J. Phys. Chem. 1992,96,9703-9709
(16) Rettig, W.; Wiggenhauser, H.; Hebert, T.; Ding, Adalbert Nucl.
Instrum. Methods Phys. Res. 1989, A277, 677.
(17) Williams, E. R.; Loh, S.Y.; McLafferty, F. W.; Cody, R. B. Anal.
Chem. 1990,62, 698.
(18) Rudge, M. R. H. Meas. Sci. Technol. 1991,2, 89.
(19) Fellgett, P. J . Phys. Colloq. C2 1967, 28, 165.
(20) Gottlicb, P. IEEE Trans. Info. Theory 1968, IT-14, 428.
(21) Swift, R. D.; Watson, R. B., Jr.; Decker, J. A.; Paganetti, R.; Hanvitt,
M. Appl. Opt. 1976, 15, 159s.
(22) Harwit, M.Appl. Opt. 1971, 10, 1415.
(23) Trcado, P. J.; Morris, M. 0. Appl. Spectrosc. 1988, 42, 897.
(24) Treado, P. J.; Morris, M. D. Appl. Spectrosc. 1988, 42, 1487.
(25) Coufal, H.; Moller, U.; Scheider, S.Appl. Opr. 1982, 21, 116.
(26) Bowers, M. T.; Palke, W. E.; Robins, K.; Roehl, C.; Walsh, S.Chem.
Phys. Lett. 1991, 180, 235.
9703
Busch, G. E.; Wilson, K. R. J . Chem. Phys. 1972, 56, 3626.
Zare, R. N.; Herschbach, D. R. Proc. IEEE 1963, 51, 173.
Jonah, C. J. Chem. Phys. 1971,55, 1915.
Bersohn, R.; Lin, S.H. Adu. Chem. Phys. 1969, 16, 67.
Woodward, C. A.; Whitaker, B. J.; Stace, A. J. J . Chem. Sa.,Faraday Trans. 1990,87, 2069.
(32) Woodward, C. A.; Whitaker, B. J.; Knowles, P. J.; Stace, A. J. J .
Chem. Phys. 1991, 184, 113.
(33) Gotts, N. G.; Hallett, R.; Smith, J. A.; Stace, A. J. Chem. Phys. Lett.
(27)
(28)
(29)
(30)
(31)
1991, 181, 491.
(34) Woodward, C. A.; Upham, J. E.; Stace, A. J.; Murrell, J. N. J . Chem.
Phys. 1989, 91, 7612.
(35) Smith, J. A.; Gotts, N. G.; Winkel, J. F.; Hallett, R.; Woodward, C.
A.; Stace, A. J.; Whitaker, B. J. J . Chem. Phys. 1992, 97, 397.
(36) Yates, F. J. R. Stat. SOC.Suppl. 1935, 2, 181.
Vibrational Transition Probabilities in the B-X and B’-X Systems of the SiCl Radical
Scott Singleton,+Kenneth G. McKendrick,*
Department of Chemistry, The Uniuersity of Edinburgh, Edinburgh EH9 355, U.K.
Richard A. Copeland, and Jay B. Jeffries*
Molecular Physics Laboratory, SRI International, Menlo Park, California 94025 (Receiued: May 14, 1992)
Vibrational transition probabilities have been measured for the B2Z+(u’=0_3)“2~(~’’=Ck10) and B’2A(u’=0,1)-X211(u”=0_2)
systems of SiCl. Individual vibronic levels of the excited states were prepared by laser excitation of ground-state Sic1 formed
in a discharge-flow system, and the resultant emission was dispersed and recorded. Independent measurements made in
two laboratories were in very satisfactory agreement. The extensive results for the B-X system were compared with
Franck-Condon factors derived from Rydberg-Klein-Rees potentials, allowing the form of the electronic transition dipole
moment function to be assessed. It was found that the electronic transition probability for the B-X system is relatively slowly
varying with internuclear distance, consistent with previous conclusions on the electronic configurations of the states involved.
The more limited data on the strongly diagonal Bf-X system were not readily reproduced from the accepted form of the
potentials and the anticipated electronic transition dipole moment.
I. Introduction
Quantitative spectroscopic information is valuable from at least
two perspectives. It provides fundamental insight into the electronic and geometric structure of molecules, and it is also esscntial
in the applied use of spectroscopy for the monitoring of concentrations of particular species. In this paper, we report experimentally-determined vibronic transition probabilities for the
BZZ+-X211and B’2A-X211 systems of the Sic1 radical, which has
been the subject of recent interest in the context of dry etching
and deposition of silicon materials in the semiconductor industry.’-3
In addition to presenting this potentially useful information, we
consider what these results reveal about the electronic character
of the states involved.
The Sic1 radical was first detected spectroscopicallyin 1914
by Jevons,4 who observed structure in the ultraviolet emission from
the products of the reaction of S i c 4vapor with active nitrogen.
Subsequent early studies5v6revealed that many of the bands in
the 200-300-nm region could be assigned to transitions involving
a doublet state with a splitting of -200 cm-l. It was concluded
that the ground state had 211 symmetry.’ Following further
investigation?-” the first rotationally resolved spectraI2J3 established conclusively the 211,2Z+, and 211 character of the X,
B, and C states, respectively.
Some outstanding difficulties remained over the assignment
of the bands in the 280-nm r e g i ~ n but,
, ~ after varied speculations?J1J4 higher resolution spectra established the presence of
an additional Bf2Astate.IsJ6 In an extensive series of investigation~,”-~’
Bredohl and co-workers have characterized systematically the rotational structures of the A-, B-, Bf-, C-, D-,E-,
*Towhom correspondence should be addressed.
‘Current address: Port Sunlight Laboratory, Unilever Research, Merseyside L63 3JW. U.K.
0022-3654/92/2096-9703$03.00/0
and F-X electronic transitions, improving on earlier work.’z’sJ6.~
Good agreement was found with the molecular constants for the
X 2 n state derived from microwave measurement^.^^ More recently, the very high resolution Lamb dip measurements of Meijer
et a1.25J6on the E X system have confirmed the values of constants
deduced by Bredohl’s groupI8and also provided hyperfie splittings
and the excited-state natural lifetime. A further recent
has shown that Sic1 may be observed by resonance-enhanced
multiphoton ionization through the C-, D-,and E-X systems.
