Optical-optical double-resonance spectroscopy of BaO

JOURNAL

OF

MOLECULAR

Optical-Optical

SPECTROSCOPY

82, 310-338 (1980)

Double-Resonance The Low-Lying

Spectroscopy States

RICHARD A. GOTTSCHO,’ J. BROOKE KOFFEND,’ Department

of Chemistry,

Massachusetts

Institute

of BaO

of Technology,

AND

ROBERT W. FIELD

Cambridge,

Massachusetts

02139

Optical-opticai double-resonance (OODR) induced photoluminescence into the lowest excited electronic states of BaO--a%+, A’Z+, b311, and A’ ‘II-from C’S+ is described. These low-lying states are deperturbed to obtain spectroscopic constants and potential energy curves: a32+ T, (cm-‘)

w, (cm-‘) 0,x, (cm-‘) weye x lo2 (cm-‘) B, (cm-‘) (Y, X lo3 (cm-l) ye X lo6 (cm-‘) & (A)

16 5%(3)

469.0(7) 1.48(4) 0.2594(5) 1.44(5) 2.1294(20)

A’X+ 16 807.345(10)

499.620(19) 1.7lq8) 2.14(9) 0.2583908(26) 1.111(3) 7.0(7) 2.133512(11)

b3U 17 502.6(10)

447.62(8) 2.287(12) 0.2242q16) 1.18(4) 2.2901(8)

A’ III

17 619.7(2) 447.95(22) 2.139(8) 1.02(3) 0.22385(16) 1.15(4) -4.0(21) 2.2922(8)

where uncertainties of la are given in parentheses. The results of this deperturbation the presence of additional low-lying, A states which perturb bW and A’ III.

suggest

I. INTRODUCTION

The power of optical-optical double-resonance (OODR) spectroscopy in accessing and characterizing electronic states of BaO with =4 eV excitation energy was demonstrated in the preceding paper (I). More importantly, OODR is a vehicle by which low-lying, metastable electronic states can be populated and structurally characterized. This paper presents: (i) the analysis of OODR-induced BaO ClIZ+ + a3C+, b311, and A’ III photoluminescence spectra,2 and (ii) subsequent deperturbation3 of the low-lying (~2 eV) BaO electronic structure. As discussed in the preceding paper (I), C’P + A’2 excitation spectra and C’S+ photoluminescence spectra are studied in order to establish population probes for the long-lived a3C+, b311, and A’ III states which are chemically produced in many flame reactions. ’ Present address for Richard A. Gottscho: Department of Physics, Massachusetts Institute of Technology, Cambridge, Mass. 02 139. Present address for J. Brooke Koffend: JILA, University of Colorado, Boulder, Colo. 80309. * The b3Il state has recently been renamed (2) and was formerly known as a3H. 3 See preceding paper (I ) for a brief discussion of the deperturbation procedure. 0022-2852/80/080310-29$02.00/O

OODR SPECTROSCOPY

OF BaO

311

CC+ + b311, and CV + A’ III emission spectra reported previously (3) (OODR II) were obtained using broad bandwidth (AvWHM= 1 cm-l) tunable dye lasers. OODR using two, single longitudinal mode, frequency-stabilized, dye lasers results in a substantial increase (50x) in * + X1x+ uv fluorescence* signal-tonoise ratio owing to enhanced pumping efficiency of C’Z+ (1). The resultant higher steady-state population in C’Z+ allows detection of C’s+ -+ a3Z+ (2) and C’Z+ + b31&,emission. The latter is reported for the first time here. Studies of the low-lying electronic structure of BaO date back to Mahanti (4), who first correctly analyzed the vibrational structure of the A%+-X12+ band system. Lagerqvist, Lind, and Barrow (5) (LLB) rotationally analyzed 11 bands (through V’ = 5) of the AlZ+-X’Z+ system and detected numerous perturbations in A’P but were not able to definitely determine perturbing state symmetries. Field (6) reexamined LLB’s data and from perturbation patterns and magnitudes, as well as the vibrational variation of interaction matrix elements, assigned the perturbing state symmetries as b311 and A ’ Ill and determined the zero-point energies (u = 0) ofthese states with respect toX’Z+. His analysis was subsequently verified by the detection ofA’ III + X’C+ chemiluminescence (7,8), time-resolved laser-induced A’ III + X12+ fluorescence (9), and broad bandwidth OODR-induced CIZ+ --, A’ III and b3111fluorescence (3). Precise X1x+ and A’C+ rotational constants and dipole moments have been obtained from microwave (N-13) and microwave-optical double-resonance (MODR) (14-17) experiments. Ar+ and broad bandwidth dye laser OODR was used in Ref. (18) (OODR I) to extend the vibrational analysis of X’Z+ through ZI”= 34 and consequently improve X’Z+ vibrational constants. The major emphasis of this work is to deperturb the lowest excited electronic states of BaO--a3Z+, A’Z+, b311, and A’ III-in order to obtain potential energy curves, interaction matrix elements, and mixing coefficients. Potential energy curves are useful in calculating vibrational matrix elements as well as providing a physical picture of the electronic state structure. Interaction matrix elements can be used to determine: (i) the atomic orbital composition of the molecular orbitals (i.e., LCAO-MO coefficients) (Z9-2Z), (ii) vibrational numberings for perturbing states (2, 6, 22), and (iii) higher-order interaction parameters (23-27). Mixing coefficients provide a prescription for composing eigenstates (and hence eigenstate properties) from deperturbed basis states; In short, deperturbation provides a model with which data can be interpreted in a physically meaningful fashion as well as reliably extrapolated to unobserved spectral regions. Two criteria are used to define complete deperturbation: (i) observed minus calculated transition frequencies must be random and comparable to experimental error, and (ii) perturbation matrix elements and higher-order constants must be internally consistent. The data presented here are combined with data from Refs. (5, 16) in deperturbing all the known low-lying excited electronic states of BaO: a3Zf, A%+, b3n, and A’ III. The results of this deperturbation have been used to vibrationally * Throughout this paper u*J*, u’J’, and v”,J” are used to denote the OODR final, intermediate, and initial rovibronic levels, respectively. u,J denotes the terminal level of v*J* OODR-induced photoluminescence.

312

GOTTSCHO ET AL. TABLE I Observed C’P+ Emission Band9 Band (v’ .v)

Band W'.V)

c’E+ + l3,61

14

(3.7)

*

a3I: + 674.9

AAir Head hn)

oHead(cm-%

A1t+

(cont.)

12 074

828.0

14

11 621

860.3

(3,8)

13

ClC+ + b3nl 16 264

12

614.7

(2,ll)

15 044

631.0

15 833

631.4

15

631.7

(2.12)

11

AIZ

c1z+ (3,O) (2,O)

17

(3.1)

16 16

(2811

16 0#4)

(3.2)

16

(O,O)

16

(1.1)

15

(2.2)

15

(1.2)

(3.3)

15

(O,l)

15

648.5

15

390

649.6

14 973

667.7

14 973

667.7

14

964

668.1

14 952

668.6

14

540

687.6

14 535

687.8

14 120

708.0

13 705

729.5

13 700

729.7

13 294

752.0

15

(2,3)

15

(3.4)

15

(0,2)

15

(1.31

14

(2.41

15 416 16

(1.0)

(1,2)

826

13

284

752.6

12

888

775.7

12

829

779.3

12 467

801.9

12 410

805.0

12 oe9

827.0

12 012

832.3

14

(3,5)

14

(0.3)

14

(2,5)

14

(3.6)

14

C'C+

(2,6)

13

16 551

604.0

(3.7)

13

15 689

637.2

(l,b)

13

15 238

656.1

(2.7)

13

14

818

674.7

(3,8)

13

14

810

675.1

(2,8)

13

14

385

695.0

(3,9)

12

14 364

696.0

(1.9)

12

13 965

715.9

+ b3n

"Band head positions are calculated from C'r+ constants in Table VII in Ref. (1); a3Z+, A'X+, b3n, and R'ln constants are taken fr;m Table XI (this work) except for the energies of A", and bJn, for which the perturbed values, voo = 17 577 cm-1 (7-9) and 17 322 cm-l (6) respectively, were used. C'e+ energies from Table "II in Ref. (11 were changed so that calculated C t A heads agreed ijith those observed in Table I in Heads are accurate + 5 cm-l or y;.3'i; (see text).

