B1Π ∼ c3Σ+ perturbation in NaK: Vibrational numbering in the c3Σ+ state

JOURNAL

OF MOLECULAR

B’II

-

SPECTROSCOPY

151, 303-3 11 (1992)

c32+ Perturbation in NaK: Vibrational Numbering in the c32+ State P. KOWALCZYK

Institute of Experimental Physics. Warsaw University, Hoza 69, 00-681 Warsaw. Poland AND

J. DEROUARDANDN.SADEGHI Laboratoire de Spectromitrie Physique (CNRS lJR.4 OS), Universite'Joseph Fourier/Grenoble I, BP. 8 7. 38402 Saint-Martin-d’H@res Ckdes, France

Fragments of the B’II-X’Z+ system perturbed by the c%+ state are observed in 23Na39Kand ‘jNa4’K molecules by laser excitation spectroscopy. The isotopic shift of the c3E+ state is investigated and matrix elements for the B - c perturbation are determined for several pairs of interacting vibrational levels. The existing controversy about vibrational numbering in the c3Z+ state is discussed with the conclusion that the lowest experimentally observed level in this state is Ug= 16. Q 1992 Academic Press. Inc. INTRODUCTION

Mutual perturbations in spectra of diatomic molecules attract the continuing interest of spectroscopists (see Ref. (1) and references therein). In particular, perturbations of levels of different multiplicities can provide a wealth of information about states otherwise inaccessible from the molecular ground state. A well-known example is the B’II-X’2+ band system of NaK, where the B state is subjected to a number of interactions with the neighboring c3Zf and b31Tstates. In recent years a great deal of work has been done on this complicated molecular system. The B’II state has been well characterized in the unperturbed regions (2-4) and the perturbations B ‘II c3iZ+ (2-7) and B’II - b311 ( 7) have been studied. Although large portions of the spin-forbidden c’Z +-X ‘2’ band system have been observed in these experiments under high-resolution conditions, knowledge of the c3L:+ state is in a natural way limited to the range of vibrational levels which can be perturbed by the B’II state. As the c state potential well is deeper than that of the B state (Fig. 1 ), the lowest vibrational levels of the c state are inaccessible to a direct experimental observation. Consequently, indirect methods have been used to establish vibrational numbering in the c state. Following the previous papers (4-7) we label by ~1~the first vibrational level of the c3Z+ state lying above o = 0 in the B’II state. Derouard and Sadeghi (5) by comparison of their experimental data with electronic structure calculations by Stevens et al. (8) tentatively assigned v. = 20 + 2. Kowalczyk ( 7) studied the spin-orbit perturbation matrix element ,$between the c and B states. It is known (I ) that t can be factored to an electronic part and a vibrational overlap integral, 6 = [,, ( v 1II’), where I v ) and ( II’) are vibrational wavefunctions corresponding to B ‘II and c32 + states. Kowalczyk calculated sets of Dunham coefficients of c3Z+ for several trial u. values and deduced the overlap integrals (U 1II’) for each u. value. He found that for u. = 16 f 1 the 303

0022-2852192 $3.00 Copyright 0

1992 by Academic Press. Inc.

All rights of reproduction in any form rewed.

304

KOWALCZYK,

0.3

DEROUARD,

0.5

0.4

AND SADEGHI

0.6

0.7

R b-1 FIG. 1. Potential energy curves of the NaK molecule for states corresponding to the two lowest Na( 3’S) + K(4’S) and Na(3*S) + K(4’P) asymptotes (from Ref. (8)).