The potential curves for the known, lower, bound states of SiC1,
derived by the well-established Rydberg-Klein-Rees (RKR)
p r o c e d ~ r e ~ from
~ - ~ ~the published molecular constants,’s~’7-2’~2s.27~3’~32
are shown in Figure 1. The excited states
of interest in this study are the near-degenerate B22+and B’2A
pair, around 35 OOO cm-1 above the X211ground state. As can
be seen from this figure, the equilibrium internuclear separation
(re = 2.036 A)Iss2’of the B’2A state is very similar to that of the
ground state (re= 2.058 A),18*21325
whereas that of the B22+state
is a little shorter (re= 1.971 A).’892s It is therefore to be expected
that the B’ZA-X211 system will be strongly diagonal, with predominant Au = 0 vibronic transitions, in contrast to the B22+-X211
system which will exhibit longer progressions in vibration in
emission (or absorption) from a given vibronic level.
In this paper, we present experimental measurements of the
fluorescence spectra emitted from single vibronic levels in the B2Z+
and Br2Astates to various vibrational levels of the X211ground
state. The excited-state levels were prepared by selective laser
excitation of ground-state radicals generated in a microwave
discharge-flow system. The vibrational levels spanned were u’ =
0-3 in the B22+state, emitting to uf’ = 0-10 in the X211state,
and uf = 0 and 1 in the B’2A state, emitting to u” = 0, 1, and 2
in the X211 state, respectively. The measurements were made
independently in two laboratories (at Edinburgh University and
0 1992 American Chemical Society
Singleton et al.
9704 The Journal of Physical Chemistry, Vol. 96, No. 24, 1992
a) EXPERIMENTAL
B-X (1,O)
1.80
2.00
Q,
A Y1
2.20
60 h
I
50m
0
-
.-I
7
Gp:
1
40-
-
b) SIMULATION
w
z 30W
IJ
4
Z
w
20-
-
b
0 10-
a
34980
0
1.50
2.00
2.50
3.00
3.50
34940
34900
34860
-
INTERNUCLEAR SEPARATION/A
Figure 1. Potential curves of the lower bound states of SEI, constructed
using the RKR procedure. Inner repulsive limbs were extrapolated according to an r-12dependence. The 42state predicted by ab initio calculation4’to have a minimum around 23 000 cm-’, but not yet observed
directly experimentally, is not shown. The inset shows the region of
near-degenerate B2Z+ and B’2A levels of most interest in this study.
LASER FREQUENCY/cm-’
Figure 2. (a) LIF excitation spectrum of the B2Z+(u’=l)
X211,,2(u”=O) subband. Total fluorescence was collected without temporal or
spectral discrimination. The signal is not corrected for variations of dye
laser intensity with frequency which were not significant over this frequency range. (b) Simulation of the spectrum with an assumed rotational
temperature of 302 K and a nominal line width of 0.5 cm-’. Line
strengths calculated as described in the text.
SRI International): the level of agreement is considered below.
The fluorescence spectra have been analyzed to deduce relative
transition probabilities for individual vibronic bands. These are
themselves useful in the determination of excited-state vibrational
populations, for example in investigations of energy transfer between the excited state^.^^-^^ They have also been compared to
the results of vibrational wave function overlap calculations
(Franck-Condon factors), using potential curves derived by the
RKR procedure. We consider what this reveals about the form
of the electronic transition dipole moment function for each of
these electronic transitions, and hence about the electronic orbital
occupancy in the states involved.
SR250). Selected temporally resolved fluorescence decay traces
were obtained at SRI using a transient digitiser (DSP Technologies, 100 MHz). In Edinburgh, signals were output to a stripchart recorder and peak areas were integrated using an imageanalyzer system (Kontron IBAS); at SRI, the boxcar-integrated
signal for each laser shot was digitized and linearly averaged.
Gases were supplied by the following manufacturers with the
indicated stated purities: at Edinburgh, Ar (BOC, 99.998%), SiC14
(kindly provided by Dr. S. Cradock, Edinburgh University; original
purity, >99.999%); at SRI, Ar (Liquid Carbonics, 99.998%), He
(Liquid Carbonics, 99.998%), SiC14 (Aldrich, 99.9%).
11. Experimental Section
The two independent experimental systems were very similar
in principle. The SRI apparatus is described in detail elseIn both cases ground-state Sic1 radicals were produced
by microwave discharge in a mixture of SiC14vapor and argon
or helium carrier gas. The discharge products passed into the main
tube of a flow system maintained at a total pressure of typically
a few Torr by a high-throughput mechanical pump. Fluorescence
was excited from the radicals well downstream (-0.5 m) of the
discharge, using the pulsed frequency-doubled output of a Nd:
YAG laser-pumped dye laser (Edinburgh, Spectron Laser Systems
SL801 and Quanta Ray PDL2) or excimer laser-pumped dye laser
(SRI, Lambda Physik EMG 50 and FL 2001).
The fluorescence was collected orthogonal to the laser beam,
dispersed through a monochromator (Edinburgh, Hilger and Watts
Monospek 1000, 1 m; SRI, Heath, 1/3 m), and detected by a
photomultiplier tube (Edinburgh, EM1 9789QB; SRI, EM1 9558).
The wavelength dependence of the sensitivity of each of the
detection systems was determined by recording the spectrum of
a calibrated standard source (Edinburgh, Optronic Laboratories
245A tungsten-halogen lamp; SRI, Optronic Laboratories UV40
D2lamp). In the SRI experiments the total fluorescence was also
observed through a UV-pass, broadband filter (Schott, UG5) for
normalization purposes. Gated signals were captured by boxcar
integrators (Edinburgh and SRI, Stanford Research Systems
III. Results
III.1. Excitation Spectra. A preliminary survey of the laserinduced-fluorescence (LIF) excitation spectrum in the 275-295-nm
region was undertaken to establish unambiguously appropriate
wavelengths at which selected vibrational levels of the B and B’
states of Sic1 could be excited. Transitions were identified from
each of the spin-orbit components of u” = 0 of the ground state
to u‘ = 0, 1, 2, and 3 of B2Z+ and to u‘ = 0 and 1 of Bf2A,
respectively. The relative intensities of transitions from the 2rI.,/2
and 2113/2 ground-state components, separated by 207 cm-’, mdicated a spin-orbit temperature of 308 f 20 K.