.

.

0

OODR SPECTROSCOPY

313

OF BaO

TABLE I-Continued

C’Z+

*

b'no

(cont.)

c*r+* A”il

(-1

087)

13 550

737.8

(2,3)

14 725

678.9

(2,6)

13 545

738.1

(3,4)

14 714

679.4

(388)

13 139

760.9

(1‘2)

14 705

679.8

(3,9)

12 733

785.1

(2.4)

14 294

699.4

(2.8)

12 719

786.0

(0,2)

14 288

699.7

810.7

(3,5)

14 287

699.7

615.2

(1.3)

14 270

700.6

(3,101

12 331

(I,81

It 264

(3.11)

12 934

037.7

(2.5)

13 867

720.9

(1,9)

11 a57

843.1

(3,6)

13 864

721.1

Cl,41

13 839

722.4

(3,7)

13 445

743.6

(2.6)

13 444

743.6

(3.6)

13 029

767.3

(237)

13 024

767.6

(3,9)

12 618

792.3

818.8

CIZC * A'lil (3,l)

16 018

624.1

(2,l)

15 598

640.9

11.0)

15 588

641.3

(3.2)

15 580

641.7

to,01

15 171

659.0

(3.10)

12 210

(1,l)

15 144

660.1

(2,91

12 197

819.6

lO,l)

14 727

670.8

(1.61

12 154

822.6

assign thea3P state (2), improve the spectroscopic constants for all ofthese states, and suggest that additional low-lying (~2 eV), reservoir states (e.g., 3A and ‘A) exist and perturb both b311 and A’ Ill. The experimental details for these experiments can be found in the preceding paper (I), Ref. (28), and references therein. OODR-induced photoluminescence transition frequencies are given in Section II below. In Section III deperturbation models are specified and the deperturbed constants presented. The viability of usingC’Z+-a3Z+, C’Z+-b311, C’S+-A’ ‘II, and ClZ+-A%+ band systems to probe lower-level populations and to precisely specify modes and rates of collisioninduced intersystem transfer is evaluated in Section IV. II. C’Z+ PHOTOLUMINESCENCE

SPECTRA

Different vibrational levels of C’Z+ were pumped as described in the preceding paper (I) and photoluminescence from CY into a3L;+, A%+, b311, and A' ‘II was resolved (Ah = 0.2 A). A. Electronic and Viibrutionul Assignments C%+ + b311 and A’ ‘II fluorescence assignments are based upon the constants for the lower states as reported by Field (6) as well as the rotational structure observed: P,R doublets for b3110and P,Q,R triplets for b3111and A’ ‘II (3). The former implies Arll = 0 and the latter implies A0 = k 1, where fl is the projection of J onto the internuclear axis (29,30). u3Z+ assignments are made from (i) the pat-

314

GOTTSCHO ET AL.

tern of emission (PP, pQ, RQ, and RR branches, where the superscript denotes the change in N = J, J + 1) (31); and (ii) observation of a%+ - A’ ‘II perturbations which are described below. Emission ascribed to u3C+ could not be accounted for by any other known lower state. Typical C’Z+ + a3P, and C’Z+ + A’ III emission spectra can be found in Refs. (2) and (3), respectively. a3P vibrational assignments are made from the variation of a3Z+ - A’ ‘II matrix elements with u, and r)A’[see below and Ref. (2)]. Observed C%+ emission bands are given in Table I along with calculated band head positions. Bandheads are not observed since emission from a single C’S+ rovibronic level is monitored; evidence for CIZf rotational relaxation (which could produce a bandhead) in the form of collisional satellite lines is not apparent at total pressures ~1 Torr. In order to provide estimates of bandhead positions useful to the experimentalist, perturbed A’ III and b31’11energies,5 17 577 cm-’ (7-9) and 17 322 cm-’ (6), respectively, are used. C18+ perturbed energies are obtained by correcting the deperturbed energies in Table VII of Ref. (I) by the difference between observed lTable I in Ref. (I)] and calculated [from constants in Tables VII in Ref. (I ) and Table XI of this paper below] C’Z+-A%+ bandhead positions observed in excitation. Differences between perturbed and deperturbed energies for the remaining states are neglected since large, low-J interactions responsible for shifting bandheads from their expected positions are not present (see below). The heads calculated in Table I are accurate to &5 cm-‘. Emission from C’Z+ (u* = 4), D’Z+, and E’Z+ to states other than X%+ was not examined. B. Rotational Analysis Thirty-two of the bands listed in Table I are rotationally analyzed. Transition wavenumbers and rotational assignments are given in Tables II-V [also see Ref. (1) for additional CC+-A%+ bands]. The bands are only partially analyzed since emission from a single rovibronic level populates at most four (e.g., C’P + a3Z+ emission) and as few as two (e.g., C’P + AlIZ+ or b3110)lower levels. To obtain complete rotational analyses it is necessary to painstakingly retune both pump and probe lasers and then rescan the monochromator from ~600 to 2850 nm. Instead, a grid of C’Z+ levels spanning J* = 9 to 40 was used to sample the lower levels over the same J range. Typically 15 lines per band were recorded. Rotational assignments are straightforward from knowledge of J* determined from C’Z’ t A%+ excitation spectra (1) and AJ selection rules (29). However, in perturbed spectral regions where the relative positions of P, Q, and R branches are anomalous, assignments are more difficult. From predicted perturbation patterns (32) and random differences comparable to experimental error between calculated and observed term values (see below), the rotational assignments made in these regions are verified. In the case of C’Z+ + a3Z+ emission from a single J* level where the lower levels are not perturbed (0, = 11 and 12), it is not possible to distinguish the P from Q and R from Q lines in the P-form and R-form branches (3Z), respectively.s This 6 It is possible to determine C. by examining emission from bothJ* andJ* + 2 where the term values for all of the 3Z+ spin sublevels for N = .I* + 1 can be unambiguously measured and assigned. P-form

OODR SPECTROSCOPY

315

OF BaO

TABLE II

tI’

9

CV-a%+

Transition Frequencies

RRW-l)

w

(cm-‘)t

PQO

P

14

804.3

14

808.5

800.6*

14

804.0'

P(J'+l)

(3~6) 14

818.1

13

14

818.0'

14 a15.0*

14

20

14

815.5

14 812.3

14 792.8

14

795.2

30

14

810.0

14

806.3

14

14

779.0*

40

14 004.4*

14

797.3

14 745.8

14

763.5

9

14

368.2

14

366.4

14

356.8

14

358.9

13

14

368.3'

14

366.5*

14

353.5'

14

355.4.

