david e. reisner et al- vibration-rotation and deperturbation analysis of a^2-pi-x^2-sigma^+ and...

8/2/2019 David E. Reisner et al- Vibration-Rotation and Deperturbation Analysis of A^2-Pi-X^2-Sigma^+ and B^2-Sigma^+

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JOURNAL OF MOLECULAR SPECTROSCOPY 89, 107-124 (1981)

Vibration-Rotation and Deperturbation Analysis of A21I-X22+and SC+-X22+ Systems of the Cal Molecule

DAVID E. REISNER, PETER F. BERNATH, AND R. W. FIELDDepuriment of Chemistry und Spectroscopy Laboratory. Massuchusetts Institute of Technology.

Cumbridge. Mussuchusetts 02139

Doppler-limited laser excitation spectroscopy employing narrow-band fluorescence de-tection was used to obtain a rotational and vibrational analysis in the (0, 0) and (1, 1) bandsof the A*rI-X?P system and the (4, 2) (3, l), (0, 0), (0, I), (1, 2). (2, 3), and (3, 4) bandsof theBY-X22+ system of CaI. The A andB states are deperturbed to obtain spectroscopicconstants and Franck-Condon factors. Deperturbation was necessary because of the smallseparation of the A and B states relative to the A - B interaction strength and the AIIspin-orbit splitting. The main deperturbed constants (in cm-r) are

XXT, 0WC 238.7496(33)%J, 0.62789(64)B, 0.0693254(84)a, x 104 2.640(35):: (A)

-2.8286(2)

AII B%15 624.67(S) 15 700.52(12)24 1.19(7) 242.63( 17)

0.53(S) (Pekeris) 1.17( 12) (Pekeris)0.070460( 14) 0.071572(22)2.15(10) 3.95(2)45.8%8(52) -2.8057(3) 2.7839(4)

where la uncertainties are given in parentheses. The molecular constants provide insightinto the orbital composition of the A and B states.

I. INTRODUCTIONThe first CaI A211-X2Z+ and B 2C+-X2C+ spectra were observed in absorption

by Walters and Barratt in 1928 (1). Several vibrational analyses of the A-X andB-X bandheads have been performed (2), the most recent of which was by Raoet al. in 1978 (3). CaI has also been tentatively identified in the spectra of certaincool stars (4). In spite of the early and frequent observation of CaI spectra, no ro-tational analysis has been reported.CaI is a very ionic molecule so the charge distribution is well represented byCa+II. The remaining Ca+ valence electron resides in a nonbonding metal-centeredorbital (5). Transitions from the X2C+ state correspond to excitations of the 4s(rnonbonding electron to higher nonbonding metal-centered orbitals, resulting innearly identical potential curves for the X, A, and B states. The similarity of therotational and vibrational constants in the ground and excited states causes thespectrum to be highly congested, precluding the possibility of correct rotational

1Present address: Herzberg Institute of Astrophysics, National Research Council of Canada, OttawaKlA OR6, Canada.107 0022-2852/81/090107-18$02.00/O

Copyright 0 1981 by Academic Press. Inc.All rights o f reproduction in any form reserved.


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108 REISNE R, BERNATH, AND FIELDor vibrational analyses by classical techniques. Earlier attempts at vibrationalbandhead analyses, including the most recent, were not entirely correct (2, 3).The technique of laser excitation spectroscopy using a tunable single-mode cw dyelaser, coupled with selective, narrow-bandpass fluorescence detection, has enabledrotation-vibration assignment of over 1600 lines.

The A*II nd B*C+ tates are separated by only about 90 cm-. This separationis similar to the 2113,2-111,2 eparation (60 cm-) and the 211 - *Z+ interactionmatrix element (40 cm-l), thus the usual expressions for A doubling (7), derivedusing second-order perturbation theory, are inadequate.

Nevertheless, the usual *C+ energy level expressions (Ref. (6, p. 249)) ade-quately reproduce the line positions of the B*Z+-X*2+ ransition. However, thespin-rotation constant of the B state is larger than the rotational constant becauseof the strong interaction with the nearby A*Il tate. Thus, the effective rotationalconstant of the B*Z+ tate has no mechanical significance (8).In order to fit the A-X transition and obtain mechanically significant A-X andB-X constants, A 'II B*C+ nteraction matrix elements were explicitly includedin a direct approach fit (7). The (0, 0)A-X and B-X bands were fitted simul-taneously, as were the (1, 1)A-X and (1, 2) B-X bands, in order to deperturbthe A and B state constants. For the B*Z+ tate, two sets of constants are presentedin order to provide effective constants for convenient calculation of energy levelsas well as to provide deperturbed constants for the calculation of potential energycurves.