calculated overlap integrals matched correctly the observed variation of the perturbation matrix elements ( 7). Kato ef al. (4) investigated the dispersed fluorescence spectra of the c32;+ --) a32+ emission following excitation of strongly perturbed levels in the c3Z+ state. They calculated Franck-Condon factors (FCFs) for the observed AYtransition assuming various u. values and obtained a satisfactory coincidence with the experimental intensity distribution for vo = 12 and o. = 21. They noted, however, that for o. = 21 the overlap between c and B state perturbing levels is negligible and concluded that zio = 12 (4), In view of the contradictory results mentioned above, we performed additional measurements on the (B ‘IT - c3Z’)-X’Z’ system. Three new perturbation regions were studied in the 23Na3gK molecule and the observation was extended to five perturbation regions in the 23Na4iK isotopic molecule. The attempt to establish the absolute vibrational numbering of the c3X’ state by observation of the isotopic shift of rovibronic energy levels (9) turned out to give inconclusive results. Reinvestigation of the vibrational dependence of the perturbation matrix elements with a much larger body of experimental data reinforced the numbering proposed by Kowalczyk ( 7). We discuss the results taking into account the presence of the b3fI state, being able to interact with the c3Z + and B ‘II states. EXPERIMENTAL

DETAILS

The experimental apparatus was similar to the one described previously (5). NaK molecules were formed in a Pyrex cell containing K (with the natural isotopic abun-

ELII -

c3Z+ PERTURBATION

IN NaK

305

dance) and Na in a ratio of approximately 7:3 and heated to 250°C. A continuous wave single-mode ring dye laser (Coherent Radiation 699-2 1) working with Rhodamine 6G was used to induce fluorescence from NaK. The laser wavelength was measured with a wavemeter using as a reference the 632.8 nm line of a He-Ne laser, frequency stabilized by the two-mode difference method ( 10). The molecular fluorescence was observed through a 2-m monochromator (SOPRA) at right angles to the laser beam. We recorded small portions of the B ‘II + X ’ Z f excitation spectrum including “extra” lines due to the B ‘II - c3Z+ perturbation. Then the dye laser frequency was set at the center of each B-X line by optimizing the fluorescence signal. The accuracy in determination of a given transition wavenumber was better than 0.01 cm-‘; it was estimated from the statistical deviation of the measured line positions in unperturbed parts of the B-X system compared to the positions predicted with molecular constants of Refs. (4) and (11). RESULTS

In the 23Na39K molecule we observed the perturbation of the B’II, a = 6 level by c32+, u. + 8 with the center of perturbation around J = 33; B, v = 9 by c, u. + 12 around J x 40; B, u = 10 by c, u. + 13 around J x 33; and B, u = 11 by c, u. + 14 around J e 25. In the isotopic 23Na4’K molecule we studied the perturbation of B, u = 5 by c, u. + 7 around J = 39; B, u = 6 by c, v. + 8 around J = 26; B, u = 7 by c, u. + 9 around J x 12 and also by c, u. + 10 around J x 48; and B, u = 8 by c, v. + 11 around J N 42. The additional perturbation of the isotopic B, u = 5 level around J x 25 does not fit into the pattern of crossings between the B and c state rovibronic levels and must be attributed to another perturbing state. Tables I and II give the wavenumbers of the observed lines along with their shifts from unperturbed positions, deduced from the molecular constants of the B ‘II and X ‘Z + states (4, I I ). For simplicity, we dealt only with the e parity levels in the B state which interact with one ( F2) component of the c state. In the case of perturbation of two discrete states the energy shift A between the perturbed and unperturbed molecular lines is given by (12) A(J) =

E,(J)

- E2(J) +

2

-

E,(J)

-

2

b(J)

I/2 1 1 ’

+E2

,

(1)

where E, (J) and E2 (J) are the unperturbed energies of both interacting states and ,$ is the perturbation matrix element between the two states, here assumed to be Jindependent. This formula was fitted to experimental line shifts for each of the eight Bc perturbations reported in this paper. The fit provided values of perturbation matrix elements and the (fractional) J values at which the unperturbed vibrational levels of the B’II and c3Z+ states cross each other. Our first attempt was to use the experimental isotopic data for absolute vibrational assignment in the c3Z+ state. Using positions of 185 deperturbed lines of the c3Z+X I 2 + system in the 23Na39K molecule known from the previous high-resolution study ( 7) we were able to compute sets of Dunham coefficients describing the c3Z+ state for each trial u. value ranging between 11 and 22. These data, together with the B’II and X ‘2 + state constants (4, 11)) were used to deduce positions of crossings between B’II and c3Z+ rovibrational levels in the isotopic molecule 23Na4*K (9). Table III compares positions of crossings calculated with the assumption of uo = 12, 16, and 20 with the values obtained from experimental data. Unfortunately, the results are

