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Experimental and theoretical investigation of the photoionization of hydrogen cyanide
Volume 87, number 5
CHEMICAL
EXPERIMENTAL
AND THEORETICAL
OF HYDROGEN
CYANIDE
JDrgen KREILE,
Armin
9 Apnl1982
PHYSlCS LETTERS
INVESTfGATlON
OF THE PHOTOIONIZATION
*
SCHWEIC
and Walter
THIEL
Fachbererch Pbynhlrsche Chemie der Unil ersirat Marburg, D-3550 Marburg. West Germany
Recaved 21 December 1981:m
tinal form 30 January 1982
Enpenmental Hel asymmetry parameters are reported for hydrogen cyamde. The Hcl resulrs do no: CIIIOW conclur~ons to be made on the vlbromc coupling bcrween the two lowest Ionic states. Multiple-sutterlny calcubtions predict that such conclusions may be powblr at higher photon energies. Cakuhrcd phoIoionizatlon cross sections se presented and compared wth those for acetylene.
1. Introduction The He1 photoelectron nide has been studied
spectrum
of hydrogen
by several groups [I-4].
cyaThe
and correctlon
procedures
tad previously
[7-91
experimental
condttrons
The analyzer
have been descrrbed
m de-
so that we shall only specify
the
used presently.
was operated
in rhe constant-energy
regton between 13.5 and 14.5 eV is quite complex due to strong vibronic interactions between the closely
mode with
a preselected
to a fwhm
of =30
spaced 2 211 and x 2 Zi
The number of data potnts In a gtven section of the spectrum was chosen such that the energy difference
the vtbronic accepted
coupling
mechanism
there are different
assignment
of individual
Since ADPES spectroscopic) the measured
seems to be generally
approaches
[3-S].
photoelectron
the present
paper reports
parameters
for hydrogen
photoionization
parameters
energies up to 50 eV. They experimental
the isoelectronic
are presented are compared
cross
molecule
points did not ehceed 2 meV.
time at each data point was 16 ms, and of scans was 1536 in the 13.5-14.5
section and 1-304 in the 19.0-20.0
eV
eV sectton. The
spectrum was recorded at the magtc snglc of IX 3” and at 14 angles in the range from 30 to ISO” with increments
of IO’.
for
Hydrogen
with
stated mintmum
data and with the results for
acetylene
meV
two adjacent
the number
bands [6,7], calculated
between
The sampling
He1 asymmetry
In addition,
the available
to the detailed
peaks In this region
(angulardependent
sections and asymmetry photon
_Although
data may be useful for the interpreta-
tion ofvibronic cyanide.
ionic states [3-S]
pass energy of I eV which led for the 2P~,z peak of argon.
further
cyanide
supplied
purtty
by Degusn
of 99.0%
with a
was used without
purilication.
[8,9]. 3. Theory
7. Experimental Photoiomzation The ADPES ADES
measurements
400 photoelectron
tific Ltd. The apparatus,
were carried
spectrometer
out with an
of VG Scien-
data acquisition,
data analysis,
’ Part 97 of Theory and Appticahon of Photoelectron Spectroscopy.
0 009-2614/82/0000-OOOOls
02.75
0 1982 North-Holland
parameters proxunation
representing
molecular
orbttak
scattering
conttnuum
formalism
cross sectrons u and asymmetry
fl were calculated [IO]
state by 4-3 IC
and the final state by multiplefunctions
and the numerical
tlon of the transition
m the dtpole length ap-
the imtial
moments
[I I]. The theoretical procedures
for the evalua-
have been described
[13_1. 473
Volume 87. number 5
9 Aprd 1982
CXhlICAL PHYSICS LETTERS
The computational details for hydrogen cyamde were analogous to those ior diatomic molecules [ 121 and for acetylene [9]. The esperlmental geometry [ 131 was used in conjunction with non-overlapping rouchmg spheres. The center of gravity was chosen to be the origin for the outer sphere. The muffin-tin potential was calculated from the 4-3 IG wavefunction of the neutral molecule employing a local exchange appro\imarion [ 141 wlrh the exchange parameter a = I. The resulting potential was numerical in regions I,, conslant in region II (L’n = -0.45669 au), and coulomblc m region III due to the Latter cut-offcondlrion [IS]. The multlple-scattering elpanstons were = 3 m regons I, and at I,, = 5 in rruncated at I,, rcglon 111 [I?]. The multiple-scattering continuum functlons were orthogonalized with respect to the occupied J-3 IG molecular orbltals.
