The 3B1-1A1 band system of sulfur dioxide: Rotational analysis of the (010), (100), and (110) bands

JOUKNAL

OF MOLECULAR

SPECTKOSCOPS

45, 404-411

(1073)

The 3B,-1A, Band System of Sulfur Dioxide: Rotational Analysis of the (OlO), (1001, and (110) Bands l J. C. D. BRAND, 11epavtrllent

V. T. JONES,~

AND C. DI LAURO~

qf Chemistry, Unizwsity sf Western Ontario, London, Ontario

The (OlO)-(000) band of the 3B1 + ‘A, system of sulfur dioxide has been rotationall) analyzed and constants for the magnetic interactions in the (010) vibrational level determined. Partial rotational analyses are given for the rotationally perturbed (loo)-(000) and (llO)-(000) bands of the system. The extensive perturbations in this band system are provisionally attributed to: (i) vibronic interaction with a 3A 2 state, visible (a) as a large negative anharmonicity in higher bands of the 3B1 system, and (b) as a AK = 0 resonance perturbation in low-lying vibrational levels of the 3B1 state; and (ii) a R, K + 1 N-dependent perturbation possibly due to rotational-electronic coupling with a agr state, though evidence on this point is incomplete. Evidence bearing on these conclusions is discussed.

IXTRODUCTIOS

The triplet-singlet 3B1 + ‘rl I absorption bands of sulfur dioxide occur in the region 3900-3400 A. A low-resolution profile (Fig. 1) shows that the bands at higher energ> have irregular contours and are obviously strongly perturbed. These perturbations are of interest in that they contain information on states of sulfur dioxide which interact with the 3B1 state but are not otherwise detected in absorption from the ground state. Table I contains a vibrational analysis of main features in the system, based on measurements taken from the low-resolution profile in Fig. 1. The analysis, except that it is reinforced by data for the S’Y& isotope, is equivalent to that given by Hochstrasser and Marchetti (1) for the solid state absorption. The most visible anomaly is the large negative anharmonicity which accumulates in higher bands of the system. As Hochstrasser and Marchetti have pointed out, this must be due to a vibronic interaction of the 3B1 state with a 3Az state lying at higher energy in the crystal. The solid state spectrum, however, does not show the twin-band structure apparent in the vapor profiles at 3590, 3610, and 3623 A. These bands are so strongly perturbed in their rotational structure that the prospects for analysis are poor. The formation of twin bands in only. the vapor spectrum indicates a relative shift of energy levels between vapor and solid, probably signifying that different electronic states are involved in the interactions. Another index 1Work supported by the National Research Council. Contribution No. 46 from the Photochemistr! unit, University of Western Ontario. 2 Present address: Geophysical Laboratory, Superior Oil Company, Houston, Texas 77077. 8 Present address: Group Kazionale Struttura della Materia de1 C.N.R., Istituto Chimico dell’ Vniversitb, Napoli, Italy. 404 Cogryright All rights

0

1973 by Academic

of rewoduction

Press,

in any form

Inc. reserved

40.5 r

P‘Ic. 1. Profile

of the 8B,-L.-IL system

under

low resolution

TABLE

(pressure-path,

I

VIDKATIONALSTKUCTI~KE IN THE~B,cI.~~

Y

(S’W2) 25258

Assignmentn

Au

-

25776

26137 26494 26680 2683Y 27032 2 738.j 27524 27620 27842 2794.5 28329 28637 28838 29058 2910x *Displacements Xarchetti (1).

518 0 361 718 904 1063 1256 1609 17481 1844/ 20661 2169j 2553 28611 3062 i 3282 ‘1 3332 f

800 torr m).

