Laser velocity modulation spectroscopy of TiCl+: observation of the A 3Δ(3d2) state and deperturbation of the X 3Φ-A 3Δ complex

Article abstract of DOI:10.1063/1.475313

Absorption through an ac glow discharge associated with a velocity modulation detection technique efficiently recorded spectra of TiCl⁺. Owing to the high sensitivity of this technique, it was possible to analyze the weak and/or overlapped transitions, the study of which allowed the identification of the A ³Δ(v = 0) state located 350 cm^-1 above the X ³Φ(v = 0) state. From the study of the contributions of the basis functions to the eigenvectors of the diagonalized matrix it was possible to determine the mixing ratio of the Ω = 3 components of the A ³Δ(v = 0) and X ³Φ(v = 1) states and to evidence a reversal of the leading character of these components.

Full text of DOI:10.1063/1.475313

Laser velocity modulation spectroscopy of TiCl + : Observation of the A 3 Δ(3d 2 ) state
and deperturbation of the X 3 Φ−A 3 Δ complex
C. Focsa, B. Pinchemel, J.-L. Féménias, and T. R. Huet
Citation: The Journal of Chemical Physics 107, 10365 (1997); doi: 10.1063/1.475313
View online: http://dx.doi.org/10.1063/1.475313
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/107/24?ver=pdfcov
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Laser velocity modulation spectroscopy of TiCl؉: Observation
3
3
3
of the A ⌬„3d2… state and deperturbation of the X ⌽؊A ⌬ complex
C. Focsa and B. Pinchemel
Laboratoire de Dynamique Moleculaire et Photonique, URA CNRS 779, Centre d’Etudes et de Recherches
Lasers et Applications, Universite des Sciences et Technologies de Lille 59 655 Villeneuve d’Ascq cedex,
´
´
France
´
´
J.-L. Femenias
´
´
Institut Non-Lineaire de Nice, UMR CNRS 129-UNSA, Universite de Nice Sophia-Antipolis,
1361 route des Lucioles, 06 560 Valbonne, France
T. R. Hueta)
Laboratoire de Spectroscopie Hertzienne, URA CNRS 249, Centre d’Etudes et de Recherches Lasers
´
et Applications, Universite des Sciences et Technologies de Lille, 59 655 Villeneuve d’Ascq Cedex, France
͑Received 8 July 1997; accepted 22 September 1997͒
A single mode cw dye laser along with velocity modulation was used to record weak bands of TiClϩ
in the spectral region 17 100–18 600 cmϪ1. The ions were produced in the positive column of an ac
glow discharge with a gas mixture of He/TiCl4. These new bands have been identified as linking the
3
upper already known 17.8 3⌬(3d4s) state to respectively the X ⌽( ϭ1) state and to a newly
͓
͔
v
observed A ⌬( ϭ0) state located 350 cmϪ1 above the X ⌽( ϭ0) state. As suggested by Focsa
3
3
v
v
et al. ͑J. Chem. Phys. 106, 9044 ͑1997͒͒ the A ⌬(3d2) state was found to be responsible for the
3
perturbations observed in the X ⌽(3d2) state. The spin-orbit components of the A ⌬( ϭ0) and
3
3
v
3
the X ⌽( ϭ1) states revealed interaction leading to homogeneous and heterogeneous
v
perturbations. A set of deperturbed parameters has been determined with the help of a full
3
3
matrix-based handling of the A ⌬( ϭ0) and the X ⌽( ϭ0,1) states. Study of the contributions
v
v
of the basis functions to the eigenvectors of the diagonalized matrix displayed evidence of a reversal
3
3
of the leading character of the ⍀ϭ3 spin-orbit components of the A ⌬( ϭ0) and the X ⌽(
v
v
3
ϭ1) states. A remarkable example of avoided crossing has been observed between the A ⌬ ( ϭ0͒
and the X ⌽ ( ϭ1) spin-orbit components. © 1997 American Institute of Physics.
v
1
3
v
2
͓S0021-9606͑97͒02748-7͔
ground state of TiClϩ. Moreover the observation of inter-
combination ⌬⍀ϭ0 transitions between the 17.8 3⌬ and
I. INTRODUCTION
͓
͔
The spectroscopic study of diatomic radicals and ions
has been the subject of numerous papers in the past because
strong emission spectra were observed from the visible to the
UV range. However, it is rather limited in the case of ions
containing heavy atoms, like metals, due to the technical
difficulties associated with the generation and detection of
these species. Very few high-resolution experimental data
are available, and most of them consist of emission spectra
recorded from electrical discharges.1–6 With the develop-
ment of sensitive and selective detection schemes, the study
of heavy diatomic and polyatomic molecular ions produced
in appropriate sources has been made possible.7,8 The experi-
mental setup that we are developing in Lille aims to study
such species by means of laser velocity modulation spectros-
copy.
3
the X ⌽( ϭ0) states allowed the first experimental deter-
v
mination of the spin orbit constants of the two states. In that
3
paper we noted that the X ⌽( ϭ0) state was affected by a
v
perturbation which prevented the description of this state by
a full matrix-based representation.
Using the same experimental velocity modulation
technique10,11 as in our first paper on TiClϩ we have re-
corded new spectral regions and congested ones in order to
identify weak remaining bands.12 No less than 16 new bands
have been identified, all of them sharing the same upper
17.8 3⌬( ϭ0,1,2) state.
