Franck-Condon factors and r-centroids for the E1Σ+−X1Σ+ bands of SiS and SiSe

J. Quant. Spectrosc. Radiat. TransferVol.42, No. 6, pp. 631-634, 1989

0022-4073/89 $3.00+0.00 Copyright© 1989PergamonPresspie

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FRANCK-CONDON FOR

THE

FACTORS E1E+-XIZ SiS A N D

AND

r-CENTROIDS

÷ BANDS

OF

SiSe

SUNANDA K., SHEILA C-OPAL, B. J. Srma'a'v, and G. LAKSHMINARAYANA'~ Spectroscopy Division, Bhabha Atomic Research Centre, Bombay-400085, India (Received 7 September 1988; received for publication 5 July 1989)

Abstract--By using the computer program TRAPRB developed by Jarmain and McCallum, Franck--Condon factors and r-centroids have been calculated for the EIY.+-X~E + bands o f the SiS and SiSe radicals. Intensities of these bands have been visually estimated from the emission spectra photographed on a 3.4 m Ebert grating spectrograph (5 A/mm). A comparison of the Franck-Condon factors with these estimated intensities shows reasonable agreement.

INTRODUCTION The electronic spectra of the homologous group of radicals SiO, SiS, SiSe, and SiTe, which have been well investigated in the recent past, have been found to be comprised mainly of the following three band systems: A I/-/-XlY,+, E I ~ + - X I ~ + and a 3 I I - X ~ E + . 1 It has been observed that the emission bands of the E - X system of SiO, SiS and SiSe lie in two distinct regions as follows: for SiO, 1600-2000A, and 3100-3600 A, for SiS, 2200-2500/~, and 3500--6600/~, and for SiSe, 2400-2800/~ and 400045000 ~.2~ F o r SiS and SiSe, band assignments were established by isotopic and rotational structure studies. For SiS, the 2100-2400/~ bands arise out o f transitions from the 0 ~< v ~< 15 vibrational levels of the E~E + state to the 0 ~ v ~< 9 levels of the X~E ÷ state, while the 3500-6600/~ bands involve transitions from the 1 ~< v ~< 17 levels in the EIE + state to the 20 ~< v ~< 51 levels of the X~E + state. 7-~° In SiSe, the 2450-2800/~ bands involve the vibrational levels 4 ~< v ~< 14 in the E~Z + state and the levels 0 ~< v ~< 7 in the X~E + state, while the 4000-6000/~ bands involve the 0 ~< v <~ 13 levels in the E~E + state and the 25 ~< v ~< 52 levels of the XIE + state. 4'6 The unusual occurrence of the E - X bands of the SiS and SiSe in two distinct regions is related to the relative positions of the potential energy curves involved in these transitions. Furthermore, since some of these radicals have been observed in the interstellar medium, H-~3 the unusual intensity distribution a m o n g the E - X bands may be expected to have a bearing on the population distribution among the high-lying vibrational levels in the ground electronic state (XIy~+). The computation of F r a n c k - C o n d o n factors (FCFs) for the E - X bands of these radicals m a y serve to shed light on the intensity distribution a m o n g these bands. Here, we report F C F s and visually estimated intensities for the E - X bands of SiS and SiSe radicals.

M E T H O D OF C O M P U T A T I O N We have used the computer program T R A P R B developed by Jarmain and McCallum ~4 to evaluate the F r a n c k - C o n d o n factors and r-centroids for these bands. In this program, the K l e i n - D u n h a m series are used to represent the spectroscopic input data, namely, the vibrational and rotational constants. The R K R potential curves are then calculated. The Schr6dinger wave equation is solved numerically and the resulting vibronic eigenfunctions are used to calculate F r a n c k - C o n d o n factors and r-centroids. ?To whom all correspondence should be addressed. 631

SUNANDA K. et al

632

Table 1. Molecular constants (in cm -~) used in the calculation of FCFs and r-centroids.

