Upper state molecular constants for the (0, 0, 3) and (1, 0, 3) vibration-rotation bands of nitrogen dioxide

JOURNAL OF MOLECULARSPECTROSCOPY33, 109-118 (1970)

Upper

State Molecular Constants for and (1, 0, 3) Vibration-Rotation of Nitrogen Dioxide’ R. E. BLANK,

Department

11.

of Physics,

D.

OL~IAN,~ AND C.

Michigan State University, Michigan 4882s

the (0, 0, 3) Bands

D.

HAUSE East Lansing,

High-resolution absorption spectra of the (0,0,3) and (1,0,3) vibrationrotation bands of 1aN’60~ and 15N1602 were analyzed. Initial values for the ground state constants and predicted values of A, B, and C for the upper states of the (0,0,3) and (1,0,3) bands were taken from previous work. Improved values of the upper stat,e constants including centrifugal distortion and empirical PC terms have been obtained. Further refinement of the ground state constants was not possible. Spin splitting was observed and analyzed for a number of transitions in the (0,0,3) band of both isotopes. Effective spin-rotation coupling constants were obtained for the excited states. Due to the weakness of absorption and lack of resolution no spin splitting was observed in the (1,0,3) bands. I. INTRODUCTION

Since nitrogen dioxide is one of the few stable gases with a single unpaired electron, it has been the subject of spectroscopic investigation in almost all accessible regions. The work represents a continuation of the work of Olman and Hause (1) on the analysis of high-resolution absorption spectra of the vibration-rotation bands of NO2 in the near-infrared. Nitrogen dioxide is nearly an accidentally symmetric prolate molecule with an asymmetry parameter K = -0.994. The electronic angular momentum is “quenched” so that the major effect of the unpaired electron in the absence of external fields is an N.8 interaction. This leads to small but observable doubling of the low LV lines. II. EXPERIMENTAL

METHODS

The ;\lichigan State University high-resolution, near-infrared spectrometer as previously described (2) was employed to produce the (0 ,O, 3) and (1 ,O ,3) absorption spectra. Two runs of the (0 ,O, 3) band were made at a pressure of 15-18 Torr and an absorbing pathlength of 6.3 m. Several runs of the weaker 1 Supported in part by the National Science Foundation. 2 Present address: Sandia Corporation, Albuquerque, New Mexico. 109

110

BLANK,

OLMAN,

AND

HAUSE

(1 ,O ,3) band at 50 Torr and 15.75-m pathlength were required since calibration lines overlapped the band. The method of calibration has been described by Rao et al. (3). The spectra were calibrated using the precise near-infrared absorption frequencies measured by Rank and co-workers (3). The standard errors of the least squares fits to obtain calibration constants averaged 0.003 cm-l for the (1,0,3) and 0.002 cm-’ for the (0,0,3) band. The effective resolution obtained was approximately 0.03 cm-’ for the (0,O ,3) and 0.05 cm-’ for the (1,0,3) band. III.

SELECTION

RULES

Nitrogen dioxide has C2V symmetry with the b-axis corresponding to the symmetry axis. Thus only half of the allowed energy levels are populated (4). The resulting missing lines simplify the spectrum and permit the use of symmetric rotor notation without ambiguity. Only bands with upper states having an odd multiple of v3 were observed so the conditions for a level to be populated are : K-1

+

K-1 +

K+1

is odd for upper states

K,l

is even for the ground state

The observed bands are all of type A and correspond to parallel bands in the prolate limit. Thus the selection rules are: AK_1 = 0, AN=O,fl fl

AN = IV. ENERGY

EXPRESSIONS

if

&#O,

if

K-1=0.

(1)

INCLUDING

SPIN SPLITTING

A detailed account of the theoretical energy expressions for the slightly asymmetric molecule has been presented in Ref. (1). The energy expressions are based on a perturbation expansion including rigid rotor energy, centrifugal distortion terms, and empirical-P terms. The complete energy expression can be written:

N(N+l)+ + Taaaax1 + + H,xN’(N

Tbbbb

[ X2

+

ATaabb

(+>Ix3

+

Tabab

x4

+

H,N3(N

+ 1)3

(2)

+ 1)2(Pz2) + HKNN(N + l)(Pz”> + S&8

In this expression A, B, and C are the molecular rotational constants, N represents the rotational angular momentum, and w is the Wang energy. The T’S are treated as parameters and account is taken of possible vibrational dependence by allowing the T’S to be determined independently in the upper and lower states.

