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The low-lying states of silylene
Volume 107, number 4,5
8 June 1984
CHEhiiCAL PHYSICS LETTERS
THE LOW-LYLNG STATES OF SILYLENE
J.E. RICE and N.C. HANDY University Chemical Laboratory.
Received 22 February
Lettsjicld Rood. Gutbridge
CK? IEW,
UK
1984; in foal form 29 hlarch 1984
hfC SCF calculations have been performed on the&! surfacesof the t At ,3Bt, tB1, JA2, *AZ, 2 tA1.3.%, and 3B2 states of sifylene. These states are important in the collisional removal of Si by molecular hydrogyn. Of parricullr mtwst are the barriers in the 3B1 and ’ I31 surfaces,which are substantives reduced on tntersction xvitb 3.~2 and 1 .+2 in C, symmetry, and the small-angle minima of the latter states.
I. Introduction
tive orbit&. F&owing the suggestion of Roos [St. improved cakxdations were also performed by adding the 7at and 3bt orbitals to the active space. States considered were 3B,, 3A2 and ;B2, which correlate with Si(3PJ)+ Hl,rind l-41, ‘B*,:! “Al and lAz_ which correlate with Si( ID) + H,. The j.tt srare was also considered. AU calculationswere performed in C,, geometry.
There has been increasing interest recently in the low-lying states of silylene. The first two states are known to be the ‘A, and 3B,, with the ‘A, the iowest, as determined by Kasdan et al. [I 1 using photoelectron spectroscopy on SiHz _Schaefer and Meadows 13-1carried out a theoretical calculation for the s~g~e~-t~pl~t separation, which gave good agreement with experiments. Husain and Norris [3] have reported rate data for the collisional removal c~S~((~PJ), (“D), (IS)) by moiecukr hydrogen, Si + H, -+ SiH + H ,
2. Vertical transition
Vertical transitions energies were calculated at the experimental geometry of the ground state (I Ai): Si-H = 1.516 ii and f3 = 92.1” [6]. The larger XIIVC space was used with a double-zeta plus polarisation basis set (Si( 1 is7pld~6s4pld~ and H(4s~p~~slp}~ developed from that of Dunning [?] and Nuzkaga [S], with q&G) = 0.4 and 0rJH) = 1 .O and a hydrogen scaling factor of 1.2. Some Rydbeg functions (a,($) = 0.03 and r+,(Si) = 0.02) were added because it apperued possibfe thak some of rhe hider states may need them, although the results indicate that it is xhe smallest exponents, a,(%) = 0.09932 and o4,(Si) = 0.09699, of the standard basis which are more important. The results of these calculations xre gven in table I. The ordering of the lowest seven states agrees with the results of Wirsam. The need for a m~ti~on~gur~tion deception of these states is weli known by com-
(11
and they constructed a correlation diagram through the states of SiH,, using the results of some ab initio calculations of Wirsam 141. Wirsam performed configuration interaction calculations for various angles 6 (60” G 8 G 180”) and bond lengths. In view of the ~provement of ab initio procedures in the last ten years, in particufar the advent of MC SCF calculations and gradient methods, we decided to repeat these calculations, optimising bond lengths for various bond angles. Furthermore, some of the states have interesting small-angle minima which have not been previously investigated. The MC SCF method used was CAS SCF, with the Si Is, 2s and 2p orbit& as core orbit& and the valence orbitals4a1.2bZ.2bl. 5aI,3bz and 6a, asac0 009~2614/84/S 03.00Q Elsevier Science Publishers ~o~h-Hol~~d Physics Publi~~ng Division)
energies
B.V.
365
Volume
107. number 4.5
Table 1 The predicted
CHEMICAL
PHYSICS
order and relative energies in eV of the exited
8 June 1984
LETTERS
states of silylene
zi the experimental
geometry
Energy
Main confgwations
Energy
1 ‘BZ
7.305
(0_99)2b$Sa13bz
7.871
23B2
6.827
(0.90)2b#a12b:
State
of the ground
state
[4] a)
+ (0.37)2biSat3b2 + (0.13)2b%Zb:4a13b2
13A1
5.998
(0.98)2b$5a16al
8.940
2’A,
5.459
(0.94)2b;Zb:
5.248
- (0.16)Sa:Zb: - (0_13)2bz5a: + (O.l4)2b$a16al + (O.l0)2b:4alZbzSa13bz
l’A2
4.636
(2)
(0_96)2b2Sa:2bt
4.276
- (0.12)5a~4ai2b12b26a1 + (O.l2)5at2bt2b26at
1 ‘AZ
4.233
3.887
(0.96)2b25a:2bl + (0.12)5a12b12b26al
2.138
l’B,
2530
(0.97)2bs5a12b,
l3B1
1.096
(0.98)2a;Saltbl
0.680
X’A,
0.0
(0.97)2b$Sa:
0.0
- (0.17)2b;Zb; a) Energies read from the graph of ref. j4 1.
parison with calculations on CH2, but in addition it is noticed that the 6a, orbital is important for some states, as must follow from the increased proximity
of the higher orbitals with second-row atoms. The energies of the first five excited states relative to the ground state are consistently 0.4 eV above the results of Wirsam (Wirsam’s calculations used a minimal basis set and included electron correlation by performing a Cl calculation from the ground-state orbitals with all excitations from 4al, 2b2, 5al + 2bl, 6al, 3b2 and 7al). The energies of the higher states are markedly different. Wirsam predicted the 3A1 energy to be 8940
366
eV above the ground state, com-
pared
to the value of 5.998
eV determined
in this
work. This state is well described by one configuration and thus the minimal basis set of Wirsam seems unable to fully describe the orbitals of these higher states. Sauer et al. [9] have recently reported semi-empirical results for the silylene system. The order of the
first four states is the same, but the order of the next sixstatesispredicted to be 3Al,1A2,3B2,2 ‘A,, 2 3B2 and lB2, the 3A1, 2 ‘Al, 2 3B2 and lB2 states being represented by configurations different from those found in the present study. The relative energies of the states are therefore also widely different.