͓
͓
͔
v
In the present paper we report the observation of a new
17.8 3⌬(3d4s)ϪA ⌬(3d2) system of TiClϩ. The
3
͔
A ⌬(3d2) state has been identified and fully characterized
3
As a first stage, we recently published8 the analysis of
in its ground vibrational level, which is located only
3
the 17.8 3⌬–X ⌽( ϭ0) transition of TiClϩ which had
͓
͔
v
3
3
350 cmϪ1 above the X ⌽( ϭ0) state. In addition the ͑0,1͒
been observed and tentatively assigned as a ⌸–3⌬ transi-
tion by Balfour and Chandrasekhar,6 while a theoretical
study by Kaledin et al.9 suggested the ground state to be
v
and ͑1,1͒ vibrational bands of the 17.8 3⌬(3d4s)
͓
͔
ϪX ⌽(3d2) system were observed. The newly observed
lines combined with our previous results8 have been fitted in
order to determine a consistent set of deperturbed parameters
3
3
3
a ⌽ state. Our study confirmed the ⌽ symmetry of the
3
3
for the A ⌬( ϭ0) and X ⌽( ϭ0,1) states.
a͒
v
v
Author to whom correspondence should be addressed. Electronic mail:
therese.huet@univ-lille1.fr
The present work is the first experimental study leading
J. Chem. Phys. 107 (24), 22 December 1997
0021-9606/97/107(24)/10365/8/$10.00
© 1997 American Institute of Physics
10365
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Focsa et al.: Spectroscopy of TiClϩ
10366
FIG. 1. The energy level diagram and the observed transitions of the 17.8 3⌬(3d4s)ϪX 3⌽(3d2) and the 17.8 3⌬(3d4s)ϪA 3⌬(3d2) visible systems
͓
͔
͓
͔
of TiClϩ. The states are located at their effective positions in agreement with Table I.
3
to a fully comprehensive energy diagram of TiClϩ below
1000 cmϪ1
of the X ⌽ as lower state. Both main and intercombination
bands are observed. We can notice that the distances between
the ϭ0 and ϭ1 vibrational levels of the X ⌽ state do
.
3
v
v
not lead to a common ⌬G1/2 value for the three spin-orbit
components, suggesting the presence of perturbations in
some of the spin-orbit components of this state. Obviously,
we can notice that the Pekeris and Kratzer15 expressions,
II. EXPERIMENT
The experimental apparatus has been described in detail
in our previous paper.8 Only the main characteristics are re-
minded. A Coherent 899-29 ring cw dye laser pumped by an
Arϩ laser ͑Coherent CR20͒ was employed to record a spec-
trum of TiClϩ. The ions were produced in the positive col-
umn of an ac glow discharge driven at 30 kHz with typical
sinusoidal current of 300 mA peak-to-peak and voltage of 1
linking the vibrational ␻ and ␻exe parameters to the B and
e
3
D rotational parameters, are best accounted for in the ⌽4
ϭ0 and ϭ1 substates which can be assumed to be free of
v
v
perturbations in absence of any ⍀ϭ4 level of a close lying
electronic state.9,16 The second system is located between
kV peak-to-peak, and in
a
gas mixture of
17 400 and 17 500 cmϪ1 for the ⌬ ϭ0 sequence and be-
v
He/TiCl4ϭ7/0.1 Torr. The velocity modulation detection
technique10,11 and a noise subtraction technique13 were used
in order to eliminate signals from the neutral species and to
reduce the noise fluctuations from the lasers and the dis-
charge, respectively. The spectra were recorded using the
Coherent Autoscan software and were calibrated against io-
tween 17 950 and 18 000 cmϪ1 for the ⌬ ϭϩ1 sequence.
v
In the absence of Q branches, these bands fairly equally
spaced are characteristic of ⌬⍀ϭ0 transitions involving
a
3⌬ state. In addition, very weak intercombination ⌬⍀
ϭϪ1 bands linking the 17.8 3⌬ state to the newly ob-
͓
͔
served 3⌬ state, which will be now labeled A ⌬, have been
observed around 17 300 cmϪ1 and 17 850 cmϪ1. These red
shaded bands are mostly headless up to Jϭ60 in our spectra.
The presence of intercombination bands allows each vibra-
3
dine lines14 with an accuracy of 0.005 cmϪ1
.
Revisitation of the 17 100–18 600 cmϪ1 region has been
performed in order to record weak features of the spectrum
and to identify bands overlapped by intense and already
known transitions.8 Therefore most spectra were recorded
with a time constant of 300 ms and a sensitivity of 500 ␮V.
In addition we have scanned the 14 700–17 100 cmϪ1 spec-
tral region, in which no signal has been observed.
tional level of the three electronic states ͑except the ϭ2
v
level of the 17.8 3⌬1 state͒ to be involved in two to four
͓
͔
transitions. This leads to a confident energy level diagram
3
͑Fig. 1͒. Due to the close lying positions of the A ⌬(
v
3
ϭ0) and X ⌽( ϭ1) states, it obviously appeared that per-
v
turbations could be expected between the two states. The
III. OBSERVED BANDS
most striking feature is the closeness of the two ⍀ϭ3 spin-
3
3
orbit components of the A ⌬( ϭ0) and X ⌽( ϭ1)
Two systems of new bands have been identified ͑Fig. 1͒,
and all of them reach the well-known upper 17.8 3⌬ state.8
v
v
states. Neither the intensity of the main and intercombination
͓
͔
The first system is concerned with the ϭ1 vibrational level
bands nor the shape of these bands which all share a lower
v
J. Chem. Phys., Vol. 107, No. 24, 22 December 1997
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Focsa et al.: Spectroscopy of TiClϩ
10367
TABLE I. Effective parameters ͑in cmϪ1͒ for the spin-orbit components of the X 3⌽( ϭ0,1), A 3⌬( ϭ0), and 17.8 3⌬( ϭ0,1,2) states of 48Ti35Clϩ ͑all
v
v
͓
͔
v
uncertainties are 1␴͒.