II. EXPERIME NTAL DETAILSCaI was produced in a Broida-type oven (9) by the reaction of ethyl iodide,C2H51, with calcium vapor produced by heating calcium metal in an alumina

crucible. Operating pressure was typically 1 Torr of argon carrier gas. Four wattsof 514-nm radiation from a Coherent CR 10 Ar+ laser pumped a Coherent Model599-21 dye laser (l-MHz bandwidth) operated with rhodamine 6G (50 mW) orrhodamine 101 (30 mW). The dye laser was used to excite fluorescence in theAu = 0 band sequence of the A-X system and the AU = 2, 0, and - 1 band se-quences of the B-X system.Fluorescence was viewed (10, I I) through a l-m monochromator (spectral slit-width, l-2 cm-) which provided the narrow bandwidth detection necessary toisolate transitions in a selected branch. While fluorescence detection was generallydone in the same band in which the laser excitation occurred, on occasion it wasadvantageous to view fluorescence in another band sequence, which might possessmore convenient bandhead separations or more favorable Franck-Condon factors.Each of the bands in the B-X system displays double heads, as expected fromthe large spin-rotation constant in the B state, and is shaded to the violet. Thesingle-mode dye laser was scanned through a selected P or R branch and fluores-cence was detected exclusively in the corresponding R or P branch (of the sameparity), respectively. The spectral bandwidth of the monochromator could beadjusted to discriminate against, or controllably allow for, detection of fluorescencefrom other bands of the sequence. Similar scans were made for the A-X system.


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Ca I AZIl AND EzZ2+-X28+ 109Although many branches occur in the same spectral region, overlapped lines

coming from different branches often have different N values. This difference in Nmeans that the separations between resultantP( N + 1) andR(N - 1) fluorescencelines are different, permitting the lines in a given small spectral region to be sortedinto branches. The different branches in the same spectral region give rise tofluorescence that occurs in distinct spectral regions. By using the monochromatoras a narrow-bandpass filter, fluorescence arising from excitation in a specific branchcan be detected selectively. When the laser is scanned and the monochromatorused as a filter, the excitation spectrum is simplified.Overlapping sequence bands can result in more than 100 lines/cm-. Without thesimplification provided by narrow-band detection, our analysis would have beenimpossible. The technique is illustrated by Figs. 1 and 2 of Ref. (II ).

The fluorescence excitation spectrum was calibrated with respect to I, B O:-X 'C,+ines (12) by simultaneously recording I, and CaI excitation spectra as wellas fringes from a 300-MHz FSR semiconfocal Fabry-Perot etalon. The absoluteaccuracy of unblended lines is kO.003 cm-l. The estimated precision, from rmserror of the fit, is 0.003 cm-. The line positions and band origins given have notbeen corrected by subtraction of 0.0056 cm-, contrary to the suggestion by Ger-stenkorn and Luc (13).

III. RESULTS AND DISCUSSIONInitial fluorescence excitation spectra of CaI were recorded in the A v = 2,0, and

-1 sequences of the B-X system. Attempts to analyze the Au = 1 bands wereTABLE I

B2P+-X3+ Ban dhea ds (cm-)

B 2 Z + - X 2 Z + -IB a n d He a d s (in cm )(VVW) Pie P 2 f ( V ' . V" ) P i e P 2 fO,O) 1 6 1 9 1 . 7 0( 3 . 1 ) 1 6 1 9 0 . 0 6( 4 . 2 ) 1 6 1 8 8 . 3 6( 5 . 3 ) 1 6 1 8 6 . 6 1( 6 . 4 ) 1 6 1 8 4 . 7 9( 7 . 5 ) 1 6 1 8 2 . 9 1( 8 . 6 ) I 6 1 8 0 . 9 5( 9 . 7 ) I 6 1 7 8 . 9 2( l , O) 1 5 9 5 0 . 5 9

( 2 , 1 ) 1 5 9 5 0 . 5 9( 3 3 2 ) 1 5 9 5 0 . 5 4

1 6 1 8 7 . 4 4

1 6 1 8 6 . 1 41 6 1 8 4 . 7 91 6 1 8 3 . 3 6I 6 1 8 1 . 8 2I 6 1 8 0 . 2 01 6 1 7 8 . 4 7

_ _

1 5 9 5 4 . 6 8

I 5 9 5 4 . 3 61 5 9 5 3 . 9 7

( 4 , 3 ) 1 5 9 5 0 . 4 7 1 5 9 5 3 . 5 7( 5 , 4 ) I 5 9 5 0 . 2 8 - -( 6 9 5 ) 1 5 9 5 0 . 0 0 - -( 7 , 6 ) I 5 9 4 9 . 6 1 - -( 8 . 7 ) I 5 9 4 9 . 1 1 - -( 0 , 0 ) I 5 7 1 2 . 2 2 I 5 7 1 6 . 2 9( l , l ) 1 5 7 1 3 . 5 9 1 5 7 1 7 . 2 8( 0 . 1 ) 1 5 4 7 5 . 1 7 1 5 4 7 8 . 8 5C l . 2 1 1 5 4 7 7 . 7 9 1 5 4 8 1 . 1 0( 2 . 3 ) I 5 4 8 0 . 3 3 I 5 4 8 3 . 3 2( 3 , 4 ) I 5 4 8 2 . 7 9 - -

