Rotational analysis of the d 3∆i-a 3 Πr transition of

carbon monosulfide

D. Cossart

To cite this version:

D. Cossart. Rotational analysis of the d 3∆i-a 3 Πr transition of carbon monosulfide. Journalde Physique, 1980, 41 (6), pp.489-502. <10.1051/jphys:01980004106048900>. <jpa-00209272>

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Submitted on 1 Jan 1980

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489

Rotational analysis of the d 30394i-a 303A0r transition of carbon monosulfide

D. Cossart

Laboratoire de Photophysique Moléculaire du C.N.R.S. (*),Université de Paris-Sud, Bâtiment 213, 91405 Orsay, France

(Reçu le 27 novembre 1979, accepté le 15 février 1980)

Résumé. 2014 L’utilisation d’une nouvelle source d’émission a permis d’obtenir le spectre de la transition d 30394i-a 303A0rdu radical CS dans le proche infrarouge. 11 bandes ont été analysées (v’ = 5-12, v" = 0-2). Les transitions inter-système vers l’état fondamental avaient précédemment fourni des données surtout sur les sous-états 03A9=1. Avecles nouveaux spectres, des données expérimentales sont obtenues sur les composantes 03A9 ~ 1.

Un des résultats du traitement de déperturbation des niveaux vibroniques impliqués dans la transition d-a est ladétermination du paramètre spin-orbite vrai ainsi que du paramètre spin-spin dépendant de la parité. Ces valeurssont comparées avec les valeurs théoriques correspondantes. L’étude des perturbations du second ordre sur lessous-niveaux de l’état 30394 a conduit à la localisation en énergie de l’état 10394, jusque-là non identifié. Les constantesdéperturbées des états a 303A0 et d 30394 sont les suivantes (toutes données en cm-1):

Abstract. 2014 Use of a new emission source facilitated recording the near infrared spectrum of the d 30394i-a 303A0rtransition of the CS radical. Eleven bands have been analysed (v’ = 5-12, v" = 0-2). Intersystem transitions tothe ground state have previously given information mainly on the 03A9 = 1 components.The new spectra provide experimental data on the 03A9~ 1 components. As a result of the deperturbation treatmentof the vibronic levels involved in the d-a transition, improved values are obtained for the true spin-orbit andparity-dependent spin-spin parameters. They have been compared with the corresponding theoretical values.The study of second order perturbations of the 30394 sublevels allowed an estimate of the energy of the 10394 state notpreviously identified. The deperturbed constants for the a 303A0 and d 30394 states are the following : (all data in cm-1).

J. Physique 41 (1980) 489-502 JUIN 1980,

Classification

Physics Abstracts33.20K

1. Introduction. - The diatomic molecules belong-ing to the IV-VI or V-V groups in Mendelev’s classi-fication present favorable circumstances for the

study of spin-orbit perturbations, since vibronic

(*) Laboratoire associ6 a l’Universite Paris-Sud.

levels of the first excited electronic configurationn4 O’n*(a 3n, A l II states) are interspersed among -the vibronic levels of the second excited configurationn3 0’2 7r*(a , 3,E +, d 34, e3,E -, A ’ 1 E+, 1.r -, 1 L1 sta-

tes). It has been shown [1] ] that the electronic spin-orbit matrix elements between a state belonging tothe first group and a state belonging to the second

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01980004106048900

490

group, are proportional to a single integral involvingthe wavefunctions of the 7c and a outer orbitals i.e.,in the case of CS :

where al + is the equivalent one electron spin-orbitoperator.The same can be said for the electronic rotation

matrix elements which may be obtained, in the singleconfiguration approach as a function of an 1-uncoupl-ing integral

The coefficients of proportionality which relate thephenomenological spin-orbit and rotation-orbit matrixelements to the a and b values can be calculated appro-ximately assuming on one hand, the separation of theelectronic and vibrational integrals (R-centroid appro-ximation), and on the other hand a single electronicconfiguration with the same orbitals for all the states.

For rovibronic levels I u7r *, v, J &#x3E; and I n3 7r*, v’, J &#x3E;the ratio :

characterize approximately the relative magnitudeof rotation-orbit to spin-orbit interactions.The particular situation of the CS radical is empha-

sized by comparison with isoconfigurational species :

i) The homonuclear molecules as N2, P2, As2...do not present the corresponding spin-orbit pertur-bations in their spectra, since the states arising fromthe two first excited configurations have different

symmetry relatively to the exchange of the nuclei.

ii) In the heavier species as : CSe, SiS, AsN, theratio s is so small that the rotational perturbationparameters can be neglected in the Hamiltonianmatrix.

iii) In the isoelectronic radical SiO, the polariza-tion gives rise to a large spatial separation of 7r and 6orbitals leading to small n I al + I a &#x3E; integrals sothat forbidden transitions are not observed.

iv) Finally, the molecule which is most similar toCS is carbon monoxide. The perturbation effectsin the valence states of this latter molecule have been

already extensively studied, specially by Field et al. [1] ]and Hall et al. [2].