14

815.9

779.0'

(3.7)

20

14

367.1

14

364.6

14

345.9

14

347.1

27

14

364.9

14

361.7

14

338.9"

14

338.9*

14

335.1

30

14

363.0

14

358.5

14

334.0

40

14

338.5

14

350.7

14

305.2

20

13 920.6

13 918.7

13

892.4

30

13

907.9

13

914.7

16

12

166.8

12

165.8

12

150.1

12

151.1

22

12

165.4*

12

165.4*

12

143.8

12

144.8

32

12

163.61

12

163.0'

12 131.3

12

132.5

43

12

153.2*

12

152.7'

12 110.6

12

112.0

(3,8)

L2,ll)f

(2.12)f 16

11 735.4

11

734.4

11

22

11 734.3'

11

734.3'

11 712.5

11 713.6

32

11 733.1'

11 732.5'

11 701.0

11 702.1

43

11 723.5'

11 723.5'

.ll 681.2

11 682.3

#Assignments

chosen

qreater than assignments. +J'

is ClY+

0.

correspond

See

rotational

text

718.5

to 6. (a'L+

for discussion

quantum

11

719.5

spin-spin of the

constant)

branch

number.

l

Blended or otherwise discussion.

degraded

line.

see

text

for

corresponds to an ambiguity in the sign of the a3Z+ spin-spin constant, C,. In Table II, C, > 0 has been assumed. For perturbed 3X+ levels, the sign of C, is unambiguously determined because A ’ Ill - a32+ interactions are diagonal in J and not N; each 3Z+ spin sublevel with a different value of J is perturbed by A’ III differently (32). In this case, only one sign for C, (i.e., one set of line assignemission fromJ* populates the.! = J* (fparity) and J = J* + 1 (e parity) sublevels of the N = J* + 1 %+ level; R-form emission from J* + 2 populates the J = J* + 1 (e parity) and J = J* + 2 (f parity) sublevels of the same N = J* + 1 level.

316

GOTTSCHO ET AL. TABLE III C’C+-A’S+ Transition Frequencies

(cm-‘)?

J’

R(J'-1)

9

I4 406.2

13

14 405.8

14

392.6

20

14 404.6

14

384.2

27

14 400.8

14

373.0

30

14 397.9

14

367.1

40

14 386.8

14

345.7

919.4

P(J'+l) (3.6) 14 396.9

(3,7) 9

13 928.8

13

13

13 926.5

13 914.8

20

13 926.2

13 905.5 13

896.6

30

13

13

888.6

20

13 451.9

13

431.6

30

13 445.8

13 415.1

13

12 978.6

12 965.0

27

12 973.4

12 946.4

27 916.9 (3,8)

(3,9)

tJ I is ClX+

rotational

quantum

ments) yields a calculated spectrum with random residuals comparable mental error.

to experi-

III. DEPERTURBATION3

A. Data Preparation Transition frequencies in Tables II-V are converted to term values, relative to X’C’ (u” = 0, J” = 0), by subtracting the frequencies in Tables II-V from PC+ term values (I, 28). This does not degrade the data precision since E(u*,J*) is precise to 0.01 cm-’ (I, 28) whereas the fluorescence transition frequencies are measured to an accuracy of only 0.5 cm-’ and a precision of 0.2 cm-i.’ Term values can be found in Ref. (28). In the least-squares fits, differences between frequencies corresponding to transitions in different branches of the same band, weighted according to their uncertainties of 0.2 cm- l,‘**as well as term values for each level, ’ The discrepancy between precision and accuracy results from calibration of spectra against Ne and Ar reference lines: absolute wavelength measurements made on different days varied by as much as 0.02 nm (~0.5 cm-‘) because of irreproducibility in alignment of the standard atomic pen lamp with respect to both OODR-induced fluorescence and the monochromator slit. Interpolation between atomic lines separated by more than 5 nm is accurate to no better than 0.02 nm. On the other hand, frequency differences between OODR fluorescence lines separated by less than 3 nm are precise to ~0.01 nm (-0.2 cm-‘) from day to day. Thus differences between emission line frequencies for given J* are weighted more heavily than absolute term values. * The weights are 1 cm-*/g: , where Si is the experimental error in cm-’ associated with the ith datum.

OODR SPECTROSCOPY

OF BaO

TABLE IV C’I+-b3Kl Transition Frequencies

(cm-l)t

assigned uncertainties of 0.5 cm-l, were fit. Blended line (indicated by an asterisk in Tables II-V) uncertainties are estimated to be 1.0 cm-’ absolute accuracy and 0.5 cm-’ relative precision. In order to more precisely deperturb the low-lying states of BaO, A 5’ + X2+ transition frequencies from Ref. (5) and MODR frequencies from Ref. (16) are included. Reference (5) A lZ+-XIZf transition frequencies are first converted to term values by the addition of ground-state term values calculated from Ref. (13) (rotational energies) and Ref. (18) (vibrational energies). Although not statistically rigorous, the superior precision with which X1x+ rotational constants are known effectively breaks correlations between A 5+ and X’Z+ term values. The term values so obtained from Ref. (5) are assigned uncertainties of 0.05 and 0.25 cm-’ for

318

GOTTSCHO ET AL. TABLE V C’Z+-A’

Z’

R(J1-l)

III Transition

Frequencies R(J

po

30

14 334.0

14 317.0

14 306.8

40

14 361.3

14 334.7

14 324.2

p(J

p(J’

(cm-‘)

J’

(O,O) 18 27 34

15

191.0

15 199.2 15 206.8

p(J

(3,s) (cont.)

15 182.7 15 186.6 15 189.8

1s 174.4 15 174.6 15 175.2 0,6)

48

15 233.9

15 209.4

15 189.4 9

13 697.4

13 893.3

13 889.1

13

13 899.6

13 893.2

13 887.5

20

13 903.4

13 902.4

13 885.2

27

13 907.9

13 902.9

13 881.8

30

13 923.0

13 903.8

13 895.0

40

13 931.9

13 914.7

13 896.5

(0.11 1s 27 34 48

14 751.6 14 760.6 14 769.5 14 799.7

I4 743.2 I4 748.4 14 753.7 14 776.2

14 735.0 I4 735.9 14 736.1' 14 755.3

IO.21 0.7) 18

14 314.4

14 306.4

14 298.1

27

14 324.6'

14 312.4.

I4 300.0*

34

14 331.7

14 316.5

14 301.5

48

14 363.8

14 342.4

14 320.3

9

13 478.7

13 474.6

13 470.6

20

13 488.6

13 479.6

13 470.2

30

13 497.9

13 485.2

13 472.3

40

13 511.7

13 494.2

13 476.9

13 062.2.

13 058.4

13

13 063.8

13 058.3

13 052.2

20

13 071.7

13 063.4

13 054.7

(3,2) 13.8) 9

15 616.9

15 612.9

15 608.2 9

13 40

15 618.2 15 640.8

15 612.6 15 623.1

15 604.9

(3,4) 9

14 739.7

14 7M.l

13 053.8'

15 606.4

13

14 750.6

14 744.6

14 738.6

20

14 751.6

14 745.4

14 736.5

30

14 762.2

14 747.6

14 735.2

40

I4 770.7

14 766.2

27

13 077.2

13 065.6

13 053.7

30

13 082.8

13 069.9

13 056.5

40

13 096.9'

13 079.6

13 062.1

(3.91 9

12 649.2

12 645.2*

12 641.0

13

12 650.8

12 645.7*

12 639.9

20

12 659.0

27

12 665.2

12 653.7

12 641.8

9

14 320.5

14 316.4

14 312.2

30

12 670.3

12 657.6

12 644.3

13

14 322.6

14 316.8

14 310.8

40

12 685.7

12 668.5

12 651.1

20

I4 327.6

14 317.8

14 309.3

27

14 333.1

14 319.0

14 308.6

0,s)

+J’

(3,101 9

12 239.5

12 235.6

12 231.4

is c’s+ rotational quantum number.

l

Blended or otherwise degraded discussion of precision.

line.