Volume 107, number 4.5
Since reaction (1) is likely to produce excited states of silylene initiaily, the energy differences between the ~~1~~~~~~ structures are of particular interest. For each of the states lAI, %t , “AZ, 3A2 and f.B, , the Dunning-Huzinaga basis with potarisation functions was used with the six active orbit&. The
bond length was optimised for many bond angles to produce the potential energy curves in fig. I ~The optimised e~u~brium structttre of each state is given in tabie 2. The larger active space was used for the 2 IAt , 3A, and %3, states. For the 2 IAt state, a smallexponent p function (or,(%) = O.OZ>was added to the basis set, and for the 3A1 and 3B2 an s function (cr(Si) = 0.03) was also added. The curve for the 2 IA, state is displayed in fig- 2. Also included for comparison in this graph are a few points of the t A,, 3A7 and 1A, surfaces, also calculated at this accuracy.%e morr$complex 3At and 3B2 surfaces are displayed in figs. 3 and 4, The Sit 1I>) -t H2 energies are nor equivafent
8 June 1984
CHEMXCAL PHYSICS LETTERS
for all the correlating
ine~u~v~ence of the d orbit&, since the symmetry of the Si atom cannot be constrained ta D,, in our CAS SCF program. The optimised structures for a8 the states with &helarger active space and basis set are given in table 3. These calculations are compared with those of Wisam. We now discuss the ~d~~du~ states in more detail.
4. The first three states:
lAl,
3ES1and II),
Experimentat information is ~no~v~ on the equilibrium geometry of these states, and they have also been studied by S&t&r and coworkers [Z,iOl. The groun stats is I At : the D and x orbitals are sufficient& far
apart for the singlet state to be more energetically stable than the triplet, unlike the valence isoelectronic radical rneth~~e~e. The ~~~o~o~~~~rat~o~ dexription is also confirmed for the lA,, whereas one con@ &ration describes the >Bl and I Bl states over the regions shown. Probably the best calculations on these three states are by Calvin et al. [ 101, who performed
double-zeta plus polatisarion basis calculations with S~~~on~vo(tAt~orone(?3~, fBt)rsference(sj. The results of these workers and Wirsam and our own
states (I AII i Bk) ffigs. I and 2). This is due to khe
Fig. 1. Potential energy curves for the efectrunic states of tigiene caicuktslted u&g the zi.active-orbm+space metksod. fhe 3As BF&2 * A1 curves cakulared with the eight-active-space method are scaled here for comgarixm. Energies in hatxee.
Volume 107, number 4.5 Table 2 ~u-~~urn
CHEMICAL PHYSICS LETTERS
structures calculated with the si!-active-space
state
Main cmlfiitions
method Bond angle (de& H-5-H
Bond length (A) Si-H
Energy (ev)
3,238’
2.50
120.2
I.519
2.09
123 j6f
1.487 [S]
I.93 [6]
12.8
3.401
1.63
118.3
1.497
0.72
9.35
1540
0.0
92.1 [6]
1.516 f6]
0.0
13.4
(~.98}2b*5a~2bt
8 June 1984
+ (ti.J 1)2bz3b$2b, + (0.11) kxture
“Bl exp.
3A2
(0.98)lb&2b, + (O.l4)2b~2b,6a~ - (0.1 1)2b25a;2bt3b;
3B1 X’At
a)
(0~9)2b~Sat2br (0.97) 2b$Sa:
- (O.i9)2b~2b~ esp.
al This con&uration
does not include 4ai.
Fig. 2. Potential energy curves for the electronic in hartree.
368
states of silylene calculated using the e~t~ctiv~rbit~~~a~
method.
Energies
Volume
107. number
CHEMICAL
4.5
-289
PHYSICS
8 June
LETTERS
1984
9
Fig. 3. Potential energy curves face. Energies in harlree.
for the 3A1 state of silylene.
The dominant
confwrations
are shown
for each section
of tie sur-
LO:2 b; 50,3 b,
+mixture(see
Fig. 4. Potential energy
curve for the 3Bz state of silylene. The dominant
results for the equilibrium structures are compared in table 4. The X lA,-3B, splitting has not been well defied experimentally, but Schaefer [lo] feels that an analy-
text)
confiurations
are shown.
Energies
in haruee.
sis of his theoretical results and Lineberger’s experiments [ 11 suggests a value near 20 kcal/mole (0.867 eV). An MR SDCI calculation will be necessary to improve upon our result of 0.760 eV. (An equivalent cal 36s
Volume 107. number 4.5 Table 3 Equilibrium
State
3B2
strucbures
CHEMICAL
calculated with the eight+xtive-space
hlain confirations
(0.96)2b$5a13b2
PHYSICS
8 June
LETTERS
1984
method length
Energy
(A)
Bond angle (deg) H-Si-H
Bond Si-H
this work
ref. [4]
this work
ref. [4]
this work
ref. [4]
77.95
1.686
1.667
5.697
6.244
2.104
-
5.099
1.703
-
3.163
1.489
1.566
3.716
2.996
67.4
3.470
1.746
2.572
3.858
125.62
1519
1577
2.122
1.624
65.7
3.330
1.736
1.826
3.391
117.1
123.63
1.496
1.551
0.759
0.207
92.7
97.46
1534
1.582
0.0
0.0 a)
92.1
(W
+ (0.17)6a12b25a:
3A*
(0.91)5a:2b23bz
54.1
- (0.26)2b;5a16ar - (O.l6)6a:
2b23b2
+ (0.14)2b:5ar6al + (0.10)5a16at3b$
-
180
(0.97)2b;5ar6al + (0.15)2b,5a16ar3ba
21Ar
162.5
(0_56)2b:Sa;
180
+ (0_77)2b;2b: - (0.24)2bz6a:
‘442
12.6
(0.98)5a:2br2b2 + (0.13)6a;2b12b, - (0.10)
‘Bl
mixture
120.7
(0.98)2bz5a12bl + (0.11)4a12b~5ar2b16al
3A:
(0.98)5a:2b12b2
12.6
- (O.l4)6a:ZbrZba
“Bl
(0.98)2b:Sar2br
X’A,
(0.97)2b:5a: - (O.i1)2bf2b:
a) Ground-state
370
energies:
-290.065223
(this work) and -289.91422
(ref.
[4])
hartree.