Figure 2a shows the LIF excitation spectrum of the B2Z+(u’=1)
X2IIII2(u”=O)subband (we shall adopt for convenience the
contracted notation B-X1/2(l,O)), obtained by collecting the total
emitted fluorescence without spectral or temporal resolution. This
is a typical example of one of the isolated B-X transitions not
overlapped by B’-X features. The characteristic QI and PI heads
are apparent, with partially resolved rotational structure, and a
clear 35C1/37C1isotope splitting is evident. Also shown in Figure
2b is a simulation of the spectrum with an assumed rotational
temperature of 302 K and rotational line strengths calculated from
the expressions first derived by Earls.36 The agreement is quite
satisfactory.
In contrast, the near degeneracy of certain B and B’ vibrational
levels results in spectral overlap of some transitions. For example,
Figure 3a illustrates the coincidence of the B-XIl2(2,0) and
-
The Journal of Physical Chemistry, Vol. 96, No. 24, 1992 9705
B-X and B’-X Systems of the Sic1 Radical
a)
B’-X(0,O)
Q1l
B-X(2,0)
l
the fluorescence emitted at the earliest times following excitation,
effectively eliminating emission from degenerate B’(u’=O). B(u’=3) can be excited in isolation from X211,/, (due to the different
vibrational spacings in the B and B’ states, only the single pair
B2Z+(u’=2) and B’2A(u’=0) is nearly degenerate (see Figure 1);
however, the X-state spin-orbit splitting compensates to overlap
the B-X3,2 (3,O) and B’-XIj2 (1,O) subbands).
In contrast, it is not so straightforward to excite or observe
fluorescence from isolated B’2A levels, since, quite apart from
spectral overlap with B22+levels, some collision-induced transfer
is inevitable at the pressures of our experiments. Regardless of
these effects, the prominent Q I heads of the B’-X(0,O) and -(l,O)
bands remain the obvious features to select for excitation of B’2A
vibrational levels. We describe the less extensive data which we
have obtained on B’2A state emission probabilities in section 111.2.2,
below.
111.2. Fluorescence Spectra: Transition Probabilities. The
intensity, Id,,,,of fluorescence emitted on a particular vibronic
transition between vibrational level u’, of an excited electronic state
and level u”, of a lower state, is very well known37to be given by
I,tdt = N,rhc FAdd,
(1)
where Nd is the population of the upper level and P is the frequency
of the emission (in units of cm-I). The Einstein coefficient, Add,,
represents the rate of spontaneous emission of photons on this
particular transition, and may be decomposed to
= (64r4/3h)s3 pddt
(2)
The vibrational transition probability, pddtris fundamentallyrelated
to the wave functions of the states involved through the relationship
Ad,,,
Pdd’
35670
35630
35590
35550
LASER FREQUENCl/cm-’
Figure 3. LIF excitation spectra in the region of the B’-X,,,(O,O).and
B-X,,,(2,0) bands. Signals collected were (a) total fluorescence integrated over all times following the laser pulse, (b) fluorescence in a 10-ns
gate overlapping the laser pulse, and (c) fluorescence at times >lo0 ns
following the laser pulse.
B’-X1 2(0,0) bands. (The overlap is similar in the transitions from
the X I II3,2 component not shown in this figure.)
The contributions from the different excited states can be
distinguished by exploiting their disparate radiative lifetimes
(approximately 10 ns and 1 ps for the B and B’ states, respect i ~ e l y ~ ~In, ~Figure
~ ) . 3a, the total integrated emitted fluorescence
was recorded, whereas in Figure 3b only the emission in a IO-ns
gate overlapping the excitation laser pulse was detected, revealing
almost entirely B-X excitation features. Correspondingly,Figure
3c shows the excitation spectrum obtained when only emission
at longer times (>lo0 ns) was observed, resulting in isolation of
the B’-X system. (In fact, in this latter case of Figure 3c, the
emission would not be exclusively from B’-state molecules, since
collisions transfer population between the B’ and B states.
However, the Sic1 molecules which emit at long times must all
have initially been excited to the B’ state. The collision-induced
transfer of population between states is the subject of separate
publication^.^^-^^)
Figure 3c shows that the B’-X(1,l) “hot band” QI head is
almost exactly resonant with the B-X(2,O) Q1head, so extra care
must be taken to avoid not only the more obvious B’-X(0,O)
features when attempting to excite B22+(u’=2) in isolation. The
ratio of B’-X(1,l) to B’-X(0,O) intensities (making use of vibrational transition probabilities in Table I1 discussed further
below) yielded a vibrational temperature of 317 f 25 K. This
is consistent with the rotational and spin-orbit temperatures above
and, as expected, is close to the ambient temperature in the
laboratory.
In summary, the u’ = 0 and 1 levels of B22+ can be excited
from either spin-orbit component of X211 without interference
from B’2A levels. B(u’ = 2) can best be observed virtually in
isolation by pumping the B-X (2,O) PIhead and monitoring only
[
= J-*dRe(r)*,<t dr]
2
(3)
where qdand qd,are the vibrational wave functions of the upper
and lower states, respectively. The quantity &(r) is the familiar37
electronic transition moment, which describes how the overlap
of the upper and lower state electronic wave functions, and hence
the electronic transition probability, depends on internuclear
separation, r.
Vibrationally-resolved fluorescence spectra emitted from selected vibrational levels of an excited electronic state, once appropriately corrected for the frequency (or, equivalently, wavelength) dependent sensitivity and bandpass of the detection system,
allow the relative values of the vibrational transition probabilities,
p0.,,,, to be deduced.
III.2.I. B-X Emission. Figure 4a shows a series of fluorescence
spectra observed from selectively populated u’ = 0, 1, 2, and 3
levels, respectively, of the B2Z+state. The closely-spaced pairs
of bands correspond to transitions to each of the spin-orbit components of successive vibrational levels of the X211ground state.
