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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. Journal de Physique, 1980, 41 (6), pp.489-502. �10.1051/jphys:01980004106048900�. �jpa-00209272�
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 303A0r
du 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. Avec les 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 la détermination du paramètre spin-orbite vrai ainsi que du paramètre spin-spin dépendant de la parité. Ces valeurs sont comparées avec les valeurs théoriques correspondantes. L’étude des perturbations du second ordre sur les sous-niveaux de l’état 30394 a conduit à la localisation en énergie de l’état 10394, jusque-là non identifié. Les constantes
déperturbées 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 303A0r
transition of the CS radical. Eleven bands have been analysed (v’ = 5-12, v" = 0-2). Intersystem transitions to the 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 treatment
of the vibronic levels involved in the d-a transition, improved values are obtained for the true spin-orbit and parity-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 not
previously identified. The deperturbed constants for the a 303A0 and d 30394 states are the following : (all data in cm-1).
Classification
Physics Abstracts
33.20K
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 configuration n4 O’n*(a 3n, A l II states) are interspersed among - the vibronic levels of the second excited configuration n3 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 to
the 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 involving
the wavefunctions of the 7c and a outer orbitals i.e.,
in the case of CS :
where al + is the equivalent one electron spin-orbit operator.
The same can be said for the electronic rotation matrix elements which may be obtained, in the single configuration approach as a function of an 1-uncoupl- ing integral
The coefficients of proportionality which relate the
phenomenological spin-orbit and rotation-orbit matrix elements to the a and b values can be calculated appro-
ximately assuming on one hand, the separation of the
electronic and vibrational integrals (R-centroid appro-
ximation), and on the other hand a single electronic configuration with the same orbitals for all the states.
For rovibronic levels I u7r *, v, J > and I n3 7r*, v’, J >
the ratio :
characterize approximately the relative magnitude
of 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 from
the two first excited configurations have different
symmetry relatively to the exchange of the nuclei.
ii) In the heavier species as : CSe, SiS, AsN, the ratio s is so small that the rotational perturbation parameters can be neglected in the Hamiltonian matrix.
iii) In the isoelectronic radical SiO, the polariza-
tion gives rise to a large spatial separation of 7r and 6
orbitals leading to small n I al + I a > integrals so
that forbidden transitions are not observed.
iv) Finally, the molecule which is most similar to CS is carbon monoxide. The perturbation effects
in 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 and CS are due almost exclusively to different orders of magnitude of spin-orbit and rotation induced inter- actions, the CS radical appeared to be the best species
to further test the fine structure model proposed in
the 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 in interstellar cloud reactions. Some of the properties
of 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 particular
interest of these spectra are the following :
a) The detection of radiation of extraterrestrial
origin is more easy in the long wavelength range than in the UV region where the optical spectra of CS were observed up to now. These new line measurements
might help in the observation of CS in astrophysical
spectra.
b) The knowledge of long wavelength transitions,
with the metastable a 31I state as the lower state, could permit selective laser excitation and lifetime measurements of triplet levels.
c) The analysis of the IR bands attributed to the d 3,j -a317 transition provide new experimental data
on 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 with the ground state X ’.E+ as the lower state. These
transitions borrow their intensity mainly from the
A 1 ll-X 1.r+ system.
Direct spin-orbit coupling with the A ’17 state
favors the appearance of the subbands involving
Q = 1 triplet state components. The other subbands may then borrow intensity from the S2 = 1 subbands
if spin uncoupling by rotation is sufficient. The inten-
sity ratio between the bands involving Q =1= 1 and
Q = 1 upper levels is about 16 times smaller in CS than in CO, causing the relative scarcity of experi-
mental data on the 3nO,2 and 3L12,3 substates when
compared to the CO case.
The deperturbation treatment of the first 9 vibra- tional levels of the A 1 n state, which will be published shortly by Bergeman and Cossart [4] is one of the
most complex cases in diatomic spectroscopy and has proved to require knowledge of the term values
obtained in the present work. , Though the principal results of this work are men-
tioned again in the longer report [4], the analysis given here is relative, on one hand to a particular
transition appearing in a different spectral region of special interest, and on the other hand to a more
detailed deperturbation treatment of the 3 n and 3 L1 levels involved. This paper is part III of the CS valence- valence perturbations analysis. After pionier work
on the rotational analysis of the CS optical spectra by Barrow et al. [5], and the observation in the vacuum
UV of the A’ ’Z+-X 1.r+ transition by Bell et al. [6], part I and II of the present series have been published respectively by Cossart and Bergeman [7] who have
estimated the off-diagonal spin-orbit and spin-spin parameters for the valence states and by Cossart
et al. [8] who have given the rotational analysis of the
a 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 obtained by means of an emission source already used in the
production of fluorobenzene ion spectra analysed by Cossart-Magos et al. [9]. The details of the experi-
mental device are given by D. Cossart [10]. A low
pressure (10-2 to 10- 3 torr) d.c. discharge is establish- ed between plane parallel electrodes 1 cm apart and submitted to a 500 to 1 000 G magnetic field perpen- dicular to the electric field. The resulting confinement of the cathodic glow causes the discharge to operate
at lower pressures than in the absence of magnetic
field and also lowers the cathode fall in the cathodic dark space (hollow cathode effect). After the dis-
charge is initiated, the potential between electrodes is about 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, whereas
the CS bands, in particular those of the a 311_X 12:+
and d 3d-a 3II systems, appear with intensity much
increased relative to those of the A-X transition when
compared to the spectra obtained previously by Cossart, 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 unambiguous
since term values for 3 A 1 sublevels up to v = 10 and for the 3HJ states are known from triplet-singlet
transitions in the ultraviolet. The UV spectra also provide some information on the substates 3 A2
and 317o.