17.8 3⌬( ϭ0)
17.8 3⌬( ϭ1)
17.8 3⌬( ϭ2)
͓ ͔ v
͓
͔
v
͓
͔
v
⍀ϭ1
⍀ϭ2
⍀ϭ3
⍀ϭ1
18 381.064͑1͒
⍀ϭ2
⍀ϭ3
⍀ϭ1
Tv
17 873.181͑1͒
0.177 953͑3͒
0.796͑7͒
17 984.744͑1͒
18 104.657͑1͒
18 492.433͑1͒
18 612.183͑1͒
0.178 150͑3͒
0.938͑7͒
18 884.354͑1͒
Bv
0.178 532͑3͒
0.881͑5͒
0.179 005͑3͒
0.916͑6͒
0.177 102͑3͒
0.860͑6͒
0.177 673͑3͒
0.878͑5͒
0.176 244͑4͒
0.892͑10͒
107Dv
X
3⌽( ϭ0)
X
3⌽( ϭ1)
A
3⌬( ϭ0)
v
v
v
⍀ϭ2
⍀ϭ3
⍀ϭ4
⍀ϭ2
⍀ϭ3
⍀ϭ4
868.089͑1͒
⍀ϭ1
⍀ϭ2
⍀ϭ3
Tv
Bv
0
188.555͑1͒
382.727͑1͒
473.910͑1͒
700.136͑1͒
0.176 412͑3͒ 0.173 614͑3͒
Ϫ1.78(1)
Ϫ0.49(1)
431.261͑1͒
0.180 479͑5͒
0.80͑3͒
558.613͑1͒
0.179 692͑4͒ 0.178 793͑4͒
0.10͑1͒
Ϫ0.50(1)
635.187͑1͒
0.173 912͑3͒ 0.174 111͑3͒ 0.174 029͑3͒ 0.174 621͑4͒
107Dv 0.888͑6͒
1011H
0.882͑5͒
0.831͑6͒
2.04͑1͒
1.55͑2͒
0.796͑7͒
3.73͑1͒
0.27͑2͒
Ϫ1.12(5)
3
⍀ϭ3 spin-orbit component can help to identify the two lev-
localize the ⍀ϭ3 spin-component of the A ⌬( ϭ0) level.
v
3
els observed at 635 cmϪ1 and 700 cmϪ1 as the A ⌬ (
The observation of the other components of this level and of
the three components of the X ⌽( ϭ1) level, and more
v
3
3
3
ϭ0) or the X ⌽ ( ϭ1) state. The same observation can be
v
v
3
done on the ⍀ϭ2 spin-orbit components which are located
precisely the effective values of the parameters, suggested a
strong perturbation between the X ⌽( ϭ1) and A ⌬(
v v
3
3
at 474 cmϪ1 and 559 cmϪ1
.
The presence of perturbations was confirmed by rota-
tional analysis based on a polynomial effective model used
to describe each of the spin-orbit vibrational levels of the
ϭ0) levels. A preliminary deperturbation procedure, taking
into account perturbation contributions up to the fourth or-
der, allowed us to predict the effective parameters of the
3
3
3
three X ⌽, A ⌬ and 17.8 3⌬ states. This has been done
A ⌬ ( ϭ0) component: the energy origin was estimated to
͓
͔
v
3
only on the most abundant isotopomer 48Ti35Clϩ because of
the weakness of the observed bands. Table I summarizes the
parameters derived from this fit which allows an easy re-
lie between 626 and 654 cmϪ1, the effective rotational con-
stant Beff between 0.1766 and 0.1779 cmϪ1, and the effective
centrifugal stretching Deff about 4ϫ10Ϫ7 cmϪ1 ͑that is an
exceptionally large value in the present case͒. The observed
values were finally 635.187 cmϪ1, 0.178793 cmϪ1, and
3.73ϫ10Ϫ7 cmϪ1, respectively ͑see Table I͒.
building of the experimental data. Numerous values listed in
3
this table indicate that the lower states A ⌬( ϭ0),
v
3
3
X ⌽( ϭ1) and even X ⌽( ϭ0) cannot be considered as
v
v
isolated
states
following
the
Born–Oppenheimer
In the following, we shall use the notation of Brown
et al.19 and Lefebvre-Brion and Field.17 The effective Hamil-
tonian used for the analysis of the spin-orbit and rotational
structures is given by the following expression:
approximation15 to the contrary of what it is observed for the
17.8 3⌬ state. We can see, for example, that large and even
͓
͔
negative D values are derived from the fit; moreover, chaotic
evolution of the B rotational parameters is noted in the two
states considering both their spin-orbit and vibrational evo-
lutions. These observations enforce the idea that the assign-
ment of a set of constants to a given ⍀ϭ3 spin-orbit com-
HϭHEVϩHSOϩHSSϩHROT
,
͑1͒
where HEV is the vibronic part of the Hamiltonian, and the
spin-orbit, spin-spin ͑or second-order spin-orbit22͒, and rota-
tional parts are defined respectively by the forms
3
3
ponent of the A ⌬( ϭ0) or the X ⌽( ϭ1) states based
on the effective rotational parameters stays meaningless at
v
v
this state of the work.
1
HSOϭA r͒L S ϩ A r͒ LϩSϪϩLϪSϩ͒
͑
͑ ͑
z
z
The above considerations sustain the idea that the
2
3
3
X ⌽( ϭ0,1) and the A ⌬( ϭ0) states must be treated by
v
v
a full direct approach matrix-based method17 which will give
an useful insight on the assignment of the ⍀ϭ3 and ⍀ϭ2
spin-orbit components. It is noticeable that no local pertur-
bation has been observed nor any fine structure in the studied
bands.
1
2
ϩ
AD JϪLϪS͒2,L•S
,
͔
ϩ
͑2͒
͑3͒
͓͑
1
HSSϭ ␭ϩ␭ JϪLϪS͒2,S2Ϫ S2
,
͑
ͫ
ͬ
D
z
3
ϩ
1
IV. THEORETICAL MODEL AND LEAST-SQUARES
PROCEDURE
HROT
ϭ
J2ϪJ2͒ϩ L2ϪL2͒ϩ S2ϪS2͒
͓͑
͑
͑
͔
z
2␮r2
z
z
Many authors have dealt with diatomic Hamiltonians,
including spin-orbit and rotational structure, and other higher
order effects.17–21 Particularly, the diagrammatic method
shown in Ref. 18 has been successfully used in order to
1
ϩ
LϩSϪϩLϪSϩ͒Ϫ JϩSϪϩJϪSϩ͒
͑
͓͑
2␮r2
Ϫ JϩLϪϩJϪLϩ͒ ϪD JϪLϪS͒4.
͑4͒
͑
͔
͑
J. Chem. Phys., Vol. 107, No. 24, 22 December 1997
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Focsa et al.: Spectroscopy of TiClϩ
10368
For an unperturbed 3⌬ or 3⌽ state described in the
neously fitted in order to derive the deperturbed molecular
constants of the involved states. 1740 lines are newly ob-
served ͑the set of assigned lines has been placed in Physics
Hund’s case ͑a͒, one obtains a 3ϫ3 matrix as used in our
previous paper.8 In these expressions the 1/2␮r2 factor ͑r is
the internuclear distance and ␮ the reduced mass of the mol-
ecule͒ originates the well-known rotational Bv parameter.