CHEMICAL PHYSICS LETTERS
Volume 107, number 4.5
8 June 1981
Table 4 Equilibrium structures of the three lowest-lying states of silylene (‘At, 3Bt and ’ Bt)
state
Predicted geomeuies (bond length (.X)/bond aTIe (de_e))
cxp. [6]
ref. (41
ref. IlO]
this work
lB1
l-487/123
3Rr X’A,
l/516/92.1
1.486/1235 1.471/117.6 1.508j94.3
1.468/122.6 1.466/118.1 1.505193.9
1.519/120.1 1.497/118.3 1.534j92.75
Predicted energies relative to the ground state (ev) a)
exp. [6]
‘BI 3R1 X’A,
1.925 (0.0)
ref. [4]
ref. [ 101
this work
2.299
2.168
2.120
0.807
0.728
(0.0)
a) Totd energies (in hartree) for the X ‘A, state are -290.04890
culation on CH2 for the 3B1-1Al splitting yielded 0.425 eV [ 1 I], compared to an experimental value of 0371 eV [12].) From tables 2,3 and 4, there are discrepancies between the theoretical predictions and the experimental determinations for the bond angles and lengths. Whereas the SCF method [2] yields short bond lengths, the CAS SCF method is known to yield bond lengths which are too long unless a large active space is used. With the six/eight active space, the ‘A1 bond length is too long by 0.024/0.018 A. However, such discrepancies will not affect the overall shape of the potential energy surfaces we are discussing. The IA, curve is well represented by two contigurations along its length, from the separate Si(tD) + H?(lZi) through its minirnum at 92.1° to its linear 1%: structure. The 3B,, which correlates with Si(3PJ) + H2(‘Zi), is seen to have a maximum (e-82 eV) at approximately 32.5” before dropping to its minima. It is well represented by 2bs5a12bt for 0 > 325”. but needs 5ai6at2bt to describe the dissociated Si(3PJ) + H-,(1X:) for 0 =G30”. Similarly,the IB,, which correlates with Si( lD) + H2( 1I$), has a maximum (G35 1 eV) at approximately 40”, being well represented by 2bgSat2bt for 0 > 45O and 5a:6a12bt for e G 350.
0.759
(O-0) (ref. [4]), -290.10268
5. The small-angle
(0.0)
(ref. [lo]) and -290.065223
states:
(this ~vork).
3 A2 and 1 A2
These states, predominantly represented by 5a$?b ,2b 7,, are valence isoelectronic with the 3A2 and lA2 states of CH2 and NHf. This state of NH; has been shown to have small b&d angles in DZP Cl calculations of Schaefer and co-workers [ 131, and this phenomenon was rather straightforwardly esplained with reference to the Walsh diagram [ 141. It must be expected, therefore, that the 3A2 and JA2 states of SiH2 wiU ha;e small bond angles, if local . muurna exrs:. From table 2, using the six-active-space model, the bond angles for the 3A7_ and lA2 states are 12.8” and 13.4O, and for the eight-active-space model 12.6O for both. The 3A7_ minimum is 0.012 eV lower than the reactants Si(3PJ) + Hz at the six-active-space level, but is higher at the eight-active-space level (0.303 eV). The lA7 state, however, is 0.016 eV below the reactants Si(jD) + Hz at the six-actiw-space level and has the same energy as the reactants (0.000 eV) at the eight-active-space level. From the tables it is seen that both states are predominantly represented by the main configuration although for the 3A, the configuration 6a:2bt2bz has coefficient 0.14. The bond lengths of these states are long, and the states may be viewed as complexes (eight-active-space results):
371
Volums
107. number
CHEMICAL
4,s
PHYSICS
LETTERS
8 June 1984
Table =
Impel -xx confgurations
Angie
Bond
(aes)
length
Confwurations
Energy relative to minimum (ev) 2bfZbj
2bz6a:
2b:Sai
0.14
0.94
-0.07
0.14
1.364
0.21
0.93
-0.10
0.07
0.384
1.489
0.56
0.71
-0.24
O.O!
0.0
1.485
0.66
0.66
-0.30
(A)
2b$5a:
100
1.519
130
1.492
1625 lS0
Si
0.731
across she 2 LA, surrace
x
0.162
X
lA2
Due to the extreme values for the bond lengths and bond angles, we must expect that these predictions will change by a significant percentage if larger calculations are performed. The 3A1 surface plays an important role in C(3PJ) + Hz collisions to form the ground 3Bl state of CH,. Schaefer and co-workers [ 141 could find no minimum on the 3A, surface, but found that the lowest point of intersection of 3A;, and 3B, to be only 9 kcal/ mole above the C(3P;) + Hz reactants. Because such an intersection
is avoided in C, symmetry,
this sug-
gested little or no barrier to the direct formation of the 3Bl state of CH2. This problem has recently been examined in detail by Harding [ 151, who has looked at Cs geometry and the effect of basis sets. He concludes that the crossing is weakly avoided with a barrier of the order of 2.5 kcal/mole. Furthermore, he found a very shallow 3A, minimum (depth -0.25 kcal/mole) with (apparently) a similar geometry to the 3Az geometry we .ind for SiH2. A similar picture .vill hold for SiH,. We fmd the lowest point of C,, intersection of 3B1 and 3A7 to be at Si-H = 1.a275 A and 0 = 59.3”, with an energy 21.2 kc_‘,‘mole (0.917 eV) above Si(3P,) + Hz, using 01:~ largest basis set and active space. (This result was determined by calculating the energy at each of a grid of points (bond angle/bond length) for the two 372
0.22
states (3B,, 3A,) and finding the lowest energy at which the energy difference between the two states was less than 0.000003 hartree.) This means that the barrier to the formation of SiH,(3Bl) from Si(3PJ) + Hz is also much smaller (five times) via the 3 A2 state than along the 3B, surface. For the ‘El and 1A-, states we expect the situation to be similar, but we have not investigated this crossing.
Si
3A2
6.The21A1
state
This state was considered with the larger active space. We must expect it to be a low-lying valence state, due to the presence of 2bs2bf in the description of the X IAl state. In table 5 we show the decreasing importance of the 2bs3_bf CSF as 0 increases from 100” to lSO”, compensated by an increase in the significance of ZbsSa: and lb$6a:. The potential well at 162.15~ is wide and shallow (0.223 eV), the energy only rising rapidly from 130’ to 100°. Previous calculations on methylene determine the 2 1 Al state to be only slightly non-linear [ 161. Bauschlicher and Yarkony [ 161 used a DZP CI method,with the two references 3ailb$ and lb:lbs. Because we find a third configuration to be important in SiH2,we recomputed the X3Bl, 1 lAt and 2 lAl states of CH,. The results are reported in table 6. These determined the minimum of the 2 1Al at 17 1 -lo, not at linearity, with the 1b$4a: CSF having a coefficient of 0.049. The 6a, orbital is more significant for SiH?, as must be expected from a comparison of the internuclear distance correlation diagrams. The basis functions with smallest exponents did not enter significantly into the orbitals, and it therefore seems that the 2 1A, state of SiH2 is a true valence state.