4. Results and discussion The relevant parts of the He1 photoelectron spectrum of hydrogen cyamde are displayed in figs. I and 2, together with plots of/l versus the lomzatlon energy (IQ. In the 13.5-14.5 eV section, the measured asymmetry parameters vary between 0.38 f 0.06 and 0.68 f 0.05, without any obvious regular trend. In the 19.0-20.0 eV section, they range from 0.66 2 0.07 to 0.28 IO.09 showing some decrease with decreasing
-10 iz 3 -
6
z si E z
L
0 1878
1903
19 53
1928
1978
IE (EV) Flp 2. He1 photoelectron bands (a = 90”) md asymmetry parameters B for the B 2I+ lonizstlon of hydrogen cyanide as funcuons of rhe lonizsuon energy.
photoelectron energy. The observed asymmetl)r parameters at the respective vertical ionizatton energies are hsted in table I, along with the calculated values. The deviations between theory and expenment are of similar magnitude as with other molecules where discrepancies of typically 0.3-0.4 have been found [9.12] The use of ADPES data for studying vlbronic coupling is based on the following argument [6] : the excitation ofa smgle quantum ofa non-totally symmetric vibration IS forbidden during photoiomtation. If such a vtbrational
sub-band is observed it must have borrowed its intensity from another ionic state of the appropnate symmetry, and must therefore show an angular photoelectron distribution characteristic of the latter state. In the case of hydrogen cyanide, e.g. a single excitation of the bending vibration in the % ?fl ionization may be vlbromcally induced by coupling to the X LE+ state. Thus, If one follows the assignment of ref. [4], the peaks at 13.644 and 13.85 1 eV should
II II
lot
Table I
I/JVLI 1318
13
La
iLoa
1378
IE
Fd;mentd
IL
38
rig 1. Hel photoelectron bands (0 = 90”) and asymmetry parametersp for the x 2l1 and x2 X+ ionizations of hydrogen cysnrdc as functions of the lonlzatlon energy. 474
lomc state
IE (ev)
LJc\p
fltheor
X2n x2x+ ‘ij&+I
13.61 11.01 19.86
0.68 f 0.05 0.63 5 0 03 0.38 2 0 04
0.79 0.98 060
IL68
(EL’)
and theoretical He1p values for hydrogen cya_
a) AU values refer to the vertical ionization energies [a] lined
9 Aprd 1982
CHEMICAL PHYSICS LEITERS
Volume 87, number 5
exhrbit the angular distribution of the x22+ tomzation although they appear within the 2 ?ll band. Similarly, according to the more refined theoretical analYSISof ref. [S], the 13.5-14.5 eV section of the spec. trum should contain peaks both with 2 *If-type and X ‘X+-type asymmetry parameters. The measured He1 j3 vah~es in thus sectton, however, are fairly umform (see fig. lJ. The He1 asymmetry parameters for the % 2ll and A 2Z+ romzations arc obv~ously quite close to each other, m agreement wrth the theoretical prediction (see tablel). Therefore the present He1 results do not allow any conclusions on the vibronic coupling between the two lowest ionic states of hydrogen cyanide to be made. Fig. 3 shows the calculated asymmetry parameters as functions of the photon energy. The curve for the X*ll ionization rises monotonically with Increasing photon energy and is similar to the corresponding
curve for the isoelectronic acetylene molecule [9] whde the /I values for the two 2X’ lonrzations depend on the photon energy in a more complicated way. Contrary to the He1 case, the calculated asymmetry parameters for the %‘-ll and x ?X+ lomzations differ IKN
1
strongly at other photon energies, e g. HeII.Our theoretical results thus suggest that vtbronic coupling effects may be observed m He11 ADPES measurements with hydrogen cyanide. Due to the low intenstttes involved, however, such an investigation is not feasible with our present expertmental setup. Fig. 4 compares the calculated photoronizatton cross sections for the first three ionizations of acetylene and hydrogen cyanide. The curves for the z ‘ll ionizatrons are obviously quite similar whde those for the ?Z? ionizationsdtffer apprecrably in the low-energy region. In acetylene, a o,-type shspe resonance causes the pronounced maximum m the A ‘Xi curve around 19 eV which has no counterpart in therein curve due to the usual drpole selection rules. In hydrogen cyanide, there is no symmetry-related distinction between the ?Z+ iontzattons, and the x 2C+ and E 2Z’ curves are sunilar m showmg only small humps tn the low-energy region. Wrth regard to these qualitattve features, the 3x+ photoromzation cross sectrons for acetylene and hydrogen cyanide are thus reminiscent of those for the isoelectromc molecules rutrogen and carbon monoxide [I?, 16- 191. In the case of hydrogen cyanide, no other theoretical or experrmental data seem to be avatlable for comparison with the calculated cross sections(fig. 4). As
n
ij
2:’
1%.