As the differences of behaviour between CO andCS are due almost exclusively to different orders ofmagnitude of spin-orbit and rotation induced inter-actions, the CS radical appeared to be the best speciesto further test the fine structure model proposed inthe case of CO.

It should also be remarked that Penzias et al. [3]have established, by microwave spectroscopy the

presence of CS in dense regions of the interstellar

medium and shown that CS appears very often ininterstellar cloud reactions. Some of the propertiesof CS discussed here could be of interest in further

astrophysical work.The new spectra presented here are in the visible

near-IR region (7 000 to 9 000 A). The particularinterest of these spectra are the following :

a) The detection of radiation of extraterrestrialorigin is more easy in the long wavelength range thanin the UV region where the optical spectra of CS wereobserved up to now. These new line measurementsmight help in the observation of CS in astrophysicalspectra.

b) The knowledge of long wavelength transitions,with the metastable a 31I state as the lower state,could permit selective laser excitation and lifetimemeasurements of triplet levels.

c) The analysis of the IR bands attributed to thed 3,j -a317 transition provide new experimental dataon the Q =1= 1 triplet sublevels.

A significant gap existed indeed in the data concern-ing the 3 nand 3,j states obtained from the UV spectra(1 800 to 3 850 A). In this region all transitions involv-ing triplet states are intersystem transitions withthe ground state X ’.E+ as the lower state. Thesetransitions borrow their intensity mainly from theA 1 ll-X 1.r+ system.

Direct spin-orbit coupling with the A ’17 state

favors the appearance of the subbands involvingQ = 1 triplet state components. The other subbandsmay then borrow intensity from the S2 = 1 subbandsif spin uncoupling by rotation is sufficient. The inten-sity ratio between the bands involving Q =1= 1 andQ = 1 upper levels is about 16 times smaller in CSthan in CO, causing the relative scarcity of experi-mental data on the 3nO,2 and 3L12,3 substates whencompared to the CO case.The deperturbation treatment of the first 9 vibra-

tional levels of the A 1 n state, which will be publishedshortly by Bergeman and Cossart [4] is one of themost complex cases in diatomic spectroscopy and hasproved to require knowledge of the term valuesobtained in the present work. ,

Though the principal results of this work are men-tioned again in the longer report [4], the analysisgiven here is relative, on one hand to a particulartransition appearing in a different spectral region ofspecial interest, and on the other hand to a moredetailed deperturbation treatment of the 3 n and 3 L1levels involved. This paper is part III of the CS valence-valence perturbations analysis. After pionier workon the rotational analysis of the CS optical spectraby Barrow et al. [5], and the observation in the vacuumUV of the A’ ’Z+-X 1.r+ transition by Bell et al. [6],part I and II of the present series have been publishedrespectively by Cossart and Bergeman [7] who haveestimated the off-diagonal spin-orbit and spin-spinparameters for the valence states and by Cossart

491

et al. [8] who have given the rotational analysis of thea 31I-X ’E’ bands corresponding to the first vibra-tional levels of the a 3Il state (v’ = 0-4).

2. Experimental. - The new spectra were obtainedby means of an emission source already used in theproduction of fluorobenzene ion spectra analysedby Cossart-Magos et al. [9]. The details of the experi-mental device are given by D. Cossart [10]. A lowpressure (10-2 to 10- 3 torr) d.c. discharge is establish-ed between plane parallel electrodes 1 cm apart andsubmitted to a 500 to 1 000 G magnetic field perpen-dicular to the electric field. The resulting confinementof the cathodic glow causes the discharge to operateat lower pressures than in the absence of magneticfield and also lowers the cathode fall in the cathodicdark space (hollow cathode effect). After the dis-

charge is initiated, the potential between electrodes isabout 100-200 V and the electric current is 20 mA.If pure carbon disulfide is introduced into the dis-

charge tube, one obtains intense spectra of CS2(A-X and B-X systems) along with CS A 1 ll-X 1 E+bands of low intensity. If helium is added to the CS2,the CS’ bands disappear almost completely, whereasthe CS bands, in particular those of the a 311_X 12:+and d 3d-a 3II systems, appear with intensity muchincreased relative to those of the A-X transition when

compared to the spectra obtained previously byCossart, Horani and Rostas [8] in hot cathode dis-charge tubes.The spectra of the d 3A-a 311 transition were

photographed on Kodak IN plates, ammonia sensi-tized, by means of a Ebert 3.40 m spectrograph operat-ing in the lst order of a 1 200 lines/mm plane grating.Inverse spectral dispersion is of the order of 2.2 A/mm.With a slit of 30 Il, lines 0.08 cm -’ apart can be resolv-ed. The measurement accuracy of the visual semi-automatic comparator used, is better than 0.05 cm-1.