SYSTEM V(PO?)

u(S’601) - Y(S’W2)

(Ooo-(010, (Ooo- (000) (OlO)-(000, (020)- (000)

Origin Y2 2v, - 4[-31 ;1, - 20-91

25791 26139 26481 26652 26799

Y, + w - 9[--61 Y, + 2ur - 17[-201 2vl - 60[-2271

26990 27339 2i47.5

42 16 49

(210)-(000)

2u, + Y? -

(300)- @OO) (310)-(000)

3v, - 159[-1161 3u, + Y:!- 212[-2051

(32W(OOO)

3~ + 2~~ -

27784 27870 28244 28546 28731 28949 28993

5x 7.5 Xi 01 1Oi 109 1 15

(loo)-(000) (030)- (000) (llO)-1000) (120)-(000) (200)- (0001

in square

brackets

are

recorded

103[ -561

152[-16.11

for the c.r!-stal

spectrum

-

15 2 13 40 LX

1,~ Hochstrasser

an(l

406

BRAND,

JONES,

AND

DI LAURO

of vibronic effects is the isotope shift, which becomes very irregular in higher bands of the system. This paper reports the rotational structure of three bands, (010))(000), (lOO)-(000) and (llO)-(000), lying in the less-perturbed region 3650-3850 A. Only the (010) transition analyzes as an unperturbed band, analogous to the (000))(000) transition reported previously (2). The theory and other pertinent background material required for the analyses is discussed in some detail in the earlier paper (2) and is not repeated here. Perturbations in the (110) band of this system have also been described by Merer (.?). II. EXPERIMENTAL

The bands under investigation were photographed in the 15th and 16-th orders of a 3.4 m Ebert spectrograph, using a pressure-path of 100~1500 Torr m at room temperature. Lines of an Fe hollow cathode lamp were used for calibration. The low-resolution profiles of Fig. 1 and Table I were obtained with a 0.5 m Jarrell-Ash monochromator, using a pressure-path of about 800 Torr m : these measurements (f2 cm-‘) refer to the prominent “spike,” 8-10 cm-’ to high-frequency- of the band origin, which marks the head of S-form branches (AAT = +2) of low R (3). A 1ow-resolution profile of S” OZ was obtained under similar conditions4 III.

ROT.~TIONAL

ANALYSES

Rotational structure in the (01(l), (loo), and (110) bands is sufficiently like that of the O-O band that many assignments can be made by inspection. The stronger lines in the high-frequency wing of the band belong to SR~-, @J3- and QPS- subbranches (the superscript capital letter indicates the form AiY of the subbranch) which have common upper levels in the FP component of the triplet state. These subbranches are strong for higher values of K and closely follow symmetric rotor formulas for line position and intensity. In the low-frequency wing the QRI-and Qpr- subbranches, which are very strong for K = 0 and 1, contain useful information on the asymmetric rotor region of the band. A preliminary analysis could be drawn up on the basis of these two groups of lines. The next stage involved a building-up of assignments in other branches guided by calculations based on the preliminary set of constants. This step is essential for determination of the magnetic interaction constants, since the Fr and F3 components of the multiplet state are almost degenerate and F2 assignments are required to disentangle the spin-spin and spin-rotation interactions. In the final stage the assigned frequencies provided the input to an iterative least-squares asymmetric rotor program to obtain the best set of values for the triplet state constants. Ground state constants required for this program, taken directly from the microwave/far infrared analysis of Gebbie and others (q), were not varied in the refinement. Since the ground state centrifugal distortion constants are expressed as DN, . . ., R6 this form is retained in the upper states in spite of the implied redundancy (5). In practice, only the (010) analysis progressed satisfactorily through these three stages. The (100) band has perturbations which prevented the second stage from being completed, while the (110) perturbations prejudiced even the preliminary set of assignments. As each band presents different problems the results are discussed separately-. 4\Ve thank Dr. Roger Nanes for providing

this recording.

(‘INSTANTS 0~ THE (0101 LEVEL OF THE :‘I?, ST;\TE (in cm-‘).

Constants

for the (010) level of the “U1 state

are in Table

II. This analysis

proceeds

routinely although blending critical for the determination

where assignments are of lines in the K’ = 1 subband, of the constants b and /3, is more severe than in the O-O

band.

are given

The various

in order that of about that

constants

to more figures

the\, may be used to reproduce

0.06 cnl-1.5 Comparison

yt! affects

mainly

with results

coefficients of P,Ti, 11 = 2, 1, . * . . It is curious that the zero-field spin-spin statistically Tinti

significant,

(6)

oretically

has than

Hamiltonian therefore

0.004 cm-’ though

pointed a positive

out

for spin multiplet becomes

states

responsible

rather

fundamental

increasingly

coupling

a

states

for the estensive

within

(2) shows, in the energ!-

constants

PUlo differs

for the (000) state. are not well determined

negative

It should

1;

is

more

be kept in mind

(7) is derived

ineffective

difficulties

for the O-O band

determined

the constants that

value.

frequencies

A, DK, . . . which appear

the constants

the value /300(l= 0.007 f

than are statisticall!-

the measured

under

matrices

as

in sign from results

seem

for either

band.

explained

the-

electronic

states

conditions.

in the 3R1 s>.stem unperturbed

as espected,

the Van Vleck effective

for separated

near-resonance

perturbations

even in relatively

readily

that

Both

significant, a tolerance

Thus

and the

rnax give rise to

hands.