-1Ac c u r a c y + 0 . 0 1 c m


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110 REISNER, BERNATH, AND FIELDTABLE II

Franck-Condon Factors Calculated from Deperturbed Constants

Y~~l_____tl_______!_______~_______~_______~0 0.814 0.159 0 . 0 2 3 0 . 0 0 3 - - - -l 0.175 0 . 5 3 0 0 . 2 3 2 0 . 0 5 3 0 . 0 0 9 0 . 0 0 12 c t . 0 1 0 0 . 2 8 6 0 . 3 4 8 0 . 2 5 6 0 . 0 8 0 0 . 0 1 7; 0 . 0 0 1_ 0 . 0 2 4- 0 . 0 4 0. 3 5 7 0 . 4 0 2. 2 3 1 0 . 2 5 4. 1 5 7 0 . 2 3 8. 1 0 35 _ _ - _ _ _ 0 . 0 5 4 0 . 4 3 3 0 . 1 1 0

Ail - X2X*

V~a.____o_._____!______~_______~_______0 0 . 9 4 2 0 . 0 5 4 0 . 0 0 3 - - - - - -I 0 . 0 5 7 0 . 8 3 0 0 . 1 0 4 0 . 0 0 8 0 . 0 0 1 - -2 0 . 0 0 1 0 . 1 1 3 0 . 7 1 9 0 . 1 4 9 0 . 0 1 6 0 . 0 0 2; _ __ 0 . 0 0 3- 0 . 1 6 8. 0 0 6 0 . 6 1 2. 2 2 0 0 . 1 8 7. 5 1 0 0 . 0 2 6. 2 1 75 _ _ - _ _ _ 0 . 0 1 0 0 . 2 6 9 0 . 4 1 5

Y~\yA______O_______!_______2________3____0 0.957 0 . 0 4 1 0 . 0 0 2 - - - - - -1 0 . 0 4 3 0 . 8 8 8 0 . 0 6 4 0 . 0 0 5 - - - -2 _ _ 0 . 0 7 1 0 . 8 4 7 0 . 0 7 5 0 . 0 0 7 - -; _ __ - -- 0 . 0 8 6_ 0 . 0 9 2. 8 2 8 0 . 0 7 6. 8 2 7 0 . 0 1 0. 0 7 05 _ _ - - S W _ - 0 . 0 8 9 0 . 8 3 8

On l y v a l u e s ? 0 . 0 0 0 5 h a v e b e e n i n c l u d e d .

frustrated by extreme sequence congestion and spectral overlap, as evidenced bythe head of heads shown in Table I. The (0, 1) band was found to be relativelyfree of overlap and was analyzed first to obtain preliminary constants for the X andB states. These constants were then used to guide the analysis of the remainderof the bands in the B-X system. The B-X data were fitted using standard C energylevel expressions (6, p. 249), but y and y were strongly correlated.The X-state constants were then used to assign the AU = 0 bands in the A-Xsystem. Analysis of the A-X system and a combined fit of the A-X bands withselected B-X bands provided well determined values for y. The B-X bands werethen refit with y fixed.The standard ZII-2~+ Hamiltonian uses A doubling and spin-rotation parametersderived using the Van Vleck transformation (8). In CaI, the % - 2+ interactionis so strong that second-order perturbation theory cannot adequately explain theA doubling of the A "IItate. In order to fit the A-X transition, the 211 - 72+ inter-action parameters 3 and 5 (14) were explicitly used in combined A-X and B-Xfits. These fits also provided estimates of the true mechanical B and o constants,uncontaminated by magnetic contributions introduced by Born-Oppenheimerbreakdown (8).