10 -
10
20
30 ro hwleV1
50
Fg 3. Calculated asymmetry parametersior hydrogen cyanide WINS photon enerey.The measuredHe1 valuesare in-
cluded.
20
30
LO
20
30
LO
nl,llevi Tip. 4. Calculated photoionuanon crossYXIIOIIS for acetylene and hydrogen cyanide versusphoton energy The ekperlmental dats for acetylene 1201 are Included.
475
Volume87. number 5
CHEMICALPHYSICS LETTERS
for acetylene, the results for the % ‘ll, ionization have been dtscussed previously [9]; the rapid vanation of theexpenmerttalvahtesarottnd 14eVisdue toanautotonization process [9,20] not included in the present theorettc~ formalism. The calculated cross sections for thexZSi andEilG ronuations are too high when compared to recent expenmental data [20] and to discrete-basis-set cakulat~ons [ZO, 311. The extstence of a o,,-type shape resonance close to threshold (maximum m the x ‘Z: curve, see fig. 4). however, is confirmed by these studres [20,2 i 1, Acknowledgement Thts work was supported by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie. The caiculattons were carried out at the TR 440 computer of the UmversrtZt Marburg We are grateful to Professors Bradshaw and Langhoff for sendmg preprmts of refs. [7_0,2. I].
References
[I 1 D.W.Turner, C Baker. AD. Baher and CR Brundle, blolcc~lar phoIoefcc+ronspecuosEopy (~ibq.~cw~ork, 1970). (2 [ J.hl HOllas and T A. Sutherley, Mol. Pnys 24 (1972) 1123.
9 April 1982
[ 31 D C. Frost, S.T. Lee and C A. hlcDoweU,Chem. Phys. Letters 23 (1973) 472. 141 C.Fridh and L.Asbrink, J. Electron Spectry. 7 (1975) 119. {51 H. Koppel. L.S. Cederbrum, IV. Domcke and W. van
Niessen.Chem. Phvs. 37 II9791 303. Phy& Scr& l&(1979) II. I71 J Kreileand A. Schweig. J. Electron Spectry. 20 161 \V. Do&e.
(1980) 191. [S] J. Krerle and A. Schwei@,Chcm.Phys. Letters 69 (1980) 71 19J J f&tie, A. Schweig and w. Thiel. Cbem. Phys. Letters 79 (1981) 547. [ 101 R. Dttchfiefd. W.3. Hehre and J.A. Pople, J. Chrm. Phys. 54 (1971) 7’4. [lil D.Dllland J.L.Dehmer, J.Chem.Phys.61 (1974)69X [ 121\I’. Thhlel,Chem. Phys. 57 (1981) 217. [I31 C.C.Cosram, J.Chsm. Phys 29 (1958) 864. 1141 J.C.Sktter,Phys Rev.81 (1951)385 [ ISJ R. Latter, Phys. Rev. 99 (1955) 510 [ 161 J W. Da=xport. Phys. Rev. Letters 36 (1976) 945. [ I71 E,\V. P1ummer.T. Gustafsson, W. Cudat and D.E Eastman. Phys. Rev. AIS (1977) 2339 1181 TN. Rescgno, Cr. Bender. B.V. hkKoy and P IV Langhoff, J. Chem. Phys. 68 (1978) 970. [ 191 J.L. Drhmer. D. Ddl and S. %iIxe, Phys. Rev Letters 13 (1979) 10031. IZO] P.\V. LanghofZ, B.V. McKay, R. Unk~ and A M. Bradshav,Chem. Phys. Letters 83 (1981) 270. [211 LE. Machsdo, E P. Leal. C. Cszmak,B.V. McKay and P.\v. Langhofi, to be pubhshed.