See text for

unblended and blended lines, respectively. MODR data from Ref. (Z6) are used as reported and are weighted according to the quoted uncertainties. B. The Hamiltonian

The Hamiltonian matrix in a Hund’s case “a” basis is given in Table VI. The matrix is composed of one a3E+ (v,) level, one A’ III (uAp)level, two A%+ (uAand vA2)levels, one b311 (Cl = 0, 1, and 2) (Q,) level, and an additional b311(only 4I = 2) (vaz) level. These matrix elements have been derived previously but with a phase

OODR SPECTROSCOPY

319

OF BaO

TABLE VI Hamiltonian Matrix Used for Deperturbation II= 11

of Low-Lying States of BaO”

- KS, + BA X-DA x21

822 - EA, +BA.,x-l)-DA',x-1~2 "33

- Eb + BbCx+l)

- Ob,X2 + 4x + I,-Ab-Cb

HII - Eb + eb,x+l)

- DbQ

"55 - Eb + Bbk31

- Db(X2 - 4x+5) + l\b - Cb

f - [Ea + e,,x+21 "66 n77

+ 6X - 3) + 2Cb

- D,,x*+8x+41

= E& + Bax-D,[x*

+ 2x,171)1-

+ 2c,-2r,l Cg -T*

Ii= = [En2 + BA2X - DA2X21 88 H99

- Eb2 f Eb2,x-Zlk-

I-I;*- HZ1 --24

222)-Db2[0.5(1+4~)~-1~*

,"=.

+ &XIX%

E-I;3- I-l& - 2&C& HTg - Es& - leb,r,l+4x)f-ll/,ULb2JI

2

cAb2

n24 - "42 * 'A'b "27 = '72 - 'A'a H2* - He* = -2'rnAVA2x4 %4

- -izx>'l IBb - 2 ,XCllDbl'l

* 843

= 2DbIx,x-2)l~

"35 = %a H&

- E-I:,=

*['ba - 'ba'

H37 = H73 = 5 x ', llba H&

- xt3

- 2kCn2b

H45 = "54

- -[2,x-2~1~~Bb-2,x-1~obl

f r, II:, - Hg4 - ,2x1 "bs Es,, - Ii,, - ,PPKb

w5,

- w75 - -,x-tAba

47

- 6

nt,J

-

- -2x* le.-z(x+l)D, - r,/21

where X - J,J+l) 1,2,...,9danot~

A'r+,v,),A",,,v,,,,

bgIl,,vb).

b’n,Wb),

b*n,,vb,,

.31;,v,l,

aQ;,v,l,

Ah+,vA

I),

+

A2 danotw

b'flp,vb+l), r*lp*ctively r'r+,v,+U

b2 dancat.

b'nl,vb

k vibtonie

.n.rgy

I -

&

s

b’n

c

mph-npin

II

dlatortion

#pin-orbit

,3z11-l

con.t.nt

cmutmt

con*tant

lpin-rotation

A+

- YIP41

92'

een.t.nt

rOtatiQnd1

D centrifugal

7.

+ 1)

con.t.nt

+ I/3 + ‘X W~Y-11-4/9-2xl

Y - Ab/Bb "ij Lij -

rotation-electronic spin-orbit

interaction

interaction

and

320

GOTTSCHO ET AL. TABLE VII Summary of A%+ - b3LI Perturbations J8

A'Z+l"A )

b'n(vb) "=2

CAb/WAIVb> (cm-1)

5Ab km-l~b

0

1

1=

0

45.1

60.3

89.6

11.02(2)

22.79 (41

2=

1

27.6

43.6

79.7

-2.78(4)

22.7

3=

2

18.8

68.7

-7.89(2)

21.92 (6)

4=

3

55.6

-6.485112)

22.76 (4)

38.3

-1.52(31

20.8

11.(S)

38.

(17)

3.50)

26.3

(22)

54.

(6)

01

7.OB(fixed)

4=

4

SC

4

97.7

SC

5

6

5


7

6


88.9

14.0(21)

(4)


aJ value at which unperturbed levels would be degenerate. b Uncertainties in parentheses are b Oefined in Table VI.

estimates.

CAlI+ - XIE+ transitions from Ref.l5)and MODR data from Ref.(l6)were used.

convention (27,33) different from that of Condon and Shortley (34) which is employed here, (S, 2 k IIS&

2) = +[S(S

+ 1) - X(C k I)]“*,

(1)

where S is the total spin, 2 is the projection of S onto the internuclear axis, andS, is the spin ladder operator. The plus sign in Eq. (1) is similarly employed in the evaluation of all angular momentum ladder operator matrix elements. The secondb3112 (62) diagonal matrix element (Hoe) is taken from Ref. (29) and is accurate for any degree of spin uncoupling. The interaction of this state with A lx+ is expressed as a product of aJ-dependent b3110- b311, mixing coefficient and the b31-Io- A%+ spin-orbit matrix element (,&J since no first-order interaction between b3111zand A%+ exists (32). Only those parameters which could be determined from the data are included in the matrix (Table VI); in particular, A’ III and b311 A-doubling terms are not included. The computer program is listed in Ref. (28). C. Description of Perturbations Terms in the Hamiltonian W’ = -B[J+L_

which connect different case “a” basis states are + J-L,

- L,S_

- L-S+] + C &li.si, 1

(2)

where ci( = CK (ZK/r3M) and Z, is the Kth nuclear effective charge; riK is the ith electron-Kth nucleus separation; li and sf are one-electron orbital and spin angular momenta, respectively; and all other constants have their usual meanings (30). The term in Eq. (2) multiplied by -B is simply a part of the rotational Hamiltonian,

OODR SPECTROSCOPY

321

OF BaO

TABLE VIII Summary of AlI+

- A’ ‘II Perturbations

1

0

104.0

zc

1

96.0

-0.0212

0.11117(11) (19)

1.0114 0.64

(6) (3)

3c,d

2

85.7

-0.0512

(21)

0.61

4=

3

75.7

-0.0700

(4)

1.128

(6)

5C

4

63.9

-0.0149

(9)

1.37

(8)

P

5

0.063

(20)

0.9

(3)

7

6

28.5

-

0.088

(14)

1.44

(23)

8

7


0.086

(16)

1.4

(3)

- 1.014



'See

footnote

a in Table

See

footnote

b in Table

VII.

'See

footnote

c in Table

VII.

b

d

(10)

An additional was determined

+ 0.024

unitless

VII.

interaction to be -9.3

parameter, which is multiplied + 0.3 x 10-6 cm-l.

by x 3/2

(see Table

VII,

BR2, where R is the rotational angular momentum (30); this term connects states of the same multiplicity and is responsible for A%+ - A’ III and some a32+ - b3TI perturbations. The second term in Eq. (2) is an effective spin-orbit operator (35) and causes A%+ - b311, A’ III - a3Z+, and b311 - u3Z+ mixing. All perturbations are diagonal in J and electronic reflection parity (e orf) (36). A’C+ - A’ III perturbations are characterized by a single crossing and a J-deTABLE IX Summary of A’ ‘II - dZ* A’ lntvA, 1

aJr+(vJ

PI(f)

JCJa

F*(e) Fj(f)

F;sa

&$vA,Iva>

0

2

(57.51C

35.9

(13)

64.3

(23)

1

3

(55.5)

25.

(8)

94.

(30)

4

6

39.5

-19.5

(7)

58.1

(21)

5

7

(45.0)

37.5

31.2

-16.48 (29)

58.5 (10)

6

0

34.8

28.5

20.1

- 8.6

52.

7

9

11.2

=See footnote a in Table "II. Fl, F2, N-l, respectively, where N = J-S m. b

Perturbations

See

footnote

'J,, values

b in Table

in parentheses

1.0 (6)

and F3

refer

VII. are extrapolated

(7)

values.

to levels

(4)

38. (23) = SE.9 + 2.7 Cm -1

with

J = N + 1. N,

and

GOTTSCHO ET AL.

