Predissociation dynamics of the A 2Σ+ state of SH and SD

Article abstract of DOI:10.1063/1.475108

The technique of cavity ring-down spectroscopy has been used to investigate predissociation in the A ²Σ⁺ state of the SH and SD radicals. Spectra were recorded of the A-X (1,0) band of SH and the (1,0), (2,0) bands of SD. Linewidth measurements of transitions to individual rovibrational levels of the A state revealed increasing predissociation rates with vibrational and rotational quantum number. These and all other available data have been reproduced, quantitatively, by Fermi Golden Rule calculations employing the best (experimentally determined) analytic potential for the A state and ab initio repulsive potentials and spin-orbit coupling matrix elements.

Full text of DOI:10.1063/1.475108

Predissociation dynamics of the A 2 Σ + state of SH and SD
Martyn D. Wheeler, Andrew J. Orr-Ewing, and Michael N. R. Ashfold
Citation: The Journal of Chemical Physics 107, 7591 (1997); doi: 10.1063/1.475108
View online: http://dx.doi.org/10.1063/1.475108
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2
Predissociation dynamics of the A ⌺؉ state of SH and SD
Martyn D. Wheeler, Andrew J. Orr-Ewing,a) and Michael N. R. Ashfold
School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
͑Received 8 July 1997; accepted 11 August 1997͒
The technique of cavity ring-down spectroscopy has been used to investigate predissociation in the
2
A ⌺ϩ state of the SH and SD radicals. Spectra were recorded of the A–X ͑1,0͒ band of SH and the
͑1,0͒, ͑2,0͒ bands of SD. Linewidth measurements of transitions to individual rovibrational levels of
the A state revealed increasing predissociation rates with vibrational and rotational quantum
number. These and all other available data have been reproduced, quantitatively, by Fermi Golden
Rule calculations employing the best ͑experimentally determined͒ analytic potential for the A state
and ab initio repulsive potentials and spin–orbit coupling matrix elements. © 1997 American
Institute of Physics. ͓S0021-9606͑97͒00543-6͔
I. INTRODUCTION
ing of the electronic predissociation of the A-state. More
recently the SH A–X transition has been employed as a
probe to measure nascent rotational distributions arising
from the 266 nm photolysis of H2S using the technique of
degenerate four-wave mixing ͑DFWM͒ which, unlike LIF
as a detection scheme, should not suffer from signal loss due
to nonradiative processes such as predissociation.
The SH radical is of importance in fossil fuel combus-
tion processes and as an intermediate in a wide variety of
naturally occurring reactions yielding sulphur containing
pollutants. It is a direct product of H2S photolysis in the
upper atmosphere, and is of astrophysical relevance given
the significant abundance of sulphur in the interstellar me-
dium.
17
2
Predissociation rates for SH and SD A ⌺ϩ ϭ0 were
v
Ј
determined accurately by LIF studies. Ubachs et al.18,19 re-
corded high resolution LIF spectra of SH in a molecular
beam to measure lifetime broadening of spectral lines and
2
2
The SH A ⌺ϩ –X ⌸ electronic transition was first ob-
served in absorption by Lewis and White,1 and has been the
subject of numerous subsequent studies.2–7 Ramsay,8 and
later Johns and Ramsay9 used flash photolysis of H2S and
D2S to obtain UV spectra of the ͑0,0͒, ͑1,0͒, and ͑2,0͒ bands
observed an N dependence to the A ⌺ϩ ϭ0 predisso-
2
v
Ј
Ј
ciation rates. The natural lifetimes decrease monotonically
from 3.2Ϯ0.3 ns for N ϭ0 to 0.95Ϯ0.02 ns for N ϭ9, with
Ј
Ј
2
2
of the A ⌺ϩ –X ⌸ transition of SH and SD using a grating
spectrograph and performed a detailed rotational analysis.
These workers reported sharp rotational lines in the ͑0,0͒
band while the ͑1,0͒ and ͑2,0͒ bands of SH were observed to
be diffuse, indicating the onset of rapid predissociation.
e-parity levels ͑corresponding to the F1 components of the
2
A ⌺ϩ state͒ having slightly shorter lifetimes than the
f-parity (F2) levels. These lifetime values are in good agree-
ment with the results of quenching20 and time-resolved fluo-
rescence decay experiments.10 Kawasaki et al.21 measured
Ramsay8 estimated rotational linewidths in the ͑1,0͒ band of
2
fluorescence lifetimes of SD A ⌺ϩ, ϭ0, N ϭ0–13 and
v
Ј
Ј
ϳ0.1 cmϪ1 implying a lifetime of SH A ⌺ϩ,
ϭ1 of
2
v
Ј
observed a monotonic decrease with increasing N from
Ј
ϳ50 ps. In comparison, the radiative lifetime of SH A ⌺ϩ
2
198Ϯ7 to 44Ϯ1 ns, with e-parity levels again having
slightly shorter lifetimes.
ϭ0 was experimentally deduced to be 820Ϯ240 ns ͑730
v
Ј
10
Electronic structure calculations22–24 suggest that the in-
Ϯ180 ns for SD͒ in fairly close agreement with ab initio
calculations giving an estimate of 704 ns.11 Further evidence
2
teractions resulting in predissociation of the A ⌺ϩ states of
for the predissociation of the A ⌺ϩ state came from flame
2
SH and SD are similar to those occurring in the OH radical.