3. Vibrational and rotational analysis. - The assign-ment of the new observed bands is unambiguoussince term values for 3 A 1 sublevels up to v = 10and for the 3HJ states are known from triplet-singlettransitions in the ultraviolet. The UV spectra alsoprovide some information on the substates 3 A2and 317o.The d 3 A i-a 3 n transition shows 3 subbands

3A1-3no, 3A2-3ll1 and 3A3-3ll2 which appear in thisorder for a given vibrational transition and increasingwavelength. Absence of branches with åE =F 0 con-firms that the two states belong to Hund’s case aand the order of the subbands is consistent with a

regular 3I1 state and an inverted 3d state, as observedin the UV spectrum and as expected from the elec-tronic configuration.Each subband consists of 6 branches Re, Rf, Pe,

Pf, Qe and Qf, all of which are red degrated. The eor f index refers to the parity of the a 3II levels involv-

ed. The A doubling in the d 3 A state is always lessthan the experimental resolution and the same canbe said for the sublevels 3I11 and ’172- On the contrary,the A doubling appears to be greater than the experi-mental resolution in the 3 no sublevels., As a conse-quence the rotational lines of index e and f are super-imposed except in the case of the subbands 3 A1-3 nowhere the separation between the lines of the branchesRe, Pe, Qe and Rf, Pf, Qf is equal to the A splitting ofthe 317o state. This, added to the fact that the 3 A1 1levels have another deactivation channel, via coupl-ing with A ’H levels and intersystem transitions,makes the 3 A1 _3 n 0 subbands much weaker than the3 A2,3-3 n 1,2 subbands. For this reason, the 3 A1-3 nosubbands could not be measured in the bands (10, 2),(11, 2) and (12, 2).Table I presents separate Deslandres tables for the

3 classes of subbands of the d 3d-a 317 system. Theentries correspond to the prominent R-branch heads.The spectrum of the (7, 0) band of the d 3 A-a 3IIsystem is shown in figure 1. Table II gives the rota-tional assignments of this (7, 0) band. The correspond-ing term values have been useful in the fitting ofA lIl (v = 2) levels and the quasi-degenerate sub-

Table I. - Deslandres tables of the d 3 Ai-a 3 n r sub-bands (all data in cm-1).

For easier identification, the most prominent R-branch heads aregiven. When these branch-heads are not easily discemable, we givethe frequency of the shortest wavelength R-line measured.

492 JOURNAL DE PHYSIQUE

493

Table II. - Measured lines for the d 3 J-a 3 Il{7,O) band (all data in cm-1).

states. The deperturbation treatment of these levels,as well as the term-values corresponding to the other10 bands, will be given elsewhere by Bergeman andCossart [4].

Table III shows the Franck-Condon factors calcu-lated from the d3 L1 and a 3II R.K.R. potentialcurves obtained via deperturbed molecular parame-

Table III. - Franck-Condon factors for the d 3 L1i-a 3nr transition.

The underlined figures correspond to observed bands.

ters. In the spectral interval under consideration

(7 000 to 9 000 A) the observed bands are indeedthose of largest Franck-Condon factors. Moreover,it should be mentioned that for the e ’2: --a 317transition, analoguous calculation of Franck-Con-don factors leads to a prediction that the (3, 0), (4, 0)and (5, 0) bands of this system could be observed.In fact, these bands do appear at the proper wave-lengths but with much less intensity than the d 3,j -a 311system so that the rotational analysis proved impossi-ble. Most unassigned lines in figure 1 belong to the(3, 0) band of the e 3L --a 317 system. It should benoted that for 3 L:I: states belonging to Hund’s case b,spin-orbit interaction with the A lIl state is of thesame order of magnitude for the 3 componentsof each 3 L state and, as a consequence, informationabout each of these sublevels is accessible from the

triplet-singlet transitions.

4. Deperturbation of the a 3H and d 3d states. -

The analysis of the interactions between the a 3IIand d 3d vibronic levels and the neighbouring statescan be split into 2 parts corresponding to the 2 steps ofthe deperturbation treatment.

4.1 FIRST ORDER DEPERTURBATION. - The dimen-sion of the corresponding Hamiltonian matrix is

494

equal to the number of neighbouring substates whichcross the 3II or 3 L1 levels or which interact so stronglythat second order perturbation formulae are incor-rect.

The results obtained from fitting to such a modelare first order deperturbed molecular parameters ofthe a ’17 and d 3L1 sublevels and off-diagonal inter-action matrix-elements between the states considered.

In contrast with the lower vibrational levels of thea 3I1 state, the d 3L1 upper levels are interspersed amongvibronic levels of the A 1II and other triplet states.As a consequence, the d 3 L1 experimental term valuesmust be fitted together with the term-values of theneighbouring states which are obtained from the UVspectra. This deperturbation treatment involvingas large as 15 x 15 Hamiltonian matrices will be

presented elsewhere by Bergeman and Cossart [4].Only the results concerning the first order deperturb-ed d 3d parameters are used here. In this paper arepresented only the first order deperturbation detailsfor the a 3I1 vibrational levels involved in the d-atransition. Although such a deperturbation was

Table IV. - Summary of the data available on thea 317 substates.

