The Schumann-Runge absorption bands of 16O18O in the wavelength region 175–205 nm and spectroscopic constants of isotopic oxygen molecules

JOURNAL OF MOLECULAR SPECTROSCOPY

134,362-389 (1989)

The Schumann-Runge Absorption Bands of 160160 in the Wavelength Region 175-205 nm and Spectroscopic Constants of Isotopic Oxygen Molecules A. S.-C. CHEUNG, ’ K. YOSHINO, D. E. FREEMAN, R. S. FRIEDMAN,* A. DALGARNO, AND W. H. PARKINSON Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138

High-resolutionabsorptionspectraof ‘60’s0 have been photographed,at 300 and 78 K, throughoutthe region 175-205 nm, in the first order of a 2400 lines/mm gratingin a 6.65-m vacuum spectrograph at a dispersion of 0.06 nm/mm. Precise wavelength measurements and rotational analyses of the Schumann-Runge bands (2,0)-( 16,O) have been completed. Spectroscopic constants of the B’S; state of ‘bO’*O for 2 < D=Z16 have been determined. Rotational perturbations are observed in the (16,O) band. The concept of mass-reduced vibrational quantum numbers, P-“~(u + f), has been used to combine isotopic molecular constants from 16Q, ‘60’*0, and “‘02. It has been shown that the functions of the vibrational spacings, p”2AG.+‘12, rotational constants FB,,, and p2 D,, spin-spin constants, X,, and spin-rotation constants, py,, are isotopically invariant functions of p-‘12(u + 4). The isotopic dependence of the spin-spin constants X, is discussed in terms of the unique perturber approximation. Values of yu and X, have been obtained by interpolation for the levels u = 2-8, which correspond to bands of ‘60’80 with unresolved triplet structure. In a theoretical investigation, the calculations of level shifts and perturbations have been reexamined. Excellent agreement between calculated and experimental level shifts has been obtained for ah three isotopic molecules. 0 1989 Academic Prw. Inc. 1. INTRODUCTION

160 180 constitutes 0.4% of atmospheric oxygen and it is the sixth most abundant atmospheric gas. It is spectroscopically distinct from I602 in at least two important respects: (a) I60 ‘*O, being a heteronuclear diatomic molecule with nuclei of zero spin, has twice as many populated rotational levels as 1602 and (b) the rovibronic levels of I60 “0 are shifted significantly in energy from those of “Oz, Recently, Cicerone and McCrumb ( 2 ) have concluded, from rough calculations of the atmospheric photodissociation rate of I60 180, that I60 I80 may be a nonnegligible source of odd oxygen, i.e., of 0 and OS, in the upper atmosphere and mesosphere. More realistic calculations by Blake et al. (2) have indicated that this source of odd oxygen is much smaller than suggested by Cicerone and McCrumb (I). However, the abundance of heavy ozone, “Oj, in the atmosphere remains a controversial matter (3-5)) and detailed experimental information on absorption wavelengths, spectroscopic constants, and cross sections of I60 ‘*O may be required for its satisfactory solution. ’ International Exchange Scholar, Smithsonian Institution, 1986-1987, Present address: Chemistry Department, University of Hong Kong, Hong Kong. 2 Also Department of Chemistry, Harvard University. 0022-2852189 S3.00 Copyright 0 1989 by Academic Press. Inc. All rights of reproduction in any form reserved.

362

SCHUMANN-RUNGE

BANDS OF ‘60’80

363

Halmann (6) has measured, at an instrumental bandwidth of 5-20 cm-‘, the wavelengths of the absorption bandheads of the (4,0)-( 11,O) bands3 of ‘60’80, but the pressure was 1 atm and only some rotational structure was partiahy resolved. Halmann and Laulicht ( 7,8) have also calculated the Franck-Condon factors based on Morse functions for the B32;-X32; transition of various isotopic oxygen molecules. With the present 6.65-m spectrograph, Hecht et al. (9) have photographed and partially analyzed some Schumann-Runge absorption bands of 160 “0, but detailed analyses and high-resolution cross-section measurements for 160 ‘*O have not been published previously. More recently, in work directed primarily toward the determination of band oscillator strengths and predissociation linewidths from equivalent widths measured with a 2.2-m spectrometer, Lewis et al. (10) have presented a limited rotational analysis of the Schumann-Runge bands (3,0) through (16,0), but they suggest their results should be treated as a guide only. In this paper, we report the high-resolution spectrographic wavelength measurement and rovibronic analysis of the Schumann-Runge bands of I60 180, and also the detailed isotopic relationships among the spectroscopic constants of 1602, 160’*0, and ‘*OZ obtained by use of the concept of mass-reduced molecular constants described by Stwalley ( I1 ) . Finally, in an extension of the calculations of Julienne and Krauss ( 22) and Julienne (13), we obtain theoretical values of the level shifts and demonstrate that a consistent deperturbation can be found for all three isotopic molecules. 2. EXPERIMENTAL

DETAILS

The apparatus and procedure for this work are the same as described in our previous paper (14). The spectrum was photographed by a 6.65-m McPherson Model 265 vacuum spectrograph, described previously ( 15 ) , in the first order of a 2400 line/ mm grating coated with MgFz . The reciprocal linear dispersion is approximately 0.06 nm / mm. This is the same instrument as that used for our recent high-resolution studies of the Schumann-Runge bands of I602 (14, 26-18). The relative accuracy of the measurements is estimated to be 0.000 1 nm ( kO.03 cm -‘) for the sharpest lines, and the absolute accuracy is 0.0003 nm (20.09 cm-‘). The background continuum is obtained from a dc discharge ( -200 mA) in hydrogen ( -2 Torr). Typical exposure times with Kodak SWR plates are 6-20 min with an entrance slitwidth of 0.010 mm. The absorption ceil, isolated from the discharge tube and spectrograph by two fused silica windows (Suprasil-1), provided a 50-cm optical path length and can be cooled by liquid nitrogen. The isotopic oxygen (MSD Isotopes, 52.6% atomic ‘*O) was introduced into the absorption cell and the pressure was varied from 0.6 to 3 18 Torr at 300 K and 0.2 to 154 Torr at 78 K. The isotopic mixture contains 1602, ‘60’80, and “Oz in the approximate molecular ratio of 1:2: 1. Since the absorption spectrum of the heteronuclear molecule I60 ‘*O possesses twice as many rovibronic lines as that of either of the homonuclear molecules 1602 or ‘*O*, the intensities of the bands of all three molecules are roughly comparable in this mixture. The wavelengths of the absorption spectra of the O2 molecules are determined from the wavelengths of the Fourth Positive emission lines of CO, photographed in the same order of the grating. 3 In the present paper, the symbol (I), 0) labels the Schumann-Runge transition B(u)%; + X(O)“Z;.

absorption band for the vibronic

364

CHEUNG ET AL.

I 183.0

I

I

I

I

I 183.8

FIG. 1. The (9,O) Schumann-Runge bottom at 300 K.

nm

band of oxygen isotopes. Top spectrum was taken at 78 K and

The CO wavelengths are obtained from the known rovibronic term values of the A and X states of CO ( 19). The accuracy of the CO term values is better than 0.05 cm-‘. 3. BRIEF DESCRIPTION AND ASSIGNMENT OF THE SCHUMANN-RUNGE ABSORPTION BANDS OF 160’80

The gas sample used in this experiment contains approximately 25% 1602, 50% I60 l8O, and 25% “Oz. Consequently, the photographic spectra of such oxygen samples have overlapping bands, which are shown in Figs. 1 and 2. Because of the isotope effect, the band origins move to longer wavelengths for a heavier oxygen isotope. Figure 1 shows the (9,0) bands of the isotopes; the upper spectrogram corresponds

‘6@30

I

179.5

‘802

I

180.0

“,,,

FIG. 2. The (12,O) Schumann-Runge band of oxygen isotopes at 78 K. &(N) and F’s(N) components of rotational lines are rarely separated at this size of enlargement.

SCHUMANN-RUNGE

BANDS OF I60 ‘*O

TABLE I Wavenumbers of the Rotational Lines of the (2,0) through ( 16,O) Schumann-Runge Absorption Bands of I60 “0’ a.

Wavenumbers of the B(Z)-X(0)

N

band

R(N) 50 50 50 50 50 50 50 50 50 50 50 50 50

0 ;

3 4 : 7 8 9 10 11 12 b.