5984.705 7.4140 0.423211 0.399358 (-1.29 (-1.540 (8.6

intervals

0.0065

214

I

(1.07

0.0199

233

*Ob971) 323

x

10-e

5874.951 f 0.010 7.0791 f 0.0057 0.42355 f 0.00016 0.398728 zk 0.000065 (-0.99 f 0.15) x 10-a (-1.39 f 0.40) X 10-e (6.8 f 1.0) x 10-b -8.175 X 1OV

throughout.

f 0.0048 zt 0.0087 f 0.000939 f- 0.000017 * 0.19) X 10-Z f 0.076) X 1O-6 f 2.1) x 10-S -8.215 X 1OV 0.0 0.0 301

u 95y0 simultaneous confidence b Calculated values.

identified No. of lines used SD of fit

H KN HK No. of lines

Tobobb

Tanbb

Tbbbb

Taaaa

c

n

A

vu

103

TABLE

0.0082

416

f 0.006 zk 0.0012 & 0.000032 f 0.000024 z!= 0.025) X f 0.14) x =t 0.38) X -8.215 X (-1.77 zk 0.31) x (2.961 f 0.093) X 550

4754.209 7.3427 0.425457 0.402916 (-0.992 (-1.51 (9.06

UPPER STATE CONSTANTS FOR NO2 (cm-l)

1OP 10-e 1O-6 1OW 10-r 10-b

003

(0.29

0.0092

X

0.009 0.0019 0.000046 0.000036 0.044) X 0.19) X 0.81) X -8.175 X zx.17) 466

4655.228 f 7.0217 f 0.425781 f 0.402214 f (-0.836 f (-1.58 f (7.26 f

10-S

lo-* lO-‘j lo-& 10-o

112

BLANK,

OLMAN,

AND

HAUSE

As in the previous work, Tabab was fixed at the theoretical value given by Chung and Parker (5). Explicit expressions for the x’s are given by Hill and Edwards (6). The H’s represent empirical constants (7) and the {P& are expectation values of the operator P, = P, . The expression can be put in a form suitable for least squares analysis as discussed in (1) and used to fit the observed spectrum. The ground state constants were fixed at the values given in the earlier work since no changes resulted from the additional data. The upper state constants were calculated using the ground state constants plus observed transitions to determine the set of upper state vibration-rotation energy levels which were fit to the theoretical expression. The upper state constants for the (0 ,O, 3) and (1 ,O ,3) bands are presented in Table I. The frequencies used together with their weights and deviations are given in Ref. (8). &G-Rotation

Interaction

The N f S interaction as applied to NO2 has been discussed by Lin (9)) and the result is a doubling of the spectral lines for K $ 0. The spin-rotation HamilJ

N

N+3/2

N+l

-
+ ‘/2

UPPER STATE

N

,-

\N

--l/2 P

Q

ii

FIG. 1. Schematic diagram displaying the splitting of asymmetric energy levels due to spin-rotation interaction. Each level is doubled except for ICI = 0. Only AJ = AN trsnsitions have been observed.

MOLECULAlt

toni:ln

It

CONSTANTS

OF

1 1.> ‘V

NO,

has t#he form:

is .dkicut to uw the approximation E;,; = 0 for ,i # j. Since the electronic spin is $1, there are two CMX:

The resulting

corrections

to the asymmetric

energies

have the form:

E,‘, = I&N/“, hTE = -K,,(N

CM-1

I

5959

+ 1)/Z.

I spu

5975

.. woo

FIG. 3. -4 portion of the (1,0,3) band of “NO: showing part, of the K-, = 0 and /i_, = 1 subbands. Due to the asymmetry of the molecule and the presettcc of t,wo identical nuvgctt nuclei there are twosubbands for X1 = 1 and higher: an even subband with odd :V lines tnissing and att odd one with even N lines missing. For K-1 = 0 otdy the even S lines arc present.

FIG. 4. 1%portion

of the

(0,0,3)

band

of 14NO:! showing

part

of the K-1

= 0 s[tbhand.

BLANK,

114

OLMAN,

AND

HAUSE

Where

K2E Km = N(N + 1) ’

(6)

and E is an effective constant defined by c

=

Eaa -

Ebb + ’

2

Ccc

(7)

.