Molecule

State

@e

~eXe

~eYe

Re

oe

-0.028 0.0005

0.22137 0.30353

0.00139 0.00147

9722 § 51780 t

0.1392 0.1920

0.0011 0.0007

I0000 ~ 45489 t

SiS

FI

405.60 749.64

1.6 2.57

SlSe

F 1 y* X I ]~*

308.44 574.87

1.98 1.659

t From Ref. I ;

*extrapolated value;

DO

§ from the thesis of S. Gopal.

Table 2(a). F r a n c k - C o n d o n f a c t o r s and estimated intensities for the E - X s y s t e m o f SiS in the 2100-2400~ region. V 11

0

1

I 2

012

2

3

4

5

6

7

8

9

016

063

181

392

665

892

938

743

[21

[4]

450

725

838

656

282

017

062

201

[3] 3 4

5

012

027

038

162 [4]

417 [5]

700 [61

761 [4]

481

101

022

300

091

317

626

729

440

060

064

383

480

[8]

[9]

[71

494

712

500

084

056

379

416

010

[s]

[8]

179

6

056

300

633 [7]

613

7

099

430 [4]

676 [7]

380

8

160

549

603

140

[21

[7]

628

440

9

235

320

648

[2] 183

572

015

322

404

086

052

207

416

129

032 [4]

321

384

232

262

285

320

044

[7] 232

[2] 10

[3]

356

028

[5] 246

028

363

[7] 174

029

[1] 11

410

605

088

148

353

154

023

184

310

[11 131

037

[7]

[2]

256

218

[8] 12

493

510

282

226

017

294

084

[8]

[4]

086

262

RESULTS AND DISCUSSION To make a visual estimate of the band intensities, the E - X bands of SiS and SiSe have been excited by a microwave discharge through a sealed quartz tube containing small quantities of silicon and sulphur or selenium, along with neon gas, at a pressure of about 2 torr. The spectra have been photographed at medium dispersion (5 .~,/mm) on a 3.4 m Ebert grating spectrograph using Kodak 103 aF and SA1 photographic emulsions. Care was taken to allow for variations in spectral response of the photographic emulsions and for any overlapping bands. The FCFs and r-centroids have been calculated for the E - X transitions of SiS and SiSe by using molecular constants from Refs. 6 and 10 (Table 1). Representative values of FCFs and their estimated band intensities are given for SiS in Table 2 and SiSe in Table 3; comprehensive data for FCFs and r-centroids may be obtained from the authors on request. Bands belonging to the lower sequences (Av = 0, 1. . . . ) are weak and hence not observed. The observed band intensities are proportional to the FCFs and also to the population of the initial level and the transition frequency.

F r a n c k - C o n d o n factors and r-centroids

633

Table 2(b). F r a n c k - C o n d o n factors and estimated intensities for the E - X system of SiS in the 3500-6600 A ~on. 29

30

31

32

33

34

35

36

37

5

518 [3l

310 [6]

161 [3]

073

029

010

6

827 [7]

740 [6]

534 [7]

322 [71

166

075 [Zl

030

010

[3]

328

667

818 [6]

739

533

320

[7]

[8]

164 [9]

073 [4]

028

[8]

7

38

39

8

056 [5]

036

324

664 [5]

813 [81

728 [81

519 [9]

307 [9]

154 [5]

067

026

9

462 [4]

320 [6]

050 [4]

043

342

678 [6]

810 [7]

710 [10]

494 [8]

286 [7]

141 [4]

i0

011

263

459 [6]

297 [5]

036 [4]

060 [1]

378

703

806

683

462

[8]

[10]

[9]

[7]

455 [3]

261 [4]

018

089

429

732

797

[9]

[8] 490

Ii

12

13

344 [4]

099 ~[4]

021 [5]

289

019 [4]

271

325

071 [4]

040

326

444

215 [S]

005 [4]

133

298 [3]

080

038

298

295

040

073 [4]

367 [o]

423 [5]