687.98R 687.98R 687.20 685.13 681.73 677.03 671.14 663.25B 655.64 646.03 635.30 623.13 609.87

Wavenumbers of the B(3)-X(0)

P(N) 50 50 50 50 50 50 50 50 50 50 50

683.37B 679.86 674.78 668.01 660.63B 651.93 641.71 630.44 617.89 604.00 589.16

band

P(N)

N

0

51 312.69R

: 3 4 5 6 I

51 51 51 51 51 51

312.69R 310.17 306.76B 301.73 295.57 288.22

51 51 51 51 51 51

310.17B 304.79 300.07 293.52 285.72 276.79 266.55

: 10 11 12 13 14 15 16 17

51 51 51 51 51 51 51 51 51

279.34 269.75 258.76B 246.30B 232.60 217.36 201.58 184.07 165.80 145.18B

51 51 51 51 51 51 51

254.88 242.20 227.87B 212.71 196.33 178.27 159.31 139.26

c.

Wavenumbers of the B(4)-X(0)

N 0 ::

3 4 5 6 7

:

10 11 12 13 14 15 16 17 18

band

W-1 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51

914.73R 914.73R 914.73R 912.8OP 908.73P 903.39 896.94B 889.65 880.93 870.31 858.82B 846.52B 832.28B 816.30B 800.28 782.96B 762.95B 742.35 721.52

J’(N) 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51

912.80R QO8.73R 902.44 895.38 888.98 879.33 868.61 856.81 844.14 830.86 814.31B 796.87 779.10 759.75 738.85B 716.45 692.81B 668.79

“The symbols in Table I have the following meanings: R or P after a wavenumber indicates overlap with a R or P branch line; R(N) s indicates an incompletely resolved me; B indicates overlap with another line; Q indicates shoulder to the main R(N) or P(N) 1’ questionable identifications.

365

366

CHEUNG ET AL. TABLE I-Continued d.

52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52

:

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

22 23 24 25 26 e.

9

10 :a 13 :: 16 17 18 19 20 21 22 23 z:

f.

1

494.05R 494.05R 493.57 491.18P 486.86P 481.86P 475.17P 467.18P 458.46 447.78 435.92 422.52B 408.34 392.62 375.33 356.81B 337.44 316.72 293.34B 269.57B 245.56 219.36 191.66 162.85B 132.42 100.87 070.25B

Wavenumbers of the B(6)-X(0)

53 53 53 53 53 53 53 53 53 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52

6 7 8

0

Wavenumbers of the B(S)-X(0)

044.98B 044.98B 043.79 041.11 037.04P 031.68P 024.93P 016.81P 007.35P 996.5OP 984.3OP 970.84P 955.98P 939.75P 922.06P 903.1513 882.82P 861.23P 838.2OP 813.84P 788.17P 760.98P 732.65P 702.92P 671.75P

Wavenumbers of the B(7)-X(0)

53 568.61R 53 568.61R

band

52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52

491.18R 486.86R 481.86R 475.17R 467.18R 457.82 447.18 435.18 421.24 407.58 391.44 374.20 35.5.45B 335.56 314.40 292.21 267.59B 243.04 216.48 188.85 160.07 129.48 097.60 064.73

band

53 53 53 53 53 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52

037.04R 031.68R 024.93R 016.81R 007.35R 996.50R 984.3OR 970.84R 955.98R 939.75R 922.06R 903.15R 882.82R 861.23R 838.20R 813.84R 788.17R 760.98B 732.65R 702.92R 671.75R 639.33R 605.40R 570.32R

band

53 565.02R

SCHUMANN-RUNGE

BANDS OF I60 “0

367

TABLE I-Continued f.

Wavenumbers

N

band

R(N) 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 g.

P(N)

567.80 565.02P 560.81P 555.38P 548.49P 540.27P 530.63P 519.13 506.82 492.60 477.38B 460.77 442.59 423.00 403.53B 379.81 356.11 330.84 304.14 276.63 247.62 216.27B 184.63

53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53

Wavenumbers of the B(8)-X(0)

560.81R 555.38R 548.49R 540.27R 530.63R 519.47 507.17 493.40 477.98 461.68 443.57 424.30 404.36 381.51 358.23 333.24 306.73 279.26 250.33 219.54 187.97 154.42

band

N

R(N)

0

54 061.66R

; 3 4

54 061.66R 060.48 54 057.62P 54 053.32P

54 057.62R 053.32R 54 048.07 54 041.30

i 7

54 047.50 040.29 54 031.48

54 033.08 023.25 54 011.97

: 10 11 12 13 14 15 16 17 18

54 53 53 53 53 53 53 53 53 53

021.28 009.65 996.67 982.24 966.47 948.91B 930.46 910.31 888.35 865.77 841.35B

53 53 53 53 53 53 53 53 53 53

999.31 985.21 969.63 952.53 934.17 914.35 892.91 870.55 846.37 820.65B 793.88

fi 21 22 23 24

53 53 53 53 53

787.93 815.39 759.35 729.24 697.31 664.27

53 53 53 53

736.21B 765.48 704.59B 671.56 637.74

h. N

of the B(7)-X(0)

RI(N)

Rz(N) 54 54 54 54 54 54

P(N)

Wavenumbers of the B(9)-X(0) MN)

523.59R 54 525.83 522.OOR 54 522.21 518.9OR 54 519.46P 514.25R 508.15R 500.57R

band

PI(N) 54 54 54 54 54 54

519.46R 515.61P 510.12P 503.03P 494.47P 484.4OP

PAN)

54 54 54 54 54

515.61P 510.12P 503.03P 494.47P 484.4OP

Pa(N)

CHELJNG

368

ET AL.

TABLE I-Continued h.

N

RI(N)

;

Wavenumbers of the B(9)-X(0)

W”)

Rz(N)

band

PI@‘)

Pz(N)

PdN)

54 491.49R 480.92R

54 491.49R 480.92R

54 491.78 481.22

54 472.88P 459.853

54 472.88P 459.85P

54 460.12

lo” 11 12 ::

54 54 54 54

468.92R 455.39R 440.49R 424.05R 386.74R 406.05R

54 54 54 54

468.92R 455.39R 440.49R 424.05R 386.74R 406.05R

54 54 54 54

469.18 455.74 440.80 424.43 387.15

54 54 54 54

445.35p 429.36p 412.11P 393.09P 350.82P 372.68P

54 54 54 54

445.35p 429.36p 412.11P 393.09P 350.82P 372.68P

54 445.73 429.65

15 16 17 18 19 20 21

54 54 54 54 54 54 54

365.83R 343.45R 319.64R 294.33R 267.49R 239.21R 209.40R

54 54 54 54 54 54 54

365.83R 343.45R 319.64R 294.33R 267.49R 239.21R 2OQ.40R

54 366.30

54 54 54 54 54 54 54

327.49P 302.71P 276.46P 248.64P 219.41P 188.59P 156.51P

54 54 54 54 54 54 54

327.49P 302.71P 276.46P 248.64P 219.41P 188.59P 156.51P

54 327.79 54 303.13

;z 24

54 178.12R 145.35R 54 111.18R

54 087.65P 122.8QP 54 050.98P

54 087.65P 122.89P 54 050.98P

54 088.20

53 973.15P

53 973.15P

53 973.93

54 178.12R 145.35R 54 lll.18R

54 54 54 54 54

320.20 294.78 267.87 239.81 210.25

54 179.12 54 112.44

;: i. N

RI(N)

0

54 950.28R

; 3 4

54 950.28R 948.69 54 945.44R 54 940.62R

: 7

54 934.20R 926.29R 54 916.83R

: 10 11 12 13

54 54 54 54 54

905.88R 893.42R 879.35R 863.871 846.71R 828.24R

:z 16 17 18

54 54 54 54

808.21R 786.59R 762.83B 738.41 712.12

f: 21 22 E

54 684.34 655.14B 54 623.96 54 557.68

MN) 54 54 54 54 54 54 54 54 54 54 54 54 54 54 54 54 54 54 54

1

55 339.63R 55 339.63R

z 4

55 337.70 334.13 55 328.94

: 7 8 9 10 :2

55 55 55 55 55 55

322.42 314.26R 304.13 292.73 279.72 265.05 231.25 248.91

&P’)

948.85 945.44R 940.62R 934.20R 926.29R 916.83R QO5.88R 893.42R 879.35R 866.87R 846.71R 828.24R 808.21R 786.59R 762.83B 738.99R 712.72R 684.95R 655.53R

54 558.44

j.