(The simulations of these spectra shown in Figure 4b are described
in section IV.l, below.) An analysis of the positions of the bands
yields vibrational constants (for the 28Si3sC1isotopomer) of W /
= 535.7 cm-I and w,”x/ = 2.2 cm-l for the X211state, in good
agreement with previous higher resolution (but slightly less extensive) measurements. I
A qualitative inspection of the intensities of the bands reveals,
as expected, a general (although not monotonic) increase in the
number of nodes in the spectrum with increasing upper state
vibrational quantum number. Quantitative analysis of the integrated intensities of individual bands, appropriately corrected for
frequency-dependent terms, produced the relative vibrational
transition probabilities, pdutr,presented in Table I. The sum of
the pduttvalues originating from a given u’level has been (arbitrarily) normalized to 1OOO. Two sets of experimental results are
included, corresponding to the independent measurements made
in the Edinburgh and SRI laboratories. It can be seen that the
overall level of agreement is very satisfactory, with virtually all
significant transition probabilities agreeing to within 10%. The
global sum of squares of differences between the puldlsets, incorporating 35 bands, is 1361, corresponding to a root mean square
difference of 6.2/1000.
9706 The Journal of Physical Chemistry, Vol. 96, No. 24, 1992
Singleton et al.
a ) EXPERIMENTAL
Bv'=O
m
2 34
v"= 0 1
5
Bv'=l
VI4=
m
0 1 2 3 4 5 6 7
Bv'=2
Bv'=3
v"= 0 1 2 3 4 5 6 7 8 9
V"=
m
i
ilE!id56it!iQ!O
m
u
-.
w
Ir;
b) SIMULATION
0
3
280.0
300.0
320.0
280.0
300.0
320.0
300.0
280.0
320.0
280.0
300.0
320.0
F LUORE SCE NCE WAVE LE NGTH / nm
Figure 4. (a) Dispersed fluorescence spectra from selectively populated vibrational levels of B22+emitting to vibrational levels of X211as indicated,
Signal intensities have been corrected for the wavelength-dependent response of the detection system. (b) Simulations of the fluorescence spectra in
(a), using the appropriate form (SRI data) of a linearly-decaying R,(r) function described in the text.
TABLE I: Vibrational Transition Probabilities for the E
(090)
(1,O)
(191)
( 1,3)
(1 $4)
(~5)
(1~5)
(~7)
(290)
(291)
(2J)
~ 3
(2,4)
(2,5)
(2h)
~ 7
(2.8)
(3m
(3J)
(3.2)
(3,3)
(3,4)
(395)
(36)
(3,7)
(3,8)
(3,9)
(3,101
(9)
(9)
(6)
(4)
(2)
(2)
339 (5)
360 (6)
194 (3)
78 (3)
22 (2)
5 (1)
336
36 1
200
76
22
5
360
356
183
65
330 (9)
3 (2)
159 (5)
248 (8)
167 (6)
68 (5)
21 (3)
4 (3)
173 (7)
156 (5)
117 (3)
15 (1)
162 (4)
196 (6)
116 (4)
48 (2)
13 (2)
4 (2)
320 (7)
3 (1)
150 (6)
251 (3)
171 (6)
77 (5)
22 (1)
5 (1)
167 (5)
143 (6)
111 (3)
11 (1)
162 (1)
210 (3)
126 (3)
54 (1)
14 (1)
2 (1)
366
3
141
236
160
68
21
5
202
149
116
8
146
190
120
50
15
4
356
172
165
65
-
61 (4)
222 (7)
16 (2)
159 (6)
21 (2)
56 (4)
166 (6)
167 (7)
92 (5)
32 (4)
8 (3)
62 (3)
221 (12)
13 (4)
158 (6)
19 (3)
56 (5)
174 (8)
171 (7)
85 (4)
34 (4)
8 (2)
73
249
11
157
21
46
158
155
87
34
10
334
362
203
74
22
5
(0,1)
(092)
(OJ)
(0~4)
(0~5)
)
)
X Svstem of SiCl
-
-
-
-
-
-
-
-
-
-
-
330
361
203
78
23
5
319
359
208
82
25
6
353
3
141
240
165
71
22
5
333
3
141
247
174
78
16
6
190
143
113
8
148
196
126
53
17
6
173
134
108
8
151
205
136
59
19
5
68
235
10
153
21
47
163
162
93
37
11
60
213
9
147
20
48
171
174
163
42
13
322
1
207
81
-
345
217
233
101
-
-
-
-
-
"Vibrational transition probabilities, as defined in eqs 2 and 3. Numbers in parentheses represent l o uncertainties in the last digit, calculated from
statistical variations in the measurements between runs. The sum of pdo" values from a given u'level is normalized to 1OOO. "Data collected in the
Edinburgh laboratory. 'Data collected in the SRI laboratory. dFranck-Condon factors, as defined in eq 5. The sum of qddfvalues from a given u'
level is normalized to IOOO. 'Calculated from RKR potentials, this work. /Calculated from Morse potentials, ref 39. Walculated using the best fit
to the Edinburgh data of the linear form of Re(?)in eq 8, p = 0.25 A-', r' = 2.0 A. Sum of pdu" values from a given level normalized to 1OOO.
*Calculated using best fit to SRI data of R,(r) in eq 8, p = 0.65 A-I, r' = 2.0 A. Sum of pJd,values from a given u'level normalized to 1000. From
ref 39. Sum of values from a given u'level renormalized to 1000. 'Apparently misprinted in ref 39.
The Journal of Physical Chemistry, Vol. 96, No. 24, 1992 9707
B-X and B’-X Systems of the Sic1 Radical
111.2.2. BCX Emission. In principle, by exciting at the strong
head of an appropriate B’-X vibronic band and then monitoring
emission beyond a short initial delay during which the small
underlying component of directly excited B2Z+ population would
fluoresce, it would be possible to record uncontaminated B’-X
fluorescence spectra. However, as noted above, in the pressure
regime within which Sic1 a u l d be generated in our apparatus,
B’2A-state molecules have a significant chance of undergoing
collisions during their 1-119 natural radiative lifetime. Efficient
B’ B collision-induced t r a n ~ f e r J >then
~ ~ results in B-X emission
which substantially overlaps the B’-X bands.
Qualitative inspection of the emissions from u’ = 0 and 1 of
B’2A revealed them both to be strongly diagonal, with dominant
(0,O)and (1,l) bands, respectively, as expected. Slightly different
strategies were adopted in the SRI and Edinburgh laboratories
to eliminate the contribution from overlapping B-X bands and
obtain quantitative transition probabilities for the B’-X systems.
Although limited in extent, these data might allow some assessment of the form of the electronic transition moment, Re@),for
this transition.