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TABLE IIIB*Z+-X*X+ Observed Transitions (cm-l)


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112 REISNER, BERNATH, AND FIE LDTABLE IV

B2Z+-X2H+ Rotational Constants (cm-)

5 = 0 1 2 3 4_______________________________________________________________~__________________________________6 X lo2 7.16292tlY) 7.13135(34) 7.09543(35! 7.065704(66) 7.03562(36)D, , x 1 0 ' 3 . 0 9 9 ( 1 2 ) 3 . 0 6 9 ( 2 7 ) 3 . 0 7 9 ( 3 1 ) 3.lOOb 3. IOObrv -0.140017(26) - 0 . 1 2 3 3 3 4 ( 4 0 ) -0.108778(381 -0.095699 (83) -0.084701(58)Ye x IO6 2.306(17) 2.250(25) 2.274(22) 1.981(41) 2.004(60)

Yx = 0 1 2 3 4--_______-_-_______--______________________________*_______________~_______________________________5 X 10 6.91928(19) 6.89300(19) 6.86814(33) 6.83842(331 6.81461(19)D\ , x 1 0 8 2.34 2.34 2.34 2.34 2.34Y, x 104d 56.01 55. JO 55.39 55.08 54.77Nu mb e r s i n p a r e n t h e s e s a r e l o u n c e r t a i n t i e s .a T h e B2 C* c o n s t a n t s a r e n o t d e p e r t u r b e d a n d mu s t n o t b e u s e d f o r g e n e r a t i o n o f p o t e n t i a l e n e r g y c u r v e s .b .F i x e d a t t h e v a l u e f o r v ' = 0 . V a l u e s c a l c u l a t e d u s i n g p r o g r a m DHL ( u ) .d Va l u e s o b t a i n e d f r o m A- X f i t s f o r v " = O a n d I a n d e x t r a p o l a t e d f o r v=2,3,4 using ay = -0.00031.

The B-X bands were also fit alone, since the simple %S energy level ex-pressions adequately reproduce the spectra. However, the B-state constants areto be treated as effective parameters because of the strong % - Y;+ nteraction.These constants must never be used to derive RKR potentials.A. lEti+-X2x+ Adysis

The most recent vibrational bandhead analysis was performed by Rao et al. (3),but they made several vibrational band misassignments. In addition, the parity as-signment of the P, and P, bandheads was reversed. Extreme spectral congestionrendered it virtually impossible to disentangle a head of heads that occurs in theA v = 1 sequence. Also, small Franck- Condon factors (see Table II) for the (2,O)and (3, 1) bands prevented their observation by nonlaser methods, and led to anincorrect absolute numbering of the bands in the A u = 2 sequence. A list of meas-ured bandheads appears in Table I.

Even in our initial laser excitation survey of bandheads, detecting total fluores-cence, the heads belonging to the (2, 0) and (3, 1) bands were overlooked. Therapid decrease in Franck-Condon factors (Table II) with decreasing U evel out-weighs the increase in population. The weak (2, 0) and (3, 1) bands were buried

2 Proper assignment of eifparity ( t5) should have been possible on the basis of the known orderingof the A and B states in Cal. The presence of a fPP+ state to higher energy than theA ?l state suggests anegative value of the spin-rotation constant (7). This information is sufficient to determine the correctparity assignments of the P, and PC heads using the standard energy level expressions (6, p. 222).


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114 REISNER, BERNATH, AND FIELDTABLE VI

Equilibrium Molecular Constants for BY%+ nd X2X:+States

T eweWe XeB e x I O2

x I O 4a eD O x I O 8

Ye = x I O4

? c x I O4Y x 1 0 4YR , G,

X 2 2 + E S +

0 . 0 15 7 1 6 . 1 7 1 3 ( 3 0 )2 3 8 . 7 4 9 6 ( 3 3 ) 2 3 9 . 9 1 8 3 ( 3 7 )

0 . 6 2 7 8 9 ( 6 4 ) 0 . 6 4 9 8 5 ( 7 9 )6 . 9 3 2 5 4 ( 8 4 ) 7 . 1 7 9 1 6 ( 1 1 6 )2 . 6 4 0 ( 3 5 ) 3 . 2 5 5 ( 6 6 )2 . 3 4 b 3 . 0 9 9 ( 1 2 )

5 6 . 1 7 ( 9 J d - I 4 9 0 . 6 5 ( 2 2 )- o . 3 1 ( l l ) d 1 8 5 . 7 4 ( 3 1 )

_ _ - 9 . 4 9 2 ( 6 5 )2 . 8 2 8 6 _ _

a B s t a t e v a l u e s a r e e f f e c t i v e c o n s t a n t s t h a t r e p r o d u c e l i n e p o s i t i o n s .T h e s e c o n s t a n t s mu s t n o t b e u s e d t o g e n e r a t e p o t e n t i a l e n e r g y c u r v e sf o r t h e B2 E+ s t a t e .