0

Wavenumbers of the B(lO)-X(0)

55 55 55 55 55 55 55 55 55 55

54 54 54 54 54 54 54 54 54 54 54 54 54 54 54 54 54 54 54

948.85 945.76 940.62R 934.42 926.61 917.19 906.35 893.42R 879.35R 863.87R 847.08 828.24R 808.21R 787.18 762.83B 738.QQR 712.72R 684.95R 655.53R

54 558.95

;: 54 54 :: 54 it 54 54 54 54 54

942.37 936.95P 929.75B 920.81B 910.73P 898.92P 885.62P 870.66P 854.31P 836.81B 816.96P 795.97P 773.64P 749.66P 723.95 697.22P 668.52P 638.451

54 573.41B

55 55 55 55 55 55 55 55 55 55

337.95R 334.37R 329.17R 322.68R 314.26R 304.55R 293.11R 280.13R 265.54R 249.34R

54 157.02B

Pz(N)

54 54 54 54 54 :: 54 54 :: 54 54 54 54 54 54

936.95P 929.75B 921.02P 910.73P 898.92P 885.62P 870.66P 854.31P 836.81B 816.96P 795.97P 773.64P 749.66P 724.39P 697.22P 668.52P 638.45P

54 573.41B

PdN)

54 930.12B 921.02P :: 910.73P 54 898.92P 54 885.62P 54 871.41 54 854.64 836.81B :: 816.96P ;: 54 54 54 54 54

:E:t’4: 749.66P 724.39P 697.22P 668.52P 638.45P

54 573.89B

54 464.44

Wavenumbers of the B(ll)-X(0)

337.95R 334.37R 329.1lR 322.68R 314.26R 304.55R 293.11R 280.13R 265.54R 249.34R

54 249.07 54 219.82

band

PO’) 54 54 54 54

54 393.27 54 372.92

55 55 55 55 55 55 55 55 55 55 55 55

335.77 331.87 326.11 318.60 309.82 299.28 286.95 273.36 258.17P 241.07 222.38 202.79

band

55 55 55 55 55 55 55 55 55

326.41 318.84 310.12P 299.51P 287.21P 273.61B 258.17P 241.49P 222.98P

55 55 55 55 55 5; 55 55

318.84 310.12P 299.51P 287.21P 273.36B 258.17P 241.49 222.98P

SCHUMANN-RUNGE BANDS OF ‘b”0

369

TABLE I-Continued j. N 1.3 14 15 16 17 18 :i 21

RIP’) 55 55 55 55 55 55 55 55 54

211.95 190.57 166.24 144.03 118.72B 090.99 062.02 031.78 QQQ.44B

N

212.52R 191.42R 168.96 144.75 119.45R 091.94R 063.17R

55 000.81R

2 3 4 x 7 8 9 10 11 12 13 14 15 :; 18 19 20 21 22 23 24 25

689.84 689.44 687.27 683.47 678.02 670.94 662.21 651.83 639.81 626.15 610.85 593.91 575.30 555.05 533.17 509.61 484.43 457.56 429.04 398.85 366.98

55 261.34

55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55

;

55 997.99 997.47 55 995.15

3

55 99l.OQ

: 6 7 8 Q 10 11 12 13 14 15 16 17 18 19

55 55 55 55 55 55 55 55 55 55 55 55 55 55 55

985.26B 977.73 968.55 957.66 945.01 930.66 914.60 896.75 877.31 856.11 833.17 808.46B 782.07 753.94 724.04 692.43

181.OQ 157.68 133.08 106.69 078.75 049.54 018.07

PW 55 55 55 55 55 55

55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55

688.55 684.53 678.98 671.92 663.23 652.89 640.91 627.37 612.09 595.29 576.75 556.54 534.80 511.42 486.31 459.58 430.99 401.03 369.28

55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55

685.99 681.79 675.88 668.31 659.07 648.19 635.67 621.50 605.70 588.26 569.16B 548.43 526.06 502.06 476.44 449.13 420.13 389.41B 357.31 323.19B 287.66 250.45

998.63 996.30R 992.29R 966.53R 979.06 969.85 956.96 946.35 932.03 916.01 898.21 878.85 857.71 834.85 810.19 783.89 755.82 726.01 694.65B

56 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55

001.11 QQ6.30R QQ2.2QR 986.538 979.16 969.97 959.12 946.57 932.31 916.39 698.74 879.37 858.30 835.50 810.94 784.66 756.73

55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55

55 695.67B

QQ4.09B 989.98 983.95 976.18 966.67 955.45 942.51 927.86 911.51 893.45 873.55 852.21 829.03 804.09 777.50 749.09 719.02 687.24B 653.66

682.57 676.60 669.04 659.84 648.98 636.46 622.33 606.56 589.16 570.05B 549.38 527.07 503.14 477.49 450.25 421.32B 390.80 358.59 324.89B 289.18 252.00

55 172.66

Pa(N)

55 55 55 55 55 55 55 55

677.13 669.26 659.99 649.13 636.59 622.49 606.72 589.32

55 55 55 55 55

549.71 527.40 503.44 477.92 450.72

55 391.36 55 359.24 55 289.96 55 252.91 55 173.67

band

PI(N) 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55

181.4OP 158.33P 133.80 107.38P 079.43P 050.15P

54 986.13P 54 952.31

PAN)

Wavenumbers of the B(13)-X(0)

fW’)

PdN) 55 55 55 55 55 55

band

C(N)

55 171.11 55 128.91

Rz(N)

161.40P 158.33P 133.54 107.38P 079.43P 050.15P

54 986.13P

55 OOO.81R

55 262.97

55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55

PI(N) 55 55 55 55 55 55 55

Rs(N)

55 368.43

RIP’)

0

212.52R 191.42R 169.30 145.19 119.45R 0Q1.94R 063.17R

band

Wavenumbers df the B(12)-X(0)

690.11 688.05 684.22 678.82 671.77 663.04 652.69 640.71 627.10 611.83 598.89 576.34 556.11 534.32 510.79 485.67 458.83 430.37B

I. N

55 55 55 55 55 55 55

Rz(N)

RI(N) 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55

RdN)

MN) 55 55 55 55 55 55 55

k.

0 1

Wavenumbers of the B(Il)-X(0)

PdN) 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55

QQlOQB 985.26P 977.33P 967.81 956.65P 943.74P 929.15P 912.84 694.82 875.06 853.62 830.49 805.63 779.00 750.72 720.74 688.99 655.55B

h(N)

55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55

985.26P 977.33P 967.93 956.65P 943.74P 929.15P 912.95 895.04B 875.30 853.98 830.88 806.10 779.59 751.48 721.45 689.80B 656.50B

CHEUNG

370

ET AL.

TABLE I-Continued

I.

Wavenumbers of the B(13)-X(0)

N

R,(N)

Rz(N)

22: 22 23

55 623.90

55 661.16

m. N 0

1 2 3 i F !I 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

R,(N) 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 55 55 55 55

262.56 262.01 259.44 255.04 248.87 240.91 231.16 219.63 206.32 191.21 174.37 155.70 135.18 112.80 088.74 062.98B 035.08 005.49 974.14 940.89 905.88B 868.91

55 789.52B 55 747.06B

0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

484.17 483.30B 480.51B 475.94B 469.27B 460.81 450.44 438.23 424.14 408.34B 390.05B 370.63 349.14

56 56 56 56

300.19 272.92 242.90 212.61

56 144.62 56 107.72

&(N)

263.88B 261.09R 256.81R 250.65R 242.63R 232.91R 221.45 208.20 193.18 176.54B 157.65 137.36 115.09 091.11 065.26

56 55 55 55 55

008.12 977.17B 943.82B 909.02B 872.19B

55 793.02

56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56

266.27 261.09R 256.61R 250.65R 242.63R 232.91R 221.67 208.51 193.60 176.80 158.29 138.04B 115.98 092.05 066.24 038.72 009.39

55 945.05B 55 910.44B 55 835.48B 55 794.88

PI(N) 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 55 55 55 55 55 55 55 55

258.98 254.78 248.65 240.65 230.80 219.12 205.71 190.54 173.58 154.75 134.30 112.01B 087.83 061.98 034.18 004.69 973.35 940.24 905.30B 868.48 829.89 789.52B 747.06B 702.96

485.56B 482.86 478.22 471.65 463.44 453.20R 440.98 426.98 410.97 393.19 373.69 352.41 328.96 303.73 276.56 247.63 216.60 183.90