322

JlJ+Il

x lO-3

FIG. 1. A%+ vibration-rotation energy vs J(J + 1) illustrating perturbations by b3& (0), b311, (Cl), bW, (O), and A’ III (x). Data for vA = 0 through 5 comes primarily from Ref. (5).

pendent (heterogeneous) matrix element. A’S+ - b31’Iperturbations exhibit three crossings corresponding to the three b311 spin components: 3110, 3111, and 3111,. Since spin-orbit interactions are diagonal in R, only 5’ - 311,,interactions are nonzero but when the spin uncouples from the internuclear axis (via BJ,Ss terms in the Hamiltonian (29, 30)) the three spin components of 311 are mixed and all may then perturb A’Z+ according to their 3110character. A’ llI - a3Z+ spin-orbit interactions are characterized by three crossings: the e-parity crossing occurs at J values between twof-parity crossings. See Ref. (32) for additional details. Tables VII and VIII and Fig. 1 summarize the A’C+ - b311 and A’Z+ - A’ ‘II perturbations observed here as well as those observed and analyzed previously (5,6). a3Z+ - A’ III perturbations are summarized in Table IX and Fig. 2. Per“6 II IO 9 8 7 6 5 4 3 2 I 0

0

I

2

1 3

I 4 JIJ+Il

I I 5 6 x IO-’

I 7

1 8

’ 9

1 IO

FIG. 2. A’ ‘Cl vibration-rotation energy vsJ(J + 1) illustrating perturbations by a3Z’ F3 (O), F2 (O), F, (m). and A’I+ (x). Note double crossing. A’ In - u”X~ - A%,’ at Jo = 28.5 in II.,, = 6.

OODR SPECTROSCOPY

OF BaO

TABLE X Deperturbed

Constants for Low-Lying States= of BaO

323

324

GOTTSCHOETAL. TABLE

X-Continued

OODR SPECTROSCOPY

OF BaO

325

TABLE X-Continued

turbations and the corresponding deperturbation model for each level are described below. The final sets of parameters are given in Table X. Correlation matrices for each fit can be found in Ref. (28). A%+ term values calculated by diagonalizing the matrix in Table VI with the parameters in Table X were used in converting * c A%+ transition frequencies to * term values as reported in Ref. (Z).9 Not all parameters in Table X are varied but some are fixed at estimated values in order to obtain physically significant varied parameters.1o Centrifugal distortion constants are fixed at 2.8 x lo-’ cm-l, the value reported for A%+ in Ref. (5), except where noted. Fixed energies and rotational constants are calculated from Ref. (5) (A%+), Ref. (6) (A’ III and b311), or Ref. (2) (~~2’). When indeterminate, b311 spin-orbit constants (A*) and b311 - A’ III spin-orbit interaction matrix elements (&,,J are fixed at - 100 cm-‘, which is approximately the final mean value for both Ab and tAra. b311 and a32+ spin-spin constants, Cb and C,, respectively, and u3x+ spin-rotation constants, ya, are fixed at zero except where noted. All off-diagonal elements which could not be varied are fixed at values calculated from the product of electronic [Ref. (6) for AT - A’ ‘II, AT+ - b311, and a32+ - b311 and Ref. A’ ‘II] and vibrational factors, (2) for u32+ (A%+ IH’ jb31&) = 2?5~

= 2l’*( 631-I~~HSo~~A %+) (Z.‘,b )VA) ,

(A’ TIlfZ’ jA’I;+) = -21’27),A,x1’2= -21’2~“2(A’ ‘II~(L+~(A’Z+)(vAt~BIv,),

t3a) (3b)

s A *Z+ term values and copies of the least-squares fits are avaiiable from the authors upon request. lo For example, if one spin component of a slI state (other than sIIl), perturbs a ‘Z+ state with larger rotational constant, but the other components lie below the IP+ origin and do not perturb ‘P+ significantly, the W spin-orbit constant, An, cannot be determined. However, ifAn is fixed at zero, the energy fit for the V level will be incorrect by an amount comparable to An. Generally, it is useful to calculate and fix perturbation matrix elements which cannot be determined in order to obtain physically significant rotational and centrifugal distortion constants.

326

GOTTSCHO ET AL.

P+

L I.6

25

I

I

I

2.0

2.2

2.4

2.6

R ti,

FIG. 3. RKR potential energy curves for the lowest electronic constants in Table XI.

(A’

‘IIlH’(a3Z+) = tAta

(b3rIo~H’ p&v

= (A’

states of BaO generated

1~~~SOllu3~+)(u,~~u,),

= 2[5ba - Th] =

2[(b3n(lHSOlla3C+)(vb

-

(~31-W-lla3Z+h(~

from

(34

Iv,>

[dl,

(34

and similarly for the remaining b311 - a32+ matrix elements, where Hso is the spin-orbit (second) term in Eq. (2), the reduced matrix elements are electronic factors assumed to be independent of internuclear distance, 5 and 7 are vibronic interaction matrix elements defined in Table VI, x = J(J + I), and all other symbols have their usual meanings. The vibrational matrix elements in Eq. (3) (e.g., (u_,~1v,)) are calculated by generating Rydberg-Klein-Rees (RKR) potential curves (37) from spectroscopic constants in Ref. (5) (A%+), Ref. (6) (A’ III and b311), and Ref. (2) (a32+) and then numerically solving the Schriidinger equation to obtain vibrational wavefunctions and matrix elements. The validity of the Born-Oppenheimer-type separation of rotational, vibrational, and electronic degrees of freedom in Eqs. (3) is discussed in Refs. (38,39). Briefly, Eqs. (3) are expected to be valid when the R centroid for one pair of mutually interacting levels is equal to the R centroid for any other pair of interacting levels, where

OODR SPECTROSCOPY

R centroid

=

OF BaO

(#IV’) (t+‘>

327

(4)

and R is the internuclear distance, u and u’ are vibrational quantum numbers for the pairs of perturbing vibrational levels. (38,39) For the above states, the average R centroids for mutually perturbing levels are - b311) = 2.26 + 0.04 A,

(5a)

R centroid (A lx+ - A’ ‘I-I) = 2.26 k 0.04 A,

(5b)

R centroid (a3X+ - A’ ‘II) = 2.34 k 0.15 A,

(5c)

R centroid (A’P

where the uncertainties quoted represent the range ofR-centroid values sampled.” As expected these values correspond to the internuclear distances where the potential energy curves intersect (Fig. 3) (39). D. The Least-Squares

Fits

Fit 1. VA= 0, vb = 0 (fixed), VA’ = 0 (Jixed). No perturbations in A’X+ (VA = 0) are observed so this level is fit with b31’I(ub = 0) and A’ ‘n (VA’ = 0) constants held fixed. Fit 2. VA = 1, t.+,= 0, VA’ = 0, u, = 2. In addition to AW - b311 and A%+ - A’ III perturbations reported in Ref. (5), A’ III A doubling resulting’from interaction with a3Z+ is detected although no u3P - A’ III crossings are observed in the J range sampled. The A’ III - A%+ perturbation at Jo = 104.0 is poorly characterized since the A%+-XIZ+ (1,O) band analysis in Ref. (5) ends at this point. Although Db could be determined, DA, could not be and is fixed at a preliminary value ofDb which is nearly equal to the final Db fitted value. It was also necessary to vary Cb although it is only marginally determined. Fit 3. VA = 2, vb = 1, VA’ = 1, ua = 3. In addition to the perturbations reported in Ref. (5), a3Z+ - A’ III interactions are again observed in the form of A doubling and level shifts of the A’ llI state at J > 40. No crossings are observed in the J range sampled. Fit 4. VA = 3, vb = 2, VA’ = 2, va = 4 (fixed). No new perturbations are observed; however, these term values could not be fit without varying a phenomenological centrifugal distortion A lx+ - A’ In interaction parameter, r)&‘, which was not required for any other perturbation. Other problems are apparent when this fit is compared with others: (i) the A’ III energy is anomalously low by ~35 cm-‘; (ii) both the b311 spin-orbit constant, Ab, and the b311 - A’ ‘II spin-orbit interaction parameter, 4;(‘b, are anomalously large by -15 cm-‘; (iii) the b311 spin-spin constant, cb, is also unusually large by = 15 cm-‘; and (iv) the b3n rotational constant, Bb, is larger than expected by 20.003 cm-l, which is 10 times the la error. Attempts to force the program to converge about the expected parameter values were unsuccessful. Nor did varying the b311 spin-rotation constant or the third-order A%+ centrifugal distortion constant, H, diminish the magnitude I1 These R centroids were calculated from RKR curves generated with the final spectroscopic stants determined here (Table XI).