emission spectra12 which showed the SH A–X ͑0,0͒ band
and the SD A–X ͑0,0͒ and ͑0,1͒ bands, but no emission for
2
Predissociation of the OH A ⌺ϩ state has been much stud-
ied both experimentally25,26 and theoretically.27,28 The
2
A ⌺ϩ state of OH is crossed by three repulsive electronic
Ͼ0. Similarly, laser induced fluorescence ͑LIF͒ studies of
v
Ј
states that dissociate to the atomic fragments O(3Pj)
ϩH(2S). These repulsive 4⌺Ϫ, 2⌺Ϫ, and 4⌸ states are
SH and SD failed to detect fluorescence from Ͼ0 levels of
v
Ј
the A ⌺ϩ state.13,14 Excitation of SH on the A–X transition
has been used to study SH–Ar and SH–Ar2 van der Waals
complexes15 and SH embedded in matrices of argon and
krypton.16 The presence of one or more Ar atoms bound to
2
2
coupled to the bound A ⌺ϩ state via spin–orbit couplings,
and the extent to which these states affect the predissociation
2
rate varies with the vibrational level of the OH A ⌺ϩ and
2
SH A ⌺ϩ increased the fluorescence lifetime of ϭ0 lev-
2
the rotational quantum number; for example, for OH A ⌺ϩ,
v
Ј
ϭ3 rates are 0.33ϫ1010 sϪ1 for N ϭ0 and 1.58
els to as long as 600 ns; for Ar–SH the increase in the
natural lifetime depended on the number of quanta of exci-
tation of the Ar–SH stretch. SH contained within a rare-gas
matrix showed complete quench-
v
Ј
Ј
ϫ1010
s
Ϫ1 for N ϭ14, with rates for e-parity (F ) levels up
Ј
1
to 10% higher than for f-parity (F2) levels. Recent Fermi
Golden Rule calculations of the predissociation rates of OH
2
A ⌺ϩ, , N levels employing ab initio electronic wave
v
Ј
Ј
functions for the A ⌺ϩ, ⌺Ϫ, ⌺Ϫ, and 4⌸ states and com-
2
4
2
a͒
Author for correspondence. Fax: ͑0117͒ 925 1295; Electronic mail: a.orr-
ewing@bristol.ac.uk
puted values of the spin–orbit coupling between these states
J. Chem. Phys. 107 (19), 15 November 1997
0021-9606/97/107(19)/7591/10/$10.00
© 1997 American Institute of Physics
7591
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7592
Wheeler, Orr-Ewing, and Ashfold: Predissociation dynamics of SH
showed excellent agreement with the available experimental
data.28
The 532 nm output of a Nd:YAG ͑Quantel YG680͒ laser
was used to pump a dye laser ͑Spectra Physics PDL-3͒ op-
erating with DCM and Rhodamine 610 dyes. The dye laser
output energy was typically ϳ30 mJ and had a bandwidth of
ϳ0.07 cmϪ1. Part of the dye laser fundamental was sepa-
rated from the main laser beam using a quartz flat and di-
The SH A ⌺ϩ state is similarly crossed by ⌺Ϫ, ⌺Ϫ,
and 4⌸ repulsive states that correlate with S(3Pj) and H(2S)
at large internuclear separation. Riad Manaa24 performed de-
tailed ab initio electronic structure calculations of the poten-
tial energy curves for all four of these states and for the
spin-orbit and Coriolis couplings between the states. Predis-
sociation rates based on these ab initio results were not, how-
ever, calculated. The experimental data with which to com-
pare such calculated rates has, until now, been sparse, and
2
4
2
´
rected into an iodine LIF cell and an etalon ͑free spectral
range 0.492 cmϪ1͒ for accurate wavelength calibration. The
standard deviations of fits to the well-documented I2 B–X
spectra34 and etalon fringes were Ͻ0.01 cmϪ1. The remain-
´
ing laser beam was frequency doubled in a KDP crystal
housed in a homebuilt autotracker and the residual funda-
mental light was removed using a filter. The resultant UV
beam had an energy of 3–6 mJ per pulse and was injected
into the ring-down cavity ͑RDC͒ through one of the cavity
end mirrors. The UV mirrors ͑Research Electro-Optics, 7.75
mm diam, 4 mm thick quartz substrates͒ had a specified re-
flectivity of Ͼ99.9% at 320 nm and a 2 m radius of curva-
ture. They were mounted 1.6 m apart in PTFE disks con-
nected to the glass flow cell by flexible bellows. Fine control
of the mirror positions was achieved using micrometer
screws located alongside the bellows, and mirror alignment
was assisted by a helium–neon laser. Light escaping from
the RDC was detected by a photomultiplier ͑EMI 9592͒
mounted behind one of the mirrors. Background fluorescence
arising from the UV laser beam passing through the mirror
substrates was eliminated by a filter placed in front of the
PMT. The signal from the PMT was digitized using a digital
oscilloscope ͑LeCroy 9400͒ and transferred to a PC via a
GPIB interface for analysis. Care was taken to ensure that
the ring-down signal was a single-exponential decay. Ring-
down times (1/e) were typically ϳ10 ␮s at 306 nm. Spectra
were recorded by monitoring the variation of the ring-down
time with wavelength.
measurement of accurate lifetimes for SH and SD
A ⌺ϩ, ,N levels has been restricted to ϭ0.10,18–21
A
2
v
v
Ј
Ј
Ј
2
comparison of predissociation rates of SH A ⌺ϩ with the
much-studied OH A ⌺ϩ should highlight the effects of the
2
different spin–orbit interactions in these first- and second-
row hydride radicals.
The technique of cavity ring-down spectroscopy
29–31
͑CRDS͒
enables spectroscopic probing of the predisso-
ciated ,N levels of SH and SD A ⌺ϩ for Ͼ0 because
2
v
v
Ј
Ј
Ј
it is a direct absorption technique and because the high sen-
sitivity of CRDS allows measurement of SH and SD spectra
at low pressures where collision-induced broadening is neg-
ligible. We have recently demonstrated the power of CRDS
for studies of molecular predissociations in which the life-
times of the predissociated states are less than ϳ500 ps.32
CRDS therefore provides a complementary method to LIF
which is better suited to study the decay of longer-lived
states. In an earlier communication,33 we reported a high-
2
2
resolution cavity ring-down spectrum of the A ⌺ϩ –X ⌸
͑1,0͒ band of SH. From the accurately determined spectral
2
linewidths, we extracted predissociation rates for SH A ⌺ϩ,
ϭ1, N ϭ0–8 and compared the experimental data with
v
Ј
Ј
Fermi Golden Rule calculations using a combination of the
ab initio spin–orbit coupling values and repulsive state po-
tentials of Riad Manaa24 and a potential for the A ⌺ϩ state
2
The flow tube consisted of a 25 mm diam glass tube with
several ports along its length for pressure gauges and gas
inlets. The flow tube was evacuated by a rotary pump ͑Ed-
wards͒ connected close to one end of the tube by a vibration-
isolating bellows. The pressure in the cell was monitored by
capacitance manometer gauges ͑0–10 and 0–1000 Torr͒ and
could be regulated using a throttling valve before the rotary
pump. SH was formed in a continuous flow via the reaction
of hydrogen atoms with H2S. The hydrogen atoms were
formed by microwave discharge of H2 ͑BOC High Purity͒ in
a phosphoric-acid coated mullite tube ͑10 cm long, 12 mm
o.d.͒ and were introduced to the RDC 33 cm from one end;
they reacted in the RDC with a few mTorr of H2S ͑Mathe-
son, 99.5% purity͒ introduced further upstream. Typical
pressures of H2 in the discharge were 0.5–1.0 Torr and the
microwave discharge operated at ϳ50 W input power. Care-
ful control of the gas mixes using needle valves suppressed
the formation of S2 which was observed as a by-product of
the reaction to form the SH. Measurement of the widths of
nonpredissociated lines in the S2 B–X spectrum35 in the
wavelength region of the SH experiments established the UV
laser linewidth in our experiments as 0.09 cmϪ1 FWHM,
with the line shape well described by a Gaussian function.