306

KOWALCZYK,

DEROUARD,

AND SADEGHI

TABLE I Measured Lines of the B’II(e, u’, J)-X’Z+(o” = 0, J) Transitions in 23Na39Kand Their Shifts from the Unperturbed Positions (All Values in cm-‘) _I’

observed line

d, shift

16,O) band PC281 PC291 PC301 PC311 PC321 PC331 PC34) PC351 PC371 P(38) PC391 PC401

27 28 29 30 31 32 33 34 36 37 38 39

R(341 R(35) R(37) RC38) R(39)

35 36 38 39 40

R(40) R(41) R(42) R(43) RC44) P(47)

41 42 43 44 45 46

P(28) P(29) PC301 P(31) P(32) PC331 PC341 R(321

27 28 29 30 31 32 33 33

PC351 R(33) PC361 PC371 PC381 PC391 PC401

34 34 35 36 37 38 39

P(19) P(ZO) Pczl) Pf22) PC23) PC241 PC251 PC261

18 19 20 21 22 23 24 25

P(27)

26

PC281 PC291 PC301 PC311 PC321

27 28 29 30 31

17316.561 314.626 312.627 310.565 308.438 306.229 303.924 301.760 296.887 294.373 291.800 289.159

-0.002

-0.003 -0.006 -0.008 -0.012 -0.034 -0.088 0.062 0.014 0.004 0.003 -0.002

L9,Ol band 17465.388 462.999 458.002 455.366 452.554 453.324e 450.097 447.218 444.296 441.309 438.248 417.625

-0.003 -0.011 -0.025 -0.059 -0.194 0.576 0.101 0.048 0.027 0.017 0.008 0.001

(10,Ol band 17518.572 516.311 513.978 511.562 509.063 506.471 503.706 516.370 517.400e 501.447 514.486 498.544 495.646 492.689 489.665 486.572

-0.013 -0.019 -0.022 -0.033 -0.052 -0.088 -0.222 -0.220 0.810 0.227 0.230 0.107 0.069 0.048 0.037 0.033

(11,O) band 17581.168 579.519 577.795 575.989 574.103 572.125 570.032 567.761 568.822e 565.126~~ 566.246 563.839 561.445 559.003 556.492 553.911

-0.048 -0.056 -0.063 -0.075 -0.090 -0.119 -0.186 -0.353 0.708 -0.807 0.313 0.165 0.108 0.081 0.063 0.054

Note. e denotes an “extra” line of predominant c-X character. u Relative to positions calculated with molecular constants of Refs. (4) and ( I1 )

B’rI -

c’Z+

PERTURBATION

307

IN NaK

inconclusive and we are not able to choose the correct vibrational numbering based on them. Therefore we decided to study the vibrational dependence of the perturbation matrix elements between various vibrational levels in the B’II and c3Z+ states. Table IV shows the values of perturbation matrix elements determined in this experiment along with results of previous works. For the B, II = 5 - c, v. + 7 perturbation in 23Na4’K the line positions were too irregular for assignment of the perturbation matrix element with a reasonable uncertainty. We constructed RKR potentials for the c3Z ’ state according to several assumed vibrational numberings in the c state. Estimates of vibrational overlap integrals between B and c state levels for J values of observed perturbation culminations were then compared with the experimental values of perturbation matrix elements. Only one numbering scheme, in which u. = 16, gave satisfactory agreement (Table V). Thus the numbering proposed in Ref. ( 7) has been reinforced. Results presented in Table V make it possible to exclude the numbering proposed by Kato et al. (4) (v. = 12). With their numbering the strongest observed perturbation between 2, = 12 in B ‘II and u. + 15 in c3Z + should be negligibly weak: other observed values of perturbation matrix elements are also contrary to the predicted ones in this case. DISCUSSION