RdN) 56 56 56 56 56 56 56 56 56 56 56 56 56

488.54B 483.30B 478.40B 471.88B 463.58B 453.20R 441.30 427.53 411.70 394.12 374.61 353.12 329.99

56 185.38

480.51B 475.94B 469.82B 461.56 451.44 439.43 425.49 409.69B 392.09 372.58 351.32 328.04B 302.87 275.88 246.96 216.25 183.56 148.93 112.23

55 584.40 55 545.80 55 505.45

band

56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 55

256.64 250.17 242.2OP 232.30 220.82P 207.38 192.35P 175.33 157.18P 136.43P 114.05 089.97 064.30B 036.49 007.06 976.20B

55 55 55 55

907.93 871.38 833.15B 792.51

55 706.39

J%(N)

56 56 56 56 56 56 56 56 56 56 56 56 56 56

250.65B 242.2OP 232.55 220.82P 207.50 192.35P 175.63 157.18P 136.43P 114.45 090.52 064.55B 037.43 008.04

55 943.82B 55 909.02B 55 834.19 55 794.01 55 70802

band

PI(N) 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56

h(K)

P,(N)

Wavenumbers of the B(l5)-X(0)

Rzb”) 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56

55 620.30 583.43 55 544.70 55 504.27

Wavenumbers of the B(14)-X(0)

56 56 56 56 56 56 56 56 56 56 56 56 56 56 56

R,(N) 56 56 56 56 56 56 56 56 56 56 56 56 56

PdN

PI(N) 55 618.39 581.41B 55 542.60

RANI

n.

N

h(N)

band

Pz(N) 56 56 56 56 56 56 56 56 56 56 56 56 56

478.40B 471.88B 463.58B 453.60 441.73P 427.97P 412.20 394.94 375.33 354.23 330.99B 305.80 278.99

56 187.21 56 152.54

PdN)

56 56 56 56 56 56 56 56 56 56 56

472.58 464.19 453.95 441.73P 427.97P 412.33 395.64B 375.82 354.668 331.54 307.02B

56 250.90 56 188.43 56 117.98

SCHUMANN-RUNGE

371

BANDS OF ‘60’*0

TABLE I-Continued o.

Wavenumbers of the B(16)-X(0)

N 0

1

i

4 5 6 7 8 9 10 11 12 13

RdN) 56 56 56 56 56 56 56 56 56 56 56 56

663.19B 662.19B 659.29B 654.10B 647.02 637.95 626.86 613.73 598.66 581.50 562.26 541.16B

56 56 56 56 56 56 56 56 56 56 56

667.71B 664.76 659.59R 652.49 643.42R 632.58R 619.72 604.93B 588.23 569.63 549.00

56 56 56 56 56 56 56 56 56 56

665.40 659.59R 652.88 643.42R 632.58R 619.90 605.15 588.63 569.85 550.25B

P,(N) 56 56 56 56 56 56 56 56 56 56 56 56 56

659.29B 655.03B 648.63 640.18 629.67 617.17 602.64 586.16 567.52 547.04 524.59B 499.98B 473.31

band

Pa(N)

P2P)

56 56 56 56 56 56 56 56 56 56

660.46 654.10B 645.79 635.17P 622.57P 608.16P 591.99P 573.66P 553.48 531.33

56 481.03

56 56 56 56 56 56 56 56 56 56

662.19B 655.03B 646.12 635.17.P 622.57P 608.16P 591.99P 573.66B 553.68 531.62

56 482.55

to a temperature of 78 K and the lower one to 300 K. From left to right, the bandheads belong to 1602, I60 “0 and “02, respectively. The (12, 0) bands have sharp lines ( 17, 20), and Fig. 2 shows these bands with triplet splittings resolved. The apparent linewidths of different bands of I60 ‘*O go through maxima at u = 4 and o = 7. Detailed work to extract individual linewidths is in progress (21) . The SchumannRunge band system of I60 I80 has twice as many spectral lines as that of either homonuclear molecule, for which rotational levels with even values of the ground-state rotational quantum number N are not populated. We observe qualitatively that the lines of I60 IgO are weaker than the corresponding lines of 1602. This result is in accord with the predictions of Blake et al. (2) who find that the ratios of the band oscillator strengths of ‘60’80 to those of I602 lie in the range 0.64-0.86 for the (1, O)(12,O) bands. The measured line positions and rotational assignments of the principal branches of bands ( o, 0) with u = 2- 16 are given in Table I. Satellite and forbidden lines, which are weak, are observed only in the crowded bandhead regions. The wavenumbers of satellite and forbidden lines with N = 1-9, calculated for bands (9, 0)-( 15, 0) from B-state molecular constants (see Sect. 4)) derived from the principal branch lines and known ground-state term values (22), are given in Table II. Our measured values, when available, are given immediately beneath the appropriate calculated values. 4. LEAST-SQUARES FITTING RESULTS AND SPECTROSCOPIC CONSTANTS OF THE B”Z; STATE OF ‘60’80

The Hamiltonian for the ‘Z electronic state described in this paper and the matrix elements used, in Hund-Mulliken case (a) basis sets, can be found in Cheung et al. (I 7). The term values of the B32 ; levels are calculated from the transition Iiequencies in Table I and the ground-state term values (22)) and are fitted to the Hamiltonian. From the available data, it was not possible to determine the parameter An which therefore was omitted for all the bands studied. For u = 12-15, six parameters (B, D, A, y, yD, and the band origin T) were varied. For t, = 9 and 11, because of the limited

372

CHEUNG

ET AL.

resolution of the Fz and F3 components, the parameter yn was omitted. For 0 = 28, the triplet structures of the bands (8, 0) are unresolved, and so the spin parameters y and X cannot be obtained directly from the fit. Furthermore, for u = 2-5 and 7, the large predissociation widths cause di5culty in determining the centrifugal distortion constants, D, which, therefore, are fixed at the values calculated from those of 1602 ( 17) by use of the isotopic relationship (23) (see Sect. 5 (ii)). The molecular spectroscopic constants obtained are tabulated in Table III, where the uncertainty, which is a 1u limit for the parameters, is given in parentheses below the parameter value. The column headed RMS gives the root-mean-square deviations between computed and observed term values. The values of y and X in square brackets are interpolated by procedures described in Section 5. A plot of AG,+,,* values, derived from Table III, versus u, is shown in Fig. 3, in which the solid curve is obtained from the following polynomial formula with the vibrational constants of I602 ( 17): T(u) = To + pw,(u + f) - p&X&

+ f)’

+ P3We(U + 0’ + P4W,(U + f)” + P5Me(U + 4)‘.

(1)

The vibrational constants of the B state of I60 I80 can be calculated from those of 1602 and the ratio p2 of reduced molecular masses. They are compared in Table IV with those obtained from the least-squares fit to the vibrational formula with u = 213. The level shifts, arising mainly from the interaction of the repulsive II states with the B32; state, are discussed in Section 6. The tendency seen in Fig. 3, for the plot of AG,+ I 12 versus u for I60 ‘*O to show slightly positive curvature at high u values, was noted previously for 1602 ( 17), and makes difficult the determination of the dissociation energy by extrapolation of the plot to higher u values. A plot of our B(u) values from Table III is shown in Fig. 4, in which the solid curve is obtained from the following polynomial formula with mass-reduced rotational constants from those of 1602 ( 17): B(u) = p2Be - p3a,(u + 1) + ,o~Y~(u + 4)’ + ,&(u

+ 4)‘.

