The B
3
R
state of the SO radical
Ching-Ping Liu
a, Nicola L. Elliott
b, Colin M. Western
b,*, Yuan-Pern Lee
a,c,
Reginald Colin
da
Department of Applied Chemistry and Institute of Molecular Science, National Chiao Tung University, Hsinchu 30010, Taiwan
b
School of Chemistry, University of Bristol, BS8 1TS, UK
cInstitute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan dLaboratoire de Chimie Quantique et Photophysique, Universite´ Libre de Bruxelles, Brussels, Belgium
Received 9 April 2006; in revised form 8 May 2006 Available online 12 May 2006
Abstract
Spectra of the B3R– X3Rtransition in SO above the first dissociation limit are recorded using degenerate four wave mixing. These spectra are combined with earlier work involving laser induced fluorescence, absorption spectra and Fourier transform emission spectra, to enable a rotational analysis and deperturbation of vibrational levels of the B state up to v0= 16. Numerous perturbations were noted
within the B3Rstate, and the origin of these is discussed. In a number of cases, these perturbations can be attributed to interactions with specific other electronic states of SO, such as A3P, C3P, d1P, and A00 3R+
. 2006 Elsevier Inc. All rights reserved.
Keywords: SO; Radicals; DFWM; Perturbations; Electronic spectroscopy
1. Introduction
The B 3R–X 3Rtransition dominates the absorption spectrum of SO between 41 000 and 52 000 cm1. The first major work on the electronic spectroscopy of SO was Mar-tin’s study of this B–X transition[1], which recorded emis-sion spectra from the v0= 0, 1, 2, and 3 levels of the B state
in a discharge tube. Predissociations within these first four vibrational levels were noted, and were attributed to a crossing with a3Pstate. A number of further flash photol-ysis studies of the B–X transition, this time in absorption, extended the coverage of the B state to what appears to be v0= 30, close to the dissociation limit [2–4]. Variations
in the level of diffuseness of the vibrational bands indicated additional predissociation mechanisms, around v0= 14 and
v0= 17. Later, the high-resolution Fourier transform
emis-sion spectra of Clerbaux and Colin[5]enabled analysis of the B–X transition to be carried out in much greater detail for levels below the dissociation limit. The rotational
struc-ture of the v0= 0 and v0= 1 levels was analysed, and a set
of molecular constants for these two B state vibrational lev-els was obtained. Based on the N dependence of the break off in emission in v0= 0–3 the first dissociation limit was
determined to be at 43 680 cm1.
All these studies indicated various perturbations in most, if not all, the vibrational levels of the B state, though a detailed analysis of the origin of these irregularities was not possible. Perturbations were very evident in the flash photolysis absorption spectra recorded by Colin, although only a limited amount of rotational analysis was possible due to the resolution of these spectra. Clerbaux and Colin identified several irregularities in the rotational structure of v0= 0 and v0= 1 although again, no suggestions as to the
cause of these perturbations were made.
This work provides a more complete rotational analysis and deperturbation of vibrational levels within the B 3R state of SO, by combining new experimental measurements with previous data. A range of techniques were employed to obtain absorption and emission spectra of the B 3R– X 3R transition. These included degenerate four wave mixing (DFWM), laser induced fluorescence (LIF),
photo-0022-2852/$ - see front matter 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2006.05.005
*
Corresponding author. Fax: +44 0 117 925 1295.
E-mail address:C.M.Western@bristol.ac.uk(C.M. Western).
graphic plate absorption, and Fourier transform emission spectroscopy. Combining a range of spectra, taken under different conditions using different techniques, has provid-ed the information necessary for the analysis of the more perturbed vibrational levels of the B state, and in some cases allows us to see the perturbing states directly.
More recent work on other electronic states of SO has enabled the source of several B state perturbations to be identified here. There are a number of electronic states of SO which are known to be candidates for perturbation of the B state; a potential energy diagram showing all the known bound states in the region is shown in Fig. 1. As the lowest levels of the B state are just below the first dis-sociation limit, any state correlating with this limit can interact with the B state. Of these, only the A 3P state has been reasonably well characterised up to the dissocia-tion limit[6]. The ground state (X3R) and the lowest lying excited states, a1Dand b1R+, have been well characterised by microwave[7]and infra-red[8–10]studies, and the Fou-rier transform emission study[5]of the B–X transition pro-vided information up to X v00= 21; however, none of this
work extends all the way up to the dissociation limit. There are also a number of other states, which are known to be bound, but about which very little information is available. The c1Rstate has been observed in Ar and Ne matrices
[11], and more recently in emission in the gas phase [12], but these experimental data are limited. Similarly, little is
known of the A00 3
R state, although it has also been observed in emission [13]. Apart from matrix work [11], there is only indirect experimental evidence of the A0 3D
state [14] and even less is known of the bound 5P state shown inFig. 1, which has only been postulated from the-oretical calculations[15]. SO is unusual in that two bound states, the C 3P and d 1P states, have been found just above the dissociation limit[15], using 1 + 1 multiphoton ionisation spectroscopy. The d state was found to be weak-ly bound, with the highest level being v0= 3; the C state
supports significantly more vibrational levels although only v0= 0 and v0= 1 have been observed experimentally.