The numbering recently proposed by Kato et al. (4) has a sound motivation in the observed intensity pattern of the c3Zt + a32Z+fluorescence. In fact, we checked that with u. = 12 the FCFs of the c-a transition are in good coincidence with the reported experimental spectra. (It must be noted that for another numbering with u. = 2 I, ruled out by Kato et al. (4) only because of insufficient overlap between the c and B states, we found no relationship between the calculated c-a FCFs and the experimental line intensities reported in (4)). Therefore we have to find an explanation of why the three apparently correct methods presented above for establishing the vibrational numbering in the c3Z+ state give contradictory results. We believe that the reason may be in the presence of another molecular state, namely b311, in the same energy range where the B’II and c3X+ states are situated. The mutual positions of the b 311and c3X + potential curves displayed in Fig. 1 indicate the possibility of strong interaction between these states. The curves cross at E x 17 000 cm-’ and their outer parts become nearly parallel, providing a large overlap of vibrational wavefunctions over a wide range of u values. In fact the b311 - c3Z+ perturbation has been observed experimentally ( 7). This additional perturbation can explain the failure of our isotopic shift experiment. The c3Z+ state has been deperturbed with respect to interaction with the B’II state, but not with the b311 state. Therefore the observed levels in the isotopic 23Na4’K molecule are not only shifted by the isotopic effect (9) but also irregularly displaced by the neighboring b311 state levels. On the other hand, in the studied energy range both repulsive and attractive limbs of the B’II and b311 state potentials are far apart and the vibrational overlap (BI b) between them is of the order of lo-l2 (13). We believe that the reported B’II - b311 perturbations ( 7) were due to a second-order interaction through the c3ZZ+state, with an interaction matrix element of the type ( I ) HBh = (B/c)(clb).(y

-EC)-’

.

(2)

308

KOWALCZYK,

DEROUARD,

AND SADEGHI

TABLE II Measured Lines of the B’II(e, v’, J)-X’Z+(o” = 0, J) Transitions in 23Na4’K and Their Shifts from the Unperturbed Positions (All Values in cm-‘) J'

observed

line

shifta')

(5.0) band RC7.1) R(221 R(23) R(24) R(25) R(27) R(301 R(311 R(32.1 R(33) R(34) A(351 R(36) R(37) R(38) R(39) R(40)

22 23 24 25 26 28 31 32 33 34 35 36 37 38 39 40 41

PC191 P(20) PC211 PC221 PC231 P(24) PC251 PC261 PC271 P(B) R(27) R(B) R(29) R(30) R(31)

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

R(7) R(8) R(9) R(10) R(11)

8 9 10 11 12

R(Q) PC141 PC151 PC161 PC171 P(18) PC191 PC201 PC211 P(221 R(40) R(41) R(43) R(44) R(45) R(46) R(47) P(49) P(50)

17275.129 273.974 272.757 271.459 270.170 267.328 262.613 260.929 259.178 257.367 255.508 253.567 251.582 249.520 247.479 245.263 243.027

0.004 0.003 -0.002 -0.028 0.014 0.011 0.002 0.006 0.003 0 0.009 -0.003 0.001 -0.011 0.058 0.014 0.010

(6.0) band 17328.654 327.326 325.927 324.462 322.926 321.332 319.679 317.937 316.092 314.473 323.127 321.524 319.868 318.156 316.377

-0.004 0.008 0.011 0.008 -0.004 -0.012 -0.019 -0.052 -0.127 0.085 0.039 0.023 0.016 0.015 0.011

(7,O) band

13 13 14 15 16 17 18 19 20 21

17396.308 395.913 395.433 394.852 394.102e 394.767 393.978 388.951 387.813 386.650 385.431 384.155 382.821 381.422 379.960 378.438

-0.052 -0.063 -0.097 -0.167 -0.344 0.321 0.170 0.176 0.111 0.085 0.067 0.055 0.049 0.041 0.035 0.033

41 42 44 45 46 47 48 48 49

17349.776 347.245 341.996 339.262 336.452 333.588 330.829 312.918 309.441

-0.003 -0.008 -0.005 -0.011 -0.025 -0.025 0.143 0.135 0.020

Note. e denotes an “extra” line of predominant c-X character. a Relative to positions calculated with molecular constants of Refs. (4) and (II).