The SRI data were processed digitally. Spectra recorded34
following excitation to each of B’2A, u’ = 0 and 1, contained
emissions from various B2Z+ vibrational levels whose relative
using the B-X relative transition
populations could be
probabilities presented above. The net contribution from B-X
emissions to each spectrum could therefore be self-consistently
subtracted, leaving only residual B‘-X emissions. Each B’-X band
was then integrated and the results were converted to the relative
vibrational transition probabilities, pdutT,presented in Table 11.
It was not straightforward to analyze the Edinburgh data in
quite the same way because of the analogue method used to record
signals. Nevertheless, we were still able to perform a careful
quantitative investigation of the emission from B’2A(u’= 1). The
B’-X( 1,O) band is spectroscopically isolated, even in the presence
of B-X emission from vibrational levels lower in energy than
Bf2A(u’= 1) (which are the only B-state levels populated in the
collisional transfer process from this B’ l e ~ e l ~ ~However,
- ~ ~ ) . the
dominant, diagonal B’-X( 1,l) band is overlapped by the B-X(2,O)
band, which is itself a relatively strong transition from B(u’=2)
(see Table I). We therefore measured the pressure dependence
of the ratio of the B’-X(1,0) intensity to the combined B’-X(1,l)
B-X(2,O) intensities. The extrapolated zero-pressurevalue of
this quantity was 0.174 f0.005,which, when corrected for frequency-dependent terms, produces the normalized ratio of pdvt,
values also included in Table 11. The agreement with the SRI
data is good.
More qualitative limits on the relative probabilities of other,
weaker, off-diagonal bands were also estimated from the Edinburgh data. These again agreed well with the SRI values, as
shown in Table 11. One observation which will prove to be of
significance in the later discussion is that the B’-X( 1,0) band is
clearly substantially more intense than the B’-X( 1,2) band.
-
-
+
IV. Discussion
The measured vibronic transition probabilities are useful
quantities in themselves for the reduction of observed fluorescence
spectra to excited-state vibrational population^.^^-^^ They also
reveal something about the electronic character of the states
connected by the transitions, through the form of the electronic
transition moment, R,(r).
If &(r) happens to be independent of r, then it can be removed
from within the integral in eq 3 and pu,d.can be written as
Pdu”
= Rc24dd(
(4)
where R, is a constant and qddk the well-known Franckqondon
factor,37the square of the vibrational overlap integral:
Even if R,(r) is not constant, but is a slowly varying function of
r, then pdd,can be approximated by the product of an effective
or average value of the square of the electronic transition moment,
-
and the Franck-Condon factor, qddt:
-
Pdd’
=~e(~)2c7uw
(6)
-
This relationship is exact if R,(r) is linear, in which case R,(r)
may easily be shown to be the value of R,(r) at the “r-centroid”,
p, given by
F =
s
PdrP, dr/
s
PdPvttdr
(7)
Provided that the difference between upper and lower state
potential curves is monotonic in the region of significant wave
function overlap, semiclassical arguments imply that transitions
associated with a given vibronic band will occur predominantly
at a single internuclear separation. The relative intensity of each
vibronic band will therefore indicate the strength of the electronic
transition moment
at the dominant value of r, which may be
identified with R,(r) in eq 6.
Hence, if the Franck-Condon factors, qdU,,,
can be obtained
independently, the experimentally measured values of the vibrational transition probabilities, pddJ,may be used to deduce the
relative values of the electronic transition moment d a t e d with
internuclear distances particular to individual vibronic transitions.
We have carried out this procedure for the B-X system. We also
made an attempt to apply it to the much more limited B’-X data.
The potential curves for the B, B’, and X states were constructed
by the well-established RKR p r o c e d ~ r e , ~ *using
- ~ ~ published
molecular c o n ~ t a n t s ’ ~ ~ with
’ ~ ~ the
~ ’ .results
~ ~ ~ ~already
’
presented
in Figure 1 . Vibrational wave functions were subsequently obtained by standard numerical solution3*of the radial Schrainger
equation. Franck-condon factors could then be calculated, which
in practice was done by evaluating the integral in eq 3 with &(r)
set at unity; the value of r at which the contribution to the integral
was maximized was also recovered from the calculation for each
vibronic band. The ratios putdt/qddltherefore provided a first
approximation to the form of R,(r). In a second iteration, this
functional form of R,(r) was incorporated in the evaluation of
predicted pddrvalues through eq 3 and the results for each band
finally compared with the experimental observations.
IV.1. B-X System. The Franck-Condon factors calculated
for the B-X system by the procedure described above are included
in Table I. Also listed are the only previous values of which we
are
which were generated by a more approximate method
employing Morse potential curves and less accurate molecular
constants, and covering a more limited range of vibronic bands.
Agreement is reasonable for bands originating from B2Z+, u’ =
0, but is less satisfactory for u’ = 1
Table I further contains the computed pdd’ values arrived at
iteratively with R,(r) functions adjusted to best match the experimental pUtd.sets. (The Edinburgh and SRI data sets were
treated independently to allow comparison.) The R,(r) function
was found to be relatively constant over the range of internuclear
distances, 1.85 A < r d 2.15 A, sampled by the maxima of the
observed vibronic bands.
In terms of a linear, decreasing functionM
I
R,(r) = c(1 - p(r - r?)
(8)
where c is an arbitrary constant and r’ = 2.0 A is the midpoint
of the range in which R,(r) was determined, the best-fit values
of the slopes were p = (0.25 f 0.56) A-‘ and p = (0.65 f 0.85)
A-l for the Edinburgh and SRI data sets, respectively. These
values correspond to respective declines of 7% and 18%in R,(r)
over the range 1.85 A d r d 2.15 A. Another way of expressing
the statistical significanceof the slightly declining &(r) functions
relative to those constant with r is to compare root mean square
differences over the entire data set. Recall that the qufdfvalues
are effectively pddrvalues for constant R,(r). The root mean square
differences over all bands were 1 1 . 1 and 13.3 for comparison of
the respective Edinburgh and SRI experimental pdu” data sets
directly with the qdg values. These were reduced to 8.1 and 7.6,
respectively, for comparison of the experimental pddjvalues with
those calculated from the appropriate R,(r) function. Simulated
fluorescence spectra using the appropriate R,(r) function are
9708
The Journal of Physical Chemistry, Vol. 96, No. 24, 1992
Singleton et al.