The-oretical calculations on the C state [15,16] show that it undergoes an avoided crossing with a repulsive state at r 2.05 A˚ ; this can be seen in Fig. 1. Note that Fig. 1
includes RKR curves derived from experimental data (solid lines) and the results of high level ab initio calculations (dashed lines) from references [15,16] supplemented by a few calculations described in the text below.
In this paper, we extend the detailed rotational analysis of the B state to a much wider range of vibrational levels, which allows us to identify some specific interactions of other electronic states with the B3Rstate, and perform a deperturbation for selected cases. Interactions involving A3P, C3P, d1P, and A00 3R+
are discussed, though it is without question that some, if not all, of the other electron-ic states shown inFig. 1will also interact with the B state. A greater understanding of the interactions between B3R and its nearby electronic states enables a clearer picture of the spectroscopy of SO to be formed.
2. Experimental
This paper presents new spectra of SO, mainly degener-ate four wave mixing spectra taken in Taiwan. The analysis also included spectra from previous work recorded using a number of different techniques, which are also described briefly in this section.
2.1. Degenerate four wave mixing
A SO2/He mixture was prepared in a stainless steel
res-ervoir before expansion through a pulsed nozzle (General Valve, orifice diameter 1 mm); the reservoir was filled with SO2to a pressure of 300 Torr near 296 K and diluted with
ultrahigh purity helium to a total pressure of 3000 Torr. The pulsed nozzle was operated at 10 Hz with an opening period of 0.50 ms. The stagnation pressure was typically 1.3 atm. SO radicals were produced from the photolysis of SO2 with an ArF excimer laser (Lambda Physik, LPX
120i or GAM laser, EX100H) operating at 193 nm. The photolysis laser beam was slightly focused several nozzle diameters downstream from the orifice.
The degenerate four-wave mixing (DFWM) experiments are similar to those described previously for two-colour resonant four-wave mixing (TC-RFWM) experiments, but here only one laser was used [17,18].
30000 35000 40000 45000 50000 1.5 2 2.5 3 3.5 4 0 1 23 45 67 89 1011 1213 X3 – a1 b1 + c1 – A'3 A''3 + A3 5 0 1 0 1 0 12 3 0 1 2 3 4 5 6 7 8 9 10 1112 13 1415 16 18 1920 21 22 2324 25 26 27 28 29 30 17 B3 – C3 d1 e1 r / Å / cm–1
Fig. 1. Overall potential energy diagram showing all currently known states of SO below 55 000 cm1. The solid lines are generated from RKR curves; the dashed lines are based on high level (MRCI) ab initio calculations.
The frequency-doubled output from a dye laser (Lambda Physik, Scanmate 2E, using dyes LC4200, LC4400, LC4800, LC5000, and selected mixtures) pumped with a XeCl excimer laser (Lambda Physik, LPX 105) at 308 nm is split into three beams of comparable intensities to provide excitation in a spectral region of 214–263 nm. Light from the dye laser had spectral widths 0.1 cm1 for the fundamental output. Typically 50–150 lJ of laser energy and a beam diameter of 1.5 mm was used.
The three laser beams of the same polarization propa-gate in the same direction and cross at small angles (1) 3 mm downstream from the nozzle. The resultant signal beam is allowed to travel 2–3 m through several irises before being spatially filtered with an iris, a convex lens (f = 10 cm) and a pinhole (diameter 0.15 mm) in combination, and detected with a photomultiplier tube (Hamamatsu, R955P). The signal was integrated with a gated-integrator (Stanford Research, SR250) and pro-cessed with a computer. A digital pulse generator (Stanford Research, DG535) served to control the timing between the pulsed nozzle, the laser system, and the boxcar integrator. The delay between the photolysis and DFWM laser pulses, typically 0.7–2 ls, was adjusted to optimize the signal. Wavelength calibration of the dye laser was achieved either with a Fe–Ne optogalvanic cell or a wavemeter (Burleigh WA-5500, accuracy 0.2 cm1). DFWM spectra to v0= 3–
9 of the B–X transition of SO were recorded. Transitions observed using DFWM mostly originated from the v00= 2
level of the X state, due to the non-Boltzmann distribution of SO produced from the SO2photolysis[19]. The
rotation-al temperature could be adjusted by adjusting the experi-mental geometry, with values around 100 K being typical. Note that the DFWM signal depends on the square of the molecular density and the cube of the laser intensity but no attempt was made to normalize the spectra with respect to the intensity of the dye laser and we did not check for saturation effects. This is sufficient for the analy-sis presented in this work which only requires accurate peak positions. Peak intensities were only used as a rough guide to assignment.
2.2. Laser induced fluorescence
In addition to DFWM spectra, a number of laser induced fluorescence (LIF) spectra were recorded. LIF spectra, covering B v0= 0–3, were recorded in Taiwan in
conjunction with the DFWM spectra, using the same appa-ratus and method of radical production; a second photo-multiplier was placed near the jet to detect fluorescence in a direction perpendicular to the photolysis beam. As for the DFWM spectra, these showed a rotational temper-ature of 100 K. LIF spectra of the B–X transition had also been previously recorded as part of the work by Archer et al. [15]. These spectra were included in analysis of the lower vibrational levels, since their lower rotational temperature (15 K) enabled transitions at low J to be eas-ily assigned. In addition, a few selected LIF spectra of B–X
hot bands were recorded in Bristol, using essentially the same experimental set-up as described by Archer et al. A molecular iodine spectrum was recorded simultaneously, allowing a detailed check on the overall calibration accura-cy. An increased laser power was used in the recording of these spectra, which enabled transitions directly to some perturbing states to be observed alongside the B–X transitions.