CHEMICAL
EXPERIMENTAL
AND THEORETICAL
OF HYDROGEN
CYANIDE
JDrgen KREILE,
Armin
9 Apnl1982
PHYSlCS LETTERS
INVESTfGATlON
OF THE PHOTOIONIZATION
*
SCHWEIC
and Walter
THIEL
Fachbererch Pbynhlrsche Chemie der Unil ersirat Marburg, D-3550 Marburg. West Germany
Recaved 21 December 1981:m
tinal form 30 January 1982
Enpenmental Hel asymmetry parameters are reported for hydrogen cyamde. The Hcl resulrs do no: CIIIOW conclur~ons to be made on the vlbromc coupling bcrween the two lowest Ionic states. Multiple-sutterlny calcubtions predict that such conclusions may be powblr at higher photon energies. Cakuhrcd phoIoionizatlon cross sections se presented and compared wth those for acetylene.
1. Introduction The He1 photoelectron nide has been studied
spectrum
of hydrogen
by several groups [I-4].
cyaThe
and correctlon
procedures
tad previously
[7-91
experimental
condttrons
The analyzer
have been descrrbed
m de-
so that we shall only specify
the
used presently.
was operated
in rhe constant-energy
regton between 13.5 and 14.5 eV is quite complex due to strong vibronic interactions between the closely
mode with
a preselected
to a fwhm
of =30
spaced 2 211 and x 2 Zi
The number of data potnts In a gtven section of the spectrum was chosen such that the energy difference
the vtbronic accepted
coupling
mechanism
there are different
assignment
of individual
Since ADPES spectroscopic) the measured
seems to be generally
approaches
[3-S].
photoelectron
the present
paper reports
parameters
for hydrogen
photoionization
parameters
energies up to 50 eV. They experimental
the isoelectronic
are presented are compared
cross
molecule
points did not ehceed 2 meV.
time at each data point was 16 ms, and of scans was 1536 in the 13.5-14.5
section and 1-304 in the 19.0-20.0
eV
eV sectton. The
spectrum was recorded at the magtc snglc of IX 3” and at 14 angles in the range from 30 to ISO” with increments
of IO’.
for
Hydrogen
with
stated mintmum
data and with the results for
acetylene
meV
two adjacent
the number
bands [6,7], calculated
between
The sampling
He1 asymmetry
In addition,
the available
to the detailed
peaks In this region
(angulardependent
sections and asymmetry photon
_Although
data may be useful for the interpreta-
tion ofvibronic cyanide.
ionic states [3-S]
pass energy of I eV which led for the 2P~,z peak of argon.
further
cyanide
supplied
purtty
by Degusn
of 99.0%
with a
was used without
purilication.
[8,9]. 3. Theory
7. Experimental Photoiomzation The ADPES ADES
measurements
400 photoelectron
tific Ltd. The apparatus,
were carried
spectrometer
out with an
of VG Scien-
data acquisition,
data analysis,
’ Part 97 of Theory and Appticahon of Photoelectron Spectroscopy.
0 009-2614/82/0000-OOOOls
02.75
0 1982 North-Holland
parameters proxunation
representing
molecular
orbttak
scattering
conttnuum
formalism
cross sectrons u and asymmetry
fl were calculated [IO]
state by 4-3 IC
and the final state by multiplefunctions
and the numerical
tlon of the transition
m the dtpole length ap-
the imtial
moments
[I I]. The theoretical procedures
for the evalua-
have been described
[13_1. 473
Volume 87. number 5
9 Aprd 1982
CXhlICAL PHYSICS LETTERS
The computational details for hydrogen cyamde were analogous to those ior diatomic molecules [ 121 and for acetylene [9]. The esperlmental geometry [ 131 was used in conjunction with non-overlapping rouchmg spheres. The center of gravity was chosen to be the origin for the outer sphere. The muffin-tin potential was calculated from the 4-3 IG wavefunction of the neutral molecule employing a local exchange appro\imarion [ 141 wlrh the exchange parameter a = I. The resulting potential was numerical in regions I,, conslant in region II (L’n = -0.45669 au), and coulomblc m region III due to the Latter cut-offcondlrion [IS]. The multlple-scattering elpanstons were = 3 m regons I, and at I,, = 5 in rruncated at I,, rcglon 111 [I?]. The multiple-scattering continuum functlons were orthogonalized with respect to the occupied J-3 IG molecular orbltals.