(2)

In Table IV, the calculated rotational constants of ‘60’80 from those of 1602 are also compared with the experimental values derived Corn the polynomial least-squares fit obtained from the B(u) values in Table III. 5. MOLECULAR

CONSTANTS

OF 1602, ‘60’80,

AND

“Oz

The accumulation of experimentally determined molecular constants ( 2 7,20) permits a detailed comparison; not only should those results be examined to confirm the relationships among isotopes, but, more importantly, with the use of all the available information, we are able to obtain those molecular constants not directly determinable because of narrow triplet splittings and large predissociation widths. Relationships among different isotopes have been discussed by several authors (II, 23-25), using the concept of the mass-reduced vibrational quantum number I-“~( u + j), where P is the reduced molecular mass. The mass-reduced functions of Stwalley (II) are applied here to various molecular constants of 1602, ‘60’80, and “02. In general, ifX(r), a

SCHUMANN-RUNGE

373

BANDS OF ‘60’s0

TABLE 11 Wavenumbers of Satellite and Forbidden Lines Calculated from Term Valuesa

B(9) - X(O) BAND N

PQ12

%3

“Q23

0

1 2 3 4 5 6 7 a 9

54 54 54 54 54 54 54 54 54

521.88 515.95 510.24 503.08 494.45 484.36 472.80 459.76 445.25

54 54 54 54 54 54 54 54 54

517.91 513.80 506.17 501.05 492.45 482.37 470.82 457.80 443.31

54 54 54 54 54 54 54 54

517.94 512.20 505.03 496.41 486.33 474.77 461.75 447.26

RQ3*

RQZl

54 54 54 54 54 54 54 54 54 54

525.74 525.60 523.94 520.80 516.18 510.09 502.52 493.41 462.96 470.96

54 54 54 54 54 54 54 54 54

522.18 520.42 517.23 512.58 506.47 496.90 489.85 479.33 467.34

RP3l

54 54 54 54 54 54 54 54 54 54

522.16 524.08 522.35 519.16 514.56 506.47 50090 491.87 481.36 469.38

TR31

54 54 54 54 54 54 54 54 54 54

530.37 532.70 533.52 532.87 530.74 527.14 522.06 515.51 507.48 497.97

NP,3

54 54 54 54 54 54 54

506.41 496.82 485.74 473.17 459.12 443.61 426.62

B(10) - X(0) BAND N

PRl3

0 1 2 3 4

54 54 54 54 54 54 54 54 54

i 6 7 a 9

B(ll)

948.64 942.73 936.96 929.69 920.90 910.59 898.76 685.41 870.54

NP13

a31

54 54 54 54 54 54 54 54 54

944.68 940.58 934.89 927.66 918.89 908.60 896.79 883.45 868.60

54 54 54 54 54 54 54 54

944.95 939.12 931.81 923.00 912.68 900.84 887.49 072.62

54 54 54 54 54 54 54 54 54 54

952.78 952.52 950.72 947.39 942.53 936.16 928.26 918.83 907.89 895.43

54 54 54 54 54 54 54 54 54

949.04 947.07 943.65 938.75 932.33 924.41 914.96 904.00 891.52

54 54 54 54 54 54 54 54 54 54

948.86 950.94 949.00 945.61 940.72 934.32 926.41 916.96 906.03 893.56

54 54 54 54 54 54 54 54 54 54

957.10 959.12 959.69 958.73 956.25 952.25 946.73 939.69 931.12 921.03

54 54 54 54 54 54 54

933.17 923.60 912.46 699.78 885.57 869.84 852.59

- X(0) BAND

N

P&3

PQlZ

0

1 2 3 4 5 6 7 a 9

55 55 55 55 55 55 55 55 55

337.87 331.93 326.06 318.62 309.61 299.03 286.68 273.15 257.85

B(12)

X(0) BAND

N

PR13

55 55 55 55 55 55 55 55 55

333.90 329.77 323.99 316.59 307.61 297.05 284.91 271.19 255.90

PQ13

0

1

55 687.98

‘Wherea observed

55 684.02

pair of wavenumbers values, respectively.

55 55 55 55 55 55 55 55

334.43 328.50 321.03 312.01 301.43 289.28 275.56 260.27

PQ*3

RQ33

RQtt

pQZ3 55 55 55 55 55 55 55 55 55 55

342.24 341.90 339.94 336.40 331.28 324.59 316.33 306.48 295.07 282.07

RQ21 55 692.59 55 692.12 55 692.14

55 55 55 55 55 55 55 55 55

338.43 336.28 332.65 327.48 320.76 312.46 302.63 291.21 278.22

RQ33 55 688.70

RP3, 55 55 55 55 55 55 55 55 55 55

338.00 340.32 338.21 334.60 329.46 322.75 314.48 304.65 293.24 280.26

a31 55 55 55 55 55 55 55 55 55 55

346.23 348.12 348.42 347.16 344.32 339.91 333.94 326.38 317.25 306.54

Rp3,

=R31

55 688.09 55 690.59

55 696.31 55 697.95 55 698.03

is given for a line, the upper and lower entries are the calculated Where a single value is given, it is the calculated value.

NPt3

55 55 55 55 55 55 55

322.40 312.80 301.55 288.71 274.28 258.28 240.71

NP*3

and

CHEUNG ET AL.

374

TABLE II-Continued

I]( 12) -

X(0) BAND

N

RQZl

PQ*3

PQr3

FR13

2

55 681.99

55 679.84

55 684.78

55 689.98

55 686.35

55 688.29

3

55 675.99

55 686.20 55 686.24 55 680.78

55 682.48

55 668.36

5

55 659.09

673.92 673.83 666.33 666.30 657.08

55 678.72

4

55 55 55 55 55

6

55 648.18

7

55 635.63

8

55 621.44 55 605.62

55 55 55 55 55 55

646.19 646.22 633.66 633.67 619.49 603.68

PQ,*

9

55 671.07

55 684.44

55 697.96 55 698.03 55 696.35

55 672.51

55 677.03

55 679.00

55 693.11

55 662.86

55 669.96

55 671.95

55 688.24

55 651.49

673.71 673.83 665.02 664.95 654.68

55 661.27

55 663.27

55 681.73

55 638.40

55 55 55 55 55

55 650.95

55 652.97

55 673.58

55 638.45 55 638.43 55 623.76

55 624.25 55 608.46

55 642.71 55 629.10

55 639.00 55 625.42

55 641.03 55 627.46

55 663.80 55 652.37

55 607.43 55 589.46

PQ*3

RQ*,

RQ3*

RP3,

TR3,

001.14 000.55 oo0.55 998.21

55 997.15 55 997.23 55 994.58

55 994.16

55 990.42

55 992.38

55 55 55 55 55 55 55 55 55

55 984.63

55 986.61

56 003.56 56 003.69 55 999.86

55 977.17

55 979.16

55 994.46

55 971.01 55 971.09 55 959.52

55 968.02 55 957.18

55 970.02 55 959.19

55 987.37 55 978.56

55 946.29 55 931.33

55 944.64 55 930.40

55 946.67 55 932.44

55 968.05 55 955.83

55 914.66 55 896.29

55 661.81 55 650.92

B(13) - X(0) BAND

N

pRlJ

0 1

55 996.15

55 992.19

2

55 990.14

55 987.98

3

55 984.02

4

55 976.20

5

55 966.66

6 7

55 955.41 55 942.46

8 9

55 927.79 55 911.42

55 55 55 55 55 55 55 55 55 55 55

981.95 982.05 974.17 974.32 964.66 964.77 953.43 940.49 940.55 925.84 909.48

55 993.34 55 993.33 55 987.15 55 979.30 55 969.78 55 958.55 55 945.64 55 931.02 55 914.70

56 56 56 55

988.41 988.46 980.95 980.80 971.79 960.92 960.91 948.35 934.06

55 996.23 55 999.05 55 996.51

56 56 56 56

NP13

004.53 005.89 005.83 005.57 55 980.68

B(14) - X(0) BAND N

PQ!Z

%3

PQ13

0

1 2 3 4 5 6 7 8 9

56 56 56 56 56 56 56 56 56

260.83 254.78 248.54 240.51 230.68 219.06 205.65 190.46 173.49

56 56 56 56 56 56 56 56 56

256.87 252.62 246.47 238.48 228.67 217.07 203.68 188.51 171.55

56 56 56 56 56 56 56 56

258.48 252.14 244.07 234.26 222.67 209.31 194.19 177.28

RQ2, 56 56 56 56 56 56 56 56 56 56

266.28 265.54 262.98 258.64 252.53 244.63 234.95 223.50 210.26 195.24

RQ32 56 56 56 56 56 56 56 56 56

262.19 259.36 254.90 248.73 240.83 231.18 219.76 206.58 191.62

TR3,

RP31

56 56 56 56 56 56 56 56 56 56

260.89 264.08 261.29 256.85 250.71 242.82 233.18 221.78 208.61 193.66

56 56 56 56 56 56 56 56 56 56

269.32 270.37 269.67 267.23 263.02 257.05 249.31 239.79 228.48 215.39

%3

56 56 56 56 56 56 56

245.36 235.65 224.04 210.60 195.35 178.31 159.48

SCHUMANN-RUNGE

- X(0)

N

rQsl*

PR13 56 56 56 56 56 56 56 56 56

375

‘60’80

BAND

pQ*S

0

1 2 3 4 5 6 1 8 9

OF

II-Continued

TABLE

B(K)