con-

328

GOTTSCHO ET AL. 0

J'= 20 P(21)

R(21)

; IF

RR(19Po(20)

C ’ X+-A’ 13.7)

PP(2l) I j POl20)

c’

I

I

I

4

2+

x+-(3.81

03x+

I

II

P(2ll C’ X+--A”n (3.6)

FIG. 4. Double perturbation between asI+ (u, = 8), A’ ‘II (Us. = 6). and A%+ (uA = 7). The a3ZC+ (F3) - A’ ‘II crossing is depicted here. The A%+ - A’ ‘II interaction which culminates at Jo = 28.5 is weak. C’P+ (u* = 3, J* = 20) is prepared by OODR. Unperturbed line positions are given by dashed lines (the C’Z+ - a3Z+ V(21) line is not observed). In addition to OODR-induced photoluminescence, A%+ + X’Z+ (1,5) emission induced by the pump laser alone occurs in this spectral region.

of these anomalies. Neither parameter could be determined. These problems suggest the presence of additional perturbing levels. FitS.v, = 4,vb = 3,vb2 = 4,vA,= 3, va = 5 (j&d). No new perturbations are detected. A second b311 vibrational level is needed to simultaneously fit the A%” (0.4 = 4) - bTI* (Vb2= 4) perturbation at Jo = 97.7 and the A lZ+ (vA = 4) - b3110 (vb = 3) perturbation at Jo = 55.6. Only the energy for b311 (vb2 = 4) is varied; Bb2 and & are fixed at preliminary Fit 6 values. The b311 (vb2 = 4) energy so determined agrees well with the value determined in Fit 6. Fit 6. vA = 5, vb = 4, vAr = 4, V, = 6. Both a3Z+ - A’ ‘II and a3Z+ - b311 perturbations are observed. No crossing for the latter is apparent since the b3110 (va = 4) origin lies below a3Z+ (v, = 6) and B, > Bb; however, both a32+ - b311 perturbation parameters, &,a and vba, are determined. One a3Z+ - A’ In crossing is observed at Jo = 39.5. A second b311vibrational level must be considered at J > 74 owing to the b3112(rb = 5) - A%+ (vA = 5) crossing at Jo = 88.9; however, this is treated differently from Fit 5 since b3& (t+, = 5) - A’Z+ (vA = 6) interactions are observed (Fit 7). Instead of including b3112(t+, = 5) in this fit, A’S+ (u,~= 5) data from Ref. (5) are truncated at J = 74 and included in Fit 7, where all three fI components of b311 (ub = 5) are fit simultaneously. The two sets of AT+ (u.~ = 5) parameters determined from Fits 6 and 7 are in agreement to within 3

OODR SPECTROSCOPY

OF BaO

329

standard deviations. Both the a3Cf spin-spin and spin-rotation constants, C, and ya, respectively, are determined. Fit 7. VA = 5, Vb = 5, VA’= 5, 2), = 7, VA2= 6. As mentioned above, A’S+ (VA = 5) .I levels above J = 74 (from Ref. (5)) are fit along with VA2= 6 OODR data. Two a3Z+ - A’ IlI crossings are observed. Although no A%+ (VA2= 6) - b3& crossing is observed, the two levels are nearly degenerate atJ = 0 and &,A2 is determined. Fit 8. VA = 7, z)b = 6, VA’= 6, v, = 8. Two new perturbations are observed: A%+ (VA = 7) - A’ ‘n (VA’ = 6) and A’ ‘n (VA’= 6) - a3C+ (v, = 8). A double e-parity crossing occurs between AT, A’ ‘II, and a32+ (F,) and is illustrated in Fig. 4. Although b3& (ub = 6) lies below the VA= 7 origin, &, could still be determined from the A’ ‘II - AY interaction owing to A’ III - b3111mixing and b311 spin uncoupling which results in finite b311,,character in the nominal A’ ‘II VA’= 6 level. These perturbations were previously observed by Sakurai et al. (40), but these authors made no attempt at analysis. = 1.Ocm-l) Fit 9. 2)A= 8, ub = 7, z).&= 7, va = 9. A very small perturbation (&_@a between A’ ln (VA’= 7) and u3Cf (v, = 9) is observed at Jo = 11.2. Although no AlIS:+- A’ III crossing is observed, vAA,is marginally determined. Fit 10. VA = 8 (fimd), ub = 8, VA’= 8, v, = 10 (&Wd), VA2= 9 (fixed). No perturbations are observed. Fit Il. VA = 9, t.$,= 9, VA’= 9, v, = 10 (fixed). No perturbations are observed. Fit 12. VA = 10 (fixed), ub = 10, 2)Af= 10, v, = 11. No perturbations are observed. As mentioned above, C’Z+ --* u3Zf P- and R-form branch emission is arbitrarily assigned such that C, > 0; if the Q-branch assignments are systematically interchanged with the P and R assignments in Table II the values in Table X change by less than the le estimates quoted, except for C,, which changes sign (but has the same magnitude). Thus, the absolute value of C, is reported. Fit 13. VA = 11 (Ji)ced), ub = 11, VA’= 11 (fixed), v, = 12. No perturbations are observed. Again, only 1C, 1 is determined. From Table X, it is seen that vibrational intervals and rotational constants, particularly those for A’ ‘II and b311, do not vary in a regular fashion. For example, AG (v + l/2) values for v = 0, 1,2, and 3 for A' III andAY are (from Table X): A’ III

V

0

1 2 3

421.7 406.4 488.6 422.7

2 * + 2

1.2 cm-l 0.7 0.4 0.2

AlZ+ 495.727 494.218 489.156 486.939

-+ 0.012 cm-l + 0.019 t 0.017 + 0.012

The precision with which second-order corrections to E and B (23-26) can be calculated (~40%) does not warrant making these adjustments. However, the magnitude of these corrections precludes their being responsible for the anomalies apparent in Table X: for example, the A' III (VA’= 2) energy is low by -35 cm-’ with respect to VA’= 1 and 3, whereas the second-order energy correction (from interaction with u32+) is estimated to be -1.0 2 0.4 cm-‘. Similarly, second-order A%+ - b31’Iand u3ZC+- b311 spin-orbit interactions, which primarily determine

330

GOTTSCHO ET AL.