obtained from spectroscopic and photochemical data. The
calculated and measured predissociation rates were in quan-
titative agreement. In this paper we extend this work to
present the cavity ring-down spectra of the SD
A ⌺ϩ –X ⌸ ͑1,0͒ and ͑2,0͒ bands. From the CRD spectra
we determine predissociation rates which we compare to
Fermi Golden Rule calculations using the same potentials
and coupling functions. As a further test of our theoretical
model, we calculate the variation of the predissociation rates
2
2
2
with N for SH and SD A ⌺ϩ ϭ0 and compare the re-
v
Ј
Ј
sults with previous experimental studies. The result is a uni-
fied experimental and theoretical picture of the mechanism
2
of predissociation of SH/SD A ⌺ϩ р2, as well as pre-
v
Ј
dictions for the predissociative behavior of higher
levels.
v
Ј
II. EXPERIMENT
The cavity ring-down spectroscopy apparatus used to
record spectra of the SH and SD A–X bands consists of a
pulsed dye laser system, a glass flow tube bounded by high
reflectivity mirrors, signal detection and acquisition electron-
ics, and wavelength calibration equipment.
J. Chem. Phys., Vol. 107, No. 19, 15 November 1997
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Wheeler, Orr-Ewing, and Ashfold: Predissociation dynamics of SH
7593
2
FIG. 1. Experimental ͑bottom͒ and simulated ͑top͒ spectra of part of the SH A
⌺
ϩ –X 2⌸ ͑1,0͒ band, with rotational line assignments indicated by the combs
above the spectra. The simulation was performed using spectroscopic constants from Refs. 9 and 38 and assumes a temperature of 300 K. The line shapes in
the simulation are a convolution of a Gaussian ͑FWHM 0.09 cmϪ1͒ and a Lorentzian ͑FWHM 1.0 cmϪ1͒ function.
SD was produced by the reaction of D2S with D atoms
formed from a microwave discharge in D2 ͑Spectra Gases,
Research Grade͒ under the conditions described above. D2S
was synthesised by the reaction of D3PO4 in D2O with FeS in
a deuterated vacuum line and was stored in a 5 l glass bulb.
Prior to studying SD, the entire vacuum apparatus was deu-
terated by overnight exposure to D2O, and the microwave
discharge tube was coated with deuterated phosphoric acid.
Although the reaction of H atoms with D2S should produce
SD cleanly, the reaction with D atoms was found to give
better SD signal with less SH contamination.
to record the SH A–X ͑2,0͒ band were foiled by a combina-
tion of poor Franck–Condon factors for the transition, the
likely very large lifetime broadening of the spectral lines,
Ϫ
Ϫ
3
3
and the strong overlapping S2 B ⌺u –X ⌺g ͑6,0͒ band that
could not be eliminated by adjustment of the H2S: H atom
mixing ratio. In addition, the reflectivities of our mirror sets
at the wavelengths appropriate to the ͑2,0͒ band were sub-
stantially less than the maximum mirror reflectivity and the
maximum ring-down time observed at 290 nm was 4 ␮s.
2
2
Figure 1 shows the CRDS spectrum of the SH A ⌺ϩ –X ⌸
͑1,0͒ band over the wavenumber range 32 390–32 670
cmϪ1 together with a simulation derived using the literature
values for the ground38 and excited9,18 states. The simulation
assumes a temperature of 300 K, a Gaussian instrument func-
tion of FWHM 0.09 cmϪ1, and a Lorentzian component of
the line profile of FWHM 1.0 cmϪ1 to allow for homoge-
neous lifetime broadening. The simulation reproduces the
observed positions, intensities and widths of the spectral
lines very well, but to interpret the effects of predissociation
as precisely as possible, we fitted unblended spectral lines as
described below to determine accurately the homogeneous
widths of individual rotational levels.
The experimental design precludes any detrimental ef-
fects of cavity modes on our spectra.36,37 The longitudinal
mode spacing of the RDC is calculated to be 0.003 cmϪ1
,
much narrower than either the laser bandwidth or the widths
of the spectral features under investigation. The lifetimes for
2
SH and SD A ⌺ϩ, as discussed below, are shorter than the
cavity round trip time of the laser pulse (ϳ10 ns), so coher-
ent effects of multiple pulses interacting with the SH/SD
excited state can be neglected. The short lifetimes of the SH
and SD A-state levels also mean that the spectral linewidths
are greater than the laser bandwidth, thereby ensuring that
conditions appropriate to Beer–Lambert law absorption are
satisfied.
The excited states of SH ͑SD͒ can, in principle, decay
via two routes, radiative decay and predissociation. If the
rate constants for these two processes are denoted as krad and
kpre, respectively, the total rate of decay of the excited state
is determined by an overall rate constant kϭkradϩkpre . The
natural lifetime of the excited state, ␶(ϭ1/k) is related to the
III. RESULTS
2
2
Spectra were recorded of the SH A ⌺ϩ –X ⌸ ͑1,0͒
band and of the SD A ⌺ϩ –X ⌸ ͑1,0͒ and ͑2,0͒ bands, all
2
2
of which fall in the wavelength range 298–317 nm. Attempts
J. Chem. Phys., Vol. 107, No. 19, 15 November 1997
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7594
Wheeler, Orr-Ewing, and Ashfold: Predissociation dynamics of SH
ϭ1, N lifetimes. Error limits in the quoted life-
2
ϩ
TABLE I. SH A
⌺
vЈ
Ј
times correspond to 2␴ in the fit of the experimental linewidths.