b Va l u e c a l c u l a t e d u s i n g p r o g r a m DHL ( Q ) .c S p i n - r o t a t i o n e x p a n s i o n c o n s t a n t s o b t a i n e d f r o m e x p r e s s i o n

Y, = Ye + c $ ( V + ; , + y y ( v + $ 2 .d Va l u e o b t a i n e d f r o m A- X f i t s f o r v " = 0 a n d 1 .

lecular constants (Table VI), in the sense that the A- and B-state interaction hasdestroyed the simple mechanical meaning of the B-state rotational and vibrationalconstants. The B-X fits were made without consideration of contributions fromelectronic perturbation parameters, and hence do not remove these electronic con-tributions from the molecular constants. This problem will be discussed in the nextsection on the A-X system. Note that the X-state constants of Table VI are free ofperturbation effects and can be considered as mechanical constants.

The large vibrational dependence of y results from the increasing size of thenondiagonal Franck-Condon factors as v increases (Table II). This allows the in-teraction of vibrational levels of the A *II state lying above a given L evel of the Bstate to partially cancel the effects of the A % vibrational levels lying below this ~1.B. AII-X*X+ Anahsis

The appearance of the A-X band system of CaI is characteristic of a transitionbetween a Hunds case (a) *II state and a *Z+ state. The Qprr, P,,,,, P,, ndQmv fm P,2ff branches belonging to the 2II3,2and *II,,* subbands, respectively,all form bandheads shaded to the violet. Laser-induced fluorescence was observedin the (0, 0) and (1, 1) bands of the A v = 0 sequence. The bandheads are listed in


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115TABLE VII

A*E-X*Z+ Bandheads (cm-l)b a n d P l z f f Ql Z e f + P l e e

ap 2 f f P 2 1 e e Q 2 e f

( 0 . 0 ) 1 5 5 7 2 . 8 7 1 5 5 8 8 . 5 3 1 5 6 3 7 . 6 6 1 5 6 4 7 . 1 2 I 5 6 4 7 . 3 5( I , l ) I 5 5 7 8 . 1 6 1 5 5 9 2 . 7 1 I 5 6 4 0 . 5 9 I 5 6 5 0 . 0 1 I 5 6 5 0 . 2 2

- IAc c u r a c y + O. Ol c m .

a Q 1 2 e f a n d Plee h e a d s a r e o v e r l a p p e d .

Table VII. The large BII - Z+ interaction causes the Qlzef and P,,, heads to occurat very low J and hence prevents their resolution. Rotational assignments in theA-X system were made in the same fashion as in the B-X system, with the addedadvantage that good X-state constants were available. The measured line positionsfor the (0, 0) and (1, 1) bands appear in Table VIII.Attempts were made to fit the A -X ransitions using the standard 211Hamiltonianwith A-doubling parameters derived using the Van Vleck transformation (17). Thisapproach was not successful because the A211,,2-A211,,2eparation of -60 cm-is about the same size as the -!JO-cm-1 A 211-B2Z+eparation. The two spin com-ponents of the A state thus have significantly different separations from the B212+state. The usual definition of a single set of o, p, and q parameters for both spincomponents of the A 211tate is clearly not appropriate in the case of CaI. In addi-tion, the 211 - 2Z+ interaction is so large that 1 ) - 2B, thus an approach basedon second-order perturbation theory will neither have the correct functional formnor provide physically meaningful parameters.

The A doubling was fitted by explicit introduction of perturbation matrix ele-ments, n and r, that connect the A Illnd B2Z+ tates (14):qo:vc= (l/2)( nIIv (B(R)/+ 2Z+v),[tip'(1/2)(n"IIv'IA(R)l+jn"Z+v).The interaction matrix elements are

(2d(2b)

H(%,z, 22) = &$ - r)(J - l/2) (e)= 5 + 7(J + 3/2) (f), (3)

H2b,2 7 2Zc) = -r)[J 2 + J - 3/4y. (4)Since the A- and B-state potential curves are similar, the interaction is approxi-mately diagonal in v for u = 0 and 1. Thus the major portion of the A doubling ofv = 0 of the A state results from v = 0 of the B state, so the (0,O) A-X and B-Xbands were fitted together. Similarly, the (1, 1)A-X and (1, 2) B-X bands [the(1, 1) B-X band was not analyzed] were fitted together.

It was found that 5 was badly correlated with TX, Tn (band origins), A, andr) and so could not be independently determined. Equations (2) suggest that


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116 REISNER, BERNATH, AND FIELDTABLE VIIIa

Observed Transitions in A TI,,,-X*Zt (0, 0) Subband (cm-)

Rlee AY R12ff Au Qlfe AU Pl2ff A,,

a Observed mmus calculated in lCi3 cm-,Lines marked with an asterisk ore blended


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CaI A2n AND S2~+-X2S+TABLE VIIIb

Observed Transitions in ATI,,,-X2~+0, ) ubband (cm-)

117

J R21ee AVO R2ff A, Q21fe AV P2ff Au

o Observed minus colculoted in 10W3crn-.Lines morked with on ostertsk ore blended.