X and d letters indicate that for a given 3nn(v) substate at leastone band was observed respectively for the a-X and d-a transition.

e) Only the R-branch heads in the a-X bands were observed.

already reported by Cossart et al. [8], the new dataobtained from the triplet-triplet transition justifieda new determination of the molecular parameters.Table IV presents schematically the whole of therotational data now available on the a 3n (v = 0,1, 2)levels.The model used to represent the a 31I (v = 0, 1, 2)

term values is the classical 3 x 3 rotational Hamil-tonian matrix of a 3Il state given in table V. Becauseof the isolated position of the a 311 (v = 0, 1, 2)levels, the effects due to states which may interactwith these levels are treated by 2nd order perturba-tion theory. The parameters characterizing these

perturbations are defined as follows :

where and

where 1 Au = 1 n 1, 1EÓ, 1 - 1 A2.Theoretical calculations of the qv parameters show-

ed that their contribution to the diagonal energiesmay be on the order of only 10-4 cm-’ and, conse-quently, these parameters were neglected in our

model calculations.

Table V. - Rotational energy matrices for a 3n state; x = J(J + 1).

The matrices are symmetric. Only the upper triangle is given.Upper and lower signs refer to the Wang sum and difference functions I/l/2 { I Q &#x3E; :t I - Q &#x3E; } respectively and give the e and f rota-

tional levels.The spin-rotation, spin-spin (except ags) and electronic-rotation parameters are neglected in the diagonal matrix-elements. The q para-

meters are neglected in the off-diagonal matrix-elements.The phenomenological parameters used are defined as :

495

For a given vibrational level a 3n(v), the numberof parameters introduced in the least-squares fitwas reduced to 9 phenomenological parameters foreach vibrational level : the 4 origins To,,., Tof, T,and T2, and the 5 rotational parameters B, D, Ao,y’ and p’ as defined in table V.

Except for the cx. spin-spin parameter participat-ing to the splitting of the 3 n oe e levels, all the spin-spin and spin-rotation parameters as well as thesecond order p(3 A) parameters are omitted in thevibronic origin expressions, since their calculatedvalues are several orders of magnitude smaller thanthe experimental uncertainty.

In principle, with the data we have on the v = 0, 1and 2 levels of the a 3I1 state, we should be able todetermine 3 x 9 = 27 fine-structure parameters.However, because of strong correlation between the ADand p’ parameters and, in the absence of data on the Adoubling in the a 3n, v = 2 level, we chose to reducefurther the number of free parameters by fitting toge-ther the entire collection of experimental data forlevels v = 0 through 2 of the a 3II state. In this simul-taneous fit the number of free parameters for the3 vibrational levels was reduced to 20. The followinghypotheses were made :

1) Deperturbed B and D parameters are consider-ed to be linear functions of v :

Moreover, calculation of fl, using Dunham’s formulagives 13e = 0.8 x 10-8 cm-1; accordingly wasfixed at this value. In fact, the introduction of a 13evalue in the range 0-0.8 x 10-8 cm-1 contributedless than 0.02 em -1 to the eigenvalues at J = 40.

2) The true spin-rotation y and spin-spin as

parameters as well as the second order parametersp(3d) are assumed to be identical for all levels a 3Il(v = 0, 1, 2). The parameter p(32 -), for which anapproximate calculation gives 4 x 10-4 cm -’, repre-sents a perturbation of the diagonal elements on theorder of 10-5 cm-1 for J = 40 and, as a consequence,was fixed equal to zero in the fitting procedure.

3) The parameter o(3E+) for v = 2 was fixed at itscalculated value - 1.68 cm-1 because of lack of dataon the a 3f! Or’ V = 2 levels.

Table VI gives the results of a simultaneous fitwith 20 free parameters, 12 of which are vibronic

origins. A comparison is made between fitted andcalculated values of the eight other fine structure

parameters. The agreement is satisfactoring for thedistortion parameters. It should be noted, to under-stand the small discrepancies observed for the p(3A)parameters, that the corresponding calculated valuesare obtained using ab initio results of Robbe et al. [1 ] for the rotation-electronic integral b = 2 n 11 ’ 17 (J).The uncertainty in the experimental determination [7]of b is indeed too large to allow the use of experimen-tal b-values in the p(3 A) calculations.

Table VI. - Molecular parameters obtained from the simultaneous fit for the a 3n (v = 0, l, 2) levels (all datain cm-1).

Calculated values are obtained from the follov references :a Classical formulae given by Herzberg [17];a’ AD = 2 DaAI(ae + 6 Bel/we) Veseth [14] ;c

y m A with M = ratio between the mass of the electron and the CS reduced mass. Van Vleck [18] ;Ax Af

d peA) = bH!;’D(Rx) v I v’ &#x3E; v 12 V’)/[Een, v) - Ee A, v’)] where 3 A = 3E +, 3-Y -, 3d.r’ R{ H;b(Rx) : experimental value of the electronic spin-orbit parameter at the potential curve crossing point ;

b : ab initio values calculated by Robbe and Schamps [11].f-symbol indicate fixed parameters. Stars indicate fitted first-order deperturbed vibronic origins. Figures in parentheses represent

3 times the standard deviation in units of the last significant digit.