2.3. Fourier transform emission spectrum
The analysis also used a Fourier transform emission spectrum of a microwave discharge in an SO2+ O2+ He
mixture, recorded by Clerbaux and Colin [5]. As it was an emission spectrum, it only included transitions from the v0= 0–3 vibrational levels in the B state below the
dis-sociation limit, but included a wide range (v00= 0–21) of
vibrational levels in the ground state. The effective temper-ature (1400 K) was much higher than the laser spectra described above, though the resolution was similar (0.2 cm1).
2.4. Absorption spectra
The last set of spectra covering the B–X transition was a series of flash photolysis absorption spectra. These were recorded on photographic plates and covered almost the entirety of the B 3R–X 3Rtransition (from v0= 4 up to
the dissociation limit at approximately v0= 30), which were
recorded in Ottawa by Colin [4]. To assist in assignment, these photographic plate spectra were transformed into trace spectra using the PGOPHERprogram [20], though line
positions were taken from original measurements from the photographic plates. As for the Fourier transform spec-trum, the effective temperature was high (700 K), though the resolution was significantly lower (2 cm1).
2.5. 1 + 1 Multiphoton ionisation spectra
The final source of data used for analysis was a set of 1 + 1 multiphoton ionisation (MPI) spectra recorded in Bristol [15], covering a range of transitions to the A 3P, C 3P, and d 1P states. Although these did not provide direct information on the B 3R state, they proved vital in the identification of the source of a number of perturba-tions seen within the B state.
2.6. Ab initio calculations
High level ab initio calculations were available as described in references[15,16], but to obtain full coverage of the quintet states and repulsive curves we undertook some additional calculations. These were MRCI calcula-tions using an AVQZ basis set with the MOLPRO package
[21] and were of similar quality to the previous calculations. In common with the previous results they gave excellent results (in comparison to the RKR curves)
for bond lengths < 2.3 A˚ , but required empirical shifts of up to 2000 cm1for longer bond lengths to give the disso-ciation limits at the right energy.
3. Analysis
The basic principle of analysis was the same for all lev-els, perturbed or otherwise. A conventional linear molecule Hamiltonian was used
^ H¼ Tvþ A^L ^Sþ B ^N2þ23kð3^S 2 z ^S 2Þ þ c ^ N ^S þ 1=2oð^S2 þe 2i/þ ^S2 e þ2i/Þ ð1Þ
to model the X, B, A, C, and d states, with terms omitted as appropriate. The PGOPHER program [20] was then used to
simulate and fit the observed spectra. The X state constants were fixed according to those determined by Clerbaux and Colin [5] using a combination of millimeter, IR, and UV data. The energies are defined such that Tv= 0 for v00= 0
of the X state, giving the lowest level, (J = 0, v00= 0) at
5.59 cm1. To assign the spectra, a rough simulation was constructed, using these known X state constants and any available constants for the B state (and other states, where appropriate). Assignment of rotational lines in the rough simulation to those in the experimental spectra was then possible, particularly given that accurate ground state common differences could be used to confirm the assignments. To model perturbations, the PGOPHER
pro-gram was set up to include all the interacting states in a sin-gle Hamiltonian matrix, with matrix elements as described later for the individual interactions. Finally, a least-squares fit was carried out to obtain revised values for the constants for the B state and the states interacting with it. It is well known that the lineshapes and intensities of DFWM spec-tra are complicated to model, but we found that simply squaring the intensities was sufficient for our analysis. The observed lineshapes were symmetrical, and common differences confirmed that there were no significant peak shifts in the DFWM spectra.
We illustrate the analysis by discussing selected bands below. Files containing observed and calculated positions for each of the fits, and the correlation matrix for the parameters have been deposited with the journal as supple-mentary data, and the PGOPHERinput files (containing the
constants derived below) have also been included for convenience.
3.1. v0= 8
The v0= 8 level of the B3
Rstate is a good example of a straightforward analysis, since no significant perturbations were present in the spectra analysed. The available data comprised DFWM spectra of the (8,2) and (8,1) vibrational bands, and a plate absorption spectrum of (8,0). The line-width and rotational temperature of the DFWM spectra were approximately 0.3 cm1 and 300 K in both cases. The resolution of the absorption spectrum was lower
(2 cm1) but the spectrum extended to a higher J, reflect-ing a higher temperature (600 K), so some assignments to (8,0) were included in the fit. Sample spectra and simula-tions are shown inFig. 2, and constants derived from the analysis are given in Table 1. An excellent agreement between the experimental spectrum and simulation was noted, with an average error of approximately 0.05 cm1 (much less than the laser linewidth), indicating no pertur-bations in v0= 8 of the B state.