Lifetime/ps
N
e parity
f parity
Ј
ϩ0.24
0
5.45
5.45
Ϫ0.22
ϩ0.24
Ϫ0.22
1
2
3
4
5
6
7
8
ϩ0.36
ϩ0.36
4.93
5.19
4.97
4.65
4.59
4.61
5.10
4.64
4.70
4.08
Ϫ0.32
Ϫ0.32
ϩ0.37
ϩ0.51
Ϫ0.33
Ϫ0.42
ϩ0.25
ϩ0.65
Ϫ0.23
Ϫ0.51
ϩ0.31
ϩ0.27
Ϫ0.27
Ϫ0.24
ϩ0.42
Ϫ0.36
ϩ0.73
Ϫ0.55
FIG. 2. Experimental ͑bottom͒ and simulated ͑top͒ spectra of part of the SD
2
A
⌺
ϩ –X 2⌸ ͑1,0͒ band, with rotational line assignments indicated by the
associated radiative and predissociative lifetimes, ␶ and
rad
comb above the spectra. The simulation was performed using spectroscopic
constants from Refs. 9, 12, and 39 and assumes a temperature of 300 K. The
line shapes in the simulation are a convolution of a Gaussian ͑FWHM
0.09 cmϪ1͒ and a Lorentzian ͑FWHM 0.14 cmϪ1͒ function.
␶
pre , respectively, via
1
1
1
ϭ
ϩ
.
͑1͒
␶
␶
␶
pre
rad
2
The deduced radiative lifetimes of SH A ⌺ϩ ϭ0 and SD
v
Ј
Torr used in our experiments, pressure broadening is ex-
A ⌺ϩ ϭ0 are of the order of 700–800 ns,10 whereas the
2
v
Ј
pected to result in a linewidth contribution of Ͻ0.001 cmϪ1
.
natural lifetimes measured in this study are less than 100 ps.
Since it is reasonable to assume only a small R-dependence
in the A–X electronic transition moment and thus a small
Figure 2 shows a portion of the spectrum of the SD
A ⌺ϩ –X ⌸ ͑1,0͒ band in the wavenumber range
32 310–32 350 cmϪ1. The signal to noise ratio in this spec-
trum is worse than in the equivalent SH band, presumably
because of the less efficient production of SD in our dis-
charge flow system. Shown with the experimental spectrum
is a simulated spectrum calculated using the spectroscopic
2
2
-dependence to the radiative lifetime of the A state, we can
v
Ј
thus safely equate the measured natural lifetimes with the
2
predissociative lifetimes of the A ⌺ϩ Ͼ0 levels.
v
Ј
As described previously,32,33 homogeneous contributions
to the widths of spectral lines were determined by fitting
unblended spectral lines to a Voigt profile. The Voigt profile
is a convolution of a Gaussian function ͑corresponding to the
combined effects of the laser line shape and Doppler broad-
ening͒ and a Lorentzian function ͑corresponding to the ef-
fects of lifetime broadening͒. The FWHM of the Gaussian
function is determined by fitting S2 transitions that overlap
the SH and SD spectra. Although the Doppler components
due to SH and S2 will differ slightly, the bandwidth of the
UV laser beam dominates the Gaussian ‘‘instrument’’ func-
tion and we determine a FWHM of 0.09 cmϪ1 that we at-
tribute primarily to the laser bandwidth. This Gaussian con-
tribution to the Voigt profile is held fixed during the line
fitting, and this fitting then determines the FWHM of the
Lorentzian component, ⌫. The homogeneous linewidths are
related to the natural lifetimes by
constants for SD in its X ⌸ and A ⌺ϩ states.9,12,39 The
closest correspondence between the observed and measured
line shapes is obtained if the 0.09 cmϪ1 FWHM Gaussian
instrument function is convoluted with a Lorentzian profile
of ⌫ϭ0.14 cmϪ1 ͑FWHM͒. This homogeneous broadening
is equivalent to an upper state lifetime of ϳ30 ps. The signal
to noise ratio and the modest homogeneous broadening pre-
vent accurate fitting of unblended spectral lines to determine
2
2
the N dependence of the predissociation rate. The line-
Ј
widths are virtually at the limit we can determine reproduc-
ibly with our UV laser bandwidth and hence we restrict our-
2
selves to the observation that the lifetimes of the SD A ⌺ϩ
ϭ1 rotational levels are у30 ps.
v
Ј
As mentioned above, we were unable to record spectra
of the SH A–X ͑2,0͒ band because of a combination of un-
favorable factors. We were, however, successful in observing
portions of the SD A–X ͑2,0͒ band and part of this spectrum
in the wavenumber range 33 430–33 520 cmϪ1 is shown in
Fig. 3. The figure also shows a simulation of the band cal-
culated as described above and including a homogeneous
contribution to the spectral line shapes with ⌫ϭ2.3 cmϪ1
FWHM. This value of ⌫ was determined by fitting the com-
plete experimental spectrum to a simulation with the line-
width as a floated parameter. The spectrum is overlapped by
a band of the S2 B–X transition, and much of the apparent
‘‘noise’’ in the spectrum is in fact sharp, unbroadened S2
spectral lines. The procedure used to determine ⌫ precludes
1
⌫ cmϪ1͒ϭ
.
͑2͒
͑
2␲c␶
The results of this fitting process are listed in Table I for SH
2
A ⌺ϩ, ϭ1, N ϭ0–8. Within the errors of the measure-
v
Ј
Ј
ments, we observe no difference in predissociation rates for
the e- and f-parity rotational levels of ϭ1. The fitting
v
Ј
assumes that unresolved hyperfine structure and pressure
broadening make negligible contributions to the lineshapes.
Hyperfine splittings of Ͻ0.03 cmϪ1 have been measured18
2
for SH A ⌺ϩ ϭ0, N ϭ14 while, at the pressures of Ͻ1
v
Ј
Ј
J. Chem. Phys., Vol. 107, No. 19, 15 November 1997
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Wheeler, Orr-Ewing, and Ashfold: Predissociation dynamics of SH
7595
relative roles of the different repulsive states in the predisso-
ciation mechanism and make apparent the origins of the ob-
served variations of the predissociation rates with
and N
Ј
v
Ј
for this system. The calculations neglect the effects of the
parity of the rotational levels but we will return to this point
later.