BANDS

482.39 476.27 469.67 461.59 451.43 439.39 425.48 409.70 392.05

56 56 56 56 56 56 56 56 56

478.43 474.12 467.80 459.56 449.42 437.40 423.51 407.74 390.10

56 56 56 56 56 56 56 56

480.62 474.13 465.83 455.69 443.71 429.88 414.19 396.65

RQ2, 56 56 56 56 56 56 56 56 56 56

488.42 487.53 484.74 480.08 473.57 465.19 454.96 442.87 428.91 413.09

TABLE

%,

"QN 56 56 56 56 56 56 56 56 56

404.27 481.19 476.41 469.86 461.51 451.32 439.30 425.43 409.71

56 56 56 56 56 56 56 56 56 56

%,

482.46 486.16 483.12 478.37 471.84 463.50 453.33 441.32 427.46 411.75

56 56 56 56 56 56 56 56 56 56

NP13

491.15 491.88 490.80 487.90 483.17 476.59 468.16 457.87 445.72 431.70

III

Molecular SpectroscopicConstants’ (cm-‘) of the B State of ‘“O”O ” 2

3

T 50 685.17 (0.06) 51 310.44 (0.06)

4

51 913.17

5

(0.06) 52 492.03

6 7 8

(0.06) 53 042.52 (0.06) 53 566.59 (0.06) 54 059.59 (0.07)

B

105D

x

--i

0.7434

0.45*

[l.?O]

(o.ozrJ

0.20

0.50*

11701

[0.020]

0.24

(0.0004) 0.7134

0.52*

Il.741

[0.020]

0.27

0.54'

[1.76]

[0.022]

0.33

0.42 (0.06) 0.59'

j1.791

[O.Oi!Z]

024

]1.83]

10.0221

0.30

0.55

ilf37l

[0.023]

0.25

1.80

0.018 (0.001) 0.021'

0.06

0.022 (0.017) 0.049 (0.001) 0.067

011

(0.0004) 0.6990 (0.0002) 0.6813 (0.0004) 0.6654 (0.0002) 0.6448 (0.0007) 0.6227 (0.0002) 0.5994 (0.0004) 0.5730 (0.0005) 0.5424

(0.13) 0.74

12

(0.0001)

13

(001) 55 996.59

0.5095

1.41

(001) 2.49

(0.01) 56 261.61 (0.02) 56 483.58 (0.02) 56 664.54 (0.11)

(0.0001) 0.4732 (O.cQo3) 0.4339 (0.0003) 0.3670 (0.0013)

(0.03) 1.71 (0.06) 2.15 (0.08) 2.48*

(0.01) 2.74 (0.02) 3.05 (0.02) 4.79

10 11

14 15 16

RMS

(0.0007) 0.7294

54 521.47 (0.02) 54 948.44 (0.04) 55 337.84 (0.04) 55 688.13

9

.lO'TD

(0.04) 0.83 (0.06) 0.87 (0.14) 1.07 (0.02)

(0.02) 1.97 (0.05) 2.13 (0.03) 2.27

(0.11)

(0.001) 0.087 (0.003) 0.133 (0.003) 0.277 (0.010)

0.17

0.21 (0.03)

004

0.27 (0.04)

0.04

0.50 (0.09) 0.50

0.08 0.07

(0.1)

a Estimated errors, which are lo limits, are given in parentheses below the Parameters in square parentheses have interpolated values. parameters. Parameters with an asterisk are fixed in computer least squares fit.

0.25

56 56 56 56 56 56 56

466.92 457.14 445.37 431.68 416.10 398.64 379.31

376

CHEUNG ET AL.

I

0

I

5

IO

15

V

FE. 3. Plot of vibrational spacings AG“+,,* versus u for the B3Z; state of I60 ‘*O. The curve is calculated from the vibrational constants of “02 and the reduced molecular mass ratio.

molecular constant as a function of internuclear distance r, is proportional to $‘, then, for different isotopes, pL-‘XVis an isotopically invariant function of the mass-reduced quantum number P-“~( 21 + 4) (25). (i) VibrationalSpacings Since AG,, I ,2, the separation between successive vibrational levels, is proportional to /,L-“2, it follows (11) that the quantity I.L~“AG~+,,~is an isotopically invariant function of p-1/2( u + 1). Such a plot is shown in Fig. 5, in which the three groups of points belonging to ’ 602, ‘60’80 and ‘*02 fall on the same curve, indicating that the agreement is excellent between theory and experiment. The positive curvature with v > 12 (or p-112( u + h) > 4.2), in Fig. 5, makes extrapolation to the dissociation limit difficult (26,27). The small level shifts predicted by Julienne and Krauss ( 12) are not noticeable on the scale of Fig. 5. (ii) Rotational Constants The implicit inverse dependence of the rotational constant on the reduced mass is consistent with the prediction (25) that pBv is an isotopically invariant function of ~-‘/~(o + 1). A plot of PB, versus p-1/2 (o + f) is shown in Fig. 6 in which all the points belonging to 1602, I60 180, and I802 fall on the same curve. Similarly, the centrifugal distortion constants of the three isotopes can be brought together in a plot of NzDVversus ~-“2( u + f), which is seen in Fig. 7. In Fig. 7, the points corresponding to 0, values derived from bands with lines extending to relatively low J values show considerable scatter, so that these D, values are of limited accuracy. The curve in Fig. 7 is obtained from a polynomial least-squares fit to our experimental

SCHUMANN-RUNGE

377

BANDS OF “‘O”O

TABLE IV Spectroscopic Constants of the B State of “O”O (in cm-‘) 1C0’80

‘COz

Exp.

T,

49 791.86

T@

49 004.75

W?

709.558

Calc.

49 026.89 689.522

EXP

49 026.89 689.414

W&

10.9193

10.3111

10.3219

%Y,

-0.01759

-0.01614

-0.00964

KS%

-0.01802

-0.01607

-0.01677

w%

0.00029

0.00025

0.00028

4

0.8188

0.7732

0.7741

a,

0.01270

0.01165

0.01302

7e

-0.000139

-0.000124

0.000147

6,

-0.000039

-0.000034

-0.000047

D,. For bands with large predissociation widths or for those measured with low Jlines only, the centrifugal distortion constants were calculated from this polynomial, and are given in Table III of this paper and Table III of (20).

FIG. 4. Plot of rotational constants B(u) versus u for the B3L:; state of I60 ‘*O. The curve is calculated from the rotational constants of 1602and the reduced molecular mass ratio.

CHEUNG ET AL.

RG .5. Plot of mass-reduced vibrational spacings p “‘AC “+,,* versus mass-reduced vibrational quantum numbers p-“*(u + 4) for the B states of 1602, r60’80, and ‘#a. The symbols 0, A, and n refer respectively to 1602, ‘60’80, and ‘*OZ.

6.40

l

. l

1

* l .

I-

1

5.60

0.80 p-" (u +4)

RG .6. Plot of mass-reduced mtational constants pB_ versus mass-reduced vibrational quantum numbers p -*lz( u + 1) for the B states of 1602, 160L80,and ‘“0,. The symbols 0, A, and l refer respectively to ‘“0,) ‘60180, and ‘*O2.

SCHUMANN-RUNGE

BANDS OF ‘60’*0

379

225 -

FIG. 7. Plot of mass-reduced centrifugal distortion constants p’& versus mass-reduced vibrational quantum numbers p-‘/‘( u t f) for the B states of 1602, I60 “0, and ‘*Q . The curve is a polynomial least-squaws fit to the experimental values for 1602, ‘60’80, and “Oz. The symbols 0, A, and n refer respectively to 1602, “O”O, and “Oz.

(iii) Spin-Rotation Constants The spin-rotation interaction parameter, y, consists of two contributions associated with the electron spin-orbit coupling operator (25) y = $‘)

+ p’,

(3)

where y (I) and y (‘) are the first- and second-order contributions. This separation of y into two parts results from the representation of the wavefunction of the rotating molecule in terms of that of the nonrotating molecule, and it is useful from the viewpoint of ab initio calculations. The first-order contribution, y (I), arises from the spinorbit coupling operator containing the nuclear momenta only, and it is much smaller than y (‘) (24)) which comes from the second-order electronic perturbation treatment of spin-orbit with the spin-uncoupling term in the rotational Hamiltonian (28). As indicated by Brown and Watson (24) and Mizushima (29), both y(l) and r(‘) arc proportional to cc-‘, so that the quantity ~7, is expected to be an isotopically invariant function of l-“2( u + 4). Aplotof-~y,versusr-“2 (u + 4) is shown in Fig. 8. All isotopic results are plotted together, and the solid curve is obtained by fitting all our ~7, results for ‘“02, I60 180, and “4 to a quark polynomial. There are no direct experimental values of yV for u = 2-7 and 10 of I84 and u = 2-8 of 160 ‘*O, simply because the corresponding bands show no resolved triplets. The spin-rotation constants of those levels have been estimated by substituting the appropriate ~1~“~(u + 1) values into the polynomial, and are given in Table III of Ref. (20) and Table III of this paper.