When two vibronic states are close enough to perturb each
other it is necessary to take into account these interactions by
adding to the 3ϫ3 matrices of the isolated states the cou-
pling elements arising from the presence of the
(1/2␮r2)LϮSϯ, Ϫ(1/2␮r2)JϮLϯ and A(r)LϮSϯ operators
in the Hamiltonian. These terms, which are usually neglected
in the Born–Oppenheimer approximation,15 link bases func-
tions which differ by at least one of the ⌳ or ⍀ quantum
numbers. According to Lefebvre-Brion and Field,17 we con-
sider the three coupling operators and the derived off-
diagonal elements as follows:
23
Auxiliary Publication Service ͑PAPS͒ ͒, while the 1269 re-
maining ones were already published in our previous
paper.8,24 All the lines were weighted to an experimental
uncertainty equal to Ϯ0.005 cmϪ1
.
Numerous studies are devoted to transitions involving
perturbed electronic states.25–31 Usually, the observation for
a given electronic state of perturbed and unperturbed vibra-
tional levels allows an extrapolation from the parameters of
the unperturbed vibrational levels to predict the expected
values of the constants of the perturbed levels. Even more,
these extrapolated values are often held fixed in the fitting
procedure in order to reduce the number of freedom degrees
of the system.26 Such an opportunity does not occur in the
case of TiClϩ where it appears that all the studied vibrational
͑1͒ 12A(r)LϮSϯ giving rise to homogeneous (⌬⍀ϭ0)
spin-orbit perturbations between states with ⌬⌳ϭϮ1:
3
3
levels of the A ⌬ and X ⌽ states are perturbed.
In the fitting procedure all the parameters were allowed
to vary freely. As explained in our previous paper,8 each of
the 3ϫ3 matrices accounting for a given vibronic state in-
cludes seven parameters to be calculated: Tv is the vibronic
term value, B is the rotational constant, A and ␭ are the first-
and second-order spin-orbit constants; to each of the three
last parameters is associated a centrifugal distortion constant,
respectively named D, AD and ␭D . A unique set of param-
1
,⌳,⌺,⍀ A r͒LϯSϮ ,⌳Ϯ1,⌺ϯ1,⍀
v
͑
v
Ј
ͯ
ͯ
ͳ
ʹ
2
ͱS Sϩ1͒Ϫ⌺ ⌺ϯ1͒,
͑
ϭ␣vv
͑5͒
͑6͒
͑
Ј
where ␣vv
ϭ
,⌳
͉
1A r͒
͉
Lϯ,⌳Ϯ1 ,
v
Ј
͘
v
͑
͗
2
Ј
͑2͒ (1/2␮r2)LϮSϯ giving rise to homogeneous spin-
electronic perturbations between states with ⌬⌳ϭϮ1:
eters ␭ and ␭ has been used for the ϭ0 and ϭ1 vibra-
v
v
D
30
3
tional levels of the X ⌽ state. Wicke et al. showed that
1
,⌳,⌺,⍀
LϯSϮ ,⌳Ϯ1,⌺ϯ1,⍀
v
Ј
v
ͯ
ͯ
͑
these two parameters are essentially independent of . This
ͳ
ʹ
v
2␮r2
is effectively observed in the upper 17.8 3⌬ state.
͓
͔
ͱS Sϩ1͒Ϫ⌺ ⌺ϯ1͒,
Following the previously described model, four coupling
parameters appear in the twenty off-diagonal terms account-
ϭ␤vv
͑7͒
͑8͒
͑
Ј
1
3
ing for the perturbations: ␣00 and ␤00 for the X ⌽( ϭ0)
v
where ␤vv
ϭ
,⌳
Lϯ ,⌳Ϯ1 ;
v
v
Ј
ͯ
ͯ
ͳ
ʹ
2␮r2
Ј
3
ϪA ⌬( ϭ0) interaction and the corresponding ␣ and
v
10
3
3
␤
for the X ⌽(vϭ1)ϪA ⌬(vϭ0) interaction. The de-
͑3͒ Ϫ(1/2␮r2)JϮLϯ giving rise to heterogeneous (⌬⍀
ϭϮ1) electronic-rotational perturbations ͑L-uncoupling͒:
10
3
3
rived molecular parameters for the X ⌽( ϭ0,1), A ⌬(
v
v
ϭ0) and 17.8 3⌬ states and the coupling parameters ␣vv
͓
͔
Ј
1
and ␤vv are respectively listed in Tables II and III. In order
to compare Table I and Table II, it should be noted that the
,⌳,⌺,⍀ Ϫ
LϯJϮ ,⌳Ϯ1,⌺,⍀Ϯ1
v
Ј
Ј
v
ͯ
ͯ
ͳ
ʹ
2␮r2
origin of the energies in the effective polynomial fit has been
ͱJ Jϩ1͒Ϫ⍀ ⍀Ϯ1͒.
͑
3
ϭϪ␤vv
͑9͒
͑
fixed to T (X ⌽ ( ϭ0))ϭ0, when it has been fixed to
Ј
v
0
2
3
In our previous paper8 we observed that it was not pos-
0
T (X ⌽( ϭ0))ϭ0 for the fully deperturbed model. The
v
3
conversion factor between these two values is T (X ⌽(
v
sible to fit the data with a fully matrix-based representation
directly derived from the Hamiltonian for the X ⌽( ϭ0)
state and we noticed that it was necessary to introduce an
effective model by sharing the matrix of the X ⌽( ϭ0)
state in two parts and that it was not out of question that this
state was perturbed. As a consequence we decided to include
0
ϭ0))ϭT (X ⌽ ( ϭ0))ϩ194.501 cmϪ1
.