Predissociation rates were calculated using a slightly
modified version of the program BCONT.40 The program re-
quires potential functions for the bound and repulsive states
involved in the predissociation mechanism and the relevant
functions are taken from a combination of ab initio calcula-
tions and experimental data. The first three dissociative
states, the 1 4⌺Ϫ, 12⌺Ϫ, and 1 4⌸ states, arise ͑predomi-
nantly͒ from the electron configurations
FIG. 3. Experimental ͑bottom͒ and simulated ͑top͒ spectra of part of the SD
A
2
⌺
ϩ –X 2⌸ ͑2,0͒ band, with rotational line assignments indicated by the
...3␴21␲44␴25␴26␴12␲2; 1 4⌺Ϫ,1 2⌺Ϫ
combs above the spectra. The simulation was performed using spectroscopic
constants from Refs. 9, 12, and 39 and assumes a temperature of 300 K. The
Lorentzian component of the line shapes in the simulation was floated as a
variable parameter in a fit to the experimental spectrum, giving a FWHM of
2.3 cmϪ1. As in previous figures, the Gaussian component of the line shape
was fixed with FWHM 0.09 cmϪ1. The sharp features in the experimental
spectrum are overlapping rotational lines of the S2 B–X transition.
4
...3␴21␲44␴25␴16␴12␲3; 1 ⌸,
and the only available information about the form of these
dissociative potentials comes from ab initio calculations. In
this work, we make use of the results of the most recent of
these ab initio studies of the potential energy functions24
which are calculated to cross the outer limb of the ͑ab initio͒
measurement of the N dependence of the predissociation
Ј
Ј
2
rate from SD A ⌺ϩ ϭ2. Direct fitting of ‘‘single’’ lines
v
2
A ⌺ϩ state potential at Rc(1 4⌺Ϫ)ϭ1.71 Å, Rc(1 2⌺Ϫ)
to establish this N dependence is not feasible because the
Ј
ϭ1.90 Å, and Rc(1 4⌸)ϭ2.04 Å, respectively. We fit the
ab initio repulsive potentials to analytic functions of the form
widths of the features mean there are in fact no isolated lines
in the spectrum. A value of ⌫ϭ2.3 cmϪ1 corresponds to a
2
SD A ⌺ϩ ϭ2 lifetime of 2.3 ps.
v
Ј
2
Vrep R͒ϭDϩA exp Ϫ b RϪR ͒ϩb RϪR ͒
,
͖
͑3͒
͑
͓
͑
͑
͔
͕
1
x
2
x
In Table II we have collected together all the available
2
experimental information on SH and SD A ⌺ϩ
predis-
v
Ј
where D, the energy at the potential asymptote was fixed at
Ϫ564 cmϪ1, measured relative to the A state minimum, so
as to be in agreement with the known41 asymptotic splitting
between the 1D and 3P2 states of atomic sulphur
(9239 cmϪ1). A, b1 , and b2 are fitted parameters, and Rx
defines the S–H bond length about which we expand the
potential. The choice of Rx is arbitrary ͑but determines the
fitted values of the remaining parameters͒ and was initially
chosen to be the ab initio value for the crossing point, Rc .
Once the repulsive potentials are fitted to functions of the
form of Eq. ͑3͒, however, the value of Rx can be adjusted to
move the whole potential function to longer or shorter R as a
means of varying the crossing point energy and internuclear
separation.
sociative lifetimes. The variation of the predissociation rate
with and with hydrogen isotope can be understood in
v
Ј
terms of the proximity of the vibrational energy levels of the
2
2
A ⌺ϩ state to the crossing points of the A ⌺ϩ and repul-
sive ⌺Ϫ, 2⌺Ϫ, and ⌸ potentials. This point will be ad-
4
4
dressed in more detail in Sec. V.
IV. CALCULATIONS
The availability in the literature of ab initio potentials
for the various electronic states of SH and for the
R-dependence of the spin–orbit coupling between the elec-
tronic states has permitted us to perform detailed calculations
of the rates of predissociation of individual , N levels of
v
Ј
Ј
2
The ab initio potential for the A ⌺ϩ state proved too
2
SH and SD A ⌺ϩ and to compare these calculations with
inaccurate for the purposes of our calculation since it did not
reproduce the known vibrational frequencies and energies of
SH ͑SD͒ nor does it asymptotically give the correct energy
of S(1D) relative to S(3P). Consequently, we chose to fit
available experimental data to obtain a more accurate A-state
our experimental data. The results of this analysis clarify the
2
ϩ
TABLE II. Summary of the variation of SH/SD A
⌺
lifetimes for
vЈ
experimentally observed levels typically over the range N Ϸ0–10.
Ј
potential. We used two sources of experimental data; the
Lifetime
42,43
results of 121.6 nm photolysis of H2S ͑and D2S͒
and of
SH
SD
vЈ
rotationally and vibrationally resolved spectroscopic studies
0
1
2
3.20–0.95 nsa
5.45–4.61 ps
•••
247–38 nsb
35–24 ps
2.31 ps
of the A–X transitions of SH and SD.8,9 The former experi-
2
ments established the well depth, De , of the bound A ⌺ϩ
state potential as Ϫ8675Ϯ100 cmϪ1 ͓relative to the
asymptotic products HϩS(1D2)͔ as well as the energies of
aTaken from Ref. 18.
bTaken from Ref. 21.
2
several SH ͑SD͒ A ⌺ϩ
levels not observed in
v
Ј
J. Chem. Phys., Vol. 107, No. 19, 15 November 1997
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7596
Wheeler, Orr-Ewing, and Ashfold: Predissociation dynamics of SH
2
ϩ
FIG. 4. Potential energy curves used in the calculations of SH and SD A
⌺
predissociation rates. The horizontal lines show the energies of the vibrational
2
ϩ
2
ϩ
levels of the A
⌺
states of SH ͑left͒ and SD ͑right͒. The zero of energy is defined as the minimum of the A
⌺
state potential.
absorption spectroscopy. The A-state potential energy curve
We parameterized these matrix elements as a Taylor expan-
sion in the shifted distance coordinate, (RϪRx), to yield an
effective coupling function HSO(R),
was constructed using an extended Rydberg function44
2
V R͒ϭϪD 1ϩa ␳ϩa ␳ ͒exp Ϫa ␳͒,
͑4͒
͑
͑
͑
e
1
2
1
HSO R͒ϭm ϩm RϪR ͒ϩm RϪR ͒2.