496

I.S

v

J!1

0

IIv

II3

ae

es

v

m-

se

v

s

ted

Ca

e

saT

497

In table, VII are given the observed and calculatedterm-values of the a 3n (v = 0, 1, 2) state levels

(overall standard deviation : 0.05 cm-1 ).

4.2 SECOND ORDER DEPERTURBATION. ESTIMATIONOF THE « TRUE » MOLECULAR PARAMETERS. - Whencalculations or estimations can be done for the 2ndorder shifts of the vibronic origins, one can deter-mine improved values for the effective vibronic para-meters which are as near as possible the true mole-cular parameters.

In this particular case, the goal of the second orderestimates was :- the determination of reliable values for the

diagonal spin-orbit parameters and their variationwith v,- the determination of a deperturbed value for

the parity dependent spin-spin parameter ass forwhich ab initio calculations have been done,- the location of the unobserved 1 d state from

the study of the relative separations of the three 3 J

components.A. The a 3n state. - The exact calculation of

second order spin-orbit shifts in the R-centroid

approximation :

requires knowledge of the potential curves of theelectronic states involved as well as the electronic

part of the off-diagonal spin-orbit matrix elementHso for any internuclear distance,

In table VIII, the perturbing states are dividedinto 3 groups according to whether :

I) the potential curves and H!’D are both experi-mentally known;

II) only the potential curve is experimentallyknown;

III) both the state position and the spin-orbitinteraction must be estimated from ab initio calcula-tions.

Concerning the first group of states which has

already been extensively studied [4, 7], table VIIIgives the 01.’( 1 n) and the 01..(3 A = 3_y+, 3_y -, 3 A)values calculated with R.K.R. potential curves andwith the off-diagonal electronic spin-orbit parametersHelSO determined experimentally by Cossart and Ber-geman [6]. The shift due to the A 1 n state

is determined by the single-configuration, fixed orbi-tal approximation. Ab initio calculations by Robbe [12] ]confirm the validity of the approximation

where A is the spin-orbit constant of the a 3II state.The 0v(3A) shifts due to the triplet states were

Table VIII. - Second order spin-orbit interaction between the a 3II (v = 0, 1, 2) levels and the 1,3A perturbinglevels (all data in cm-1).

The second order spin-orbit perturbations ove.3 A) = 2: ( 3n, v I H0161b(Re) 11.3 A, v’ &#x3E; 12j{ E(3I1, v) - Ee.3 A, v’) ) are calculated in2 ways :

v’

column a : Hslo(R,,) = Hsb(Rx)column b : H’D(R,,) = H el (Rx) { I + m 1 (Rc: - Rx) + M2 (R, - fiX)2 + ... Iso( so x i x x)

where R, and Rx are respectively the R-centroid and the potential curve crossing point internuclear distances. The mn coefficients are obtainedfrom the ab initio calculated dependence of Hsb as a function of R,,.

498

calculated in two different ways in order to show theeffect on ov{3 A) due to Hsb variations with R. Firstwe neglect these variations (columns a) :

Secondly, we introduce a variation HsÓ(Rc) deducedfrom ab initio calculations due to Robbe and

Schamps [11] (columns b), where R, is the R-centroidvalue and Rx is the internuclear distance at the cros-sing point of the potential curves. One observes thatintroduction of an R,-dependence of Hg8, althoughaffecting the absolute values of the Ot.(3 A) parameters,leaves the °t.+ 1 (3 A) - Ot.(3 A) differences only slightlychanged from one vibrational level to another.

It appears necessary to calculate approximatevalues of the Ot.( 1 L ±, 1 d ) parameters relative to

states of groups II and III in table VIII in order toobtain an estimation of the deperturbed spin-orbitand spin-spin parameters in the a 311 state.Table VIII gives estimates for the interactions with

the two 1 E+ states belonging to! the group II oftable VIII. The positions relative to the a 3Il stateof the X 1 E + and A’ 1 E+ states are experimentallyknown, but there is no quantitative data about theirinteraction with the a 3Il state. From the electronicconfigurations, one can show that

The spin-orbit electronic integral

was obtained by Robbe [12] from CI ab initio cal-culation. The calculated value °v(X 1 L+) = 0.27 cm -1 1is constant for the different levels 3II (v = 0, 1, 2).The interaction between an a 31I, v level with theground state being due up to 99.99 %, to interactionswith only three levels of X 1 L + , those with vibrationalquantum number v + 1.