162

185

281

048

069

325

253 [8]

014

120

405

223

250

019

114

342

200

[5]

14

15

244

150

Note: The FCFs are multiplied by 104 • intensities

180 [t]

The numbers i n p a r e n t h e s e s a r e e s t i m a t e d

Table 3(a). F r a n c k 4 2 o n d o n factors and estimated intensities for the E - X system of SiSe in the 2400-2800 A region. v"

0

1

2

3

4

5

6

7

001 [21

002 [2]

009 [1]

028 [t]

069

1

001 [1]

004 [2]

018 [2]

057 [1]

142

291

2

004 [3]

019 [2]

066 [2]

175 [2]

356 [1]

571

002 [4]

013 [3]

056 [2]

164 [1]

354

567

665

3 4

001 [7]

006 [9]

034 [7]

124 [3]

305 [4]

524 [3]

621

467

5

001 [7]

014 [10]

073 [4]

225 [3]

450 [3]

588 [3]

465

156 [2]

6

003 [6]

030

134

343

541

502

207

7

006

056

213

448

536

308

025

085

Ii0

019

256

143

324

[6] 8

012 [6]

094

303

510

431

9

022 [S]

144

388

507

268

386 [7]

634

SUNANDAK. et al Table 3(b). Franck-Condon factors and estimated intensities for the E-X system of SiSe in the 4000-6000 A region. 28

29

30

31

32

33

34

35

36

37

38

39

40

113

055

025

011

[4]

[4l

[2]

Ill

583 [31

413 [3]

258 [51

144 [3]

072 [2]

664

716

625 [3]

463 [2]

299 [2]

0

001 [11

1

027

012

[31

[2]

005 [21

217

121

062

029

013

005

001

[1l

[2]

[2l

[i]

13l

[11

501

333 [11

199

108

053

024

010

004

[21

[21

{21

[41

14l

[11

749

736

609

437 [2]

278

159 14l

083 [4]

039 14]

017 [5]

160

435

663 ll1

743

675

521

351

210

[3]

[51

712

707

180

455

2 3 4

670 606

5

001

[2]

6

399

187

013

055

289

7

086

325

428

283

065

557

652 [2] Note: The FCFs are multiplied by 104 • intensities

The numbers in parentheses are estimated

REFERENCES 1. K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules, Van Nostrand-Reinhold, New York, NY (1979). 2. N. Elander and A. Lagerqvist, Phys. Scripta 3, 267 (1971). 3. R. F. Barrow and T. J. Stone, J. Phys. B 8, L13 (1975). 4. E. E. Vago and R. F. Barrow, Proe. Phys. Soc. 58, 538 (1946). 5. H. Bredohl, R. Cornet, I. Dubois, and D. Wiideria, J.Phys. B 8, L259 (1975). 6. G. Lakshminarayana and B. J. Shetty, J. Molec. Spectrosc. 130, 155 (1988). 7. S. J. Q. Robinson and R. F. Barrow, Proc. Phys. Soc. A 67, 95 (1954). 8. R. F. Barrow, J. L. Deutseh, A. Lagerqvist, and B. Westerlund, Proc. Phys. Soc. 78, 1307 (1961). 9. S. Gopal, G. Lakshminarayana, and N. A. Narasimham, J. Phys. B 8, 3781 (1980). 10. G. Lakshminarayana, B. J. Shetty, and S. Gopal, J. Molec. Spectrosc. 112, 1 (1985). 11. M. Morris, W. Gilmore, P. Palmer, B. E. Turner, and B. Zuckermann, Astrophys. J. 199, L47 (1975). 12. N. Kaifu, D. BuM, and L. E. Snyder, Astrophys. J. 195, 359 (1975). 13. D. Buhl, L. E. Snyder, F. J. Lovas, and D. R. Johnson, Astrophys. J. 201, L29 (1975). 14. W. R. Jarmain and J. C. McCallum, JQSRT 11, 421 (1971).