͑5͒
͑
͑
͑
2
where ␳ϭR–Re , the distortion from the equilibrium bond
length (Reϭ1.423 Å) and a1 and a2 are fitted parameters
describing the shape of the potential. We refitted the previ-
ously tabulated experimental data for both SH and SD, si-
multaneously, to yield the following unified values of the
parameters, a1ϭ2.90 ÅϪ1, a2ϭϪ2.33 ÅϪ2, using a suit-
ably modified version of the program LEVEL.45 This program
0
1
x
x
The values of all parameters required for Eqs. ͑4͒ and ͑5͒ are
listed in Table III. Having set up the potentials we calculated
the bound, ,N͉, and continuum, E,N͉, wave functions
͗
v
͗
40
¨
using the program BCONT to solve the radial Schrodinger
equation and determine the matrix elements,
¨
solves the one-dimensional Schrodinger equation for a cho-
HSO E,N; ,N͒ϭ E,N
͉
HSO R͒
͉ ,N .
v
͑6͒
͑
v
͑
͗
͘
sen potential and minimises the squares of the residuals be-
tween the observed and calculated term values. The A-state
potential used in subsequent calculations reported in this pa-
per was shifted upwards in energy by De so that the refer-
ence zero of energy for all potential functions is taken as the
bottom of the A-state well.
The final stage of the calculation is to use the Fermi Golden
Rule approximation to evaluate the predissociation rates of
the , N levels of the A state. The rate constant for pre-
v
Ј
Ј
dissociation of a particular , N level with energy E is
calculated using
v
Ј
Ј
Figure 4 shows the bound A ⌺ϩ and repulsive 1 4⌺Ϫ,
2
1 2⌺Ϫ, and 1 4⌸ potentials used in the subsequent analysis,
along with the calculated vibrational levels of the A state for
SH and SD. From this picture it is apparent that the most
2
k
,N ͒ϭ 4␲2G /h͒
͉
E,N
͉
HSO R͒
͉ ,N
v
Ј
͉
Ј
͘
.
͑7͒
͑v
͑
͑
Ј
Ј
Ј
͗
el
Here, Gel is the ratio of electronic degeneracy factors of the
final and initial states.
significant contribution to the predissociation rate of low
v
Ј
levels of the A state is likely to be from interaction with the
Predissociation rates were calculated, as a function of
1 4⌺Ϫ state. A similar interaction has been invoked as the
the bound state
and N quantum numbers, for interaction
Ј
v
Ј
main contributor to the predissociation of low
levels of
with each of the three repulsive curves. As expected, the
v
Ј
the corresponding A ⌺ϩ states of both OH and OD.28 To
quantify the contributions to the predissociation from the
three different repulsive states, 1 4⌺Ϫ, 1 2⌺Ϫ, and 1 4⌸, we
have taken the calculated spin–orbit coupling matrix ele-
rates obtained for the SH and SD A ⌺ϩ р1 levels inter-
2
2
v
Ј
acting with the higher lying 1 2⌺Ϫ and 1 4⌸ states were
several orders of magnitude smaller than those from interac-
2
tion with the 1 4⌺Ϫ state. For SD A ⌺ϩ ϭ2 the rates of
v
Ј
2
2
ments
H
SO(A ⌺ϩ,1 4⌺Ϫ), HSO(A ⌺ϩ,1 2⌺Ϫ), and
predissociation via the 1 2⌺Ϫ and 1 4⌸ states are calculated
HSO(A ⌺ϩ,1 4⌸) which are a sensitive function of S–H
to be 103 and 105 times slower than for predissociation via
2
bond length in the region of the respective crossing points.24
the 1 4⌺Ϫ state, but for SH A ⌺ϩ ϭ2 the corresponding
2
v
Ј
J. Chem. Phys., Vol. 107, No. 19, 15 November 1997
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Wheeler, Orr-Ewing, and Ashfold: Predissociation dynamics of SH
7597
2
ϩ
TABLE III. Parameters for the potentials and coupling functions used in the calculations of the SH/SD A
⌺
,N predissociation rates. All parameters are defined in the text.
Ј
vЈ
b1
b2
D
m0
A
Rx
/Å
m1
m2
/ÅϪ1
/ÅϪ2
/cmϪ1
/cmϪ1
/cmϪ1
/ÅϪ1 cmϪ1
/ÅϪ2 cmϪ1
1 4⌺Ϫ
1 2⌺Ϫ
1 4⌸
3.26
2.20
2.53
0.13
0.17
0.27
Ϫ564
Ϫ564
Ϫ564
4626.17
6730.83
8494.46
1.68
1.87
2.00
44
50
Ϫ162
140
109
67
60
Ϫ37
54
rates are both only one order of magnitude slower, suggest-
ing the onset of significant predissociation via routes other
than crossing to the 1 4⌺Ϫ potential.
and coupling functions we have chosen for the calculations
are probably not unique in being able to model the experi-
mental data but, as is apparent from the figures, the agree-
ment between experiment and calculations for all data sets is
excellent. The calculations for SH and SD match not just the
Figures 5–9 show a comparison of the calculated and
experimental predissociation lifetimes for SH A2⌺ϩ
v
Ј
ϭ0,1 and SD A2⌺ϩ ϭ0,1,2. The experimental data in
absolute rates and lifetimes for different
states, which
v
Ј
v
Ј
Figs. 5 and 7 are from Ubachs et al.18,19 and Kawasaki
vary by about five orders of magnitude, but also reproduce
et al.,21 respectively. The data for SD ϭ0 has been con-
the N dependence for the different . The greatest discrep-
v
v
Ј
Ј
Ј
verted from fluorescence lifetimes to predissociative life-
times using the known radiative lifetime of SD A2⌺ϩ.10
The calculated data were obtained as described above
after optimization of the repulsive potentials to give the
ancies are for SD ϭ1 but, as pointed out in Sec. III, the
v
Ј
linewidths in the SD A–X(1,0) band are very close to our
experimental instrument function so precise determination of
the homogeneous contributions to the linewidths is particu-
larly difficult for this transition.