8 June 198-l
CHEMICAL PHYSICS LETTERS
Volume 107. number 4.5
Table 6 Equilibrium structures and energies for the 3 B I, 1Al and 2 1 A, states of methylene
State
2 ‘A1
this work
ref. [ 161
1.081/171.0
1.07/180
1.128/102.0
X’Ar
XaB
Ener_ey(eV)
Bond length (A)/bond angle (deg)
1
esp.
1.17/103-.4
1.098/131.7
The 3At state, which
by a number
with Si(3PJ) + 2H, was considered using eight active orbitals, together with the largest basis set _It is predominantly described by two configurations across the potential surface, as shown in fig. 3. The 2b$5a16al CSF is dominant in the region 120° < 0 < ISO”, the minimum being at linearity with Si-H = 1.703 A. The other important CSF, 5a:2b23b2, dominates in the region 30” < 0 < 70”, with a local minimum at 54.7” with Si-H = 2.104 A, 2 eV above the 2bt5a16al minimum. There is an avoided crossing in the region 70° < 0 < 120°, where the bond length will change rapidly. The configuration description also changes in the range 20” < B < 30”, becoming predominantly 4a:5a:6a ,7a 1 between O” < 0 G 20°. Due to the problem of high symmetry, our programs give discontinuous results at 180°, but indications are that 3fls, 1X; and IA lie very close in energy. ( 1 Zl lies 0.574 eV above P I$, which lies 0.043 eV above l As with the six-active calculation in C2v geometry.) correlates
8. The 3B2 state This state, whi-h .orrelates with Si(3PJ) + H,(lZi), was considered with the largest basis set ark eight active orbitals. The state is well described by one configuration, 4a:5af6a12bz, for 0” < 0 < 40’. the energy rising rapidly in this region. A structure with a very long bond length is found between SO” G 8 < 180”, with a constant energy of -289.8557 hartree across the surface. This structure can be viewed as a complex from which the hydrogen atoms are dissociating to give Si + 2H, and is described
H-Si-H
ref. 1161
2.832
2.9
-
0.0
0.393 0.0
0.425 0.0
1.11/102.4 1171 1.075/133.8 1181
7. The 3Al state
this work
of important
exp. [ 121
configurations:
= 160” ,
(0.31)lb25a13b~
+ (0.30)6ai5a12b2
- (0.41)5a~6a12bl
+ (0.11)Zb~6a,3bz
- (0.28)5a
+ (0.29)6ai5a13b2
tlb,3bi
- (0.38)5af6a13b
1 - (0.37)3bi6a12bz
.
At only one angle, 9 1.2O, was it found thar a lower sncrgy was obtained wirh shorter bond length. A lrave function predominantly 4ai2b$a13b,. with Si-H = 1.686 A. had an energy of -289.8559ha:tree at this angle. A Walshdiagram analysis predicts that the lowesr 3B7 state should be described by 4a~Sa12b~2b~. in fact, we found that at 160’ the 2 ‘B, state showed a significant contribution from this configuration.
9. Summary We have esamined in considerable detail all the Czv potential surfaces which are below the esperimentally accessible energy of Si(tS) + Hz(lEz). We note that the minima which are liable IO be offmerest to the esperimentalisr are associated with rhe following states: X ‘At(1.534
X/92.7Oj,
;A,(3.330
A/12.6”),
‘AZ(3.470
a/12.6”),
3Bt(1.497 ‘Bt(1.519
A/l 18.3O), X/!20.2”),
373
Volume 107. number
4.5
and possibly 2’A1(1.489 and 3A,(1.703
CHEMICAL
A/162.5”)
A/180.0”).
Furthermore, the high barrier to the 3Bl minimum is substantially reduced in C, symmetry from its intersection with 3A2Acknowledgement
PHYSICS
LETTERS
8 June
1984
[4] B. Wirsam.Chem. Phys. Letters 14 (1972) 214. [5 1 B. Roes. Intern. J. Quantum Chem. S14 (1980) 175. [6] 1. Dubois. G. Henberg and R.D. Verma, J. Chem. Phys. 47 (1967) 4262; 1. Dubois.Can. J. Phys. 46 (1968) 2485. [7] TH. Dunning. J. Chem. Phys. 53 (1970) 2823; TH. Dunning and PJ. Hay. in: hlodem theoretical geometry. Vol. 3. ed. H.F. Schaefer Ill (Plenum Press. New York, 1977) pp. I-27. [S] S. Huzinaga, J. Chem. Phys. 42 (1965) 1293. [9] J. Sauer, P. &sky a’d R Zahradnik, Collect_ Czech.
Chem. Commun. 47 (1982) 1149.
The authors acknowledge valuable discussions with Professor H.F. Schaefer, who also supplied a preprint of ref. [IO]. We are also pleased to acknowledge useful advice from Dr. R.H. Nobes. This investigation was stimulaied by discussions with Dr. D. Husain.
[lo] [ 111 1121
[ 131
References [l]
A. Kasdan, E. Herbst and W.C. Lineberger, J. Chem. Phys.62 (1975) 541. [2] J.H. Meadowsand H.F. Schaefer 111. J. Am.Chem. Sot. 98 (1976) 4383. [3] D. Husain and PE. Norris, J. Chem. Sot. Faraday II 74 (1978) 106,335.1483.
374
1141 [ 15 ] 1161 [ 171 [ 181
h1.E. Calvin. R.S. Grev, H.F. Schaefer 111 and J.C. Bicerano. Chem. Phys. Letters 99 (1983) 399. P. Saxe, H.F. Schaefer Hi and N.C. Handy, J. Fhys. Chem. 85 (1981) 745. A.R.W. McKeJlar, P.R. Bunker.TJ. Sears. K.M. Evenson, RJ. Saykally and S.R. Langhoff, J. Chem. Phys. 79 (1983) 5251. C.F. Bender, JH_ Meadows and H.F. Schaefer 111, Faraday Discuss. Chem. Sot. 62 (1977) 59. ME. Casida, h1M.L. Chen, RD. MacGregor and H.F. Schaefer III. lsrael J. Chem. 19 (1980) 127. L.B. Harding, J. Phys. Chem. 87 (1983) 44 1. C.W. Bauschlicher Jr. and D.R. Yarkony. J. Chem. Phys. 69 (1978) 3875. G. Henberg and J.W.C. Johns, Proc. Roy. Sot. A295 (1966) 107. P.R. Bunker and P. Jensen, J. Chem. Phys. 79 (1983) 1224.