The overall
3
3
v
2
v
0
standard deviation is 0.0056 cmϪ1 for the deperturbed
matrix-based model. This value is quite close to the esti-
mated experimental accuracy (0.005 cmϪ1). The comparison
with the overall standard deviation of the polynomial fit
(0.0054 cmϪ1) suggests that the matrix-based model used to
fit the experimental data is satisfying. Equilibrium constants
3
v
3
the X ⌽( ϭ0) state in the interaction matrix even if this
v
state is 350 cmϪ1 away from the A ⌬( ϭ0) state. On ac-
3
v
of the 17.8 3⌬ and the X ⌽ states are listed in Table IV
3
͓
͔
count of these considerations, one obtains a 9ϫ9 matrix
made of the A ⌬( ϭ0), X ⌽( ϭ0), and X ⌽( ϭ1)
for the main isotopomer 48Ti35Clϩ.
3
3
3
v
v
v
3ϫ3 matrices and of the twenty ⌬⌳Þ0 off-diagonal cou-
pling elements. Let us remember that the unperturbed upper
17.8 3⌬ state is described by a 3ϫ3 matrix for each of the
V. DISCUSSION
͓
͔
A. Deperturbed parameters
ϭ0 and ϭ1 vibronic levels.
v
v
For the main isotopomer 48Ti35Clϩ, twenty-four bands
In order to validate the theoretical model used in the
fitting procedure, it is of interest to discuss the parameters
͑Fig. 1͒ including 3009 rotational lines have been simulta-
J. Chem. Phys., Vol. 107, No. 24, 22 December 1997
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Focsa et al.: Spectroscopy of TiClϩ
10369
TABLE II. Deperturbed parameters ͑in cmϪ1͒ derived from the full matrix-based treatment for the X 3⌽(
ϭ0,1), A 3⌬( ϭ0), and ͓17.8͔ 3⌬( ϭ0,1) vibronic states of 48Ti35Clϩ ͑all uncertainties are 1␴͒.
v
v
v
3
3
3
17.8
⌬
A
⌬
X ⌽
͓
͔
ϭ1
ϭ0
ϭ0
ϭ1
ϭ0
v
v
v
v
v
T
A
18 301.314͑4͒
58.1368͑3͒
Ϫ0.142(2)
2.2751͑3͒
0.27͑2͒
17 793.615͑4͒
58.2271͑2͒
Ϫ0.135(2)
2.2674͑2͒
0.26͑2͒
348.243͑8͒
55.977͑2͒
Ϫ0.87(1)
0.6939͑5͒
7.39͑5͒
484.560͑3͒
63.7906͑2͒
Ϫ0.802(2)
0.368͑2͒
0͑fixed͒
63.5298͑9͒
Ϫ0.163(6)
0.368͑2͒
1.69͑2͒
104AD
␭
105␭
1.69͑2͒
D
B
0.177 637͑3͒
0.871͑5͒
0.178 497͑3͒
0.876͑5͒
0.180 823͑6͒
0.972͑5͒
0.173 411͑3͒
0.895͑6͒
0.174 323͑6͒
0.910͑5͒
107D
listed in Table II. Among the various points that can be
checked, we can first observe that the chaotic evolution of
the B and D parameters evidenced in the polynomial fit
͑Table I͒ for the perturbed states has been eliminated. This
can note that the possible influence of the unobserved higher
vibrational levels of the ⌬ and ⌽ states has not been con-
3
3
sidered.
3
For the A ⌬ state where no more than one vibrational
3
observation is easier to do on the X ⌽ state where two
level is observed, we can only compare the order of magni-
tude of the parameters with those of the other electronic
states. We observe that the chaotic evolution of the B and D
parameters derived from the polynomial fit is now smoothed.
In most of the transition element containing diatomic
molecules, the molecular structures are strongly related to
the configuration of the involved transition-element atom or
ion32 and more precisely to the open 3d shell. According to
Bencheikh33 and Focsa et al.,16 TiClϩ can be reasonably well
described by the Ti2ϩ–ClϪ ionic structure, and the molecular
vibrational levels are studied: D is now independent of and
v
3
close to the D values of the ⌽ ( ϭ0,1) substates which
v
4
were supposed to be almost unaffected by the perturbation.
On its side, B follows now a smooth evolution with , which
v
is comparable to what is observed in the unperturbed
17.8 3⌬ state. The deperturbed positions of the vibronic
͓
͔
states can be compared with the expected vibrational con-
stants ␻ and ␻exe derived from Kratzer and Pekeris’
e
relations15 which were revealed to be satisfactorily ac-
counted for in the upper 17.8 3⌬ state.8 These relationships
configurations of the X ⌽ and the A ⌬ states are respec-
tively ͑...͒5␲1␦ and ͑...͒11␴1␦, where the valence 1␦, 5␲,
and 11␴ molecular orbitals are essentially 3dTi atomic orbit-
als. Comparison of spin-orbit constants of the ⌳Þ0 molecu-
lar electronic states and of the atomic ones can sustain this
assumption. If the 3d(␦) and 3d(␲) orbitals are not appre-
ciably changed when the bond is formed, Lefebvre-Brion
and Field17 ͑pages 87 to 92͒ show that one can write
3
3
͓
͔
give respectively ␻eϭ487.13 cmϪ1 and ␻exeϭ2.05 cmϪ1
3
for the X ⌽ state leading to a value of 483.03 cmϪ1 for
␻eϪ2␻exe , which has to be compared15 to the distance
⌬G1/2ϭ484.56 cmϪ1 between the energy origins of the
v
3
ϭ0 and ϭ1 vibrational levels of the X ⌽ state. The dis-
v
crepancy of 1.5 cmϪ1 is fully comparable to the value
2.3 cmϪ1 observed in the unperturbed 17.8 3⌬ state.8 On
͓
͔
3
3
the contrary, the evolution of AD is less satisfactory, as it is
A(X ⌽)Ϸ␨3d/2 and A(A ⌬)Ϸ␨3d/2. In the case of TiClϩ
these relationships are well fulfilled when considering the
experimental values of the molecular spin-orbit parameters
3
3
5 times larger in the X ⌽( ϭ1) than in the X ⌽( ϭ0)
v
v
state ͑Table II͒. A similar observation has been already en-
countered on small second-order parameters in the studies of
other perturbed states.25,27 This discrepancy can find its ori-
gin in neglected terms in the Hamiltonian beyond second
order. For example, centrifugal distortion is included in the
3
3
A(X ⌽)ϭ63.5 cmϪ1 and A(A ⌬)ϭ56.0 cmϪ1 ͑Table II͒
and the atomic value ␨3d(3d2)ϭ121 cmϪ1 ͑Shadmi et al.34͒.