12/18


13/18

CaI A *n AND B2Z-XT+TABLE VIIId

Observed Transitions in A *II,,,-XI+ (1, 1) Subband (cm-)

119

J R2lee Av REff fAV Q2lfe Al/ P2ff Al/

a Observed minus calculated in 10-3cm-.Lines marked with an asterisk are blended.


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120 REISNER, BERNATH, AND FIE LDTABLE IX

D~pe~u rbed A-X, B-X Constants (cm-)

= 0 1 2B2E+ B v x I O* 7 . 1 3 7 4 7 ( 9 3 ) 7 . 0 9 7 9 7 ( 1 7 6 ) - -

Dv x I O8 2 . 3 4 4 ( 2 4 ) 2 . 0 5 4 ( 3 5 ) - _

llX IO2 6 . 2 3 1 1 ( 1 0 ) 5 . 7 7 5 8 ( 1 2 ) _ _Interaction

Ma t r i x YJ x ia7 - 1 . 7 2 ( 2 3 ) - 9 . 3 2 ( 4 9 )- _

E i e m e t l t s E aY 4 0 . 4 8 2 8 3 7 . 8 3 7 7 - _

E D" x l o 4 0 . 3 9 ( 1 1 ) 2 . 0 3 ( 2 4 )- _

R2ZB y x I O2 7 . 0 3 5 2 3 ( 4 5 ) 7 . 0 1 3 6 9 ( 9 3 ) - -Dv x I O8 2 . 4 0 1 ( 1 1 ) 2 . 6 0 4 ( 1 5 ) - _

A 4 5 . 7 0 7 5 ( 2 9 ) 4 6 . 0 8 6 0 ( 3 2 ) - _"A x I O 5Dv - 1 . 1 8 ( 4 3 ) - a . 7 2 ( 8 7 )

- _

P x I O2 - 1 . 3 6 7 4 ( 3 9 ) - l . l 4 7 5 ( 5 6 ) - _

X 2 E +B x IO2 6 . 9 1 8 2 7 ~ 1 7 ~ 6 . 8 9 1 9 2 ( 2 5 ) 6 . a 6 9 2 6 ( 3 3 )D" x I O8 2 . 3 4 b 2 . 3 4 b 2 . 3 4 bY x IO4 5 6 . 0 0 7 ( 6 9 ) 5 5 . 6 9 8 ( 8 1 ) 5 5 . 3 5 =

Nu mb e r s i n p a r e n t h e s e s r e f e r to lo u n c e r t a i n t i e s .a De t e r mi n e d b y t h e a p p r o x i ma t e e x p r e s s i o n 5 = $ / Y e + , + AT I & , .b F i x e d a t v a l u e s d e t e r mi n e d b y p r o g r a m DHL ( Q) .= Fi x e d a t a v a l u e l i n e a r l y e x t r a p o l a t e d f r o m v " = 0 a n d I levels.

ct. = A, ( UPrI) /u(c+))(v(TI) /B /u(*c+)) %where A is the ATI spin-orbit constant. The (u(T) IB / u(Z))l( v(TI) 1u(2)) ratioof vibrational integrals was computed from the vibrational wavefunctions. Theratio was found to be within 1% of Br,, so

In subsequent fits, the parameter ,$ was fixed at the value determined from Eq. (6).This procedure removed the correlation between 5 and the origins as well as be-tween .$ and g. While 3 and f account for most of the interaction between the Aand B states, there still exists a nonnegligible interaction with other (Au # 0)vibrational levels. This is especially true for v > 0, because the Franck-Condonfactors become increasingly nondiagonal as u increases.


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CaI A2Il AND II%+-X*X+ 121TABLE X

Deperturbed Band Origins (cm-)

(v .v) A*Ii - X*2+ s*z+x3+(O,O) I5 625 .905 (2) 15 702 .326(3)(!,I) 15 628.549(2) 15 705.124(3)

Nu mb e r s i n p a r e n t h e s e s a r e l o u n c e r t a i n t i e s .