L?‘n -

c3Z+ PERTURBATION

309

IN NaK

TABLE II-Continued J’

observed (8,O)

PC281 PC291 PC301 PC311 PC321 P(33) R(32) RC331 p(35j P(36) P(37) P(38) PC40) P(41) PC421 PC431 PC441 PC451 PC461

27 28 29 30 31 32 33 34 34 35 36 37 39 40 41 42 43 44 45

shift”

line band

17419.261 417.208 415.094 412.905 410.646 408,335 418.373 416.288 403.486 400.958 398.357 395.694 390.162 387.290 384.332 381.218 378.332 375.150 371.926

0.018 0.013 0.014 0.008 0 0.008 -0.001 0.002 0.001 -0.003 -0.011 -0.013 -0.016 -0.020 -0.040 -0.146 0.045 0.011 0.005

The unassigned perturbation of B, u = 5 level in 23Na41K reported in this paper is presumably of the same character. In consequence, the actual c3Z+ state has to be considered rather as a mixture of the pure c3Z+ and b311 states, described by a wavefunction of the form (Y1c) + (31b) . The method for getting the vibrational numbering in the c state employed by Kato et al. (4) was based on observation of the c3Z+ + a3Z’ fluorescence. However, as both c3Z+ and b311 states can be optically linked to the a3C:+ state, the intensity pattern of observed fluorescence lines should be compared ratherto I(arc+ /3blu)12 = ~~~~(clu)~~ + f121(bla)12 + 2c@Re (clu)(alb) than simply to )(c I u) I ‘. This cannot be done at present, since the molecular constants of the b311 state ( 14) are inapplicable for the high vibrational levels involved in this case. The method used by Kowalczyk ( 7) and applied in our paper is based on the vibrational dependence of perturbation matrix elements. The vibrational variation of the overlap integrals (BI CYC + fib) is to a very good approximation identical to that for (B )c) since, as mentioned above, (B Ib) N 0. Therefore we feel that our vibrational numbering with no = 16 is not affected by the presence of the b 311state and is favoured

TABLE III Observed vs. Calculated Positions of Crossings of e-Parity Levels of the B’II and c3Z+ States in the Isotopic ‘)Na4’K Molecule

“ll

-

“1

J Cro*I experimental

J vn=12

CT0SS

calculated 16

20

5 -

vo+7

38.7

39.1

37.8

36.8

6 -

vo+8

26.3

30.2

28.7

26.8

7 -

vo+9

11.9

18.3

15.4

12.5

7 -

vo+lo

47.9

49.5

48.2

47.4

8 -

vo+ll

42.3

43.7

42.4

41.6

310

KOWALCZYK,

DEROUARD,

AND SADEGHI

TABLE IV Experimental Values of the Perturbation Matrix Elements E (in cm-‘) perturbation J

“ll - “z

.?roem

this

matrix Ref.7

worka

elements other

works

=NaS9K vo+5

13

6 - vo+8

4 I

33

8 _ vo+10

5

0.22

0.159

0.14b’

0.221

0. 2zC’

0.400

0.398*’

8 I vo+ll

46

9 - vo+12

40

0.34

0.348”

10 - vo+13

33

0.44

0. 435c’

11 - vo+14

25

0.50

12 - vo+15

14

0.58

6 _ vo+8

29

0.19

0.266”

0.582 23Na”K

7 -

vo+9

12

0.33

7 - vo+lo

48

0.55

8 - vo+ll

42

0.38

’ With uncertainty of kO.0 1 cm-‘. *Ref. (3). ‘Ref. (13). d Ref. (4). ‘Ref. (5).