For the sake of comparison, we can note that a similar agree-
ment is observed between the spin-orbit constant of the un-
perturbed 17.8 3⌬(3d4s) state (58 cmϪ1) and the corre-
3
3ϫ3 diagonal ⌬( ϭ0), 3⌽( ϭ0,1) matrices, but not in
v
v
͓
͔
the ⌬⌳Þ0 coupling terms ␣vv and ␤vv . Moreover, we
Ј
Ј
3
TABLE IV. Equilibrium parameters ͑in cmϪ1 unless quoted͒ for the X
and 17.8 3⌬ electronic states ͑all uncertainties are 1␴͒.
⌽
͓
͔
TABLE III. The ⌬⌳Þ0 coupling parameters ͑in cmϪ1͒ accounting for the
interactions in the A 3⌬( ϭ0)–X3⌽( ϭ0,1) complex ͑all uncertainties
are 1␴͒.
v
v
3
3
Parameter
17.8
⌬
͔
X
⌽
͓
a
␻
␻exe
Ae
511.930͑3͒
2.114͑3͒
58.2672͑5͒
0.178 927͑6͒
0.000 860͑6͒
0.878͑10͒
488.66͑1͒
2.05͑1͒
e
a
Interacting states
63.399͑1͒
X
3⌽( ϭ1)–A 3⌬( ϭ0)
vЈ
X
3⌽( ϭ0)–A 3⌬( ϭ0)
vЈ
v
v
Be
0.174 779͑9͒
0.000 912͑9͒
0.917͑9͒
a
a
␣
␣
vv
Ј
␣
vv
Ј
␤
vv
Ј
21.8615͑6͒
27.40͑1͒
0.1400͑2͒
31.01͑2͒
55.86͑1͒
e
107De
b
b
a
a
Re ͑Å͒
2.15 777͑8͒
2.1832͑1͒
0.340͑3͒
a
aExperimental values.
bTheoretical values.
␻exe is derived from the Pekeris’ relation and ␻ from ⌬G1/2ϩ2␻exe
e
͑experimental ⌬G1/2ϭ484.56 cmϪ1, see Table I͒.
J. Chem. Phys., Vol. 107, No. 24, 22 December 1997
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Focsa et al.: Spectroscopy of TiClϩ
10370
sponding atomic value34
␨
3d(3d4s)ϭ114 cmϪ1
.
The off-diagonal ␣vv and ␤vv parameters can be writ-
Ј
Ј
ten as a product of vibrational and electronic matrix elements
in which the electronic part is independent from the vibra-
tional quantum numbers and
and is used as a test of the
v
Ј
v
17
correctness of the experimental values of ␣vv and ␤vv
.
Ј
Ј
The model used to fit the perturbed levels of TiClϩ is nec-
essarily somewhat arbitrary in the absence of experimental
3
information about the upper vibrational levels of the A ⌬
3
and X ⌽ states and one may be surprised by the numerical
results obtained for the off-diagonal ␣vv and ␤vv param-
Ј
Ј
eters ͑Table III͒. Using a simple harmonic oscillator model
for the vibrational levels ͑Fig. 42, p. 77 of Ref. 15͒, the
overlapping of the wave-functions is generally expected to
be large between two ϭ0 and small between a ϭ0 and a
v
v
ϭ1 vibrational levels. However, the magnitudes of the vi-
v
brational overlap integrals are strongly related to an even
slight difference of the equilibrium distances of the interact-
ing electronic states.
In the case of TiClϩ, the rotational parameters Be of the
3
3
X ⌽ state (0.17 478 cmϪ1) and A ⌬ state ͑estimated value
0.18 127 cmϪ1͒ are close. They lead to equilibrium distances
respectively equal to 2.1832 Å and 2.1437 Å. Such a differ-
ence of 0.04 Å is very slight since it is comparable to the
variation of the internuclear distance of the lowest ( ϭ0)
v
vibrational levels of these states. Despite this, the derived
vibrational overlap integrals are equal to 0.887 between
3
3
X ⌽( ϭ0) and A ⌬( ϭ0) and to 0.435 between
v
v
3
3
X ⌽( ϭ1) and A ⌬( ϭ0). Furthermore, in order to de-
v
v
termine the theoretical values of ␣vv parameters, it is nec-
Ј
essary to estimate the contribution of the electronic matrix
elements. This can be derived from ligand field
calculations16 which show that the X ⌽ state is almost ex-
3
clusively related to the 3d2Tiϩϩ atomic configuration, while
3
the A ⌬ state is a mixing of 3d2 and 3d4s atomic configu-
rations of Tiϩϩ. The derived theoretical ␣vv parameters tak-
Ј
ing into account vibrational overlap and electronic mixing
are listed in Table III.
Even though a remaining discrepancy is observed, this
calculation sustains particularly the fact that the interaction
3
3
between the X ⌽( ϭ1) and A ⌬( ϭ0) states is made
v
v
possible and of course enhanced by the proximity of these
3
two states, while the interaction between the X ⌽( ϭ0)
v
3
and A ⌬( ϭ0) is reduced by vibrational overlap. This fi-
v
nally leads to comparable values of both ␣vv parameters,
Ј
contrary to the generally accepted idea.
B. Basis functions mixing
From the basis functions’ contribution to the eigenvec-
tors of the diagonalized matrix one can derive useful infor-
mation on the nature of the observed electronic states. This is
of peculiar interest in the case of TiClϩ where two spin-orbit
FIG. 2. The squared eigenvector coefficients associated with the nine basis
3
functions are displayed against J, for the following states: ͑a͒ X 3⌽ (
v
v
components ͑⍀ϭ2 and ⍀ϭ3͒ of each of the A ⌬( ϭ0)
v
4
ϭ1), ͑b͒ X 3⌽ ( ϭ1), ͑c͒ A 3⌬ ( ϭ0), ͑d͒ A 3⌬ ( ϭ0), ͑e͒ X 3⌽ (
3
v
v
v
3
3
2
2
and X ⌽( ϭ1) states cannot be clearly assigned. Figure 2
v
ϭ1), and ͑f͒ A 3⌬ ( ϭ0). For the mixed states the denomination of a
v
1
shows the J-evolution of the fractional character of the basis
given state refers to the leading character at low J values. The basis func-
tions contributing for less than 5% to the eigenvectors have not been la-
beled.