8 June 1984
CHEhiiCAL PHYSICS LETTERS
THE LOW-LYLNG STATES OF SILYLENE
J.E. RICE and N.C. HANDY University Chemical Laboratory.
Received 22 February
Lettsjicld Rood. Gutbridge
CK? IEW,
UK
1984; in foal form 29 hlarch 1984
hfC SCF calculations have been performed on the&! surfacesof the t At ,3Bt, tB1, JA2, *AZ, 2 tA1.3.%, and 3B2 states of sifylene. These states are important in the collisional removal of Si by molecular hydrogyn. Of parricullr mtwst are the barriers in the 3B1 and ’ I31 surfaces,which are substantives reduced on tntersction xvitb 3.~2 and 1 .+2 in C, symmetry, and the small-angle minima of the latter states.
I. Introduction
tive orbit&. F&owing the suggestion of Roos [St. improved cakxdations were also performed by adding the 7at and 3bt orbitals to the active space. States considered were 3B,, 3A2 and ;B2, which correlate with Si(3PJ)+ Hl,rind l-41, ‘B*,:! “Al and lAz_ which correlate with Si( ID) + H,. The j.tt srare was also considered. AU calculationswere performed in C,, geometry.
There has been increasing interest recently in the low-lying states of silylene. The first two states are known to be the ‘A, and 3B,, with the ‘A, the iowest, as determined by Kasdan et al. [I 1 using photoelectron spectroscopy on SiHz _Schaefer and Meadows 13-1carried out a theoretical calculation for the s~g~e~-t~pl~t separation, which gave good agreement with experiments. Husain and Norris [3] have reported rate data for the collisional removal c~S~((~PJ), (“D), (IS)) by moiecukr hydrogen, Si + H, -+ SiH + H ,
2. Vertical transition
Vertical transitions energies were calculated at the experimental geometry of the ground state (I Ai): Si-H = 1.516 ii and f3 = 92.1” [6]. The larger XIIVC space was used with a double-zeta plus polarisation basis set (Si( 1 is7pld~6s4pld~ and H(4s~p~~slp}~ developed from that of Dunning [?] and Nuzkaga [S], with q&G) = 0.4 and 0rJH) = 1 .O and a hydrogen scaling factor of 1.2. Some Rydbeg functions (a,($) = 0.03 and r+,(Si) = 0.02) were added because it apperued possibfe thak some of rhe hider states may need them, although the results indicate that it is xhe smallest exponents, a,(%) = 0.09932 and o4,(Si) = 0.09699, of the standard basis which are more important. The results of these calculations xre gven in table I. The ordering of the lowest seven states agrees with the results of Wirsam. The need for a m~ti~on~gur~tion deception of these states is weli known by com-
(11
and they constructed a correlation diagram through the states of SiH,, using the results of some ab initio calculations of Wirsam 141. Wirsam performed configuration interaction calculations for various angles 6 (60” G 8 G 180”) and bond lengths. In view of the ~provement of ab initio procedures in the last ten years, in particufar the advent of MC SCF calculations and gradient methods, we decided to repeat these calculations, optimising bond lengths for various bond angles. Furthermore, some of the states have interesting small-angle minima which have not been previously investigated. The MC SCF method used was CAS SCF, with the Si Is, 2s and 2p orbit& as core orbit& and the valence orbitals4a1.2bZ.2bl. 5aI,3bz and 6a, asac0 009~2614/84/S 03.00Q Elsevier Science Publishers ~o~h-Hol~~d Physics Publi~~ng Division)
energies
B.V.
365
Volume
107. number 4.5
Table 1 The predicted
CHEMICAL
PHYSICS
order and relative energies in eV of the exited
8 June 1984
LETTERS
states of silylene
zi the experimental
geometry
Energy
Main confgwations
Energy
1 ‘BZ
7.305
(0_99)2b$Sa13bz
7.871
23B2
6.827
(0.90)2b#a12b:
State
of the ground
state
[4] a)
+ (0.37)2biSat3b2 + (0.13)2b%Zb:4a13b2
13A1
5.998
(0.98)2b$5a16al
8.940
2’A,
5.459
(0.94)2b;Zb:
5.248
- (0.16)Sa:Zb: - (0_13)2bz5a: + (O.l4)2b$a16al + (O.l0)2b:4alZbzSa13bz
l’A2
4.636
(2)
(0_96)2b2Sa:2bt
4.276
- (0.12)5a~4ai2b12b26a1 + (O.l2)5at2bt2b26at
1 ‘AZ
4.233
3.887
(0.96)2b25a:2bl + (0.12)5a12b12b26al
2.138
l’B,
2530
(0.97)2bs5a12b,
l3B1
1.096
(0.98)2a;Saltbl
0.680
X’A,
0.0
(0.97)2b$Sa:
0.0
- (0.17)2b;Zb; a) Energies read from the graph of ref. j4 1.
parison with calculations on CH2, but in addition it is noticed that the 6a, orbital is important for some states, as must follow from the increased proximity
of the higher orbitals with second-row atoms. The energies of the first five excited states relative to the ground state are consistently 0.4 eV above the results of Wirsam (Wirsam’s calculations used a minimal basis set and included electron correlation by performing a Cl calculation from the ground-state orbitals with all excitations from 4al, 2b2, 5al + 2bl, 6al, 3b2 and 7al). The energies of the higher states are markedly different. Wirsam predicted the 3A1 energy to be 8940
366
eV above the ground state, com-
pared
to the value of 5.998
eV determined
in this
work. This state is well described by one configuration and thus the minimal basis set of Wirsam seems unable to fully describe the orbitals of these higher states. Sauer et al. [9] have recently reported semi-empirical results for the silylene system. The order of the
first four states is the same, but the order of the next sixstatesispredicted to be 3Al,1A2,3B2,2 ‘A,, 2 3B2 and lB2, the 3A1, 2 ‘Al, 2 3B2 and lB2 states being represented by configurations different from those found in the present study. The relative energies of the states are therefore also widely different.