380

CHEUNG ET AL.

(iv) Spin-Spin Constants The theory of spin-spin interactions has been given in detail by several authors (25, 29-31) . The parameter X is composed of two contributions, x = A”’ + x(2’ 9

(4)

where A(‘) is sometimes called the “true” spin-spin interaction and Xt2) arises from the second-order spin-orbit interaction. The true spin-spin interaction arises from the electron spin dipole-dipole interaction (30), which has its angular momentum dependence given by( 3s: - s’). Brown et al. (25) have provided a detailed derivation of the second-order spin-orbit contribution to the spin-spin constant and have shown that its angular momentum dependence is exactly the same as that of the true spinspin interaction, Therefore, the overall X value obtained experimentally is a sum of both contributions. Moreover, the explicit form of XC2),given in Ref. (25), consists of a sum of all possible contributions from states that can be connected by the spinorbit operator, I&,

where 7 labels the vibronic state, A is the quantum number specifying the component of the orbital angular momentum along the internuclear axis, and S and Z refer,

I

0.80 p-

4 (v +4J

5.60

J

FIG. 8. Plot of mass-reduced spin-rotation constants -py. versus mass-reduced vibrational quantum numbers r(-“*(v + f) for the B states of 1602, r60’80, and ‘802. The curve is a quartic least-squares fit to the available experimental values for 160z, “0 l8O, and *‘Oz.The symbols 0, A, and n refer respectively to “02, ‘60’x0, and “02.

SCHUMANN-RUNGE

BANDS OF 160’80

381

respectively, to the total spin angular momentum and its component along the internuclear axis. Mizushima (29) has discussed the invariance of X to isotopic substitution, and he finds, in particular, that the X values for the 1)= 0 levels of the ground electronic states of isotopic oxygen molecules are nearly the same. A plot of X, versus P-“~( 8 + 4) is shown in Fig. 9. All isotopic results are plotted together, and the solid curve is obtained by fitting all our X, for 1602, ‘60’80, and ‘*02 to a third degree polynomial. The spinspin constants of the v = 2-8 levels have been estimated by substituting the appropriate pm1j2(u + 1) values into the polynomial and are given in Table V. A plot of X versus D - G, is shown in Fig. 10. The solid curve is obtained from a least-squares fit of our experimental X, values for 1602, I60 ‘*O, and ‘*02 to Eq. (6) in which L,, A, and D are variable parameters:

The least-squares fit yields & = 1.54 k 0.02 cm-‘, A = 32.0 l?r 1.3 cm-‘, and D = 57 12 1 f 28 cm-‘. The spin-spin constants of the u = 2-8 levels are estimated with these parameters and are given in the third column of Table V for comparison with those from the polynomial fit. In Eq. (6)) & is the true spin-spin interaction constant which is independent of 11. The second term of Eq. (6) can be obtained from Eq. (5) by employing the uniqueperturber method (25)) in which a submatrix connecting the electronic state of interest to a single perturbing state is constructed and diagonal&l. Thus, the second-order

FTo.9. Plot of spin-spinconstantsX,versusmass-reducedvibrationalquantumnumbersp-“2( u + f) for the B state. The curve is a third degree polynomial least-squaresfit to the available experimental values for 1602, 160’80, and ‘“0,. The symbols 0, A, and n refer respectively to ‘“0,) ‘b’80, and ‘802.

382

CHEUNG ET AL. TABLE V Calculated X of I60 “0 (in cm - ’) Calculated

”

X

PF’

UPAg

2

1.72

1.70

3

1.72

1.70

4

1.73

1.74

5

1.73

1.76

6

1.74

1.79

7

1.76

1.83

8

1.87

1.87

‘PF:

Polynomial fit of X vs. &v+%)

SUPA:

Unique-perturber

for all three isotopes.

approximation.

AZ

i.e., X = X0 + o-c,

D -

G,

(cm-‘)

FIG. 10. Plot of spin-spin constants X, versus D-G,for the B states of ‘602, “‘0’80, and 18Q. The curve is a least-squares fit to the 3-parameter formula, EQ. (6), of the available experimental X. values for 1602, I60 “‘0, and ‘802. The symbols 0, A, and n refer respectively to 1602, I60 ‘*O, and ‘802.

SCHUMANN-RUNGE

BANDS OF ‘60’80

383

perturbation treatment is replaced by a numerically exact treatment of the effect of a single perturbing state. The value D = 57 121 cm-’ from our Eq. (6) is the origin of the perturbing state, which turns out to be close to the dissociation limit of the B state, which is 57 127.5 cm-’ according to Brix and Henberg (26)or 57 136 cm-’ according to Lewis et al. (27). The value A = 32 cm-’ implies a vibrationally averaged spinorbit interaction constant of 64 cm-’ between the perturbing state and the B state. The magnitude of this interaction constant is plausible; a similar value of 65 cm-’ for the spin-orbit interaction constant has been derived from the level shifts and predissociation widths arising from the interaction between the B state and the repulsive 511ustate (12). Using Eq. (6), we have obtained the A, values of bands with unresolved triplet structure, which are given in the present Table III for 2 < D < 8 of I60 ‘*O and for 2 < v d 10 of “Oz in Table III of Cheung et al. (20). 6. LEVEL SHIFTS AND PERTURBATIONS

Several repulsive states, including the ‘II,, 31111,-?fu, and 23 2: states, contribute to the predissociation and level shifts in the B3 2; state. Julienne and Krauss (12) used numerical procedures to demonstrate that the dominant perturbing state is the ‘II state. In a related study, Sink and Bandrauk (32) derived analytical expressions for”the shifts and widths based on curve-crossing models. Their formulas illustrate the sensitivity of the shifts and widths to the potential energy curves in the crossing region. Julienne and Krauss (12) adopted repulsive state potentials of the form V(R) = K.exp(-(&lK)G

- &))

+ JL,

(7)

where V, and M, are the energies and slopes at the crossing point Rx with the B32; state, and V, is the asymptotic energy of the states dissociating into two ground-state 0( 3P) atoms. They showed by using perturbation theory that with the parameters Rx = 1.875 A, M- = 40000 cm-’ A-‘, and a 511u-B3Z; coupling strength A, = 65 cm-‘, the “IIu state alone results in a smooth deperturbation in the experimental second vibrational energy differences of 1602. We have used an alternative procedure to confirm their calculations for the 1602 isotopic molecule and also to show that the same choice of ‘IIll parameters is successful in yielding a smooth deperturbation of our measured energy levels of the I60 la0 isotopic molecule but not of our measured energy levels of the “02 isotopic molecule. We find also that the level shifts calculated by Sink and Bar&auk (32) do not result in a smooth deperturbation for all of the species. We have explored whether or not 511uparameters can be found that give a smooth variation of the second differences with D for all three isotopic molecules. For the calculation of level shifts, we used a Rydberg-Klein-Rees potential for the B32; state constructed from the rovibronic term values of Cbeung et al. (27) and we followed Julienne and Krauss (12) in choosing an exponential form for the ‘l-IV potential and in adopting a spin-orbit coupling that is independent of internuclear distance. Within the Born-Oppenheimer approximation, the potentials and the coupling arc isotopically invariant. We set up and solved the coupled equations for elastic scattering in the 511uchannel at energies at which the B’Z; channel is closed.

384

CHEUNG ET AL.