A number of DFWM spectra of this and other bands were recorded at various distances between the photolysis and DFWM lasers, corresponding to different degrees of rotational cooling, and it was noted that a range of higher J00 lines were more intense than expected from a simple
Boltzmann distribution. This was especially true for the DFWM spectra with less rotational cooling and was attrib-uted to a non-Boltzmann population distribution within the initial X state. In the DFWM experiments, SO was pro-duced by 193 nm photolysis of SO2. Felder et al.[22]found
that the average rotational energy of nascent SO fragments (v0= 0, 1, and 2) resulting from 193 nm photolysis is 30
rotational quanta, or 650 cm1. This provides an explana-tion of the appearance of the DFWM (8,2) spectrum in
Fig. 2, where there is a local maximum in intensity around 43 700 cm1, corresponding to J00 23. The same effect is
seen in the (5,1) spectrum shown inFig. 3; this was record-ed with less rotational cooling, and there is an increase in peak intensity as J increases beyond 43 135 cm1, peaking at J 28.
3.2. v0= 5
An example of a vibrational level of the B3Rstate that is known to be affected by perturbations from other elec-tronic states is v0= 5. Looking at the potential energy
dia-gram (Fig. 1), there are a number of known bound electronic states lying in the same region as the B3Rstate, just above the first dissociation limit. The C3P and d1P are obvious candidates for interaction, and the most com-prehensive analysis of these states is that of Archer et al. from a 1 + 1 MPI study [15]. Within their analysis, an interaction between the v0= 5 level in the B 3
R state and the v0= 0 (X = 0) level in the C3
Pstate was outlined. From an analysis of experimental MPI spectra of these two bands, a set of molecular constants and an interaction matrix element between the two states were derived. How-ever, although the MPI spectrum of the (0,0) band of the C–X transition showed clearly resolved rotational structure with a linewidth of approximately 0.1 cm1, the (5,0) band of the B state only showed a weak and poorly resolved spectrum with a linewidth of1 cm1(attributed to predis-sociation). In this previous work the four components (X = 2, 1, 0+and 0) of the C3Pstate were modelled sep-arately as a considerable discrepancy in effective rotational constants was noted between components. This was attrib-uted to their interaction with other states, including the B state. A simple deperturbation including the B and C states
could account for the difference in rotational constant between the 0+ and 0components, and also explain dis-crepancies in simulated intensities. However, it was not possible to take the previous analysis further because of the poor resolution of the transitions to the B state. The DFWM spectra described here provide excellent informa-tion on B v0= 5, and allow a much better study of the
inter-action between the B and C states.
As for many of the other B state vibrational levels, a number of absorption and DFWM spectra were available for the analysis of v0= 5, covering the (5,0), (5,1), and
(5,2) transitions. The present analysis concentrated on the DFWM spectrum of the (5,1) transition shown in Fig. 3, since this showed the best resolution (1 cm1) and signal to noise ratio, and also extended to highest J.
The analysis of v0= 5 also included the (5,0) absorption
spectrum, though the poorer signal to noise did not allow much extra information to be gained. Low temperature MPI spectra of Archer et al. [15] were also included in the analysis to provide information on the C and d states. Initial analysis of the (5,1) band confirmed that the v0= 5 level is significantly perturbed. The deperturbation
by Archer et al. predicted a crossing of the X = 0 compo-nent of the lowest vibrational level of the C 3P state with the v0= 5 level of the B 3
Rstate at J 20, though their experimental data only extended to J = 9. We therefore used this as a starting point for our analysis. Given this, assignment of the DFWM spectra was reasonably straight-forward, confirmed by common differences using the ground state constants of Clerbaux and Colin [5]in most cases. The analysis revealed major perturbations in all three X components, at J = 17 (F1), J = 21 (F2), and J = 27 (F3).
To model the mixing between the B and C states, both a spin orbit operator and an L uncoupling operator were required. The spin orbit operator has selection rules DX= 0 and the parameter used is the following matrix ele-ment (in an unsymmetrised basis):
hC3
P1; v¼ 0j ^HSOjB3R1; v¼ 5i
¼ hC3
P0; v¼ 0j ^HSOjB3R0; v¼ 5i ð2Þ
The L uncoupling has the conventional form:
bð^JL^þþ ^JþL^Þ ð3Þ
45840 45880 45920 45960 46000 46040 46080
Simulation Trace of plate spectrum
43620 43640 43660 43680 43700 43720 43740 43760 43780 43800 43820 Wavenumber / cm-1 DFWM Spectrum Simulation a b
Fig. 2. Spectra and simulation of (a) DFWM spectrum of the (8,2) band of the B–X transition and (b) absorption spectrum of the (8,0) band. The absorption spectrum is a trace of a photographic plate. The anomalously high intensity in the centre of the DFWM spectrum arises from the non-Boltzmann distribution of the nascent SO.