Volume 107, number 4.5
Since reaction (1) is likely to produce excited states of silylene initiaily, the energy differences between the ~~1~~~~~~ structures are of particular interest. For each of the states lAI, %t , “AZ, 3A2 and f.B, , the Dunning-Huzinaga basis with potarisation functions was used with the six active orbit&. The
bond length was optimised for many bond angles to produce the potential energy curves in fig. I ~The optimised e~u~brium structttre of each state is given in tabie 2. The larger active space was used for the 2 IAt , 3A, and %3, states. For the 2 IAt state, a smallexponent p function (or,(%) = O.OZ>was added to the basis set, and for the 3A1 and 3B2 an s function (cr(Si) = 0.03) was also added. The curve for the 2 IA, state is displayed in fig- 2. Also included for comparison in this graph are a few points of the t A,, 3A7 and 1A, surfaces, also calculated at this accuracy.%e morr$complex 3At and 3B2 surfaces are displayed in figs. 3 and 4, The Sit 1I>) -t H2 energies are nor equivafent
8 June 1984
CHEMXCAL PHYSICS LETTERS
for all the correlating
ine~u~v~ence of the d orbit&, since the symmetry of the Si atom cannot be constrained ta D,, in our CAS SCF program. The optimised structures for a8 the states with &helarger active space and basis set are given in table 3. These calculations are compared with those of Wisam. We now discuss the ~d~~du~ states in more detail.
4. The first three states:
lAl,
3ES1and II),
Experimentat information is ~no~v~ on the equilibrium geometry of these states, and they have also been studied by S&t&r and coworkers [Z,iOl. The groun stats is I At : the D and x orbitals are sufficient& far
apart for the singlet state to be more energetically stable than the triplet, unlike the valence isoelectronic radical rneth~~e~e. The ~~~o~o~~~~rat~o~ dexription is also confirmed for the lA,, whereas one con@ &ration describes the >Bl and I Bl states over the regions shown. Probably the best calculations on these three states are by Calvin et al. [ 101, who performed
double-zeta plus polatisarion basis calculations with S~~~on~vo(tAt~orone(?3~, fBt)rsference(sj. The results of these workers and Wirsam and our own
states (I AII i Bk) ffigs. I and 2). This is due to khe
Fig. 1. Potential energy curves for the efectrunic states of tigiene caicuktslted u&g the zi.active-orbm+space metksod. fhe 3As BF&2 * A1 curves cakulared with the eight-active-space method are scaled here for comgarixm. Energies in hatxee.
Volume 107, number 4.5 Table 2 ~u-~~urn
CHEMICAL PHYSICS LETTERS
structures calculated with the si!-active-space
state
Main cmlfiitions
method Bond angle (de& H-5-H
Bond length (A) Si-H
Energy (ev)
3,238’
2.50
120.2
I.519
2.09
123 j6f
1.487 [S]
I.93 [6]
12.8
3.401
1.63
118.3
1.497
0.72
9.35
1540
0.0
92.1 [6]
1.516 f6]
0.0
13.4
(~.98}2b*5a~2bt
8 June 1984
+ (ti.J 1)2bz3b$2b, + (0.11) kxture
“Bl exp.
3A2
(0.98)lb&2b, + (O.l4)2b~2b,6a~ - (0.1 1)2b25a;2bt3b;
3B1 X’At
a)
(0~9)2b~Sat2br (0.97) 2b$Sa:
- (O.i9)2b~2b~ esp.
al This con&uration
does not include 4ai.
Fig. 2. Potential energy curves for the electronic in hartree.
368
states of silylene calculated using the e~t~ctiv~rbit~~~a~
method.
Energies
Volume
107. number
CHEMICAL
4.5
-289
PHYSICS
8 June
LETTERS
1984
9
Fig. 3. Potential energy curves face. Energies in harlree.
for the 3A1 state of silylene.
The dominant
confwrations
are shown
for each section
of tie sur-
LO:2 b; 50,3 b,
+mixture(see
Fig. 4. Potential energy
curve for the 3Bz state of silylene. The dominant
results for the equilibrium structures are compared in table 4. The X lA,-3B, splitting has not been well defied experimentally, but Schaefer [lo] feels that an analy-
text)
confiurations
are shown.
Energies
in haruee.
sis of his theoretical results and Lineberger’s experiments [ 11 suggests a value near 20 kcal/mole (0.867 eV). An MR SDCI calculation will be necessary to improve upon our result of 0.760 eV. (An equivalent cal 36s
Volume 107. number 4.5 Table 3 Equilibrium
State
3B2
strucbures
CHEMICAL
calculated with the eight+xtive-space
hlain confirations
(0.96)2b$5a13b2
PHYSICS
8 June
LETTERS
1984
method length
Energy
(A)
Bond angle (deg) H-Si-H
Bond Si-H
this work
ref. [4]
this work
ref. [4]
this work
ref. [4]
77.95
1.686
1.667
5.697
6.244
2.104
-
5.099
1.703
-
3.163
1.489
1.566
3.716
2.996
67.4
3.470
1.746
2.572
3.858
125.62
1519
1577
2.122
1.624
65.7
3.330
1.736
1.826
3.391
117.1
123.63
1.496
1.551
0.759
0.207
92.7
97.46
1534
1.582
0.0
0.0 a)
92.1
(W
+ (0.17)6a12b25a:
3A*
(0.91)5a:2b23bz
54.1
- (0.26)2b;5a16ar - (O.l6)6a:
2b23b2
+ (0.14)2b:5ar6al + (0.10)5a16at3b$
-
180
(0.97)2b;5ar6al + (0.15)2b,5a16ar3ba
21Ar
162.5
(0_56)2b:Sa;
180
+ (0_77)2b;2b: - (0.24)2bz6a:
‘442
12.6
(0.98)5a:2br2b2 + (0.13)6a;2b12b, - (0.10)
‘Bl
mixture
120.7
(0.98)2bz5a12bl + (0.11)4a12b~5ar2b16al
3A:
(0.98)5a:2b12b2
12.6
- (O.l4)6a:ZbrZba
“Bl
(0.98)2b:Sar2br
X’A,
(0.97)2b:5a: - (O.i1)2bf2b:
a) Ground-state
370
energies:
-290.065223
(this work) and -289.91422
(ref.
[4])
hartree.