2
shown match with the N -dependent SH A ⌺ϩ ϭ1 ex-
v
Ј
Ј
perimental data. This optimization was done in a trial-and-
error fashion by making minor adjustments to the 1 4⌺Ϫ
state potential from which we find, by inspection, that the
V. DISCUSSION
We are now in a position to compare the variation of the
experimentally measured SH (A) ϭ1 lifetimes are repro-
v
Ј
predissociation rates of SH and SD A ⌺ϩ with hydrogen
2
duced best if the whole 1 4⌺Ϫ state potential is shifted by
Ϫ0.03 Å from the ab initio value, i.e., if Rx is decreased
from 1.71 Å to 1.68 Å. This new value of Rx is also used in
Eq. ͑5͒ for the coupling function. The crossing point of the
isotope and with vibrational and rotational level. The calcu-
lations described in the previous section reproduce quantita-
tively the magnitudes and variation of these rates and we can
use the potentials, energy levels and wave functions from the
calculations to interpret our experimental observations and to
make predictions about the predissociation for levels with
2
A ⌺ϩ and 1 4⌺Ϫ potentials then occurs at Rcϭ1.75 Å. The
repulsive potentials shown in Fig. 4 are all shifted inwards
by 0.03 Å from their ab initio crossing points with the A
state, and all other calculated results displayed in Figs. 5–9
make use of these slightly shifted ab initio 1 4⌺Ϫ, 1 2⌺Ϫ,
and 1 4⌸ potentials and coupling functions and were not
optimised for each experimental data set. The potentials
Ͼ2.
v
Ј
The predissociation rate for a particular state depends on
the extent of overlap of the bound state and continuum wave
functions46 and this overlap will be greatest for energy levels
2
ϩ
2
ϩ
FIG. 5. Lifetimes of SH A
⌺
ϭ0. Experimental results are shown by
FIG. 6. Lifetimes of SH A
⌺
ϭ1. Experimental results are shown by
vЈ
vЈ
circles, ᭹; e parity, ᭺; f parity; diamonds are the results of calculations
circles, ᭹; e parity, ᭺; f parity; diamonds are the results of calculations
described in the text. Experimental data are taken from Refs. 18 and 19.
described in the text.
J. Chem. Phys., Vol. 107, No. 19, 15 November 1997
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7598
Wheeler, Orr-Ewing, and Ashfold: Predissociation dynamics of SH
2
ϩ
FIG. 7. Lifetimes of SD A
⌺
ϭ0. Experimental results are shown by
vЈ
circles, ᭹; e parity, ᭺; f parity; diamonds are the results of calculations
described in the text. Experimental data are taken from Ref. 21.
in close proximity to the energy of the crossing point be-
2
tween the A ⌺ϩ and repulsive-state potentials. The varia-
tion of the predissociation rate with
is summarized in
v
Ј
Table II, and Fig. 4 shows a plot of the potentials for the
2
FIG. 9. Calculated bound (A
wave functions for SD. The bottom panel shows the SD A
function and the 1 4⌺Ϫ wave function of the same energy. The top panel
⌺
ϩ) and continuum (1 4⌺Ϫ) nuclear radial
2
A ⌺ϩ, 1 4⌺Ϫ, 1 2⌺Ϫ, and 1 4⌸ states used in the calcula-
2
ϩ
⌺
ϭ0 wave
vЈ
tions. These calculations demonstrate that the predissociation
2
ϩ
shows the SD A
⌺
ϭ2 wave function and the 1 4⌺Ϫ wave function of
vЈ
of the ϭ0,1, and 2 levels is dominated both for SH and SD
v
Ј
by crossing to the 1 4⌺Ϫ state and it is clear from the figure
that the large increase in predissociation rate for SH as
the same energy.
v
Ј
increases from 0 to 1 is caused by the closeness of ϭ1 to
v
Ј
the energy of the crossing. Likewise, because of isotopic
effects, the vibrational levels of SD lie lower in the potential
than those of SH with the same vibrational quantum number.
Hence, we observe a faster predissociation for SH ϭ1
v
Ј
than for SD ϭ1. The energy of SD ϭ2, however, is
v
v
Ј
Ј
greater than that of SH ϭ1 and the former state predisso-
v
Ј
ciates about twice as quickly as the latter. Our calculations of
the rate for predissociation of SD ϭ2 predict a lifetime of
v
Ј
ϳ2.3 ps in extraordinarily good agreement with the experi-
mental result. To illustrate the influence of the overlap of the
2
bound (A ⌺ϩ) and continuum (1 4⌺Ϫ) nuclear radial wave
functions on the predissociation rate, Fig. 9 shows plots of
2
the calculated SD A ⌺ϩ ϭ0 and ϭ2 wave functions
v
v
Ј
Ј
together with continuum wave functions of the same energy;
2
it is evident that proximity to the crossing of the A ⌺ϩ and
1 4⌺Ϫ potentials substantially enhances this overlap in the
latter case.
No experimental lifetime data exist for either SH or SD
for levels Ͼ2 with which to make a comparison to this
v
Ј
model. However, from a purely theoretical point of view it is
still interesting to see what predictions can be made for these
higher vibrational levels in order to understand the roles of
the ⌺Ϫ and ⌸ dissociative states ͑also shifted inwards by
Ϫ0.03 Å from their ab initio values and assuming the
calculated24 values of the spin–orbit coupling matrix ele-
2
4
2
ϩ
2
ϩ
FIG. 8. Calculated lifetimes of SD A
ϭ2 ͑bottom͒. For reasons outlined in the text we were unable to give an
experimental variation of lifetime with N for these vibrational levels. SD
⌺
ϭ1 ͑top͒ and SD A ⌺
vЈ
vЈ
ments͒. For levels with р2 the dominant predissociation
v
Ј
Ј
4
route is via the ⌺Ϫ state as already mentioned in the previ-
2
ϩ
A
⌺
ϭ1 has an experimentally measured lifetime of ϳ30 ps whilst
vЈ
that for SD A
4
2
ϩ
⌺
ϭ2 is 2.3 ps.
ous section. However, for higher vibrational levels the ⌸
vЈ
J. Chem. Phys., Vol. 107, No. 19, 15 November 1997
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Wheeler, Orr-Ewing, and Ashfold: Predissociation dynamics of SH
7599
little or no variation with e/f parity. For SH ϭ1, we ob-
v
Ј
serve no significant difference between the predissociation
rates of e and f-parity levels.