Vibrational overlap integrals between the a 3I7(v)and A’ ’Z+(v’) states were calculated from R.K.R.potential curves of the a 3Il and A’ 1 L+ states, therovibronic data for the A’ state being from Bellet al. [6]. It was found that the discrete vibrationallevels of the A’ state contribute to the sum

only to 0.5, 2 and 12 % respectively for v = 0, 1 and 2.Other calculations of the vibrational overlap integralwere done for the levels in the continuum of theA’ 1 E+ state, with various analytical forms of therepulsive potential curve for that state and using asemi-classical method already used by Child andLefebvre [13]. The repulsive part of the A’ potentialcurve was extrapolated by means of a Morse function

fitting the levels v’ = 0, 1, 2, 3, 4, 5 (for higher vibra-tional levels, the precision on the turning points inthe repulsive region is not good because their energyis near the dissociation limit). It should be noted thatan extrapolation using a Linnett function givespractically the same results. The second order shiftdue to the A’ state can be expressed as :

where H£ is the matrix element of interaction func-tion between normalized bound level and an energynormalized continuum state VE. With a constant

value for HelSO equal to J5 ( 3n1 Hj§(Rx) ) 13Et ),this latter being experimentally known, one finds

ov(A ’ ’,E ’) L-- - 0. 34 cm - ’ for each of the a3no(v = 0, 1, 2) levels. This value is a rough approxima-tion because, on the one hand, we have supposed thatthe integral 2 n I al + 7 a &#x3E; is the same for theinteractions a 3170 - a’ 3,E + and a 317" - A’ 1,E +and, on the other hand, because the percentage of then3 n* configuration in the A’ state is very much lessthan 1 for such a state whose potential curve minimumlies near the dissociation limit.

Finally table VIII gives the remaining ov(l E -, 1 L1)parameters. For the 2 states belonging to the group IIIin table VIII, the potential curves as well as the inter-action matrix elements with the a 317 state are notexperimentally known. A rough estimate of the cores-ponding 2nd order parameters was obtained assum-ing :

1) The vibrational overlap integrals between thea317 state and the 1 E -, ’.A states are the same as the

corresponding overlap integrals between the a3I1state and respectively the 3E - and 3 L1 states. This

hypothesis is satisfactory because the energy diffe-rences £(1 E -) - E(3E -) and E(’.A) - E(3,A) esti-mated respectively equal to 525 cm-1 (from ab initiocalculations [11]) and 3710 cm-1 (cf. followingsection relative to the deperturbation of the d 3,Avibronic origins), are small compared to the

differences.

2) The electronic spin-orbit integrals HelSO havebeen assumed identical between the a 3Il state andthe pair of singlet-triplet states which arise from thesame electronic configuration i.e. :

and

The two preceding hypotheses lead to an approximateestimate of the 2nd order interaction with the 12" -,1 J state :

and

499

The calculated second order parameters0(3A = 3 L:t, 3 A) and 0(1 A = 1 L:t, 1 A, 1 ll) listedin table VIII may be used to obtain from the fittedvalues of table VI (marked with an asterisk) the 2ndorder deperturbed vibronic origins given in table IX (1).Among the true molecular parameters listed in

table IX, one remarks that only the non relativisticvibronic energies Tov = Toe + G(v) can be obtainedby subtracting from the first order deperturbed T*values of table VI the sum of the 2nd order shiftsdue to the well known states belonging to the firstgroup of table VIII. Moreover, because of the pro-perty mentioned above (that the variation

is practically independent of the difference

H el (Rc) - HSÓ(Rx’J), it can be seen, by comparisonwith the We and We Xe values given in the columns (a)and (b) of table IX, that these parameters are welldetermined in this particular case without requiringa knowledge of the variation with R of the electronicspin-orbit interaction. Nevertheless, the position ofthe a 3I1 state potential curve minimum cannot

reasonably be obtained to better than a few tenths ofa wavenumber.On may test further for internal consistency of

the model :

a) Diagonal spin-orbit constant deperturbation. -The determination of the deperturbed diagonal spin-orbit parameters of the a 3I1 state involves the 2ndorder interactions with singlet states. The latter aremuch less well determined than those due to tripletstates. Nevertheless, it can be remarked that, exceptfor 0(1 A), the singlet states 2nd order parameters arepractically constant in the three first a 31I vibrationallevels.

Consequently, the v-dependence of the spin-orbitseparation in the a 3n state : aA = Av+1 - Av, isbetter determined by considering the Avl.0 values,(obtained from the E(3n1) - E(3no) differences),where the 0(1 A) parameter is not involved, ratherthan the A;.l values (obtained from the

differences). It should be noted in table IX that, aswell as for the Te, We, We Xe parameters group, if

the Ae spin-orbit equilibrium value cannot be obtain-ed to better than a few tenths of a wavenumber, theaA parameter is well determined, since the correspond-ing values in (a) and (b) columns are almost identical.Using the formulae given by Veseth [14] connecting

the aA parameter and the AD centrifugal distortionparameter, we find that the agreement between

(1) Semi-empirical calculations of the interactions between thea 31I state and the k 317 and ’17 states belonging to the diexcitedconfiguration O’n3 n*2 have shown that these interactions are alwaysless than 0.1 cm-1 and they are indeed neglected here.