CHEMICAL PHYSICS LETTERS
Volume 107, number 4.5
8 June 1981
Table 4 Equilibrium structures of the three lowest-lying states of silylene (‘At, 3Bt and ’ Bt)
state
Predicted geomeuies (bond length (.X)/bond aTIe (de_e))
cxp. [6]
ref. (41
ref. IlO]
this work
lB1
l-487/123
3Rr X’A,
l/516/92.1
1.486/1235 1.471/117.6 1.508j94.3
1.468/122.6 1.466/118.1 1.505193.9
1.519/120.1 1.497/118.3 1.534j92.75
Predicted energies relative to the ground state (ev) a)
exp. [6]
‘BI 3R1 X’A,
1.925 (0.0)
ref. [4]
ref. [ 101
this work
2.299
2.168
2.120
0.807
0.728
(0.0)
a) Totd energies (in hartree) for the X ‘A, state are -290.04890
culation on CH2 for the 3B1-1Al splitting yielded 0.425 eV [ 1 I], compared to an experimental value of 0371 eV [12].) From tables 2,3 and 4, there are discrepancies between the theoretical predictions and the experimental determinations for the bond angles and lengths. Whereas the SCF method [2] yields short bond lengths, the CAS SCF method is known to yield bond lengths which are too long unless a large active space is used. With the six/eight active space, the ‘A1 bond length is too long by 0.024/0.018 A. However, such discrepancies will not affect the overall shape of the potential energy surfaces we are discussing. The IA, curve is well represented by two contigurations along its length, from the separate Si(tD) + H?(lZi) through its minirnum at 92.1° to its linear 1%: structure. The 3B,, which correlates with Si(3PJ) + H2(‘Zi), is seen to have a maximum (e-82 eV) at approximately 32.5” before dropping to its minima. It is well represented by 2bs5a12bt for 0 > 325”. but needs 5ai6at2bt to describe the dissociated Si(3PJ) + H-,(1X:) for 0 =G30”. Similarly,the IB,, which correlates with Si( lD) + H2( 1I$), has a maximum (G35 1 eV) at approximately 40”, being well represented by 2bgSat2bt for 0 > 45O and 5a:6a12bt for e G 350.
0.759
(O-0) (ref. [4]), -290.10268
5. The small-angle
(0.0)
(ref. [lo]) and -290.065223
states:
(this ~vork).
3 A2 and 1 A2
These states, predominantly represented by 5a$?b ,2b 7,, are valence isoelectronic with the 3A2 and lA2 states of CH2 and NHf. This state of NH; has been shown to have small b&d angles in DZP Cl calculations of Schaefer and co-workers [ 131, and this phenomenon was rather straightforwardly esplained with reference to the Walsh diagram [ 141. It must be expected, therefore, that the 3A2 and JA2 states of SiH2 wiU ha;e small bond angles, if local . muurna exrs:. From table 2, using the six-active-space model, the bond angles for the 3A7_ and lA2 states are 12.8” and 13.4O, and for the eight-active-space model 12.6O for both. The 3A7_ minimum is 0.012 eV lower than the reactants Si(3PJ) + Hz at the six-active-space level, but is higher at the eight-active-space level (0.303 eV). The lA7 state, however, is 0.016 eV below the reactants Si(jD) + Hz at the six-actiw-space level and has the same energy as the reactants (0.000 eV) at the eight-active-space level. From the tables it is seen that both states are predominantly represented by the main configuration although for the 3A, the configuration 6a:2bt2bz has coefficient 0.14. The bond lengths of these states are long, and the states may be viewed as complexes (eight-active-space results):
371
Volums
107. number
CHEMICAL
4,s
PHYSICS
LETTERS
8 June 1984
Table =
Impel -xx confgurations
Angie
Bond
(aes)
length
Confwurations
Energy relative to minimum (ev) 2bfZbj
2bz6a:
2b:Sai
0.14
0.94
-0.07
0.14
1.364
0.21
0.93
-0.10
0.07
0.384
1.489
0.56
0.71
-0.24
O.O!
0.0
1.485
0.66
0.66
-0.30
(A)
2b$5a:
100
1.519
130
1.492
1625 lS0
Si
0.731
across she 2 LA, surrace
x
0.162
X
lA2
Due to the extreme values for the bond lengths and bond angles, we must expect that these predictions will change by a significant percentage if larger calculations are performed. The 3A1 surface plays an important role in C(3PJ) + Hz collisions to form the ground 3Bl state of CH,. Schaefer and co-workers [ 141 could find no minimum on the 3A, surface, but found that the lowest point of intersection of 3A;, and 3B, to be only 9 kcal/ mole above the C(3P;) + Hz reactants. Because such an intersection
is avoided in C, symmetry,
this sug-
gested little or no barrier to the direct formation of the 3Bl state of CH2. This problem has recently been examined in detail by Harding [ 151, who has looked at Cs geometry and the effect of basis sets. He concludes that the crossing is weakly avoided with a barrier of the order of 2.5 kcal/mole. Furthermore, he found a very shallow 3A, minimum (depth -0.25 kcal/mole) with (apparently) a similar geometry to the 3Az geometry we .ind for SiH2. A similar picture .vill hold for SiH,. We fmd the lowest point of C,, intersection of 3B1 and 3A7 to be at Si-H = 1.a275 A and 0 = 59.3”, with an energy 21.2 kc_‘,‘mole (0.917 eV) above Si(3P,) + Hz, using 01:~ largest basis set and active space. (This result was determined by calculating the energy at each of a grid of points (bond angle/bond length) for the two 372
0.22
states (3B,, 3A,) and finding the lowest energy at which the energy difference between the two states was less than 0.000003 hartree.) This means that the barrier to the formation of SiH,(3Bl) from Si(3PJ) + Hz is also much smaller (five times) via the 3 A2 state than along the 3B, surface. For the ‘El and 1A-, states we expect the situation to be similar, but we have not investigated this crossing.
Si
3A2
6.The21A1
state
This state was considered with the larger active space. We must expect it to be a low-lying valence state, due to the presence of 2bs2bf in the description of the X IAl state. In table 5 we show the decreasing importance of the 2bs3_bf CSF as 0 increases from 100” to lSO”, compensated by an increase in the significance of ZbsSa: and lb$6a:. The potential well at 162.15~ is wide and shallow (0.223 eV), the energy only rising rapidly from 130’ to 100°. Previous calculations on methylene determine the 2 1 Al state to be only slightly non-linear [ 161. Bauschlicher and Yarkony [ 161 used a DZP CI method,with the two references 3ailb$ and lb:lbs. Because we find a third configuration to be important in SiH2,we recomputed the X3Bl, 1 lAt and 2 lAl states of CH,. The results are reported in table 6. These determined the minimum of the 2 1Al at 17 1 -lo, not at linearity, with the 1b$4a: CSF having a coefficient of 0.049. The 6a, orbital is more significant for SiH?, as must be expected from a comparison of the internuclear distance correlation diagrams. The basis functions with smallest exponents did not enter significantly into the orbitals, and it therefore seems that the 2 1A, state of SiH2 is a true valence state.