Table 1
Summary of constants (cm1) for the B3Rstate of SO
v0 T v B D· 106 k c· 10 2 Number of observations Estimated linewidth
Perturbations Data sources
0a 41 375.105(7) 0.498859(2) 1.294(2) 3.457(1) 1.949(2) — —b Several small, unidentified (0,2) LIF, FT
1 41 991.97(1) 0.49426(9) 1.61(8) 3.20(2) 1.37(9) 440 —b SeeTable 3. A3R+v0= ?,
A3P v0= 10, and other small
(1,1), (1,2) LIF, (1,6), (1,7) FT
2 42 599.04(2) 0.4589(7) — 1.18(2) 3.7(3) 140 —b Yes, D state, and others (2,0), (2,2), (2,3) LIF
3 43 200.69(6) 0.465(1) — 1.25(8) 2.4(8) 62 —b Yes, unidentified (3,2), (3,3), (3,4) LIF,
(3,2) DFWM, (3,4) MPI
4 43 795.40(6) 0.4806(3) 4.3(3) 4.07(5) 0.9(2) 148 <3 None (4,0) abs, (4,2) DFWM
5 44 382.05(8) 0.4705(5) 0.8(6) 1.0(1) 1.9(9) 238 <0.8 SeeTable 2. C3P v= 0,d1P v= 1 (5,0) abs, (5,1), (5,2) DFWM
6 44 954.76(8) 0.4678(7) 9(1) 5.17(6) 0.85(3) 154 <1.2 None (6,0) abs, (6.2) DFWM 7 45 524.0(7) 0.4612(5) — 5.4(3) — 155 <2 C3P v= 2 (7,0) abs, (7,1) DFWM 8c 46 075.494(9) 0.45992(6) 1.39(7) 2.77(1) 0.81(3) 362 <0.3 None (8,0) abs, (8,1), (8,2) DFWM 9 46 624.59(4) 0.45024(7) — 3.45(5) 1.1(1) 244 <1.5 None (9,0) abs, (9,1) DFWM 10 47 161.0(2) 0.447(1) 2(1) 3.1(1) 1.4(4) 73 <5 None (10,0) abs 11 47 683.6(1) 0.4388(2) — 4.8(2) — 112 <1 C3P v= 5 (11,0) abs
12 48 194.01(6) 0.4360(1) — 2.89(7) 1.2(2) 109 <7 None identified (12,0) abs
13 48 691.6(1) 0.4329(5) 3.4(5) 2.31(7) 1.9(2) 115 <10 None identified (13,0) abs
14 49 935.7(5) — — — — — <20 Analysis not possible (14,0) abs
15 49 708.3(5) — — — — — <40 Analysis not possible (15,0) abs
16 50 049.9(3) 0.3822(6) — 5.2(3) — 133 <10 None identified (16,0) abs
a
Constants from reference[5].
b
Below dissociation limit; linewidths expected to be below instrumental resolution (<0.1 cm1).
c kD= 7.8 (4)· 104cm1. 218 C.-P. Liu et al. / Journal of Molecula r Spectroscopy 238 (2006) 213–223
and we define the parameter we use as the matrix element: hC3P; v¼ 0; K ¼ 1jbLþjB3R; v¼ 5i ð4Þ
For the best fit we also had to allow for centrifugal distor-tion of these interacdistor-tions, which take the form:
1=2aDb ^N2; ^HSOcþ ð5Þ
1=2bDb ^N 2; ^J
^Lþþ ^JþL^cþ ð6Þ
where [A, B]+= AB + BA. The parameters are defined by
analogy with those in Eqs.(2) and (4).
A fit including just the B v0= 5 and C v0= 0 levels gave
good results with this model for the interaction, but left a small but systematic discrepancy for the C3P1component,
which could only be fitted by using a slightly different effec-tive B value for this component. Given the close proximity of d1P v0= 1 this can be attributed to a mixing with this
state. Inclusion of a spin-orbit mixing between these two states enabled a single rotational constant (0.567 (1) cm1) to be used to describe all X components of C
3
P v0= 0, unlike in the previous work. The final
Hamilto-nian matrix used therefore included B 3R v0= 5, C 3
P v0= 0, and d 1
P v0= 1, and the final constants from a fit
to this Hamiltonian are presented inTable 2.
Given this model, a good fit to the B–X (5,1) vibra-tional band was obtained, as seen in Fig. 3. An energy level diagram, illustrating the crossing between the B
3
R and C 3P states is shown in Fig. 4. The diamonds and crosses represent ‘‘observed’’ e and f energy levels respectively, obtained by adding observed transition fre-quencies to the known ground state energy levels. From this diagram, it can be seen that there are some missing assignments at low J. During the fitting process, it was evident that some transitions around J0= 9 were
dis-placed by up to 2 cm1 from the model positions. The spectra we had were not clear enough to provide a detailed assignment of these transitions, but it is clear that there is another perturbation. However, assignment of the state causing this perturbation is not straightfor-ward; the C 3P and d 1P states have already been accounted for, and none of the other bound states in
Fig. 1are in the right position to have an effect. The only states not included on the diagram are likely to be repul-sive states correlating to the S (1D) + O (3P) dissociation limit. It is worth noting in this context that the d1Pstate is rather unusual and previous workers reported [15] that ab initio calculations performed on the d 1P state were not easy to converge, with less accurate calculations giv-ing a completely repulsive state. This could be the case for other states correlating with the first dissociation limit; the Wigner–Witmer rules allow us to confirm that the correct number of states have been included in the diagram but given the difficulty of the calculation, as illustrated by the d 1P state, previous ab initio calcula-tions could have missed a shallow well in one or more of these states. It is likely, therefore, that there is at least one formally repulsive state that is capable of supporting some bound levels, and this is most likely the source of the perturbation.