4. Results and discussion The relevant parts of the He1 photoelectron spectrum of hydrogen cyamde are displayed in figs. I and 2, together with plots of/l versus the lomzatlon energy (IQ. In the 13.5-14.5 eV section, the measured asymmetry parameters vary between 0.38 f 0.06 and 0.68 f 0.05, without any obvious regular trend. In the 19.0-20.0 eV section, they range from 0.66 2 0.07 to 0.28 IO.09 showing some decrease with decreasing
-10 iz 3 -
6
z si E z
L
0 1878
1903
19 53
1928
1978
IE (EV) Flp 2. He1 photoelectron bands (a = 90”) md asymmetry parameters B for the B 2I+ lonizstlon of hydrogen cyanide as funcuons of rhe lonizsuon energy.
photoelectron energy. The observed asymmetl)r parameters at the respective vertical ionizatton energies are hsted in table I, along with the calculated values. The deviations between theory and expenment are of similar magnitude as with other molecules where discrepancies of typically 0.3-0.4 have been found [9.12] The use of ADPES data for studying vlbronic coupling is based on the following argument [6] : the excitation ofa smgle quantum ofa non-totally symmetric vibration IS forbidden during photoiomtation. If such a vtbrational
sub-band is observed it must have borrowed its intensity from another ionic state of the appropnate symmetry, and must therefore show an angular photoelectron distribution characteristic of the latter state. In the case of hydrogen cyanide, e.g. a single excitation of the bending vibration in the % ?fl ionization may be vlbromcally induced by coupling to the X LE+ state. Thus, If one follows the assignment of ref. [4], the peaks at 13.644 and 13.85 1 eV should
II II
lot
Table I
I/JVLI 1318
13
La
iLoa
1378
IE
Fd;mentd
IL
38
rig 1. Hel photoelectron bands (0 = 90”) and asymmetry parametersp for the x 2l1 and x2 X+ ionizations of hydrogen cysnrdc as functions of the lonlzatlon energy. 474
lomc state
IE (ev)
LJc\p
fltheor
X2n x2x+ ‘ij&+I
13.61 11.01 19.86
0.68 f 0.05 0.63 5 0 03 0.38 2 0 04
0.79 0.98 060
IL68
(EL’)
and theoretical He1p values for hydrogen cya_
a) AU values refer to the vertical ionization energies [a] lined
9 Aprd 1982
CHEMICAL PHYSICS LEITERS
Volume 87, number 5
exhrbit the angular distribution of the x22+ tomzation although they appear within the 2 ?ll band. Similarly, according to the more refined theoretical analYSISof ref. [S], the 13.5-14.5 eV section of the spec. trum should contain peaks both with 2 *If-type and X ‘X+-type asymmetry parameters. The measured He1 j3 vah~es in thus sectton, however, are fairly umform (see fig. lJ. The He1 asymmetry parameters for the % 2ll and A 2Z+ romzations arc obv~ously quite close to each other, m agreement wrth the theoretical prediction (see tablel). Therefore the present He1 results do not allow any conclusions on the vibronic coupling between the two lowest ionic states of hydrogen cyanide to be made. Fig. 3 shows the calculated asymmetry parameters as functions of the photon energy. The curve for the X*ll ionization rises monotonically with Increasing photon energy and is similar to the corresponding
curve for the isoelectronic acetylene molecule [9] whde the /I values for the two 2X’ lonrzations depend on the photon energy in a more complicated way. Contrary to the He1 case, the calculated asymmetry parameters for the %‘-ll and x ?X+ lomzations differ IKN
1
strongly at other photon energies, e g. HeII.Our theoretical results thus suggest that vtbronic coupling effects may be observed m He11 ADPES measurements with hydrogen cyanide. Due to the low intenstttes involved, however, such an investigation is not feasible with our present expertmental setup. Fig. 4 compares the calculated photoronizatton cross sections for the first three ionizations of acetylene and hydrogen cyanide. The curves for the z ‘ll ionizatrons are obviously quite similar whde those for the ?Z? ionizationsdtffer apprecrably in the low-energy region. In acetylene, a o,-type shspe resonance causes the pronounced maximum m the A ‘Xi curve around 19 eV which has no counterpart in therein curve due to the usual drpole selection rules. In hydrogen cyanide, there is no symmetry-related distinction between the ?Z+ iontzattons, and the x 2C+ and E 2Z’ curves are sunilar m showmg only small humps tn the low-energy region. Wrth regard to these qualitattve features, the 3x+ photoromzation cross sectrons for acetylene and hydrogen cyanide are thus reminiscent of those for the isoelectromc molecules rutrogen and carbon monoxide [I?, 16- 191. In the case of hydrogen cyanide, no other theoretical or experrmental data seem to be avatlable for comparison with the calculated cross sections(fig. 4). As
n
ij
2:’
1%.