Cb (25, 33, 41-M), cannot account for the anomalous value of Cb = 22.98 cm-’ determined for z)b= 2. On the other hand, these interactions, as well as secondorder A’ III - a3Z+ interactions, are of the right magnitude to explain observed C, values.12 In fact, the A’Z+ and a3Z+ E and B values are not anomalous. It is curious that in Fit 4 it is necessary to vary an additionalA’ ‘II - A’Z+ interaction parameter, qiA,. Although this centrifugal distortion parameter can be explained by second-order interactions with A ’ III and A lx+ vibrational levels not explicitly included in the Fit 4 Hamiltonian, it is peculiar that it is not required in any other fit. These problems are not unique to vAf = vb = 2: BA, (vAV= 3) is certainly too large when contrasted with BA, for VA’= 2 and 4. And the Bb values for vb = 0, 1, and 2 are the same to within experimental error, contrary to the expected monotonic decrease of B with v. The above observations are indicative of incomplete deperturbation, which in turn is a consequence of choosing an inappropriate or incomplete model Hamiltonian. Failure to achieve complete deperturbation sensitively indicates the presence of at least one additional, low-lying, “dark” state. The fact that these anomalies are manifested only by A’ III and b311 and neither A%+ nor a3Z+ leads to the conclusion that this state(s) has A symmetry (32, 35). Experiments designed to characterize this A state(s) are described below. E. Equilibrium Constants Dunham coefficients (4.5) for the low-lying states of BaO are given in Table XI. The E and B values from Table X are fit to polynomials in (v + l/2), ignoring correlations between parameters but weighting according to the uncertainties* in Table X. For A’ ‘II, G(vAt) values up to VAT = 29 from Ref. (8) and B (VA,) values up to VA’= 18 from Ref. (9) are fit along with these data.13 The Ab value in Table XI is a weighted8 average of the values in Table X. Values for C, , Cb, and ya are not averaged as they are generally small and vary significantly from level to level. The constants for a3x+, A Y, b311, and A' III have been extended and improved. The use of bandheads instead of origins and extrapolation from high v in Ref. (8) are believed to be responsible for discrepancies in A’ III constants reported here and in Ref. (8). It cannot be overemphasized that the energies in Table XI are deperturbed and should not be used to calculate spectra without diagonalizing the matrix in Table VI. The parameters in Table X reproduce the spectra to within experimental error (when used in the matrix given in Table VI) but those in Table XI do not, owing to incomplete deperturbation (see above) and neglect of correlations between parameters in the Dunham coefficient fits.14 The constants in Table XI I2 ya may similarly be explained by second-order b3Tl - n3Z+ rotation-electronic interactions. I3 G(u,,) values from Ref. (8) are given uncertainties twice those quoted because bandheads rather than origins were measured. In addition, it is necessary to adjust these energies to the deperturbed values by subtracting the difference between v00 from Ref. (8) and the deperturbed Q,, determined here. The difference of 80 cm-’ results from repulsion of A’ ‘II by b3111. I4 In order to properly take into account correlations between parameters, estimates need be made for the variances and covariances of fixed parameters. Curl’s diagnostic least-squares procedure would be

OODR SPECTROSCOPY

331

OF BaO

TABLE XI Spectroscopic

Xl2 +b VOOXlO

-4

0.0

Constants for Low-Lying States of BaO” a)I:

+

1.6496(3)

A1I+ 1.6722373(10) [1.672225]=

b39 ,;.;;;:;!lO'

.

A'ln 1.75088(12)

T,x10-4

0.0

1.6596(3)

*oo

0.0173

0.0928

-0.0611

-0.1468.

-0.1230

Y10(We)X10-2

6.6976(6)

4.690(7)

4.99620(19) [4.997lC

4.4762(E) [4.483)=

4.4795($2) l4.4245)

Y20( -Were)

2.028(17)

-1.48(4)

1.6807345(10)

-1.716 (8) f-1.64)=

Y30(weye)x102 -0.35 (11) Yqo(~aze)x105-6.3 *Ol(Re)

0.3126140(7)

2.14 (9)

0.2594(s) -1.44 (5)

0.258390!(26) fO.258321 -1.111 6 3) [-1.0701

-4.33 (24)

-2.139(e) I-1.6521f 1.02 (3)

r;.Z:M;!16) -1.18 (4) I-1.4)=

7.0 (7)

0.22385(16) 10.22441' -1.15 (4) I-1.410 -4.0 (21)

-9.49(4) 1.939677 (3)

Re(;o

-2.287(12) I-2.391a

1.76197(12)

(21)

*111 -ae)x103 -1.3921(9) Y21(r,)x106 1 A x10

1.75026(10)

2.1294(20)

2.133512(11)

2.2901(S)

2.2922(e)

aAll units are cm-l except where noted. All energies are deperturbad. Uncertainties of lu are given in parentheses. Previously reported values are given below in brackets. bXIE+ constants taken from Ref (E). 'Ref. (5). dRef.

(16).

'Ref. (6).

fRef. (8). gWeighted average of values in Table X.

are intended for calculation matrix elements.

of potential

energy curves (Fig. 3) and vibrational

IV. DISCUSSION

A. Perturbation

Matrix Elements

Weighted averages ofA’);+ - b311 A’C+ - A’ III anda3Z+ - A’ III electronic perturbation matrix elements are gken in Tables ‘VII-IX, respectively. These were obtained by dividing the vibronic matrix elements by the appropriate vibraone approach to this problem (46). If such an estimate of the complete covariance matrix were made (i.e., including fixed as well as fit parameters) then the merge procedure of Albritton et al. (47) should be used to generate Dunham coefficients.

332

GOTTSCHO ET AL. TABLE XII One-Electron

Perturbation

b(unitless) AlP+ ".A",, AIC+ s b31[ + asI: ?IA", + a3r ?Ib3n b3n

Matrix Elements a,fcm-1)

a+kn-1)

1.014 + 0.024a 63.3 + l.lb 167. + 8.' 52. + 8.d

1.26 + O.Ogd

4 A'ln

222 + 16'

b311

188 + 16f

where b = -lE+tYo>

=

nM,/ = -nba/<"bjBIva,

a+= =

% a

From

=



12j3'2C /WA/V,> = (2,3/26 /<",,l",, = _4Sba,<"b,"a> Ab A'a

= -2Ab

= 2SA,b

Table "III.

bFrom Table VII. =Fm” Table IX. d Obtained from Table

X, Fits 3 and 6, and calculated
tional factors as prescribed by Eq. (3). Electronic factors for different pairs of mutually interacting levels are seen to be approximately constant, verifying the A’ ‘II, u3Z+, and b311 vibrational assignments made previously on the basis of preliminary values for these matrix elements (2, 6). In the single configuration limit, matrix elements of operators in Eq. (2) between pairs of electronic states are related by matrix elements of one-electron operators between molecular orbitals (19, 34,35,48, 49). The lowest-lying states of BaO derive from the following electronic configurations: X’Cf a3C+

7A’S+

b311, A’ ‘TI

Z&tiWd,

69

za2yaxow?r4,

VW

zo-y&‘xowd.

(6~)

Using these configurations and the methods outlined in Refs. (19), (35), (48), and (49), matrix elements between lowest-lying states of BaO are expressed in terms of one-electron integrals in Table XII. It is seen from this table that these one-electron integrals have different values when evaluated for different pairs of interacting states indicating: (i) that the z(+, yu, xo, and w7r orbitals in Eqs. (6) are generally different for each state; and/or (ii) the single configuration approximation is invalid. In addition to the relationships in Table XII, values of b, a+, and a, (defined in Table XII) can be related to atomic integrals by employing the LCAO method: Iwm> = (fl2P), lycr) = (1 - E2)“*(a02p)

Va) +

lIcBa6s).

