionsof Penning electrons emitted from H2S in collision with He*(2 3S), The internal angular distributions involving s-, p-, and d-wave contributions are used. The values of relative kinetic energy El, and 60 meV (panel a) and 140 meV (panel b). Panel c shows a comparison of the distributions at different Et: -, 60 meV; 140 meV. The free parameters are the p-wave relative amplitude ti, the cosine of the p-wave relative phase shift cos a1, the d-wave relative amplitude t2,and the cosine of the d-wave relative phase shift cos 62. Sets of parameters: 0, = 0.55, cos 6, = 1.0, t2 = 1.0, cos 62 = -0.8; 0 , ti = 0.55, COS 61 = 1.0, [2 = 1.0, COS 6 2 = -0.9; C;l = 0.55, COS 61 = 1.0, [x = 1.0, COS 6 2 = -1.0; O,61 = 0.55, COS 61 = 0.9, 62 = 1.0, COS 62 = -1.0; V, €1 = 0.55, COS 61 = 0.8, [2 = 1.0, COS 62 = -1.0. e-,
.,
reciprocal 01 rne cnaracrerimc iengrn approximawy equal LO 21/21.,'/2as a long-range behavior.24 The overlap integral ( 41014zs) is considered to have a substantial value for I = 1 and 2, since the approach of the He* to the target causes the hybridization of the He* 2s orbital by an unoccupied orbital(s) such as He* 2p u and 3d u of the sulfur a t ~ m . ' ~ , ~ ~ Hence, the first two or three terms of eq 12 will be taken into account for further d i s c u ~ s i o n . 'If~ ~s ~and p waves are dominant, eq 12 can be simplified to
L
In the present analysis, R dependences of ( 1 and 6/ are neglected,' and their effective values will be obtained by fitting to the experimental distributions (Figure 4). Assuming that (q51slH'(~MO) has a simple exponential one may write m
W ( R ,y)
0:
exp(-KR)Il
+ I=CP/(cos y)ei61[/l2 1
(12)
where K , the reciprocal of the characteristic length, is determined as follows. For the He*(2 )S) Ar system, we adopt a reported value of K = 1.9ao-I, which was chosen to obtain the best fit to the velocity dependence curve of the total ionization cross section.2 For the He*(2 )S) + H2S system, K is evaluated as 1.55ao-' from the relation K 0: lV'l2 by using Iv(H2S)= 10.48 eV and Iv(Ar) = 15.76 eV. This is because $MO decreases exponentially with the
+
If a contribution of the d wave cannot be neglected, another expression should be used as W ( R ,y )
0:
exp(-KR)I1
+ ei61tlcos y + '/2ei62[2(3cos'
y - 1)12 (14)
Discussion Figure 5 shows Penning electron angular distributions for the He*(2 'S) + Ar system at E , = 60 meV, determined by numerically integrating W(R, y) given by eq 13 at the classical turning point on the collision trajectory. The free parameters are and 6,. In this calculation, an impact parameter is varied in steps of 0 . 6 7 ~ 1from ~ O.OOO1aoto 26.75ao, and a time interval At (24) Morrell, M. M.; Parr, R. G.;Levy, M. J . Chem. Phys. 1975, 62, 549.
Collisional Ionization of H2S and Ar with He*(2 %) 1.15
The Journal of Physical Chemistry. Vol. 93, No. 8, 1989 3067 1.2
E.
1.10
HIS
,
t He' (Z3S)
.
a. H 2 S t He' ( Z 3 S )
0
s t p t d (GOmeV)
1.05 1.00
t
B
90
100
A
0.95
0.90
A A
0.65
?
$
?0
.
0.00 1. H 2 S
2
t He*(23S)
1.t
C
3
1.0
0
0.9
C -
.-c>
- .
-
m 0.0 E
0
0.1 E.
H 2 S t He* [23S)
1.1 1.c
0.I 0.1
0.; 30
10
50
60
10
80
90
100
110
120
130
140
E l e c t r o n E j e c t i o n A n g l e / deg
V.,
~
30
40
50
60
10
BO
110
120
130
140
150
E l e c t r o n E j e c t i o n A n g l e / deg
Figure 8. Calculated angular distributionsof Penning electrons emitted from HIS in collision with He*(2 )S). The internal angular distributions involving s-, p-,and d-wave contributions are used. The values of relative kinetic energy El, are 60 meV (panel a) and 140 meV (panel b). Panel c shows a comparison of the distributions at different Ek:-, 60 meV; 140 meV. Sets of parameters (see caption of Figure 7 ) : V, = 0.55, COS 61 = 1.0, 5 2 = 0.6, COS 62 = -1.0; 0, 51 0.55, COS 61 = 1.0, 5 2 = 0.8, COS 62 = -1.0; 0 , 51 = 0.55, COS 61 = 1.0, €2 = 1.0, COS 62 = -1.0; 0, 51 = 0.55, COS 61 = 1.0, 52 = 1.2, COS 6 2 = -1.0; A,51 = 0.55, COS 61 = 1.0, t2 = 1.4, cos 62 = -1.0.