Residual p and y parameters must be inserted into the Hamiltonian to accountfor the remaining interactions with A u f 0. However, strong correlation betweenp and y prevents their simultaneous variation. This correlation was artificiallybroken by setting y(residua1) to zero. Consequently, 7, 5, and p(residual) areeffective parameters that have accomodated the small interaction parametrized byy(residua1). The results of this direct interaction fit are the deperturbed constantsof Table IX.It was found necessary to include distortion terms in the interaction parameters:

qJeff> = 7), + Q,J(J + l), (7a)&deff) = to + tD,J(J + 1). Cb)

Band origins determined from the rotational fits are presented in Table X. Thedifference between the deperturbed (0,O) band origin and the effective band originin the B-X transition would correspond to the value of the parameter ox (8)) had asecond-order perturbation theory approach been possible.The values of B. and B1 in the A and B states, determined from the combinedA-X, B-X fits, allowed determination of true mechanical constants, free ofelectronic perturbation. The results are shown in Table XI. The rotational constant(Y,was determined from B. and B 1, and used to determine the vibrational constanto,x, from the Pekeris relationship (6). The ground-state constants (0: and w:xs)and the (0, 0) and (1, 1) band origins determined from the combined fits alloweddetermination of values for AG;,* and then o: using w:x: (Pekeris). T, valueswere then obtained from the standard expression containing T,,, w,, and 0,x.:

(8)The deperturbation of the A and B states can account for a puzzling feature of theA doubling of the AYI state. For CaI, the e A component is higher in energy than

thef component of the YI,,, spin component, as expected, butfis higher than e inthe 2II3,2component. For CaF and CaBr (10, 11), e is higher thanf in both A 2111,2and A 2II3,2 spin components. When o, p , and 4 are used to try to fit the A doublingof CaI A *II, p is negative but q is positive. This is disconcerting, because examina-tion of the summation definitions of p and q, derived using the Van Vleck trans-formation, indicate that p and q must have the same sign (8). The direct perturba-tion approach accounts for the unusual A-doubling pattern with physically reason-able values of 7 and 5.


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122 REISNE R, BE RNATH, AND FIELDTABLE XI

Depertu rbed Equilibrium Molecular Constan ts for ATI and B21+ Sta tes

l a I 5 624.67(5) 15 7 0 0 . 5 2 ( 1 2 )eaw 241.19(7) 242.63(17)e

uexe ( P e k e r i s ) 0.53(5) 1.17(12)B e x I O2 7.0460(14) 7.1572(22)cre x IO4 2.15(10) 3.95(20)Do x ID8 2.40(l) 2.34(2)Re (h 2.8057(3) 2.7839 (4)

De p e r t u r b e d c o n s t a n t s f o r X2 E + a r e i n T a b l e V I . Nu mb e r si n p a r e n t h e s e s a r e l o u n c e r t a i n t i e s .a D e t e r mi n e d u s i n g w&b ( P e k e r i s ) wh i c h wa s a s s u me d t o

h a v e a n u n c e r t a i n t y o f 1 0 %.

The deperturbation of the A-X and B-X transitions is not entirely satisfactory.The obs. - talc. column of Table VIII is not completely random, although thevariance of the fits indicate that lines are fitted to within their estimated experi-mental error. In addition, the vibrational variation of several parameters, 7, Q,5, and &, in particular; seems unrealistically large (Table IX). These problemsresult from inclusion of only a single pair of II, 5+ vibrational levels in theeffective Hamiltonian matrix. The magnitudes of the perturbation parameters,however, seem reasonable in the sense that r)/q, = B/D and I[/&1 = A/A,.C. Cal Orbital Character

The interaction matrix elements 7 and ,$ provide some insight into the orbitalcomposition of the A 211and B2Z+ states. It is possible to define a nonintegral leff27- = (Mleff + 1))BIIthat characterizes the 211 - 2C+ interaction. If the molecular orbitals are ML com-ponents of pure atomic orbitals, then f,rr will have integer values and the states aresaid to be in pure precession. Note that the converse of this statement is notnecessarily true (20).For CaI, feff = 1.35, indicating some d character in the A and B states. This valueof leffcan be combined with the ratio of the A -X and B-X transition dipole moments(29) to estimate the excited-state molecular orbital composition (20). The resultsare that the A 211state is 70% 4p7r (Ca) and 30% 3d7r (Ca) while the B2Z+ stateis 57% 4pu (Ca) and 43% 3du (Ca). The A- and B-state mixing coefficientscan be used to estimate a more accurate value of 5, the off-diagonal 211-2Z+ spin-


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CaI AW AND II%-XZ+ 123orbit matrix element. The A- and B-state wavefunctions are written as

$(B*Z+) = e [4p(r (Ca)) - (1 - e2)11*3da (Ca+)),$(A%) =fl4pr (Ca)) - (1 -f2)11213d~ (Ca)). (10)

The diagonal spin-orbit interaction is given byA = f 5~ + (1 - fK&. (11)

With {J&d = 6.1, determined from the Ca+ atom, A = 45.7 cm-l for CaI, andmixing fractions 0.70 (4~) and 0.30 (3d), then cdP = 61 and tSd = 10 cm-. TheAL.S operator acting between the AII and BZ+ states gives

5 = f (AI,) = y efi& + 7 (1 - e*)*(l - f2)112&,d. (12)This leads to ,$ = 31 cm-, which is 22% smaller than the value of 40 cm- pro-vided by Eq. (6).