8 June 198-l
CHEMICAL PHYSICS LETTERS
Volume 107. number 4.5
Table 6 Equilibrium structures and energies for the 3 B I, 1Al and 2 1 A, states of methylene
State
2 ‘A1
this work
ref. [ 161
1.081/171.0
1.07/180
1.128/102.0
X’Ar
XaB
Ener_ey(eV)
Bond length (A)/bond angle (deg)
1
esp.
1.17/103-.4
1.098/131.7
The 3At state, which
by a number
with Si(3PJ) + 2H, was considered using eight active orbitals, together with the largest basis set _It is predominantly described by two configurations across the potential surface, as shown in fig. 3. The 2b$5a16al CSF is dominant in the region 120° < 0 < ISO”, the minimum being at linearity with Si-H = 1.703 A. The other important CSF, 5a:2b23b2, dominates in the region 30” < 0 < 70”, with a local minimum at 54.7” with Si-H = 2.104 A, 2 eV above the 2bt5a16al minimum. There is an avoided crossing in the region 70° < 0 < 120°, where the bond length will change rapidly. The configuration description also changes in the range 20” < B < 30”, becoming predominantly 4a:5a:6a ,7a 1 between O” < 0 G 20°. Due to the problem of high symmetry, our programs give discontinuous results at 180°, but indications are that 3fls, 1X; and IA lie very close in energy. ( 1 Zl lies 0.574 eV above P I$, which lies 0.043 eV above l As with the six-active calculation in C2v geometry.) correlates
8. The 3B2 state This state, whi-h .orrelates with Si(3PJ) + H,(lZi), was considered with the largest basis set ark eight active orbitals. The state is well described by one configuration, 4a:5af6a12bz, for 0” < 0 < 40’. the energy rising rapidly in this region. A structure with a very long bond length is found between SO” G 8 < 180”, with a constant energy of -289.8557 hartree across the surface. This structure can be viewed as a complex from which the hydrogen atoms are dissociating to give Si + 2H, and is described
H-Si-H
ref. 1161
2.832
2.9
-
0.0
0.393 0.0
0.425 0.0
1.11/102.4 1171 1.075/133.8 1181
7. The 3Al state
this work
of important
exp. [ 121
configurations:
= 160” ,
(0.31)lb25a13b~
+ (0.30)6ai5a12b2
- (0.41)5a~6a12bl
+ (0.11)Zb~6a,3bz
- (0.28)5a
+ (0.29)6ai5a13b2
tlb,3bi
- (0.38)5af6a13b
1 - (0.37)3bi6a12bz
.
At only one angle, 9 1.2O, was it found thar a lower sncrgy was obtained wirh shorter bond length. A lrave function predominantly 4ai2b$a13b,. with Si-H = 1.686 A. had an energy of -289.8559ha:tree at this angle. A Walshdiagram analysis predicts that the lowesr 3B7 state should be described by 4a~Sa12b~2b~. in fact, we found that at 160’ the 2 ‘B, state showed a significant contribution from this configuration.
9. Summary We have esamined in considerable detail all the Czv potential surfaces which are below the esperimentally accessible energy of Si(tS) + Hz(lEz). We note that the minima which are liable IO be offmerest to the esperimentalisr are associated with rhe following states: X ‘At(1.534
X/92.7Oj,
;A,(3.330
A/12.6”),
‘AZ(3.470
a/12.6”),
3Bt(1.497 ‘Bt(1.519
A/l 18.3O), X/!20.2”),
373
Volume 107. number
4.5
and possibly 2’A1(1.489 and 3A,(1.703
CHEMICAL
A/162.5”)
A/180.0”).
Furthermore, the high barrier to the 3Bl minimum is substantially reduced in C, symmetry from its intersection with 3A2Acknowledgement
PHYSICS
LETTERS
8 June
1984
[4] B. Wirsam.Chem. Phys. Letters 14 (1972) 214. [5 1 B. Roes. Intern. J. Quantum Chem. S14 (1980) 175. [6] 1. Dubois. G. Henberg and R.D. Verma, J. Chem. Phys. 47 (1967) 4262; 1. Dubois.Can. J. Phys. 46 (1968) 2485. [7] TH. Dunning. J. Chem. Phys. 53 (1970) 2823; TH. Dunning and PJ. Hay. in: hlodem theoretical geometry. Vol. 3. ed. H.F. Schaefer Ill (Plenum Press. New York, 1977) pp. I-27. [S] S. Huzinaga, J. Chem. Phys. 42 (1965) 1293. [9] J. Sauer, P. &sky a’d R Zahradnik, Collect_ Czech.
Chem. Commun. 47 (1982) 1149.
The authors acknowledge valuable discussions with Professor H.F. Schaefer, who also supplied a preprint of ref. [IO]. We are also pleased to acknowledge useful advice from Dr. R.H. Nobes. This investigation was stimulaied by discussions with Dr. D. Husain.
[lo] [ 111 1121
[ 131
References [l]
A. Kasdan, E. Herbst and W.C. Lineberger, J. Chem. Phys.62 (1975) 541. [2] J.H. Meadowsand H.F. Schaefer 111. J. Am.Chem. Sot. 98 (1976) 4383. [3] D. Husain and PE. Norris, J. Chem. Sot. Faraday II 74 (1978) 106,335.1483.
374
1141 [ 15 ] 1161 [ 171 [ 181
h1.E. Calvin. R.S. Grev, H.F. Schaefer 111 and J.C. Bicerano. Chem. Phys. Letters 99 (1983) 399. P. Saxe, H.F. Schaefer Hi and N.C. Handy, J. Fhys. Chem. 85 (1981) 745. A.R.W. McKeJlar, P.R. Bunker.TJ. Sears. K.M. Evenson, RJ. Saykally and S.R. Langhoff, J. Chem. Phys. 79 (1983) 5251. C.F. Bender, JH_ Meadows and H.F. Schaefer 111, Faraday Discuss. Chem. Sot. 62 (1977) 59. ME. Casida, h1M.L. Chen, RD. MacGregor and H.F. Schaefer III. lsrael J. Chem. 19 (1980) 127. L.B. Harding, J. Phys. Chem. 87 (1983) 44 1. C.W. Bauschlicher Jr. and D.R. Yarkony. J. Chem. Phys. 69 (1978) 3875. G. Henberg and J.W.C. Johns, Proc. Roy. Sot. A295 (1966) 107. P.R. Bunker and P. Jensen, J. Chem. Phys. 79 (1983) 1224.