Figure 9. Calculated angular distributionsof Penning electrons emitted from H2S in collision with He*(2 )S). The internal angular distributions involving s-, p-, and d-wave contributions are used. The values of relative kinetic energy E , are 60 meV (panel a) and 140 meV (panel b). Panel c shows a comparison of the distributions at different Ek: -, 60 meV; .-, 140 meV. Sets of parameters (see caption of Figure 7 ) : V, [I = 1.15, COS 61 = 1.0, 52 = 1.0, COS 62 = -1.0; 0,51 = 0.95, COS 61 = 1.0, 52 = 1.0, COS 6 2 = -1 .O; 0 , 51 = 0.75, COS 61 1.O, 5 2 = 1 .O, COS 62 -1 .O; fl, 51 = 0.55, COS 61 = 1.0, 5 2 = 1.0, COS 6 2 = -1.0; A,61 = 0.35, COS 6, = 1.0, t2 = 1.0, cos a2 = -1.0.
for each trajectory is 1.2 fs. All curves of Z(0) are anisotropic and asymmetric with respect to 0 = 90'. The slope of the distribution curve is greatly affected by the values of t1and 6,. Increasing t1or bringing 6 , close to zero results in an increase in the slope as indicated in Figure 5. The best fit to the measured Z(0,) distribution at & = 59 meV (Figure 4a) was obtained at El = 0.62 and cos 61 = 0.7.2s These values of the parameters are nearly equal to those reported by Niehaw2 Angular distribution at El, = 140 meV almost coincides with that at Ek = 60 meV, which is consistent with the experimental o b s e r v a t i ~ n . ~ ~ Figure 6 shows Penning electron angular distributions for the He*(2 %) 4- H2S system at Ek = 60 and 140 meV, determined by numerically integrating W(R,y) given by eq 13. An impact parameter is varied in steps of 0 . 3 9 from ~ ~ O.OOO1ao to 15.77ao, and At is 1.2 fs. Several distribution curves are illustrated with varying tl from 1.1 to 1.7 and cos 6, from 0.4 to 0.8. All curves of I ( 0 ) are anisotropic and asymmetric with respect to 0 = 90°, the slope of the curve at Ek = 140 meV being always greater than that at & = 60 mev for the same set of parameters (Figure 6c). For a fixed collision energy, the slope increases in the whole range of 0 with bl approaching zero or increases at 0 > 90' with increasing tI. No flat distribution beyond 90' was, however, obtained in this calculation. This suggests that the term of the d-wave
matrix element (+2,01$2s) is no longer negligible in W(R, y). Figures 7-9 show the distribution curves determined by numerically integrating W(R,y) given by eq 14. The free parameters are t , , E,, 6,, and 6,. In each figure, the dependence of Z(0) on one of the parameters with the others being fixed is depicted in panel a (Ek = 60 mev) or panel b (& = 140 mev). The comparison between curves at different energies is shown in panel c with selection of two representative sets of parameters. The more d wave is incorporated to compensate the effect of p wave by bringing 62 close to x (Figure 7) and/or increasing t2(Figure 8), the flatter the obtained curve becomes at 0 > 90'. On the other hand, the slope of the curve increases with the increasing contribution of p wave by bringing & close to zero (Figure 7) and/or increasing El (Figure 9). A number of combinations of the four parameters have been systematically tested so as to fit the calculated distributions at Ek = 60 and 140 meV to the experimental ones measured at = 59 and 141 meV, respecti~ely.~~ We cannot find any parameter sets that realize complete fitting simultaneously at the two collision energies. Nevertheless, qualitative features of the experimental distributions appear to be reproduced by our model calculation as indicated in Figure 10: Firstly, the theoretical distributions for 60 and 140 meV show similar ascending trends with 0 at 0 I90'; secondly, the curve for 60 meV levels off beyond 90'. A detailed investigation has been made on the impact-parameter dependence of the position of the classical turning points. As a result, we have observed a specific region of the impact parameter, 6 . 6 ~ 0< b < 9.0U0, in which the distance of the corresponding turning point rapidly changes from -5no to -9ao and its polar
-e,
( 2 5 ) The values of E, adopted in the fitting calculation are round numbers of Ek estimated from TOF spectra (see Experimental Section). Since the difference between EL and the measured is less than 3 meV, every I ( 0 ) curve in Figures 5-10 is practically unchanged whether or not the round number is used.
J . Phys. Chem. 1989, 93, 3068-3077
3068
-
i . 2- j
HIS x 1 1 1
30
40
1
t He'(Z3S)
50
60
80
70
90
100
e
.
I10
120
130
I40
160
E l e c t r o n E l e c t i o n Angle / deq
Figure 10. Comparison of the observed angular distributions (symbols) of Penning electrons emitted from H2S in collision with He*(2 3S) and those determined by model calculation (line graphs). Average relative kinetic energies: 0 , 59 meV; 0 , 141 meV. In calculation, the internal angular distributionsinvolving s-, p-, and d-wave contributions are used. Set of parameters: 5 , = 0.6, cos 6, = 1.0, t2 = 1.0, cos 62 = -1.0 (see
caption of Figure 7). The relative kinetic energies are 60 meV (-), 140 meV and 40 meV (--). (-a),
angle with respect to the vector of the initial relative velocity reaches the lowest value. Furthermore, the behavior of the angular distribution curve at Ek = 60 meV is found to be essentially determined by this region. These findings can be explained by the so-called rainbow effect; Le., the deflection angle of the collision trajectory reaches its most negative value owing to the long-range intermolecular attraction.26 Incomplete agreement of the experimental distribution at = 59 meV to the theoretical one at Ek = 60 meV is attributable to the effect of collision with Ek