Constants given in Table IT1 are based upon F3 assignments for K’ = 6- 16, 19 and 20 and FL assignments for K’ = 0 and 1. The fit obtained for these assignments is satisfactor)-,

but irregularities

the central ment,

region

in the low-K

of the band.

but in absence

subbands

Spin constants

of F2 assignments

prevented

the systematic

were included

the results

analysis

in the least-squares

were not considered

of

refine-

significant.

The

data in Table III show that the vibration-rotation constant o(lfi = Booc)-Hlo,l is negative, i.e.! opposite in sign from the positive value usually obtained for symmetric XI-? molecules (8). Since the signs of cxlA and (ylc are normal, this indicates the RON,is elevated 1~~. a h-axis interaction with a state of Rs vibronic symmetrv. A mild localized perturbation occurs in the -I<’ = 17 and 18 subbands where the* K’ = 17 transitions

are pushed

bA list of observed frequencies

down

and assignments

in energy is available

whilst

the

on request

K’ = 18 transitions from the Editorial

Office.

are

408

BRAND,

JONES,

AND

TABLE

DI

LAURO

III

(100) BAND CONSTANTS ~_ Band origin

Rotational constants A LG(I 2.29av B ,oo 0.29786 C,oa 0.2605~

26672.0 (mo + 906.3)

pushed

up, with displacements K’ = 15 perturbation

stronger (210)

Vibrationm rotation constants 011.4 mu ,lC AlllO

Two major

of 0.05-0.15

cm-l.

in the (ll(.)

band.

perturbations

to low frequency

occur for K’ 5

K-structure, with displacements between K’ = 15 and 16. The simplest required

in this band:

of fit

f0.019 (324 lines)

are the same as the

from

Eqs.

(7) and

operator

The interaction

is small

with

lines dis-

12, and

(ii) in the

for K’ 5 15 and a probable interaction

resonance

(011) ; the operator

(110) H

(8) of (Y), nameI\,

coupling

can be neglected

then acts independently state, with matrix elements,

HCoriolis

for K’ 2

-2CPcNc + (u” - u - b)PcSc,

ao, a, and b are the spin-rotation interaction

(i) in the ;Y-structure,

to low frequency

model for (i) is the c-axis Coriolis

can be obtained

vibration triplet

0.002, -0.052 2.7, 0.066

Its characteristics

11 and to high frequency-

f!cori<,rib =

in

lWD$ lo”n\-K lOJL)h_ 106EIh_

0.019 - 0.00062 0.00197 0.75 u. 3

SD.

Bard

placed

where

Centrifugal distortion constants

and

constants.

(1)

We assume

for a case b molecule;

identically

within

(or zero) for S = K and increases

each

with

that

the spin-

the leading

F-component

.I’ for given

term of the

K.

Low-K assignments could not be obtained for this band. A least-squares refinement based on the F3 subbands with I<’ = 7-12, including the Coriolis effects, gave the following results

: vllo

27024 cnr’

~011 27067 cm-l

141r~

2.3& cm-’ 0.2796 cm-’

ri:$

0.23.

In this calculation, centrifugal distortion constants were transferred from the (016) band and the effects of spin were disregarded. The rotational constants obtained for the (011) level (AoIl = 2.36”, BO,, = 2,2g0 cm-‘) are not reliable, a general difficulty when data are available for only one component of a coupled band. A more serious problem is that the (100) band perturbation is not explained in any obvious way by the corresponding (100) ++ (001) Coriolis interaction.

There

is relatively

4)erturbation placements

little

(ii). Based

information

in the K’ = 13 and

_y’

IO.080 1X.400

1x These

results

indicate

The selection -4, vibronic energy,

being

rules mentioned symmetry;

the perturbing

smaller

since

states

“,,l>b

Au

VP$11.