functions’ contribution to the eigenvector associated with
3
each of the six spin-orbit components of the A ⌬( ϭ0)
v
J. Chem. Phys., Vol. 107, No. 24, 22 December 1997
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Focsa et al.: Spectroscopy of TiClϩ
10371
to be quite efficient to record spectra of heavy atom-
containing molecules such as TiClϩ. Owing to the high sen-
sitivity of this technique it has been possible to analyze weak
and/or overlapped transitions, the study of which allowed the
3
identification of the A ⌬( ϭ0) state located 350 cmϪ1
v
3
3
above the X ⌽( ϭ0) state. The closeness of the A ⌬(
ϭ0) and X ⌽( ϭ1) states induces a strong interaction be-
v
v
3
v
tween the two states evidenced by abnormal effective param-
3
eters. A full matrix-based handling of the three A ⌬(
v
3
ϭ0), X ⌽( ϭ0,1) levels, including ⌬⌳Þ0 coupling
v
terms, has been carried out in order to determine a set of
deperturbed parameters. Only four coupling parameters have
been necessary to perform a fit as accurate as the effective
one. From the study of the contributions of the basis func-
tions to the eigenvectors of the diagonalized matrix it has
been possible to determine the mixing ratio of the ⍀ϭ3
FIG. 3. Avoided crossing of the X 3⌽ ( ϭ1) and A 3⌬ ( ϭ0) spin-orbit
v
v
1
2
¯
2
components: T (J)Ϫ¯T Ϫ¯BJ(Jϩ1)ϩD J(Jϩ1)
is displayed against
͓
͔
v
v
¯ ¯ ¯
J(Jϩ1); in this expression Tv , B and D are the arithmetical averages of the
corresponding parameters of the X 3⌽ ( ϭ1) and A 3⌬ ( ϭ0) states.
v
v
1
2
3
3
3
components of the A ⌬( ϭ0) and X ⌽( ϭ1) states and
v
v
and X ⌽( ϭ1) states for which the interactions are the
v
to evidence a reversal of the leading character of these com-
ponents. All these considerations explain the experimental
observation of many intercombination bands involving lower
states the symmetry of which is not strictly characterized.
It turns out that for the 3d2Ti2ϩ atomic configuration, to
most sensitive. Three points can be emphasized: First ͑Fig.
2͑a͒͒, the 3⌽ ( ϭ1) level is free of any mixing as it is
v
4
expected from a spin-orbit component ⍀ϭ4 which cannot
suffer any ⌬⍀ϭ0 interaction and which is far from any
other vibronic state. Second, Figs. 2͑b͒ and 2͑c͒ are a good
illustration of the strong mixing between the ⍀ϭ3 spin-orbit
9,16
3
3
which both the X ⌽ and A ⌬ states can be associated,
3
3
when considering the closeness of the atomic and molecular
spin-orbit constants, the well-known Hund rule is fulfilled at
least by the two first electronic states. In a very recent work,
components of the A ⌬( ϭ0) and X ⌽( ϭ1) states.
v
v
They provide the key to the labelling of these components as
3
3
either the A ⌬ ( ϭ0) or the X ⌽ ( ϭ1) states which is
v
v
3
3
Focsa et al.16 have shown that the lowering of the A ⌬ state
3
determined by the leading character which itself depends on
the predominant basis function’s contribution to the eigen-
vector of the studied state. An impressive evolution of the
fractional characters with J is observed inducing a reversal in
the characters of the two states at Jϭ50. The labelling of the
⍀ϭ3 spin-orbit components in both Table I and Fig. 1 re-
flects the leading character of the spin-orbit components at
low J values. A less important mixing is observed for the
⍀ϭ2 spin-orbit components which does not lead to a rever-
sal of the leading character if we consider Fig. 2͑d͒. Third,
Fig. 2͑e͒ should be expected to be symmetrical to Fig. 2͑d͒.
However, a strong mixing of the 3⌽ ( ϭ1) and 3⌬ (
from Kaledin et al.’s9 predicted location is made possible
only by taking into account the interaction between the 3d2
and 3d4s configurations.
The various works carried out these last years on TiClϩ
are a good illustration of the benefits resulting from the con-
frontation between theory9,16 and experiment,6,8 both of them
bringing their contribution to the enlightenment of the mo-
lecular structure of heavy diatomic ions and encouraging fur-
ther developments. From an experimental point of view, this
work reinforces the conviction that the velocity modulation
technique has been revealed to be one of the good ways in
order to observe weak ions signals.
v
v
1
2
ϭ0) is observed for J values higher than 70. This is due to
the action of the L-uncoupling operator characteristic of a
⌬⌳ϭϮ1, ⌬⍀ϭϮ1 interaction. This mixing induces a re-
versal of the leading character of the two states at Jϭ82
where the term values of the two states are closer than
10 cmϪ1. The symmetrical behavior is observed for the
ACKNOWLEDGMENTS
Dr. J. Rostas and Pr. R. W. Field are greatly acknowl-
edged for their useful comments on the deperturbation treat-
ment. The Centre d’Etudes et de Recherches Lasers et Ap-
3⌬ ( ϭ0) state on Fig. 2͑f͒. Figure 3 shows a textbook
v
1
`
´
plications is supported by the Ministere charge de la
3
example of avoided crossing of the A ⌬ ( ϭ0) and
v
1
´
Recherche, the Region Nord-Pas de Calais and the Fonds
3
X ⌽ ( ϭ1) states. This figure displays the evolution of
v
T (J)Ϫ¯T Ϫ¯BJ(Jϩ1)ϩD J(Jϩ1)
2
´
´
´
Europeen de Developpement Economique des Regions.