G’b)

OODR SPECTROSCOPY

OF BaO

333

In Eqs. (7), the molecular orbital W~Fis assumed to be localized on 0 and yu, although primarily localized on 0, has Ba6s character. Field (6) has shown that Eq. (7a) adequately accounts for the b311 spin-orbit constant, which is small (-94 cm-‘) compared with atomic Ba 3P spin-orbit splittings (833 cm-‘) (50). If l is zero in Eq. (7b) (i.e., ya is composed primarily of 02p), a+ = [&I + 1)]1’2uZ= 2%, for 1 = 1. On the other hand, if E f 0, the Ba atomic character does not contribute significantly to the off-diagonal matrix elements, a,, since two-center contributions to these integrals are small (51) and the Ba orbital has s symmetry. Thus, Ba atomic character in ya tends to dilute the ya - WETinteraction and a, can be less than a,: U+= (w7+l+lycr) = [2(1 - Ez)]%z. (8) Using the u32+ -A’ Table XII,15

III and A%+ - b311 a, values and average a, values from

l(u3C+) l(A’Z+) The A12

= 0.81,

(9a)

= 0.98.

(9b)

- A’ llI matrix element is also a measure of c(A’Z+), b = ( we 11, lycr) = [2(1 -

and from Table XII,

l(A’Z+)

l2)]112(unitless),

= 0.70.

(10) (11)

The disparity between e(A%+) determined from Eqs. (8) and (9b) and the value determined from Eqs. (10) and (11) results from the fact that different operators (e.g., Al, vs 1,) sample different properties of the electronic wavefunctions. Nonetheless, it is clear that the ya orbital has substantial Ba6s character which dilutes interactions and the rotation-electronic both the singlet - triplet spin-orbit interactions within a spin manifold. This is consistent with the conclusion reached in OODR III (I ) that excitation of A *Z+from X5+ involves partial charge transfer from 0 to Ba. B. Singlet - Triplet Energy Splittings In the single configuration limit, the u32+-A’Z+ and b311-A’ III deperturbed (i.e., without spin-orbit interactions) energy splittings are a function of the exchange integrals (52) AEx = E(A%+) - E(u32+) = ~(Y~~)xcJW

IWr12)(~a(2)xa(2))7

(124

AEn = E(A’ ‘l-l) - E(b311) = 2(w~(l)~a(l)1(1/r~~)Iw7T(2)~~2)),

(12b)

I5 The A+ - /Al (I+ and b parameters are not considered since they are poorly determined for both of two observed pairs of interacting levels.

334

GOTTSCHO ET AL.

where 1 and 2 are electron indices. If the WT, ya, and xu orbitals were identical for each electronic state and WT and yo were both composed of only 02p, AEX would equal AEn. In fact AEZ (226 cm-‘) is remarkably close to AEn (117 cm-‘). This suggests that the 12+-32+ and 111-311energy splittings in the isovalent MgO, CaO, and SrO molecules should be similar since the single configuration is a better approximation for lighter species. Assuming AEp = AEn and neglecting the effects of the 311 - llI spin-orbit interaction on E(‘lJ) we estimate: TJ3C+) (cm-‘)

MgO CaO SrO BaO

19044 11 435 10 636 16 596

* f & 2

50 50 50 3

Ref. (53) Ref. (54) Ref. (54) Measured directly by this work.

Thus the 32+ state is the lowest excited electronic state only in BaO and in all the lighter alkaline-earth oxides, 311is the lowest excited electronic state. C. Additional Low-Lying

States of BaO

As mentioned above, there is evidence for 3A and/or ‘A perturbations in both the b311 and A’ III states. The A states most likely derive from the za2yawr4v8 configuration where the US orbital is localized on BaSd. Ba is the first alkaline earth where the [ns(n - l)d] 3D state lies below the [ns np] 3P state so it is not surprising that a S5d orbital may be important in the low-lying electronic structure of BaO. In order to verify the existence of these states and better characterize their interactions with b311 and A’ ‘II, more complete C’Z+ + b311and C’Z+ + A’ III emission spectra, obtainable by exciting a finer grid of J* levels, are needed. Alternatively, C’Z’ levels which are perturbed by 0 = 1 states (i.e., heterogeneously perturbed) (2 ) could be preferentially selected and borrowed oscillator strength into fi = 1 and 2 A states exploited. D. Population

Monitoring

The band systems described above and summarized in Fig. 5 can be used in detailed rovibronic population probes of low-lying states of BaO although several points warrant consideration before proceeding with such experiments.16 Perturbations responsible for the intercombination bands observed complicate population monitoring: line intensities will generally vary with both J and v in an irregular fashion. In principle, the J variations can be computed from the deperturbation results above and those presented in Ref. (I ): the unitary transformation matrices which diagonalize the Hamiltonians provide mixing coefficients which in turn permit the relative line intensities to be calculated (30). For example, percentage Z character in the C’Z+ (II* = 3) main levels near the vibrational origin varies from Iti Pruett and Torres-Filho (55) have already used the CT+-PII, CT+-A’ ‘II, and C’P+-X’P+ band systems to probe vibrational populations in these lower states; however, they were not able to relate populations in different electronic states nor were they able to determine rotational populations.

OODR SPECTROSCOPY

OF BaO

335

64% at J = 0 to 83% at J = 20 (I ). However, competing transition moments, owing to the plethora of perturbing states in both the upper and lower levels, make reliable relative intensity calculations difficult at best.

c+4 -----:::

-J

D'

--0

.-

c

*2’

fs

,2

0.2419

-8

II

Z+

30

i In

ai In

lo

In

d t-

$ r-

U-J

I

0

ai 0,

w

m

25

6 @J , , 0.2083 0,

, , 0.2083

9-7-6-5-4-3-

0.2492 7

_

IO9876CI-

_ -

IO9a7654-

z-

=

f,,

sz:4c -

I

-

CD

cd -0

55 -

i

=0

_

A’ 2+

b311 2.40

t T

=@Z!5ZE

A’ ‘II a3 I+

19 18 17 16 15 14 13 12 II IO 9 8 -

7 6

2-----c--x’

z+

FIG. 5. BaO energy-level diagram illustrating the emission observed from a single C’X+ (u* = 3, J) level. Rotational constants are indicated on the levels; shortest and longest wavelengths of bandheads are given in nanometers along the transition arrows.

336

GOTTSCHO ET AL.

It is recommended, instead, that careful fluorescence intensity measurements be made via OODR pumping of C’Z+ prior to using these same transitions in excitation (e.g., C’Z+ t VII followed by C%+ ---, X’Z+ uv fluorescence) to monitor populations. This is particularly necessary for comparisons of populations between different vibrational levels where the upper-level perturbing-state vibrational numberings remain undetermined: for example, C-b311 Franck- Condon factors most likely determine the vibrational envelope of CIZf-PII emission intensity [see Ref. (1) for a description of c - C’Z+ perturbations]. V. CONCLUSION

The technique of optical-optical double resonance has been shown to be a sensitive means by which low-lying, long-lived electronic states can be systematically detected and characterized. Although crucial intercombination bands result from perturbations in the highly excited electronic states of the heavy BaO molecule (I), the OODR technique assisted by perturbations is by no means applicable only to this molecule. Local perturbations exist in most molecules and with the selectivity afforded by OODR these isolated perturbed levels can be prepared at will and gateways to different spin manifolds consequently created. A population-monitoring scheme for the a3Cf, b311, and A’ Ill reservoir states has been established. It is hoped that this work will stimulate such kinetic measurements in the near future. ACKNOWLEDGMENTS The basic motivation and most important techniques found in this paper originate with the late Professor Herbert P. Broida, to whose memory this paper is dedicated. We are grateful to Dr. Roger Bacis, Mr. Paul Weiss, and Mr. Warren Weintraub for experimental assistance and to Dr. .I. Gary Pruett for a critical reading of this manuscript. Dr. Ingemar Renhom kindly provided us with his derivation of the one-electron spin-orbit matrix elements. This research was supported by the National Science Foundation under Grants CHE-7505959 and CHE-7519410. RECEIVED:

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