I

mu

.5S

:::z

e

as

N

O11v

t:zIn

Cde

14)mra1:3Sv

00mie

-"Q-s

qa

epq

IX.e

mT

tgidi

as

the thf t0

ts’5

ins

ietienair

8cg

e

0or c-s.gSe au

M

g

.5-S g SU cl

pMe r

UB’’9

..

or

v eo

Sr=55

500

fitted and calculated AD values given in table VI is

satisfactory.b) Parity-dependent spin-spin parameter determi-

nation. - As can be seen in table IX, the ass valuesdo not differ in the v = 0 and v = 1 levels of the a 3IIstate. This confirms one of the hypotheses made inthe fitting of the a 3II (v = 0, 1, 2) term values. Never-theless, there is a significant difference between thevalues in (a) and (b) columns. There is an excellent

agreement between the estimated value in column (a)of the true spin-spin parameter a,,, and the theoreticalvalue of Lefebvre-Brion [15]. In spite of this agree-ment, we expect a smaller absolute value, as in thecase of CO where the theoretical absolute value of

(ass is about 20 % greater than the experimental one.

The situation is quite similar in CS, the main part ofass coming from the carbon atom spin-spin contribu-tion. As for the other deperturbed molecular parame-ters which are given in table IX, the most reliable assvalue is consequently the one given in column (b)(ass = - 0.67 cm- 1) where an R-dependence of

HelSO has been taken into account.B. The d 3 L1 state. - Vibronic origins of the 3 L1

substates obtained after the first order deperturba-tion [4] are corrected to 2nd order so as to includeperturbations due to other vibrational levels of theA 1Il and a 3Il states. Second order perturbationterms are calculated in one way taking account onlyof the R,,-dependence of the electronic spin-orbitintegrals. These values, deperturbed relative to the

Table X. - Deperturbed vibronic parameters of the d 3d 1,2,3 substates (all data in cm-1).

After 2nd order calculations of the interaction ’A - 1 n, 3 n, the effective deperturbed values are fitted with a quadratic v functionTflv) = To + (Ùeu(v + ’1 ’) - (Ùe xeu(v + !)2. Figures in parenthesis represent 3 standard deviation in units of the last significant digit.In the expressions of the effective parameters as a function of the true parameters and the remaining unknown 2nd order shifts, the 3 L1 ’" k 3 ninteraction is neglected.

known states A 1 n and a 311 , are fitted to a quadraticexpression in v :

The effective values To, wen and We xen’ for eachvalue of Q = 1, 2, 3 are given in table X. As can beseen in table XI a significant difference of 10.04 cm -1exists between the average of the effective energiesfor the Sl = 1 and 3 components and the correspond-ing value for the intermediate Sl = 2 component.This suggests that 2nd order deperturbation of thed 3d state taking into account the a 3n and A ’Hstates is not sufficient to completely deperturb themolecular parameters of that state. Among the non-observed states having direct spin-orbit interactionwith the d 3d state, the ld state belonging to the sameconfiguration seems to give rise to the most impor-tant contribution.However, one cannot exclude completely inter-

Table XI. - Equilibrium molecular parameters for thed 3 Ai state (all data in cm-1).

(a) Calculated by Robbe and Schamps [11].(b) The theoretical value (A3a = - 58.5 cm-1 ) is an Hartree-

Fock value without configuration interaction. As the 3 L1 state arises98 % from the Q2 n3 n* configuration (the contribution of the otherconfigurations is found to be negligible) one can assume that thecorresponding CI value is : A3¿j = - 58.5(0.98)2 - 56 cm- 1.

501

action with the k 3 nand 5II states with a diexcitedan 3 ?L*2 configuration :

a) In the case of CS, the 3 n orbital is practicallynon-bonding. This greatly stabilizes the states belong-ing to the Gn4 n* and Gn3 n* 2 configurations, in

particular the SII state.b) On the other hand, as mentioned above, the

spin-orbit interaction 3 A ’" k 3 n, 5n is also enhanc-ed in CS as compared to SiO because of the greaterpolarization.

This property was already mentioned by FieldLagerqvist and Renhom [16].The energies of the k 317 and 5 n states were cal-

culated by Robbe and Schamps [11] respectively at28 000 and 11 000 cm -’ 1 above the d 3 A state. In thesingle configuration approach, the 3d N 1 A, k 317, 5 ninteraction matrix elements may be expressed as :

Ab initio calculations of these integrals, with configu-ration interactions, were made by Robbe [12]. Thevalues obtained are : 3 d 2 I HelSO B1 L1 &#x3E; = - 193 cm -1and ( 3 Jt [ al + I 7 (J &#x3E; = 123 cm-1.These approximate values allow estimation of 2nd

order perturbations :

The energy differences I1Evv’ are calculated from thetheoretical values given above for the 1 J, 5 nandk 3II states, and the vibrational overlap integrals v v’ ) where made equal to ðvv’. This approximationwhich seems valid in the case of the interactions bet-ween the states 1 L1 and 3A belonging to the same confi-guration, is much less so for the other two states.As a consequence, the values obtained for o(k 3ll)and 0(5 n) should be considered as upper limits tothe absolute value. It is seen that, while the effect ofthe k 3II state is negligible, the separation of effectsdue to the d and the 5n states is more ambiguous,although bulk part of the shift of the 3A 2 sublevelis due to interaction with the 1 J state.