Table 2 also lists the parameters derived by Archer et al. [15] for comparison. Identical values are not to be expected given the differences in the models used, but it is clear that the single large spin orbit interaction of 16.61 (7) cm1 found in the previous work has been split, giving a smaller interaction of 2.4 (4) cm1, accom-panied by a significant L uncoupling perturbation. How-ever, the previous work had to make several drastic assumptions because of the limited information available,
42950 43000 43050 43100 43150 43200 43250
Wavenumber / cm-1
Fig. 3. DFWM experimental spectrum (upper trace) of the (5,1) band of the B–X transition, and simulation (lower trace). The effective temperature of the experimental spectrum is600 K. The anomalously high intensity in the centre of the spectrum arises from the non-Boltzmann distribution of the nascent SO.
including that the K doubling in the C 3P0 component
was entirely due to the nearby B state. This work does not have to make this assumption, and a significant K doubling constant (o) of 0.98 (8) cm1 is determined. Given this and other assumptions in the previous work, any discrepancies are unsurprising.
Ab initio off-diagonal spin-orbit matrix elements between the C and d states, and also between the B
and C states, are available from Figure 6 of Reference
[15]. Averaging over approximate vibrational wavefunc-tions indicated a value of 12.95 cm1 for the matrix ele-ment hC3P;m¼ 0j ^HjB3R;m¼ 5i. Comparing this with
our measured value of 2.4 (4) cm1 suggests that the ab initio calculations are at least qualitatively right. A calculated hC3P; v¼ 0j ^H
SOjd1P; v¼ 1i matrix element of
40 cm1 is also available. This could well be consistent
d1 v' = 1 C3 v' = 0 C3 v' = 0 C3 v' = 0 B3 v' = 5 Symmetry: :e :f J (Energy -0.47 ( + 1 )/c m JJ -1 0 5 10 15 20 25 30 35 44150 44200 44250 44300 44350 44400 44450
Fig. 4. Energy level diagram showing observed and calculated upper state reduced term values (term value,0.47J(J + 1)) plotted against J for B3
R state v0= 5, C3
Pstate v0= 0 (X = 2 is off the bottom of the diagram), and d1
Pstate v0= 1, showing mixing between the states. The diamonds and crosses
represent ‘‘observed’’ e and f energy levels obtained by adding observed transitions to calculated ground state energy levels. Table 2
Molecular constants for the B3Rv0= 5, C3
P v0= 0, and d1
P v0= 1 levels, and parameters resulting from a deperturbation of these statesa
State Parameter Valuea/cm1 Previous workb
B3Rv = 5 T0 44382.05 (8) 44381.4 (3) B 0.4705 (5) 0.4755c k 1.0 (1) 3.7c c 0.019 (9) D 0.8 (6) · 106 C3P v= 0 T 0 44151.8 (3) 44336.28 (1)d B 0.567 (1) 0.5697 (2) A 181.4 (1) 179c k 1.0 (4) 0c o 0.98 (8) 0c c 0.2 (1) 0c D 1.2 (2)· 105 0c d1P v= 1 T 0 44143.2 (7) 44137.90 (1) B 0.626 (5) 0.6071 (4) hC3P 1; v¼ 0 j ^HSOj B3R1; v¼ 5i 2.4 (4) 16.61 (7) ÆC3 P, v = 0, K = 1jbL+jB 3 R, v = 5æ 0.32 (3) — hC3P; v¼ 0ja DH^SOjB3R; v¼ 5i 0.0150 (9) — ÆC3 P0, v = 0, K = 1jbDL+jB 3 R, v = 5æ 4.1 (5) · 104 — hC3P; v¼ 0j ^H SOjd1P; v¼ 1i 8.7 (3) — a
Figures in parentheses are one standard deviation.
b
Reference[15].
c
Fixed at assumed value.
d
Value not directly comparable—this is the effective origin of the3P0component.
with our measured value of 8.7 (3) cm1, when the over-lap between vibrational wavefunctions is taken into account.
3.3. v0= 1
The analysis of B v0= 1 was also complicated by a
num-ber of perturbations. A partial rotational analysis of this level had been previously attempted by Clerbaux and Colin
[5]. A fit to the (1,5), (1,6), and (1,12) bands of a B3R–X
3
R Fourier transform emission spectrum had enabled a rotational analysis between J0= 10–53. Several
perturba-tions were evident, though each one only affected a few rotational levels.
Here, a more complete analysis of the v0= 1 level of the
B3Rlevel has been achieved, particularly at low J. Again, spectra from a number of different sources were used. These comprised the Fourier transform spectrum used for the earlier analysis in Reference [5], and LIF spectra of the (1,2) and (1,3) bands. Analysis of the low temperature LIF spectra (15–100 K) in conjunction with the Fourier transform spectrum (1400 K) extended to J = 55 and including the low J levels for the first time. A number of perturbations within v0= 1 were noted. One of these, at
J = 28 (F1), can be attributed to a crossing with the now known X = 1 component of A3P v0= 10, and was
mod-elled using an L uncoupling operator as for B v0= 5. In
addition, a number of perturbations were noted at lower J, as shown in Fig. 5. The pattern of displaced lines in the e and f components of B v0= 1, between J = 5–10, is
such that the perturbation can be modelled by a single
3
R+ state. One SO3R+state that tends to the first dissoci-ation limit is known; A00 3R+
. However, there is very little information available about this state. Ab initio studies
by Dixon et al.[23] and Swope et al.[24] proved its exis-tence, and an experimental observation of some part of the emission spectrum of the A00 3R+
–X 3R transition was recently observed[13], but the experimental data only extends to v0= 4. A simple extrapolation of vibrational
lev-els suggests we are observing v0= 14.