-0.438

above

and

of the the dis-

are:

perturbation

are satisfied all singlet

must

with

for the perturbing

belong

selection

state

than

if the perturbing

states

of species

to the triplet

-l.lOY -1.153 -1.121 - I .oio - 1.o;;

27131.937 30.260 2Y.il2 2Y.OY8 2X.360

27130.768 30.269 29.il2 2Y.098 28.360

-0.4337 -0.428 - 0.405 -0.11’) -0.Bi.Z

an -Y-independent

A.Y = 0, the .4 constant

dependence paragraph,

Ii’ = 1.4

21.251 20.750 20.16X 10.508 13.773

20.817 20.322 lY.763

rotational

in the previous

Av

2i121.6XO

27121.242

I-I 15 I6 17

on the

outlined

11 submanifolds

h-’ = 13 Y,,:,,e

Ytrl,*

I3

bearing

on the refinement

rules

AK = 0,

for the SB1 state.

level has either I?, and

manifold.

HI or

L42 lie higher

in

The first possibilit!-

corresponds to the interaction of “131with vibronic Br levels of a 3.4Z state, also thought to be responsible for the large anharmonicity in higher bands of the YHI + ‘rlt svstetn (see Section from

I). If this is correct,

the hypothesis

that

due to neardegenerac!. case the upper

vibronic

bound

perturbation

energy

The perturbation

“HI state

mechanism

with

interaction. outlined

al vibrational

momentum

the interaction

(i), on the other

of a b- or c-asis

the Voriolis

of the 3;14 state

in the (110) band

of the “.4? state

has no angular

are too incomplete to establish be independent of .I’. acteristic

limit to the energ!.

visible

follows

of the “14~system

is

with the (001) 1eve1 of 3.4?. It is possible, however, that the weak in (100) is also due to the 3Hr f--) 3.4q vibronic interaction, and in

K’ = 17 perturbation this

an upper

the interaction

hand,

be reduced

accordingI>,.

Unfortunately,

as independent

of I<, though

has an angular

momentum

AAc-axis interaction

earlier,

levels

should

dependence.

of the 3=12 state

it appears

dependence

could be explained

or by a rotational-electronic involved

A

the results

char-

either

coupling

to

b\.

of the

in the perturbation

(ii).

However, neither of these mechanisms simultaneously explains the rotational pcrturbation in the (100) band which has the features of a mild b-axis interaction; and an interesting possibility is therefore that the .I.-dependent (100) and (110) band perturbations both represent state! through

a b-axis

the matrix

rotational element

electronic (IO).

= -2B[.\.(.\.

It should be emphasized approrimation in which

couplin g with

& vibronic

levels

+

f

Lb; ~C&).

1) -

K(K

l)]‘(‘“B,;

of a “HZ

(,3)

that the (110) band is partially analyzed in the symmetric rotor the b- and c-axes are not distinguished. The angular momentum

dependence in Eq. (3) is unchanged from that in Coriolis coupling, Eq. (2), but for weak interaction it is absorbed into an effective constant H instead of C’. On balance, the “HI H “I$:! interaction appears to us more probable, but more evidence is needed.

410

BRAYD.

JONES, AND DJ LAURO

The conclusions of this section are then (a) that the (110) band shows effects due to a vibronic perturbation by 6, vibrational levels of a neighboring 3Az state, and (b) that the (100) and (110) levels exhibit rotational-type perturbations possibly explained by a neighboring 3Hz state. Three triplet states of $3~ may therefore lie in a narrow energy there is no direct spectroscopic evidence for the range. Apart from the perturbations, 3ila or 3B2 states, but the absorption intensity of transitions from the ground state to 3B~ (the triplet state of the a*?r configuration) are expected to be extremely weak. IV. DISCUSSION