The other possible source of differences in the predisso-
ciation rates for the e and f-parity rotational levels is the
2
difference in energy. For SH or SD A ⌺ϩ the e-parity level
lies slightly higher in energy than the f-parity level of the
same N quantum number. We have investigated the effect
Ј
of this very small energy shift on the calculated predissocia-
tion rates and find it to be negligible.
It is interesting to compare the lifetime data for the A
states of SH, SD with that of OH, OD to see the effects of a
heavier nucleus on the magnitude of the spin–orbit interac-
FIG. 10. Variation of predissociation rate with each individual dissociative
state and the total predissociation rate for the first six vibrational levels of
2
tion. In OH the crossing point of the A ⌺ϩ and 1 4⌺Ϫ states
2
ϩ
SH A
⌺ .
occurs between ϭ3 and ϭ4 and, as a result, the lowest
v
v
Ј
Ј
few rotational levels in ϭ0 and 1 show no predissociation
v
Ј
at all, however, even in ϭ3 the lifetime of the highest
v
Ј
observed25,26 rotational level is still as long as 33 ns in con-
state rapidly becomes the main predissociation channel
2
whilst the ⌺Ϫ state only ever seems to play a minor role.
trast with SH ( ϭ1) for which ␶Ͻ5 ps. This is largely a
v
This point is illustrated in Fig. 10 which shows the calculated
predissociation rates of SH (A) via each individual channel
as well as the total rate plotted against the rotationless levels
reflection of the smaller spin–orbit coupling matrix elements
associated with the first row hydride.
of ϭ0–5. The total rate reported here is simply a summa-
v
Ј
VI. CONCLUSIONS
tion of the three individual rates from a given
level
v
Ј
We have used a combination of experimental and theo-
retical methods to understand the predissociation of the low
Our calculations also reveal the origins of the rotational
dependence of the lifetimes of SH ϭ0,1 and SD ϭ0.
v
v
Ј
Ј
2
vibrational states of SH and SD A ⌺ϩ. As is the case with
The bound and continuum wavefunctions are solutions of the
OH, the first electronically excited state of SH is predissoci-
ated by three repulsive states, the 1 4⌺Ϫ, 1 2⌺Ϫ, and 1 4⌸
states, which all correlate with S(3P)ϩH(2S) at large inter-
nuclear separation. CRDS measurements of the A–X ͑1,0͒
bands of SH and SD and the ͑2,0͒ band of SD reveal the rates
of predissociation through homogeneous broadening of spec-
tral lines. The lifetimes determined from the predissociation
rates have been compared with Fermi Golden Rule calcula-
tions that make use of an experimentally derived empirical
¨
radial Schrodinger equation and, for N Ͼ0, the potential is
Ј
modified by addition of a centrifugal term giving
ប2 d2⌿
2␮ dR2
ប2
N
N ϩ1͒
R2
͑
Ј
Ј
Ϫ
ϩ V R͒ϩ
⌿ϭE⌿.
͑8͒
͑
ͫ
ͬ
2␮
The vibrational and continuum wave functions and the over-
lap between them thus depend implicitly on the rotational
quantum number and this variation in the overlap with N
Ј
2
potential for the A ⌺ϩ state and ab initio values for the
gives the observed N dependence of the predissociation
Ј
1 4⌺Ϫ, 1 2⌺Ϫ, and 1 4⌸ potentials and for the spin–orbit
coupling between the bound and repulsive states. The com-
parison of experimental and theoretical results reveals that
rate. Our calculations show that for vibrational levels lower
in energy than the crossing point of the bound and repulsive
potentials, the predissociation rate increases with increasing
molecular rotation, whereas for vibrational levels lying
the predissociation of the A state levels with р2 is domi-
v
Ј
nated by coupling to the 1 4⌺Ϫ state, but that the other re-
above the crossing point, e.g., SH( ϭ2), the effect of in-
v
Ј
pulsive potentials should start to contribute to the predisso-
creased rotation is to decrease the predissociation rate.
The calculations neglect the effect of parity of the rota-
tional levels on the predissociation rate. The experimental
data of Ubachs et al.18,19 for SH ϭ0 and of Kawasaki
ciation of higher
levels. The rotational dependence of the
v
Ј
predissociation rates determined by us for the ϭ1 level of
v
Ј
SH ͑A͒ and by others for the ϭ0 levels of the A state of
v
Ј
v
Ј
SH and SD is reproduced quantitatively by the calculations
which show the variation to be the result of centrifugal con-
tributions to the potential energy functions. The value of
CRDS as a method of studying fast molecular predissocia-
tion is clearly demonstrated.
et al.21 for SD ϭ0 show a small but significant difference
v
Ј
in the rates of predissociation for the two parities, with
e-parity levels having slightly shorter lifetimes than f-parity
levels. Similar effects have been observed for the predisso-
ciation of OH A ⌺ϩ in several vibrational levels, and cal-
2
culations of the predissociation rates for OH reproduce this
difference. The effect in OH is attributed to the nature of the
angular momentum coupling in the repulsive 1 4⌺Ϫ state; if
the coupling is pure Hund’s case ͑b͒ the e-parity levels are
predicted to show faster predissociation than the f-levels,
while for case ͑a͒ coupling the reverse is true.27 For OH
ACKNOWLEDGMENTS
We thank Professor T. Ishiwata, Professor Masahiro Ka-
wasaki, Keith Rosser, Dr. Jon Pearson, and Stuart Newman
for their help with the CRDS experiment. We are grateful to
Dr. C.M. Western for the use of the spectral simulation pro-
grams and Professor R.J. Le Roy both for providing us with
4
predissociation by the ⌸ state, the calculations suggested
J. Chem. Phys., Vol. 107, No. 19, 15 November 1997
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7600
Wheeler, Orr-Ewing, and Ashfold: Predissociation dynamics of SH
the programs LEVEL and BCONT and for helpful comments on
their use. A.J.O.E. thanks the Royal Society for the award of
the Eliz. Challenor Research Fellowship, and M.D.W. thanks
the University of Bristol for the award of a postgraduate
scholarship. Collaborations between the Bristol group and
Professors Kawasaki and Ishiwata were made possible by the
Japan-UK Cooperative Program of the Japanese Society for
Promotion of Science, the British Council and the Royal So-
ciety.
23 P. J. Bruna and G. Hirsch, Mol. Phys. 61, 1359 ͑1987͒.
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