2
¯
͓
¯
against J(Jϩ1); Tv ,
͔
¯ ¯ v
v
1 C. J. Cheetham and R. F. Barrow, Trans. Faraday Soc. 63, 1835 ͑1967͒.
2 E. A. Shenyavskaya and B. S. Ryabov, J. Mol. Spectrosc. 63, 23 ͑1976͒.
3 E. A. Shenyavskaya and L. V. Gurvich, J. Mol. Spectrosc. 81, 152 ͑1980͒.
4 W. J. Balfour and B. Lindgren, Phys. Scr. 22, 36 ͑1980͒.
5 A. J. Merer, A. S.-C. Cheung, and A. W. Taylor, J. Mol. Spectrosc. 108,
343 ͑1984͒.
B and D are respectively the averages of the vibronic term
values, and of the rotational and centrifugal distortion param-
eters of the two levels. As for the reversal of the leading
character observed in Figs. 2͑e͒ and 2͑f͒, the maximum of
the effect is observed at JϷ80.
6 W. J. Balfour and K. S. Chandrasekhar, J. Mol. Spectrosc. 139, 245
͑1990͒.
7 L. A. Kaledin, A. L. Kaledin, and M. C. Heaven, J. Mol. Spectrosc. 179,
246 ͑1996͒.
VI. CONCLUSION
8 C. Focsa, C. Dufour, B. Pinchemel, I. Hadj Bachir, and T. R. Huet, J.
Chem. Phys. 106, 9044 ͑1997͒.
Absorption through an ac glow discharge associated
with a velocity modulation detection technique was revealed
J. Chem. Phys., Vol. 107, No. 24, 22 December 1997
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Focsa et al.: Spectroscopy of TiClϩ
10372
9 L. A. Kaledin, J. E. McCord, and M. C. Heaven, J. Mol. Spectrosc. 173,
499 ͑1995͒.
stitute of Physics, Physics Auxiliary Publication Service, Carolyn Gehl-
bach, 500 Sunnyside Boulevard, Woodbury, NY 11797-2999. Fax: 516-
576-2223, e-mail: paps@aip.org. The price is $1.50 for each microfiche
͑98 pages͒ or $5.00 for photocopies of up to 30 pages, and $0.15 for each
additional page over 30 pages. Airmail additional. Make checks payable to
the American Institute of Physics.
10 C. S. Gudeman, C. C. Martner, and R. J. Saykally, Phys. Rev. Lett. 50,
727 ͑1983͒.
11 C. S. Gudeman and R. J. Saykally, Annu. Rev. Phys. Chem. 35, 387
͑1984͒.
12 C. Focsa, C. Dufour, B. Pinchemel, I. Hadj Bachir, and T. R. Huet, in
Proceedings of the 52nd Symposium on Molecular Spectroscopy, Colum-
bus, Ohio, 1997 ͑unpublished͒.
24 See AIP Document No. PAPS JCPSA-106-9044-28 for 28 pages of tables.
Order by PAPS number and journal reference from American Institute of
Physics, Physics Auxiliary Publication Service, Carolyn Gehlbach, 500
Sunnyside Boulevard, Woodbury, NY 11797-2999. Fax: 516-576-2223,
e-mail: paps@aip.org. The price is $1.50 for each microfiche ͑98 pages͒ or
$5.00 for photocopies of up to 30 pages, and $0.15 for each additional
page over 30 pages. Airmail additional. Make checks payable to the
American Institute of Physics.
13 M. G. Bawendi, B. D. Rehfuss, and T. Oka, J. Chem. Phys. 93, 6200
͑1990͒.
14 S. Gerstenkorn and P. Luc, Atlas du Spectre de l’Iode ͑CNRS, Paris,
1978͒.
15 G. Herzberg, Spectra of Diatomic Molecules, 2nd ed. ͑Van Nostrand,
Princeton, NJ, 1950͒.
25 R. C. Stern, R. H. Gammon, M. E. Lesk, R. S. Freund, and W. A. Klem-
perer, J. Chem. Phys. 52, 3467 ͑1970͒.
16 C. Focsa, M. Bencheikh, and L. G. M. Pettersson, submitted to J. Phys. B.:
At. Mol. Opt. Phys.
26 R. H. Gammon, R. C. Stern, and W. Klemperer, J. Chem. Phys. 54, 2151
͑1971͒.
17 H. Lefebvre-Brion and R. W. Field, Perturbations in the Spectra of Di-
atomic Molecules ͑Academic, New York, 1986͒.
27 R. W. Field and T. H. Bergeman, J. Chem. Phys. 54, 2936 ͑1971͒.
28 R. W. Field, S. G. Tilford, R. A. Howard, and J. D. Simmons, J. Mol.
Spectrosc. 44, 347 ͑1972͒.
18
´
´
J.-L. Femenias, Can. J. Phys. 55, 1733 ͑1977͒.
19 J. M. Brown, E. A. Colbourn, J. K. G. Watson, and F. D. Wayne, J. Mol.
Spectrosc. 74, 294 ͑1979͒.
29 R. W. Field, B. G. Wicke, J. D. Simmons, and S. G. Tilford, J. Mol.
Spectrosc. 44, 383 ͑1972͒.
20
´
´
´
J.-L. Femenias, C. Athenour, K. M. Rao, and T. M. Dunn, J. Mol. Spec-
trosc. 130, 269 ͑1988͒.
30 B. G. Wicke, R. W. Field, and W. Klemperer, J. Chem. Phys. 56, 5758
͑1972͒.
21 Y. Azuma, J. A. Barry, M. P. J. Lyny, A. J. Merer, J. O. Schroder, and
J.-L. Femenias, J. Chem. Phys. 91, 1 ͑1989͒.
31 D. Cossart, M. Horani, and J. Rostas, J. Mol. Spectrosc. 67, 283 ͑1977͒.
32 A. J. Merer, Annu. Rev. Phys. Chem. 40, 407 ͑1989͒.
33 M. Bencheikh, J. Mol. Spectrosc. 183, 419 ͑1997͒.
´
´
22 A. S.-C. Cheung, W. Zyrnicki, and A. J. Merer, J. Mol. Spectrosc. 104,
315 ͑1984͒.
23 See AIP Document No. PAPS JCPSA-107-10365-23 for 23 pages of
tables. Order by PAPS number and journal reference from American In-
34 Y. Shadmi, E. Caspi, and J. Oreg, J. Res. Natl. Bur. Stand. Sect. A 73, 173
͑1969͒.
J. Chem. Phys., Vol. 107, No. 24, 22 December 1997
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