It is similarly very straightforward that the ...(4su) molecular
Rydberg state must be within 39680 cm-' (the atomic 4s-3p
separation) of the molecular ground state if the well depth of the
Rydberg state is at least that of the ground state. The meas ~ r e d ' properties
* ~ ~ ~ of the B state (re = l .97 l A and we = 706.7
982 (10)
952
9988
(0,O)
>96OC
cm-I) suggest that it is in fact more strongly bound than the ground
(0,l)
<46
18 (10)
43
2
state, and more closely resembles5' the SiCP X'Z+ cation with
we = 680.6 cm-I, as indeed expected if the B state were a Rydberg
150
(17)
48
140
(1,O)
140 (3)*
823 (7)
875
8609
state. This increased well depth in turn consistently reduces the
(1,l)
860 (16)h
(1,2)
<36
25 (12)
62
<1
expected Rydberg-ground state separation from the 39 70O-cm-l
atomic limit toward the observed -34000-cm-' B-X excitation
OData collected in the Edinburgh Laboratory. bData collected in
energy.
the SRI Laboratory. Digital subtraction of B-X contribution, as deThe question is therefore whether the accepted (4su)-(7~)
scribed in the text. Numbers in parentheses represent lo uncertainties
in the last digit. cCalculatedfrom RKR potentials, this work. Sum of
transfer is compatible with our present observations on &(r) for
values from a given v'level normalized to lo00 (including d'not shown
the B-X system. Invoking simple linear combination of atomic
in table). dCalculated using a linear form of Re@),eq 8, with p = -4.0
orbitals (LCAO) arguments, the 7~ molecular orbital is preA-I, r' = 2.047 A, adjusted to match the observed P,,,~,
ratio for the
dominantly a weakly antibonding Si 3p, atomic orbital. This is
(1,O)and (1.1) bands. Sum of values from a given u' normalized to
supported by quantitative estimates of electron spin densities
1000 (including u" not shown in table). eLower limit, estimated as
derived from the ground-state microwave spectrum, which suggest
described in the text. /Upper limit, estimated as described in the text.
>90% Si 3p, character for this orbital.24 The estimated4 quantum
gUsed in the estimation of the X-state vibrational temperature, section
defect
for the ...(nsa) Rydberg series also suggests that the
111.1. *Derivedfrom the zero-pressureextrapolated ratio of intensities
Rydberg orbital has substantial Si character (although not as much
described in the text. Numbers in parentheses represent 1u uncertainties in the last digit, calculated from the experimental uncertainty in
as in SiF46). Hence the electronic orbital overlap between a
this ratio.
predominantly 3p orbital and a predominantly 4s Rydberg orbital
both centered on Si would not be expected to be affected strongly
by changes in the internuclear separation. It follows that the
compared with the (SRI) experimental data in Figure 4b.
transition should be strongly allowed and therefore have the obThe independent experimental measurements agree, therefore,
served26relatively short radiative lifetime (- 10 ns), comparable
within their respective uncertainties, that the B-X Re(r)function
to that of the equivalent atomic Si tran~ition.4'~
This prediction
is relatively flat, but probably slightly declining, over the relevant
of orbital occupancy is therefore consistent with our observation
range in r. Although the current results are compatible, they differ
of a relatively slowly-varying electronic transition moment, R,(r)
somewhat from the previous estimate39of the form of R&). Using
(at least over the range spanned by our measurements), and we
their less exact Franck-Condon factors (mentioned above) and
early semiquantitative emission intensities? Singh and D ~ b had
e ~ ~ conclude that our new results lend support to the accepted electronic configuration for the B2Z+ state.
obtained a more steep1 declining electronic transition moment.
IV.2. B' - X System. As described in section 111.2.2, we have
Their slope, p = 1.69
(when expressed in the form of eq 8),
much more limited data for the B'-X system. Our measurements
corresponds to a decline of 41% in R,(r) over the same range in
are restricted to the relative transition probabilities of the five
r as above. The pdUttvalues used to obtain this result are also
bands listed in Table 11.
included in Table I for comparison with those of the present work.
The Franck-Condon factors calculated from RKR curves deThere is no ambiguity about the electronic configuration of the
rived from the most recent2' spectroscopic constants for the B'
X211 ground state of SiCl.ls,24*41In the notation of the single ab
and X states are also included in Table 11. Clearly, the strengths
initio investigation of which we are aware?' the occupancy of the
higher-lying orbitals may be written . . . ( 7 ~ ) ~ ( 8 ~ ) ~ ( 5 ~ ) ~ ( 6of
~ )the
~ - off-diagonal bands, indicated by the experimental pdo,.
values, are nor well-matched by the quail values. In particular,
(9a)2(7*)'-2II.
the (1,O) band is observed to be significantly stronger than expected
Obvious configurations which give rise to Z states and which
from its qdv" value alone, whereas qdU<(for the (1,2) band comresult from single electron excitations to higher molecular orbitals
are ...(7a)2(8u)2(5~)2(6~)2(9a)2(100)1-2Z+
and . . . ( 7 ~ ) ~ ( 8 a ) ~ - fortably exceeds the upper limit of the experimental observations.
Similarly, the Franck-Condon factor for the (0,l) band would
( 5 ~ ) ~ ( 6 ~ ) ~ ( 9 ~ ) ' ( 7 ~ ) ' ( 8 * )2Z+,
' - ~ Z2Z-.
, The first of these has
suggest that it would be relatively more intense in comparison to
been identified with the lower-lying, more extended A2Z+state
the dominant, diagonal (0,O)band than was observed in practice.
by
with the equivalent state in SiF. This identification
In principle, the variation of R,(r) with r for the B'-X system
was supported by the ab initio calculations.4l However, the second
could explain the discrepancies between the pddtand qddtvalues.
has been rejectedi5as a description of the B2Z+ state, because
We have adjusted the linear form of eq 8 to yield relative pus,,
it would be expected to lie at higher energy than the configuration
values, calculated via eq 3, which match the experimental ob...(7 ~ 7 )8~ ( 5 ~ ) ~ ( 6 ~ ) I~( ~( T9 )a" )~ Awhich
,
has been accepted
servations of the (l,O):( 1,l) ratio. Taking a value of r' = 2.047
as the logical description of the B'2A state15 (to which we return
A, which lies near the midpoint of internuclear distances which
below). Hence, since the B state lies below the B' state, and once
contribute most to the overlap integrals, the necessarily large value
again by strong analogy with SiF and other related molecules,
of the slope, p, was found to be -4.0 A-'. Note that the magnitude
the B state has been c o n c l ~ d e dto
' ~be
~ ~the
~ first member of a
Rydberg series with the configuration ...(7 ~ )8a)*(
~ ( 5 ~ )6 ~~ () ~ - of Re(r)would be increasing rapidly with r, over the short range
of significant wave function overlap, for this negative value of p .