Table XI gives the effective values of Toe, (0e,

We X,l A3 A and aA for the d 3 J state. These values aredeperturbed relative to the A II and a 3 n state

interactions, but still involve the unknown 0(1 J)and o(SII ) parameters. Combinations of these effec-tive parameters give :

and

The ab initio calculated A3 a value of Robbe and

Schamps [11] ] is A3A = - 56 cm-1.

If one takes into account that the uncertainty ofthe ab initio calculations is of the order of 10 %, asis the case for CO [2] and for the A3n constant ofCS [11] (the calculations are made with the same 2 nand 3 x orbitals), one obtain a lower limit of the cal-culated value : A3a = - 50.4 cm -1.

It can be confirmed from equation (2), that theabsolute value of 0(5 n) is less than a few tenths ofa wavenumber, assuming that the 5 n state lies abovethe d 3A state. Consequently, neglecting 0(5 n) in

equation (1), we can deduce an approximate value0(1 L1) - 10.04 cm-1, and, using the ab initio

value ( 3A2 I H" 11 L1 &#x3E; = - 193 cm-’, one obtainsthe energy difference between the 1 L1 and 3A state :

The 1 L1 state can now be located at an energy

above the ground state of CS. This value is, of course,strongly dependent on the calculated 1 d ~ 3 d spin-orbit interaction. Nevertheless, this first determina-tion of the 1d state position is compatible both withthe ab initio calculation [11] E. L1 = 39 300 cm - and with the assignment to the 1 L1 state of an observedweak absorption band at 40 303 cm-’ and of twostill unassigned perturbations of the A 1 n (v = 1 and

502

3) levels. Determination of tentative D 1 L1 electronicstate parameters will be discussed in reference [4].

5. Conclusions. - This analysis of several bandsof the d ’.Ji-a 3 n transition in CS partially fills the

gap in the experimental data concerning the sub-states 3 nn and 3 L1n with Q 1= 1. These new data,joined to those obtained from the spectra of the A-Xtransition and intersystem transitions in the UV

region, lead to a more precise deperturbation treat-ment of the A Instate levels.The study of 2nd order perturbations on the vibro-

nic origins of the sublevels of the two states involv-ed allowed :

i) verification of the internal consistency of themodel used,

ii) determination of improved values for the spin-orbit and spin-spin parameters which have been

compared with corresponding theoretical values,

iii) location of the approximate energy of the

previously unidentified 1,d state.

Acknowledgments. - The help and participation ofDr. T. Bergeman in the perturbation analysis has beencrucial.

Acknowledgments are also due Drs. S. Leach,H. Lefebvre-Brion and C. Jungen for helpful discus-sions and careful criticism of the manuscript.

Finally I would like to thank Drs. J. M. Robbeand O. Atabek who have performed some of thecalculations included in this report.

References

[1] FIELD, R. W., WICKE, B. S., SIMMONS, J. D. and TILFORD, S. G.,J. Mol. Spectrosc. 44 (1972) 383.

[2] HALL, J. A., SCHAMPS, J., ROBBE, J. M. and LEFEBVRE-BRION, H.,J. Chem. Phys. 59 (1971) 3271.

[3] PENZIAS, A. A., SOLOMON, P. M., WILSON, R. W. and JEF-FERTS, K. B., Ap. J. (Letters) 168 (1971) L53.

[4] BERGEMAN, T. and COSSART, D. (to be published).[5] BARROW, R. F., DIXON, R. N., LAGERQVIST, A. and WRIGHT,

C., Ark. Fys. 18 (1960) 543.[6] BELL, S., NG, T. L. and SUGGITT, C., J. Mol. Spectrosc. 44

(1972) 267.

[7] COSSART, D. and BERGEMAN, T., J. Chem. Phys. 65 (1976) 5462.[8] COSSART, D., HORANI, M. and ROSTAS, J., J. Mol. Spectrosc.

67 (1977) 283.

[9] COSSART-MAGOS, C., COSSART, D. and LEACH, S., Mol. Phys.37 (1979) 793.

[10] COSSART, D., J. Chim. Phys. 76 (1979) 1045.[11] ROBBE, J. M. and SCHAMPS, J., J. Chem. Phys. 65 (1976) 5420.[12] ROBBE, J. M. (Private communication).[13] CHILD, M. S. and LEFEBVRE, R., Mol. Phys. 34 (1977) 979.[14] VESETH, L., J. Phys. B3 (1970) 1677.[15] LEFEBVRE-BRION, H. (Private communication).[16] FIELD, R. W., LAGERQVIST, A. and RENHORN, I., Phys. Scr.

14 (1976) 298.[17] HERZBERG, G., Molecular Spectra of Diatomic Molecules

(Van Nostrand, New York) 1957.[18] VAN VLECK, J. H., Phys. Rev. 33 (1929) 467.