The d 3 A i-a 3 n transition shows 3 subbands
3A1-3no, 3A2-3ll1 and 3A3-3ll2 which appear in this order for a given vibrational transition and increasing wavelength. Absence of branches with åE =F 0 con- firms that the two states belong to Hund’s case a
and the order of the subbands is consistent with a
regular 3I1 state and an inverted 3d state, as observed in 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 e
or f index refers to the parity of the a 3II levels involv-
ed. The A doubling in the d 3 A state is always less
than the experimental resolution and the same can
be 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 no
where the separation between the lines of the branches Re, Pe, Qe and Rf, Pf, Qf is equal to the A splitting of
the 317o state. This, added to the fact that the 3 A1 1
levels 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 the 3 A2,3-3 n 1,2 subbands. For this reason, the 3 A1-3 no
subbands 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. The entries correspond to the prominent R-branch heads.
The spectrum of the (7, 0) band of the d 3 A-a 3II system 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 of
A 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 are
given. When these branch-heads are not easily discemable, we give
the frequency of the shortest wavelength R-line measured.
492 JOURNAL DE PHYSIQUE
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 other
10 bands, will be given elsewhere by Bergeman and
Cossart [4].
Table III shows the Franck-Condon factors calcu- lated from the d3 L1 and a 3II R.K.R. potential
curves 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 indeed those of largest Franck-Condon factors. Moreover, it should be mentioned that for the e ’2: --a 317 transition, 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 311
system 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 be noted that for 3 L:I: states belonging to Hund’s case b, spin-orbit interaction with the A lIl state is of the
same order of magnitude for the 3 components of each 3 L state and, as a consequence, information about 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 3II and d 3d vibronic levels and the neighbouring states
can be split into 2 parts corresponding to the 2 steps of the deperturbation treatment.
4.1 FIRST ORDER DEPERTURBATION. - The dimen- sion of the corresponding Hamiltonian matrix is
494
equal to the number of neighbouring substates which
cross the 3II or 3 L1 levels or which interact so strongly
that second order perturbation formulae are incor-
rect.
The results obtained from fitting to such a model
are first order deperturbed molecular parameters of the 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 the
a 3I1 state, the d 3L1 upper levels are interspersed among vibronic levels of the A 1II and other triplet states.
As a consequence, the d 3 L1 experimental term values
must be fitted together with the term-values of the
neighbouring states which are obtained from the UV spectra. This deperturbation treatment involving
as 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 are
presented only the first order deperturbation details
for the a 3I1 vibrational levels involved in the d-a transition. Although such a deperturbation was
Table IV. - Summary of the data available on the a 317 substates.
X and d letters indicate that for a given 3nn(v) substate at least
one 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 data
obtained from the triplet-triplet transition justified
a new determination of the molecular parameters.
Table IV presents schematically the whole of the rotational 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. Because
of the isolated position of the a 311 (v = 0, 1, 2) levels, the effects due to states which may interact with 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 energies
may 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 > :t I - Q > } 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 :
For a given vibrational level a 3n(v), the number
of parameters introduced in the least-squares fit
was reduced to 9 phenomenological parameters for each 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 the second order p(3 A) parameters are omitted in the vibronic origin expressions, since their calculated values are several orders of magnitude smaller than
the experimental uncertainty.
In principle, with the data we have on the v = 0, 1 and 2 levels of the a 3I1 state, we should be able to
determine 3 x 9 = 27 fine-structure parameters.
However, because of strong correlation between the AD and p’ parameters and, in the absence of data on the A
doubling in the a 3n, v = 2 level, we chose to reduce further the number of free parameters by fitting toge- ther the entire collection of experimental data for
levels v = 0 through 2 of the a 3II state. In this simul- taneous fit the number of free parameters for the 3 vibrational levels was reduced to 20. The following hypotheses were made :
1) Deperturbed B and D parameters are consider- ed to be linear functions of v :
Moreover, calculation of fl, using Dunham’s formula
gives 13e = 0.8 x 10-8 cm-1; accordingly was
fixed at this value. In fact, the introduction of a 13e
value in the range 0-0.8 x 10-8 cm-1 contributed less 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 parameters
p(3d) are assumed to be identical for all levels a 3Il (v = 0, 1, 2). The parameter p(32 -), for which an approximate calculation gives 4 x 10-4 cm -’, repre- sents a perturbation of the diagonal elements on the
order 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 its
calculated value - 1.68 cm-1 because of lack of data
on the a 3f! Or’ V = 2 levels.
Table VI gives the results of a simultaneous fit with 20 free parameters, 12 of which are vibronic origins. A comparison is made between fitted and calculated values of the eight other fine structure
parameters. The agreement is satisfactoring for the
distortion parameters. It should be noted, to under- stand the small discrepancies observed for the p(3A)
parameters, that the corresponding calculated values
are 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 data
in 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 Ax with M Af= ratio between the mass of the electron and the CS reduced mass. Van Vleck [18] ;
d peA) = bH!;’D(Rx) v I v’ >
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
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