TABLE V Observed Vibrational Variation of Perturbation Matrix Elements (PME) Compared to Calculated Overlap Integrals (All Sets of Values Normalized to 100) PME observed

“II I “z

overlap vo=12

integrals,

calculated

15

16

17

20

=Na=K 4 - vo+5

27

100

42

28

20

9

6 I

38

96

58

42

32

18

vo+8

8 I

vo+10

69

68

89

74

64

46

8 -

vo+ll

46

79

66

51

41

25

9 - vo+12

60

64

79

64

55

38

10 - vo+13

76

43

89

78

70

55

11 ” vo+14

86

21

96

90

85

76

12 - vo+15

100

1

100

100

100

100

6 - vo+8

33

97

61

44

34

19

7 ” vo+9

57

86

77

60

49

31

=Na”K

7 - vo+lo

94

40

56

88

31

17

8 - vo+ll

65

79

69

54

44

27

15.1

5.7

1.6

5.7

8.7

rms deviation

B’rl

-

c3Z+ PERTURBATION

IN NaK

311

by the available experimental data. The molecular constants of the c3Z+ state corresponding to this numbering are listed in Ref. ( 7). We wish to emphasize that a direct observation of the lowest vibrational levels in the c3Z+ state would definitely end the controversy about its vibrational numbering. This can be done by a perturbation-facilitated laser-induced fluorescence experiment where a stepwise or two-photon excitation of some high-lying molecular levels in NaK of a mixed singlet-triplet character is followed by fluorescence to the c3X+ state. ACKNOWLEDGMENTS P.K. thanks the French Minis3re de la Recherche et de la Technologie for a fellowship. RECEIVED

: June 27, 199 1 REFERENCES

1. H. LEFEBVRE-BRION AND R. W. FIELD,‘*Perturbation in the Spectra of Diatomic Molecules.” Academic Press, New York, 1986. 2. R. F. BARROW, R. M. CLEMENTS,J. DEROUARD,N. SADEGHI,C. EFFANTIN,J. d’ INCAN,AND A. J. Ross, Can. J. Phys. 65, 1154-l 158 (1987). 3. M. BABA, S. TANAKA, AND H. KATO, J. Chem. Phys. 89,7049-7055 ( 1988). 4. H. KATO, M. SAKANO, N. YOSHIE, M. BABA, AND K. ISHIKAWA, J. c‘hem. Phys. 93, 2228-2237 (1990). 5. J. DEROUARDAND N. SADEGHI,J. Gem. Phyx 88,2891-2897 ( 1988). 6. P. KOWALCZYK, B. KRUGER, AND F. ENGELKE,Chem. Phys. Lefr 147, 301-306 (1988). 7. P. KOWALCZYK, J. Chem. Phys. 91,2779-2789 (1989). 8. W. J. STEVENS,D. KONOWALOW,AND L. B. RATCLIFF, J. Chem. PhJs. 80. 1215-1224 (1984). 9. G. HERZBERG,“Molecular Spectra and Molecular Structure. Vol. I. Spectra of Diatomic Molecules.” Van Nostrand, Princeton, NJ, 1950. IO. J. CACHENAUT,C. MAN, P. CEVEZ,A. BRILLET,F. STOECKEL, A. JOURDAN,AND F. HARTMANN.Rev. Phys. Appl. 14,685-687 ( 1979 ). P. Y. CHIEN AND C. L. PAN, Rev. Sci. Instrum. 62,933-935 ( 1991). Il. A. J. Ross, C. EFFANTIN,J. d’ INCAN,AND R. F. BARROW,Mol. Phys. S6,903-912 ( 1985). 12. J. KovAcS, “Rotational Structure in the Spectra of Diatomic Molecules,” Adam Hilger, London. 1969. 13. A. J. ROSS, private communication. 14. A. J. Ross, C. EFFANTIN,J. D’INCAN, AND R. F. BARROW, J. Phys. B 19, 1449-1456 (1986).