The magnitude of the splitting of a given level is

(8) The only transitions observed have AJ = AN so that the spin splitting of a level is not directly measurable as seen in Fig. (1). Denoting the J+” to Jf’ and J-” to J-’ transitions by V+ and v-, respectively, we have for AK = 0,

+ 55.)~’ _ K2(NN + %)e” N”(N” + 1) ’ N’(N’ + 1)

v- = K’(N’

v+ -

(9)

Note that even if C’ = en splitting will occur in the P and R branches due to the dependence on N. In the more typical case the effective spin splitting constants diier so that splitting arises in the Q branch. Then as shown in Fig. 1, it is possible for the spin splitting to be increased in the R (P) branch and decreased in the P (R) branch. As in the earlier work it was assumed that the electronic structure was unchanged by isotopic substitution which made it

(o&3)

"NO,

R4hO)

n

I

4752.1319 FIG. 4. Four typical as R&C?) to completely splitting is 0.0729 cm-l.

cm-’

I

4753.4709

spin doublets ranging from broadened but unresolved lines such resolved doublets such as I&(5) in which the magnitude of the

MOLECULAR

CONSTANTS

115

OF NOr

possible to combine the spin data from the isotopes of the molecule for a purtitular band (10). GENERAL

FEATURES

OF THE

BANDS

(1,0,3)

The (1,O ,3) is a weakly absorbing band located in the region from 5923 to 6000 cm-’ for 14NO: and from 5825 to 5590 cm-’ for 15KO? . A portion of the (1 ,O ,3) is seen in Fig. 2 where the K-1 = 0 and K-1 = 1 transitions are shown. Note the missing lines in the K_-, = 0 series. Q branches of the subbands were present but too weak to be analyzed. Transitions have been identified with K_1 as high as 5 and N as high as 46. Good fits were obtained for series through K_1 = 3. The K-1 = 5 series was very weak, and the K-1 = 4 series was perturbed. Spin splitting was not observed due to overlapping, low resolution in the region, and weakness of the low N lines. (0,0,3) The (0 ,O, 3) is a strongly absorbing band located in the region from 4695 to 4775 cm-’ for 14N02 and from 4611 to 4676 cm-’ for 15N02 . A previous analysis ascribed the observed structure to the overlapping of a type A and a type B band, but with the exception of one weak series underlying the (0,0,3) of WOZ , we have found that, at room temperature, the structure can be accounted for entirely by the type A band. i4nalysis has produced fits of nearly all observed lines with K-1 as high as 7 and N as high as 45. The branches of differing subbands overlap considerably, and the Q branches of the various subbands are widely separated. In the (0,O ,3) of 14N02 the Q lines for K_1 = 1 are grouped about 4752 cm-’ while for K-1 = 6 they occur about 4730 cm-l. TABLE

II

EFFECTIVE SPIN-ROTATION COUPLING CONSTANTS FOR THE (0, 0, 3) BAND OF NOa

EOOlP C201b

(8000 - ElOl)b E008C kooo - t003)o EOOld (too0 - e003)d

0.181644 0.1782 + 0.0014 0.0036 xlz 0.0010 0.1629 f 0.0013 0.0187 f 0.0013 0.1627 f 0.0012 0.0189 f 0.0012

a From microwave values. b From Ref. (1). c Fitting 14N02 and IsNO separately. d 14N0, and ISNO data combined. c 95yo simult,aneous confidence intervals

throughout.

0.173210 0.1693 f O.OOlB 0.0038 zk 0.0010 0.1555 * 0.0010 0.0177 + 0.0010 0.1556 * 0.0019 0.0176 zk 0.0019”

BLANK,

OLMAN, TASLE

AND HAUSE

III

(0,0,3) Band Spin-Splittings

(cm-l)

15~0~

14N02

K-1

N

P

2

3

+0.0515

+0.0594

P

3

4

+0.0642

+0.0595

P

5

6

+0.0491

+0.0425

Q

3

_I

3

-0.0652

-0.0465

Q

3

4

-0.0459

-0.0359

Q

4

8

-0.0440

-0.0356

Q

5

5

-0.0995

-0.0865

Q

5

8

-0.0626

-0.0523

Q

6

6

-0.1105

-0.0987

Q

6

11

Q

6

12

-0.0569

-0.0511

R

1

1

-0.0593

-0.0651

R

2

3

-0.0630

-0.0654

R

2

4

-0.0428

-0.0441

R

3

4

-0.1008

-0.0992

-0.1049

-0.0942

R

3

5

-0.0755

-0.0730

R

3

6

-0.0552

-0.0568

R

3

7

-0.0440

-0.0460

-0.0431

-0.0436

R

4

4

-0.1845

-0.1674

R

4

6

-0.1080

-0.1010

-0.0892

-0.0957

R

4

7

-0.0873

-0.0818

-0.0673

-0.0785

R

4

8

-0.0542

-0.0642

R

4

9

-0.0652

-0.0582

-0.0534

-0.0551

R

4

10

-0.0444

-0.0505

-0.0461

-0.0478

R

4

11

-0.0286

-0.0445

Branch

OBS

-0.0571

PRED

OBS

PRED

-0.0592

lli

MOLECULAR CONSTANTS OF NO? TABLE III (continued) (0,0,3) Band Spin-Splitting

(cm-l)