(9u)2(nsu)'-2Z+, with n = 4.
This assignment is both energetically reasonable and supported
However, we hesitate to attach any physical significance to this
by observed molecular constants. The Si(4sc3p) excitation energy
nominal functional dependence of Re(r),even although, having
(39 680 cm-I) and the Si ionization potential (IP) (65 740 cm-l)
forced a match to the observed (l,O):(l,l) ratio, the predicted
are known accurately.47a On the assumption that the ...(4sa)
intensities of the other weak, off-diagonal bands were also
molecular Rydberg state has a potential curve very similar to the
qualitatively improved. The suppression of the (0,l) and (1,2)
SiCP ion, the ...(4sa) state minimum should therefore lie some
bands was indeed required to improve agreement but was, in fact,
26000 cm-' below the SiCP X'Z+ minimum. The IP of
a bit excessive. In carrying out these calculations, it was apparent
ground-state Sic1 has been variously measured48 and estimatthat the relative intensities of the off-diagonal bands were quite
ed27946*49*s0
to be in the range 6.8-7.5 eV (55000-60000 cm-I).
sensitive to the assumed values of the spectroscopic constants.
Hence the ...(4su) molecular Rydberg state is expected to lie
There were significant differences between the Franck-Condon
roughly in the region of 29000-34000 cm-'above the ground state.
factors calculated from the most recent constants2' and those
This is consistent, at this level of approximation, with the obreported previo~sly,'~
for example. We were not, however, able
served'8.25excitation energy (34004 cm-I) of the B2Z+ state.
to match the observed pdd,values through variations in the conTABLE 11: Vibrational Transition Probabilities for the B'-X System
of SiCl
-
i-'
B-X and B’-X Systems of the Sic1 Radical
The Journal of Physical Chemistry, Vol. 96, No. 24, 1992 9709
51095-15-9; H, 12385-13-6; CHI, 74-82-8.
stants within the ranges of their reported uncertainties, without
having to impose a rapidly varying R,(r) function similar to that
References and Notes
indicated above.
( I ) Bruno, G.;Capezzuto, P.; Cicala, G.; Cramarossa, F. Plasma Chem.
We conclude that it is quite probable that subtle inaccuracies
Plasma Process. 1986, 6, 109.
in the construction of the potentials and subsequent calculation
(2) Sameith, D.; MBnch, J. P.; Tiller, H. J.; Shade, K. Chem. Phys. Lett.
of overlap integrals could lead to the substantial differences be1986,128,483.
(3) Rowe, M. D. J. Chem. SOC.,Faraday Trans. 2 1988,84,191.
tween observed pdvt, and calculated qddt values. We cannot
(4) Jevons, W. Proc. R . Soc. London, Ser. A 1914,89,187.
therefore be at all confident that the B’-X system has an electronic
(5) Jevons, W. Proc. R . SOC.London, Ser. A 1924,106,174.
transition probability which is increasing rapidly with internuclear
(6) Datta, A. C. 2.Phys. 1932, 78,486.
distance. To test this conclusion more rigorously, it would clearly
(7) Jevons, W. Proc. Phys. Soc. London 1936,48, 563.
(8) Garg, S. N. Proc. Natl. Acad. Sci. India 1950,A19, 23.
be desirable to have a larger and more quantitative data set than
(9) Wieland, K. 2.Phys. 1952, 133,229.
the limited results presented here.
(10) Wieland, K.; Heise, M. Bull. Sci. Fac. Chim. Ind. Bologna 1952,10,
An &(r) whose magnitude increases with r is, in fact, in conflict
12.
with simple expectations from the accepted electronic occupancy
(1 I ) Barrow, R. F.; Drummond, G.; Walker, S . Proc. Phys. Soc. London,
in the B’ and X states. The electronic configuration ...( 7 ~ ) ~ - Sect. A 1954,67, 186.
(12) Ovcharenko, I. E.; Tunitskii, L. N.; Yakutin, V. I. Opt.
. Specirosc.
.
(8~)~(5s)~(6u)~(9~)’(7u)~-~A
is the natural choiceI5 for identi1960,8, 393.
fication with the B’2A state, being the lowest-lying arrangement
(13) Ovcharenko, I. E.; Kuzyakov, Y. Y. Opt. Spectrosc. 1966,20, 14.
with the correct symmetry. This was also the configuration as(14) Thrush, B. A. Nature 1960,186, 1044.
(15) Verma, R. D. Can. J . Phys. 1964,42,2345.
sumed for the B’ state in the ab initio investigation.4I The B’-X
(16) Ovcharenko, I. E.; Kuzyakov, Y. Y.; Tatesvkii, V. M. Opt. Spectrosc.
transition should therefore involve a ( 7 ~ ) - ( 9 u )electron transfer.
Mol. Spectrosc. Suppl. 1963,2, 6.
We have already argued that the 77r orbital is predominantly a
(17) Bredohl, H.; Dubois, I.; Houbrechts, Y.; Leclerq, H. J. Phys. B 1978,
Si 3p, atomic orbital. By a similar LCAO argument, the 9u
11. L137.
(18) Bredohl, H.; Demoulin, P.; Houbrechts, Y.; Mtlen, F. J. Phys. B
molecular orbital will have a dominant contribution from the 3p,
1981. 14. 1771.
C1 atomic orbital. Therefore, the transition involves a perpen(19) MSen, F.; Houbrechts, Y.; Dubois, I.; HuyEn, B. L.; Bredohl, H. J .
dicular transfer between orbitals of u and u symmetry primarily
Phys. B 1981,14, 3637.
centered on dvferent atoms. The longer radiative lifetime (- 1
(20) Bredohl, H.; Cornet, R.; Dubois, I.; MElen, F. J. Phys. B 1982,IS,
727.
ps ”)is therefore not unexpected given the relatively poor electronic
(21) Mtlen, F.; Dubois, I.; Bredohl, H. J . Mol. Spectrosc. 1990,139,361.
overlap compared with, for example, the B-X system. It would
(22) Mishra, R. K.; Khanna, B. N. Curr. Sci. 1969,38,361.
correspondinglybe anticipated that the transition probability would
(23) Rai, S. B.; Singh, J.; Upadhya, K. N.; Rai, D. K. J. Phys. B 1974,
decrease sharply with increasing separation of the nuclei. This
7,415.