We denote the electronic wavefunctions by $i( r (R) and the nuclear wavefunctions by Fi( R), and expand the total wavefunction of the system in the form *(r, R) = f T #i(rlR)FAR),

(8)

t

where R is the vector joining the two nuclei and r represents collectively the position vectors of the electrons. The nuclear wavefunctions satisfy the coupled equations ; (

V& - V(R) + El F(R) = 0, 1

(9)

where p is the reduced mass of the system, E is the total energy, I is the unit matrix, F(R)is the column matrix with elements Fi( R),and V(R) is the symmetric potential energy matrix whose diagonal elements are the B3Z; and %, state potentials and whose off-diagonal element is the spin-orbit coupling. The resonance energies and widths are determined from the scattering phase shift of the open channel component of F(R) . The level shift is then simply the difference between the resonance energy and the discrete energy level of the uncoupled closed channel. The ‘IIUstate level shift contribution is calculated for the Fzcomponent of the Schumann-Runge band and is independent of Hund’s couplin case. The off-diagonal potential matrix element in the coupled equations is then F( 7 /6 ) A, (see Table 2 of Julienne and Krauss ( 12)). l

TABLE VI Experimental Second Vibrational Energy Differences (in cm-‘) - A’G, v

lGO*

1

22.41

2

23.90

3

23.76

22.51

21.03

4

25.98

23.88

21.83

5

29.79

28.37

26.58

6

28.42

26.42

25.28

7

33.04

31.06

27.77

8

33.98

31.20

29.13

9

37.62

34.75

32.45

10

40.59

37.57

33.92

11

42.72

39.10

36.15

12

44.50

41.78

38.95

160180

180*

385

SCHUMANN-RUNGE BANDS OF '60180

The rotational quantum number Nis taken to be 0. It was confirmed that the variation of level shift with rotation is not significant compared to the experimental uncertainty in the term values. In contrast to the procedure of Julienne and Krauss (12), the coupled equations method of determining level shifts does not invoke perturbation theory. The experimental second vibrational energy differences, A2G, = G,+, + G,_, - 2G,

(10)

obtained from the bands of the three different isotopic molecules are listed in Table VI. The level shift contribution to the second vibrational energy difference is given by A’S, = S,, I + S,_, - 2S,, where 5’” is the shift of the vibrational level with quantum number u due to the 511,-83 2:; interaction. The deperturbed second difference is given by A2 Gt = A2 G, - A2S,,. The results of calculations using the parameters Rx = 1.875 %i,M, = 40 Ooo cm-’ A-‘, and A, = 65 cm-’ are represented by the open triangles in Figs. 11, 12, and 13; those using R, = 1.880~,MX=400OOcm-‘~-‘,andA,=65cm-’arerepresented by the open circles. The second vibrational energy differences - A2G, are represented by the filled circles. Because only the 511Ustate has been considered, the low vibrational levels are not included since they are significantly affected by interactions with the ‘II, state.

e

c!

40 $

A

s .

c5 . B

"-7 _ 30 -

.

e .

6 8 . 8 . I

I

I 5

I

I

/

I

I 10

I

I V

FQG . 11.Plot of second vibrational difference, - A2G., versus u for the E state of 160z. The experimental second differences -A 2G. are represented by the filled circles. The deperturbed second differences - A*G! are represented by the open triangles for ‘II. parameters Rx = 1.875 A, M, = 40 000 cm-’ A-‘, and A, = 65 cm-’ and by the open circles for ‘II, parameters Rx = 1.880 A, M, = 40 CKMI cm-’ A-‘, and A, = 65 cm-‘.

386

CHEUNG ET AL.

.

I

@ .

Q

a

.

Q

10

V

FIG. 12. Plot of second vibrational difference, - A2Gy,versus u for the B state of ‘60’80. The experimental second differences - A2G, are represented by the filled circles. The deperturbed second differences - A2Gt are represented by the open triangles for 511, parameters RX = 1.875 A,M, = 40000cm-'A-';and A, = 65 cm-’ and by the open circles for 511uparameters Rx = 1.880 A, M, = 40000cm-’ A-',and A, = 65 cm-‘.

FIG. 13. Plot of second vibrational difference, - A2G,, versus u for the B state of “4. second differences - A’G, are represented by the filled circks. The deperturbed second are represented by the open triangles for ‘II. parameters Rx = 1.875 A,M, = 40 000 = 65 cm-’ and by the open circles for ‘Il. parameters Rx = 1.880 A,M, = 40 000 = 65 cm-‘.

The experimental diffizences - A’G! cm-’ A-',and A, cm-’ A-‘, and A,

SCHUMANN-RUNGE

387

BANDS OF ‘60’80

Figures 11 and 12 demonstrate that the second difference deperturbations are quite satisfactory for the “Ot and I60 ‘*Oisotopic molecules when the 511,state parameters of Julienne and Krauss (12) are adopted, however, the deperturbation for the “Oz isotopic molecule is poor, as seen in Fig. 13. Figures 11, 12, and 13 demonstrate that adopting 511,state parameters of Rx = l.880A,MX=40000cm-‘A-‘,andA,=65 cm-’ results in smooth second difference deperturbations for all three species.Although the deperturbation for I602is slightly poorer (see Fig. 1l), the deperturbation for “02 has been significantly improved (see Fig. 13). The calculated level shift contributions A*& using the latter 511U state parameters are listed in Table VII. A similar calculation using the 511U state potential of Saxon and Liu (33) (set at the correct asymptotic energy) yields results for A’S, that differ by less than 0.1 cm-‘, provided the same coupling strength is adopted. The close agreement is to be expected. The Saxon and Liu curve crosses the B-state potential at 1.8796 A witha slope of 40 800 cm-’ A-‘, parameters in good agreement with the empirical values we determined. Interaction parameters may also be inferred from the predissociation linewidths of the Schumann-Runge bands. Lewis et al. (34) obtained 511ustate parameters of Rx = 1.880 A,M, = 39000cm-’ A-‘, and A, = 70 cm-’ with little variation between isotopic molecules. The parameters Rxand M, are in good agreement with the empirical values derived here; however, a spin-orbit coupling strength of 70 cm - ’ does not result in a smooth deperturbation -A* G8 for all three species. 7. SUMMARY

This paper gives wavelength measurements and rovibronic assignments of the Schumann-Runge bands (2,0)-( 16,O), from which molecular spectn>scopicconstants TABLE VII The Vibrational Level Shift Contributions, A2& (in cm-‘)

3

0.68

0.55

0.40

4

0.93

1.16

1.29

5

-2.25

-2.17

-1.86

6

1.72

1.40

0.76

7

-1.38

-1.21

-0.63

8

0.94

1.13

0.90

9

-0.14

-0.63

-0.88

10

-0.46

-0.16

0.26

11

0.24

0.40

0.37

12

0.20

0.05

-0.23

388

CHEUNG ET AL.

;;_ 0

0

o * -

*

*

566700

? z

0

-*

0 0

r

0

: d

0

L

0

0

0

0 O0 56660

t 00

N(N+I) RG . 14. The rovibronicterm values of the u = 16 level of the B state, showing the effect of the perturbations. The triplet components Fl, Fz, and FJ are represented by 0, 0, and * ,respectively.

of the B3 2; state of ‘60180 are determined. Molecular constants of “j02, 160180, and “Oz have been examined by means of isotopic relationships. The spin-spin and spin-rotation constants obtained by interpolation for bands with unresolved triplets are very useful in our ongoing effort to extract the predissociation linewidths of the Schumann-Runge bands of I60 “0 from our measured absorption cross sections. We have demonstrated that, with a modification of the repulsive state parameters of Julienne and Krauss ( 12), we can satisfactorily deperturb the B-state vibrational energy levels of all three isotopic oxygen molecules using the ‘I&, state alone. The effect of the other repulsive states on the level shifts, especially at low vibrational quantum number u, is still to be addressed. The ( 16,O) band is perturbed electronically and a plot of the upper state term values of u = 16 versus N( N + 1) is shown in Fig. 14. The subtraction of the amount 0.32N( N + 1) from the term values, as shown in Fig. 14, has the effect of enlarging the scale of the triplet components, so that the perturbations can be seen clearly. In the absence of perturbations, the plots would be straight lines with slopes given by the differences between the effective B values of the triplet components and the B value used for scaling. The nature of the perturbing state is not clear, but all three components are affected, and a systematic deviation at low J values was found in the least-squares fitting of the band. ACKNOWLEDGMENTS AS.-C.C. thanks the Directorate of International Activities of the Smithsonian Institution for support. The work reported was supported by the NASA Upper Atmospheric Research Program under Grant NAG

SCHUMANN-RUNGE BANDS OF ‘60’80

389

5-484 to the Smithsonian Astrophysical Observatory, and by the National Science Foundation under Grant ATM-87 13204 to Harvard University. RECEIVED:

November 10, 1988 REFERENCES

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