It was found that, on increasing the laser power whilst recording LIF spectra of the (1,2) band, some extra peaks that could not be assigned to the B–X transition were observed. As the B–X transition saturates, a number of other peaks appear over a range of 15 cm1 to a slightly higher wavenumber than the B–X (1,2) vibrational band. While we did not make quantitative measurements, the life-times of the levels populated by these transitions is slightly longer than those of the B state but much less than that of the A3Pstate. Detailed modelling inPGOPHERallowed the
majority of the extra peaks to be assigned to the3R+state. To model the perturbation between the B and A00 states,
both a spin orbit operator and an S uncoupling operator were used, where the S uncoupling takes the form
bð^JþSþ ^JSþÞ ð7Þ
which we take as having matrix elements in an unsymmetr-ised basis of
hA003Rþ; v¼ ?; R ¼ 1jbSþjB3R; v¼ 1; R ¼ 0i
¼pffiffiffi2pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiJðJ þ 1Þb ð8Þ
Fig. 5 shows an energy level diagram for B v0= 1,
show-ing the crossshow-ings of both the X = 1 component of A v0= 10, and of some vibrational level of the A00 3
R+ state. ‘‘Observed’’ e and f energy levels for these three states are indicated using diamonds and crosses, as before. Other small perturbations within B v0= 1 were
Symmetry: :e :f 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 J 41980 41990 42000 42010 42020 42030 42040 (Energy -0 .47 (+ 1 )/c m JJ -1 A3 v' = 10 B3 v'= 1 (F1e) B3 v' = 1 (F2f) B3 v' = 1 (F3e) A''3
Fig. 5. Energy level diagram showing observed and calculated upper state reduced term values (term value,0.47J(J + 1)) plotted against J for B3
R state v0= 1, A3
Pstate v0= 10 (X = 0) and some vibrational level of the state assumed to be A00 3R+
noted at higher J as in the previous analysis, but the source of these has not been identified. There are, how-ever, several states in the region that could account for these, as can be seen from Fig. 1.
The final Hamiltonian matrix used therefore included B
3
Rv0= 1, A 3
P v0= 10, and one vibrational level of A00 3
R. Final constants from a fit to this Hamiltonian are given inTable 3.
3.4. Other levels
A summary of all molecular constants determined from analysis of vibrational levels up to v0= 16 is given inTable 1. Rotational analysis of v0= 0 level of the B3
Rstate is relatively straightforward, and a comprehensive study of this band has been carried out previously by Clerbaux and Colin [5], from fitting to the (0,6), (0,7), (0,8), (0,9), (0,10), (0,11), and (0,12) bands of the B3R–X3RFourier transform emission spectrum. A number of perturbations were observed, especially at higher J. Identification of these perturbations has not yet been achieved, as each of these only involves a few rotational levels so little information is available about the perturbing state.
Several B state vibrational levels, in addition to v0= 8,
were found to be completely unperturbed. These are v0= 4, 6, 9, and were analysed using a combination of
DFWM and absorption spectra.
Analysis of v0= 2 and v0= 3 has not been achieved
beyond the lowest J. Given that these levels are just below the first dissociation limit, a high density of states and therefore perturbations is to be expected for these levels. It is evident from the LIF spectra of various hot bands
available that there are significant perturbations affecting both these levels. Acquisition of LIF spectra for both of these levels, using a higher laser power, caused saturation and revealed extra peaks not attributable to the B state, as for v0= 1. Again, these peaks do not match with the
known A, C, or d states. The extra structure seen in the region of v0= 2 could be fitted as an X = 2 state, and could
thus be attributed to either the A0 3Dor the a1
Dstate, but no further conclusions can be reached. A simple fit (ignor-ing interactions between states) to a 1D state yielded Tv= 42 630.86 (4), B = 0.314 (1) cm1. In any case, it is
evi-dent from the number and position of perturbations in v0= 2 that there is at least one other, unidentified, state
interacting with this level. The extra structure associated with the v0= 3 level could not be assigned to any specific
electronic state, but it is clear that v0= 3 is very perturbed.
Another band which proved difficult to analyse is v0= 7.
From the (7,0) absorption band, it is clear that this band is perturbed as extra features are found near the (7,0) band head, at term values of Tv= 46 099, 46 104, 46 109, 46 123,
and 46 132 cm1. These are very likely due to an interaction with a component of the so far unobserved C 3P v0= 2.