10 -
10
20
30 ro hwleV1
50
Fg 3. Calculated asymmetry parametersior hydrogen cyanide WINS photon enerey.The measuredHe1 valuesare in-
cluded.
20
30
LO
20
30
LO
nl,llevi Tip. 4. Calculated photoionuanon crossYXIIOIIS for acetylene and hydrogen cyanide versusphoton energy The ekperlmental dats for acetylene 1201 are Included.
475
Volume87. number 5
CHEMICALPHYSICS LETTERS
for acetylene, the results for the % ‘ll, ionization have been dtscussed previously [9]; the rapid vanation of theexpenmerttalvahtesarottnd 14eVisdue toanautotonization process [9,20] not included in the present theorettc~ formalism. The calculated cross sections for thexZSi andEilG ronuations are too high when compared to recent expenmental data [20] and to discrete-basis-set cakulat~ons [ZO, 311. The extstence of a o,,-type shape resonance close to threshold (maximum m the x ‘Z: curve, see fig. 4). however, is confirmed by these studres [20,2 i 1, Acknowledgement Thts work was supported by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie. The caiculattons were carried out at the TR 440 computer of the UmversrtZt Marburg We are grateful to Professors Bradshaw and Langhoff for sendmg preprmts of refs. [7_0,2. I].
References
[I 1 D.W.Turner, C Baker. AD. Baher and CR Brundle, blolcc~lar phoIoefcc+ronspecuosEopy (~ibq.~cw~ork, 1970). (2 [ J.hl HOllas and T A. Sutherley, Mol. Pnys 24 (1972) 1123.
9 April 1982
[ 31 D C. Frost, S.T. Lee and C A. hlcDoweU,Chem. Phys. Letters 23 (1973) 472. 141 C.Fridh and L.Asbrink, J. Electron Spectry. 7 (1975) 119. {51 H. Koppel. L.S. Cederbrum, IV. Domcke and W. van
Niessen.Chem. Phvs. 37 II9791 303. Phy& Scr& l&(1979) II. I71 J Kreileand A. Schweig. J. Electron Spectry. 20 161 \V. Do&e.
(1980) 191. [S] J. Krerle and A. Schwei@,Chcm.Phys. Letters 69 (1980) 71 19J J f&tie, A. Schweig and w. Thiel. Cbem. Phys. Letters 79 (1981) 547. [ 101 R. Dttchfiefd. W.3. Hehre and J.A. Pople, J. Chrm. Phys. 54 (1971) 7’4. [lil D.Dllland J.L.Dehmer, J.Chem.Phys.61 (1974)69X [ 121\I’. Thhlel,Chem. Phys. 57 (1981) 217. [I31 C.C.Cosram, J.Chsm. Phys 29 (1958) 864. 1141 J.C.Sktter,Phys Rev.81 (1951)385 [ ISJ R. Latter, Phys. Rev. 99 (1955) 510 [ 161 J W. Da=xport. Phys. Rev. Letters 36 (1976) 945. [ I71 E,\V. P1ummer.T. Gustafsson, W. Cudat and D.E Eastman. Phys. Rev. AIS (1977) 2339 1181 TN. Rescgno, Cr. Bender. B.V. hkKoy and P IV Langhoff, J. Chem. Phys. 68 (1978) 970. [ 191 J.L. Drhmer. D. Ddl and S. %iIxe, Phys. Rev Letters 13 (1979) 10031. IZO] P.\V. LanghofZ, B.V. McKay, R. Unk~ and A M. Bradshav,Chem. Phys. Letters 83 (1981) 270. [211 LE. Machsdo, E P. Leal. C. Cszmak,B.V. McKay and P.\v. Langhofi, to be pubhshed.