(24) Tanimoto, M.; Saito, S.; Endo, Y.; Hirota, E. J. Mol. Specfrosc. 1984,
further leads us to be very skeptical about the reality of an ap103.330.
parent rapid increase in the magnitude of R,(r) with r.
~
V. Conclusions
We have measured vibrational transition probabilities for
emission from the first four vibrational levels of the B2Z+state
to levels up to u” = 10 in the X211ground state of SiCl. Two
independent sets of measurements, made in different laboratories,
were in very satisfactory agreement. We also report much more
limited vibrational transition probabilities for the strongly diagonal
B’2A-X211 system. These results are of direct utility in studies
of vibrational populations of electronically excited SiC1.33-35
By comparison of the measured transition probabilities with
Franck-Condon factors derived from RKR potentials, we have
gained some insight into the form of the electronic transition
moment, R,(r), for the B-X system. R,(r) appears to decline
slowly with internuclear distance, consistent with the accepted
(4su)-(7u), Rydberg-valence character of the transition.
The limited transition probabilities which were obtained for
the B’-X system were not well-matched by calculated FranckCondon factors. We suspect that this discrepancy is more likely
to be due to inaccuracies in the construction of the potentials and
hence the calculated overlap integrals than an implied R,(r) whose
magnitude increases rapidly with r. This would contradict the
decline anticipated from the accepted (77r)-(9u) “charge transfer”
character of the B’-X transition.
Acknowledgment. We thank Dr. K. P. Lawley for making
available computer code for the construction of RKR potentials
and the calculation of Franck-Condon factors, and for many
helpful discussions. We also thank Prof. R. N. Zare for providing
code for the computation of rotational line strengths and positions
which we made use of in the simulation of certain excitation
spectra. Prof. R. J. Donovan kindly lent the monochromator used
in the Edinburgh experiments. Mr. A. Nesbitt was involved in
preliminary experimental work in Edinburgh. Financial support
was provided by the UK SERC through an equipment grant, a
research studentship to S.S.,and a travel grant to K.G.McK.,
which we gratefully acknowledge. The SRI experimental work
was supported by internal research and development funds.
Registry NO.C2H2, 74-86-2; 0, 17778-80-2; CH2, 2465-56-7; HCCO,
~~
(25) Meijer, G.; Jansen, B.; Ter Mullen, J. J.; Dynamus, A. Chem. Phys.
Lett. 1987,136, 519.
(26) Meijer, G.;Ubachs, W.; Ter Mullen, J. J.; Dynamus, A. Chem. Phys.
Lett. 1987,139,603.
(27) Johnson, R. D., 111; Fang, E.; Hudgens, J. W. J . Phys. Chem. 1988,
92. 3880.
(28) Rydberg, R. Z. Phys. 1931,73,376.
(29) Klein, 0. Z. Phys. 1932,76,226.
(30) Rees, A. L. G. Proc. Phys. SOC.London 1947,59,998.
(31) Venkataramanaiah, M.; Lakshman, S. V. J. J . Quanf. Spectrosc.
Radiat. Transfer 1981. 26. 11.
(32) Mandrugin, A. V.; Kuznetsova, L. A.; Kuzyakov, Y. Y. Spectrosc.
Lett. 1989. 17. 259.
(33) Jeffries,J. B. In Process Diagnostics: Materials, Combustion, and
Fusion; Hayes, K., Eckbreth, A,, Campbell, G., Eds.; Materials Research
Society Symposia Proceedings 117; Materials Research Society: New York,
1988; p 41.
(34) Jeffries, J. B. J. Chem. Phys. 1991,95, 1628.
(35) Singleton, S.; McKendrick, K . G. J . Phys. Chem., submitted for
publication.
(36) Earls, L. T. Phys. Rev. 1935,48,423.
(37) Herzberg, G. Molecular Spectra and Molecular Structure I-Spectra
ofDiatomic Molecules, 2nd ed.; Van Nostrand Reinhold: New York, 1950;
Chapters 1, 4.
(38) Lawley, K. P.; Wheeler, R. J . Chem. SOC.,Faraday Trans. 2 1981,
77, 1133.
(39) Singh, J.; Dube, P. S . Indian J . Pure Appl. Phys. 1971, 9, 164.
(40) The algebriac form of eq 8 is a clearer representation of the relative
variation of R J r ) over the range of r in which it was determined than the
apparently simpler form R,(r) = c(l - pr), which becomes extremely sensitive
to the value of p as it approaches l/i. Even for less steeply varying transition
moments, this latter form leads to a nonlinear relationship between p and the
relative decline in R J r ) over the measured range.
(41) Gosavi, R. K.; Strausz, 0. P. Chem. Phys. Lett. 1986, 131, 243.
(42) Sanii, N.; Verma, R. D. Can. J . Phys. 1965,43,960.
(43) Singhal, S.R.; Verma, R. D. Can. J. Phys. 1971,49,407.
(44) Verma, R. D. Can. J. Phys. 1962,40,586.
(45) Karna, S. P.; Grein, F. J . Mol. Spectrosc. 1987,122,28.
(46) Bosser, G.; Bredohl, H.; Dubois, I. J . Mol. Spectrosc. 1984,106,72.
(47) (a) Moore, C. E. Atomic Energy Leuels, Volume r; National Standard
Reference Data Series (US.,National Bureau of Standards) 35; NBS:
Washington, DC, 1971.
Wiese, W. L.; Smith, M. W.; Miles, B. M.
Atomic Transition Proba
es, Volume II; National Standard Reference
Data Series (US., National Bureau of Standards 22; NBS: Washington, DC,
1969.
(48) Weber, M. E.; Armentrout, P. B. J . Phys. Chem. 1989,93, 1596.
(49) Hastie, J. W.; Margrave, J. L. J . Phys. Chem. 1969,73, 1105.
(50) Dewar, M. S.; Jie, C. Organometallics 1987,6, 1486.
(51) Tsuji, M.; Mizuguchi, T.; Nishimura, Y . Can. J . Phys. 1981,59,985.
~