Above v0= 1, nothing is experimentally known about the
C state, but, according to theoretical constants calculated by Ornellas and Borin[16], the C v0= 2 level is predicted
to lie somewhere in the region of B v0= 7. The poor
reso-lution of the (7,0) absorption spectrum only allowed an approximate fit to be achieved, with B state constants as given in Table 1, C state constants of Tv= 45518
(2) cm1, B = 0.566 (2) cm1and A =181.4 cm1(fixed), and ahC3
P1; v¼ 2j ^HSOjB3R1; v¼ 7i matrix element of 16
(1) cm1. Attempts to record a DFWM spectrum of (7,2) failed, since it is almost completely obscured by the (5,1) band. This is counter-intuitive, since a consideration of DFWM transition intensities indicates that (7,2) should be significantly more intense than (5,1). However, almost all the structure in the region of (5,1) and (7,2) can be assigned to (5,1), and the correctness of these assignments confirmed by the corresponding fits to (5,2) and (5,0). The DFWM spectrum of the (7,1) is of poor quality and was impossible to analyse. It should however be mentioned that the extra features found near the (7,0) band head are also observed near the (7,2) and (7,1) band heads.
Beyond v0= 9, data available for analysis was reduced,
due to small DFWM transition intensities. For v0= 11, a
poor (11,2) DFWM spectrum was obtained, but was over-lapped by (9,0). A rough fit to the (11,0) absorption spec-trum was attempted, which indicated some perturbations within v0= 11. The only known state at an appropriate
energy to interact with this B vibrational level is C 3P. According to the calculations of Ornellas and Borin [16], the v0= 5 level of the C state is predicted to lie near B
v0= 11, so it can be assumed that the C state is causing
the perturbations observed in (11,0), although we have not enough information to carry out a deperturbation.
v0= 10, 12, and 13 have been analysed using absorption
spectra alone, and appear to be essentially unperturbed.
Table 3
Molecular constants for the B 3R v0= 1, A 3P v0= 10 levels and a
vibrational level of A00 3R+
(probably v0= 14) and parameters resulting
from a deperturbation of these states
State Parameter Valuea/cm1
B3Rv = 1 T0 41991.97 (1) B 0.49426 (9) k 3.20 (2) c 1.37 (9) · 102 D 1.61 (8)· 106 A3P v= 10 T 0 41990.00 (4) B 0.4618 (5) A 134.86 (5) k 1.67 (4) o 0.45 (8) D 4· 107b A003 R+ T0 42007.35 (9) B 0.256 (3) k 2.66 (6) c 0.81 (3) hA3P 1; v¼ 10; K ¼ 1 j bLþj B3R1; v¼ 1i 0.020 (3) hA003Rþj ^H SOj B3R; v¼ 1i 1.87 (4) hA003Rþj JS j B3R; v¼ 1i 0.161 (4) a
Figures in parentheses are one standard deviation.
b
Fixed value.
Beyond v0= 13, the absorption spectra become very
dif-fuse, and identification and assignment of rotational lines becomes impossible, with the exception of v0= 16.
3.5. Linewidths
Table 1includes estimated linewidths derived simply by comparing simulations at various linewidths for transitions within each vibrational level of the B state. We have not checked for a power dependence of these widths, and have not modelled the DFWM lineshapes in detail, so these should be considered as rough upper limits only. For the levels that lie below the first dissociation limit (v0= 0, 1,
2, and 3), the linewidths are assumed to be instrument lim-ited. For levels above the first dissociation limit, linewidths are taken from DFWM spectra, where available, otherwise from the lower resolution absorption spectra. Even given the limitations in the measurements, there is a clear varia-tion in linewidth between vibravaria-tional levels. There is a def-inite increase in linewidth around v0= 9, and an even more
noticeable increase around v0= 14, and v0= 15, for which
rotational structure cannot be resolved. Rotational struc-ture is clear in v0= 16 but not for any higher vibrational
level. On the other hand, there is no evidence of a variation with spin state or J, suggesting a homogeneous mechanism. The origins of these variations in linewidth can be attribut-ed to crossings with other repulsive electronic states. The potential energy diagram inFig. 1suggests that there are two repulsive states that could be responsible for the increased linewidth at v0= 9, and there are several other
repulsive states crossing at higher energy that can account for the increase in linewidth around v0= 14 and v0= 15.
Even with our limited precision on the linewidth, we can see that while the overall trend is increasing linewidth with v0 the variation is not monotonic, which possibly reflects
interference between the possible channels for dissociation. 4. Conclusion
We have performed a detailed rotational analysis and deperturbation of the vibrational levels within the B 3R state of SO up to v0= 16, using spectra from a wide range
of sources. In a number of cases we have been able to iden-tify the origin of perturbations seen within the B3Rstate; perturbing states identified include the A3P, C3P, d1P, and A00 3R+
states, and there is no doubt that other nearby electronic states are also responsible for interactions with the B state. A clearer understanding of the interactions between states enables a clearer picture of the spectroscopy of SO to be formed.
Acknowledgments
We are pleased to thank the Belgian National Fund for Scientific Research (FRFC Convention), the Communaute´
franc¸aise de Belgique (Action de Recherches Concerte´es), the National Science Council of Taiwan (Project Nos. NSC94-2113-M-009-004 and NSC95-2113-M-009-002) and the Engineering and Physical Sciences Research Coun-cil (UK) for funding.
Appendix A. Supplementary data
Supplementary data for this article are available on ScienceDirect (www.sciencedirect.com) and as part of the Ohio State University Molecular Spectroscopy Archives (http://msa.lib.ohio-state.edu/jmsa_hp.htm).
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