The value of 5 calculated using Eq. (12) is different from that obtained from Eq.(6) because the A and B states are not pure p or d states. Experimentally, the twovalues cannot be distinguished because the variance of the fit is insensitive to themagnitude of [. For instance, changing 5 to 36 cm- changes the variance byless than 10%.

The values ofp(res) and -&es), due to interaction with Av # 0, can be estimatedfrom the values of 77and 6 (U = 0), ( ~(~2) 1v(*II)), and B,,. In particular, re-taining only the AV = 1 term:Po(res)= h lO510 (13)

~ O; V l , , 2 - v ' l , r y +

yo(res) = f h o 1 5 0 1 Bo,, (14)VI,pn,,2 vo,!p+The results are P,(res) = -0.0021 cm- and yo(res) = +0.0084 cm-. Since onlythe difference between yo(res) and P,(res) could be determined and yo(res) was setequal to zero in the fit, P(res, eff) = -0.011 cm-. This compares favorably withthe observed value of -0.014 cm-.

IV. CONCLUSION

CaI is suited neither to classical experimental techniques nor to classical tech-niques of spectroscopic analysis. Extreme spectral congestion makes single-modelaser excitation spectroscopy and narrow-band fluorescence detection a necessity.The small energy separation between the A *Ill nd B*Z+ states requires the use ofdeperturbation techniques on a system that would not normally be considered tobe perturbed because of the absence of level crossings. This deperturbation isnecessary to fit the A-X data and derive estimates of true molecular constants (8)for the A and B states. In particular, this allows calculation of Franck-Condonfactors, quantities of value in the determination of product distributions of chemical


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124 REISNER, BERNATH, AND FIELDreactions. Of perhaps even greater value is the insight obtained into the orbitalcomposition of the electronic states.

ACKNOWLEDGMENTSWe thank Bernar d Pinchemel and Claude Dufour for commu nicating their preliminary CaIA211-X*X+

fluorescence results. P .F.B. was support ed, in part , by a Natu ral Sciences and Engineering ResearchCouncil of Canada postgraduat e fellowship. Support for this resear ch was provided by Grant s AFOSR-76-3056, NSF CHE -78-18427, an d CHE -78-10178.

RECEIVED: December 30, 1980REFERENCES

I. 0. H. WALTERS AND S. BARRATT, Pr oc. Roy. Sot. Ser. A 118, 120-137 (1928).2. P. S. MIJ RTY, Y. P . REDDY, AND P. T. RAO, J. Phys. B. 3,425-429 (1970); L. K. KHANN A ANDV. S. DUBEY, Indian J. Pure A&. Phys. 11, 375-376 (1973); A. B. DARJ I AN D S. P. VAIDYA,

Indian J. Pure Appl. Phys. 11, 923-925 (1973).3. M. L. P. RAO, D. V. K. RAO, P. T. RAO, AND P. S. MURTY, Acta Phys. Pal. A54,343-353 (1978).4. P. M. RYBSKI, Publ. Astron. Sot. Pac. 85, 751-755 (1973).5. P. F. BERNATH, B. P INCHE MEL, AND R. W. FIE LD, J. Chem. Phys. 74, 5508-5515 (1981).6. G . HE RZBERG, Spect ra of Diat omic Molecules , 2nd ed., Van Nostr an d-Reinhold, New York,

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A. J . ME RER, D. A. RAMSAY, J . ROSTAS, AND R. N. ZARE, J. Mol. Spectrosc. 55,500-503 (1975).16. R. S. MULLIKEN AND A. CHRISTY, Ph ys. Rev. 38, 87-119 (1931).17. A. J . KOTLAR, R. W. FIE LD, J . I. STEI NFE LD, AND J . A. COXON, J. Mol. Spectrosc. 80, 86-

108 (1980).18. D. L. ALBRITTON, W. J . HARROP, A. L. SCHME LTEKOPF ,AND R. N. ZARE, J. Mol. Spectrosc.

46, 25-36 (1973).19. P. J . DAGDIGIAN, H. W. CRUSE , AN D R. N. ZARE, J. Chem. Phys. 60, 2330-2339 (1974).20. P. F. BERNATH, Ph .D. thesis, Massa chusett s Inst itut e of Technology, 1980.

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