14N02 Branch

OBS

15N02 PRED

K-1

N

R

4

12

-0.0260

-0.0397

R

4

13

-0.0224

-0.0357

R

5

6

-0.1351

-0.1578

R

5

9

R

5

10

-0.0876

-0.0789

R

5

11

-0.0636

-0.0695

R

5

12

-0.0729

R

5

13

R

5

R

OBS

PRED

-0.0835

-0.0860

-0.0556

-0.0747

-0.0620

-0.0448

-0.0586

-0.0592

-0.0559

-0.0491

-0.0528

14

-0.0384

-0.0507

-0.0419

-0.0479

5

15

-0.0407

-0.0464

R

5

16

-0.0422

-0.0427

-0.0269

-0.0404

R

6

10

-0.1027

-0.1093

R

6

12

-0.1036

-0.0893

R

6

15

-0.0626

-0.0668

R

6

16

-0.0440

-0.0615

R

6

17

-0.0524

-0.0570

R

6

18

-0.0461

-0.0501

R

6

19

-0.0437

-0.0468

R

6

20

-0.0403

-0.0439

R

6

21

-0.0416

-0.0437

-0.0354

-0.0413

R

6

22

-0.0403

-0.0413

R

6

23

-0.0447

-0.0369

Figure 3 shows a picture of a portion of the (0,0,3) of 14N02 with the K-1 = 0 subband designated. A perturbation was found affecting the K-1 = 5 subband in the (0,0,3) of 14X0,: . The deviation of observed from predicted frequencies increased wit#hX

118

BLANK, OLMAN, AND HAUSE

and was as large as 0.16 cm-’ at N = 42. A similar perturbation was noted in the K_, = 4 subband of 15NOsand of approximately the same deviation. Spin splitting has been observed and analyzed in the (0 ,O ,3). It is appreciable in the Q branches, large in the R branches, and small in the P branches of the subbands. The possibility of this was considered previously. Very few doublets were observed in the P branch due to the small splitting, overlapping, and weakness of the spin split lines. A small region of the (0 ,O, 3) of 14N02 is seen in Fig. 4 showing several spin doublets. Effective spin-rotation splitting constants are listed in Table II, and the observed and calculated spin splittings are shown in Table III. ACKNOWLEDGMENTS The authors are grateful to Professor T. H. Edwards for many helpful discussions. Also Dr. D. B. Keck and L. E. Bullock contributed helpful suggestions and computer programs which were very useful in reducing the data. RECEIVED: May 21, 1969 REFERENCES 1. M. D. OLMANAND C. D. HOUSE,J. Mol. Spectry. 26, 241 (1968). 2. D. B. KECK, J. L. AUBEL,T. H. EDWARDS,ANDC. D. HAUSE,in “Symposium on Molecular Structure and Spectroscopy,” Paper H-2. Columbus, Ohio, 1966. d. K. N. RAO, C. J. HUMPHREYS, AND D. H. RANK, “Wavelength Standards in the Infrared,” Appendix III and pp. 160, 161, 171. Academic Press, New York, 1966. 4. G. HERZBERG,“Infrared and Raman Spectra of Polyatomic Molecules, Molecular Spectra and Molecular Structure II,” pp. 462-465. Van Nostrand, Princeton, New Jersey, 1945. 6. K. T. CHUNGBND P. M. PARKER, J. Chem. Phys. 43, 3869 (1965). 6. R. A. HILL AND T. H. EDWARDS,J. Mol. Spectry. 9, 494 (1962). 7. L. PIERCE, N. Dr CIANNI, AND R. H. J.~CKSON, J. Chem. Phys. 38, 730 (1963). 8. R. E. BLANK, Thesis, Michigan State University, 1969. 9. C. C. LIN, Phys. Rev. 116, 903 (1959). 10. W. T. RAYNES, J. Chem. Phys. 41. 3020 (1964).