The evidence that the 3B1 state is vibronically perturbed by a neighboring 3A2 state is of three types; (i) large anharmonic displacements occur in higher bands of the 3B1 system; (ii) the band system is appreciably more complex in the vapor than in the crystalline state, with some ‘extra’ bands appearing in the vapor spectrum; and (iii) K-structure perturbations of a type consistent with a vibronic interaction are present in the (110) and (100) bands. This interaction has also been proposed bv Hochstrasser and Marchetti (I) to account for the anharmonic shifts in the crystal spectrum, and by Strickler and Howell (II) on general grounds. A second triplet state with energy approsimately equal to that of the 3B1 state has been considered in mechanisms of phosphorescence-quenching (22) and some photoreactions (13) of SOS. If the vibronic perturbation is responsible for the severe perturbations in higher bands of the 3B1 system, as seems likely, the interaction matrix element,

must increase sharply with increasing Avr and Aa, (nonzero elements have Avs = f 1). This follows from the fact that the (100) and (110) band perturbations are small except near resonance, whereas some of the higher bands are much more extensively perturbed. The ‘extra bands in the vapor absorption compared with the solid state spectrum (I) may result from accidental energy coincidences in the isolated molecule which are removed in the solid by a relative shift of energy levels. A vi-dependent matrix element indicates different structures in the 3B1 and 3Ag states. There is no direct experimental information on this point but recent calculations by Hillier and Saunders (14) predict differences of 28” in the bond angle and 0.04 a in distance. If this is granted, the vibrational integrals in (4) are favored in higher vibrational levels of v1 and zb2in either manifold; a given vibrational level of the 3R1 state therefore interacts more strongly with higher levels of the 3Ar state and undergoes a net displacement to lower energies. More work is needed to obtain a better understanding of the details of this comples interaction. h’ote added in proof: The phase convention adopted in this paper and in Ref. (2) is that the matrix elements of J, f iJ, and S, f is, in the uncoupled representation, and therefore of N, f iN, in the coupled representation, are real and positive. Energies of the spin states in the crystal given by Tinti (6) correspond to the convention that the elethe phase convention of Van Vleck (7)ments of S, 00 is, are real and positive-i.e., thus the spin--spin coupling constants ,8 in this paper and E used by Tinti have opposite sign, p = --E. Hence the positive value of /3 obtained from the analysis of the vo vapor band in Ref. (2) and the preferred tiegative value of R found in the solid-state spin-reso-

nancc experiment (6) arc mutually- consistent, though the numerical rough (/3 = 0.007 f 0.004, L; = -0.0157 cmF1). Rc:c~:w:u:

agreement

is rather

July 26, 1972

I. I<. bl. HOCHSTKASSEKAND X. P. MAKCHETTI, J. Mol. Speclrosc-. 35. 335 (1970). 2. J. (‘. D. BRAND, V. T. JONES, ANU C. DI LAUKO, J. .IloZ. Spec/ros~~. 40, 616 (1971 j.

3. A. J. .MEKEK, IX.scirss.Faruda_vSoc. 35, 127 (1963). 4. H. A. GEIWIE, S. LV. B. STONE, G. TOPPING, E. 6. GOKA, i\. S. C~orc;r<, ANI) I,‘. S. KNE!Z\S, J. .210,1. Specfrosr. 19, 7 (1966). 5. J. K. G. WATSON. J. Cheul. Phys. 46, 1935 (1967). 6. D. s. TINTL, c’l/Uii~.Phys. Ldt. 12, 169 (lYi1). 7. j. H. VAN VLECK, Rer. Mod. Ph_vs.23,213 (1951). ,Y. K. KUCHlTSU AND \‘. ~hfOKIN0, Bzd. Chm. SOC. Ja.pafz, 38, 814 (1965). Y. C. DL I,AUKO, I. .\fol. ~‘&.ctrosc.40, 103 (1971). III. K. S. HENDERSON, Ylrys. Z&Y. STKICFLEK AND D. B. HOWELL, J. C//errt. Phys. 49, lY4i (1968). 13. H. w’. SIDEHOTTOM, C. C. BADCOCX, J. G. CALVEKT, G. W. REINH.AKI)T, I<. I<. RAM, I)ANON, J. .~ir~. C/MI. &c. 93, 2587 (1971 I. 13. I:. CEHELNIK, c’. LV. SPICEK. AND J. HEICILEN, .I. .!~er. C‘l~euz.SM. 93, MT1 (1071). I-!. I. H. HILLIER AXI) V. K. S.AI’XI)ERS,MOL. Plrys. 22, 193 (1971 ).

ANI) 1~;.K.