Laser velocity modulation spectroscopy of TiCl + : Observation of the A 3 Δ(3d 2 ) stateand deperturbation of the X 3 Φ−A 3 Δ complexC. 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 Published by the AIP Publishing Articles you may be interested in A new, definitive analysis of a very old spectrum: The highly perturbed A 2Πu–X 2Πg band system of the chlorinecation ( Cl 2 + ) J. Chem. Phys. 137, 194317 (2012); 10.1063/1.4765334 Ab initio theoretical studies on U 3+ and on the structure and spectroscopy of U 3+ substitutional defects in Cs 2NaYCl 6 , 5f 2 6d 1 manifold J. Chem. Phys. 118, 5335 (2003); 10.1063/1.1555120 Rotationally resolved à 2 Π g ←X 2 Π u electronic spectrum of triacetylene cation by frequency modulationabsorption spectroscopy J. Chem. Phys. 110, 296 (1999); 10.1063/1.478065 Velocity modulated laser absorption spectroscopy of TiCl + J. Chem. Phys. 107, 7020 (1997); 10.1063/1.474944 Laser velocity modulation spectroscopy of the 3 Δ(3d4s)–X 3 Φ(3d 2 ) visible system of TiCl + andcharacterization of the spin–orbit structure J. Chem. Phys. 106, 9044 (1997); 10.1063/1.474036

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Laser velocity modulation spectroscopy of TiCl 1: Observationof the A 3D„3d 2

… state and deperturbation of the X 3F2A 3D complexC. Focsa and B. PinchemelLaboratoire de Dynamique Mole´culaire et Photonique, URA CNRS 779, Centre d’Etudes et de RecherchesLasers et Applications, Universite´ des Sciences et Technologies de Lille 59 655 Villeneuve d’Ascq cedex,France

J.-L. FemeniasInstitut 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 Laserset Applications, Universite´ des Sciences et Technologies de Lille, 59 655 Villeneuve d’Ascq Cedex, France

~Received 8 July 1997; accepted 22 September 1997!

A single mode cw dye laser along with velocity modulation was used to record weak bands of TiCl1

in the spectral region 17 100– 18 600 cm21. The ions were produced in the positive column of an acglow discharge with a gas mixture of He/TiCl4. These new bands have been identified as linking theupper already known@17.8# 3D(3d4s) state to respectively theX 3F(v51) state and to a newlyobservedA 3D(v50) state located 350 cm21 above theX 3F(v50) state. As suggested by Focsaet al. ~J. Chem. Phys.106, 9044~1997!! the A 3D(3d2) state was found to be responsible for theperturbations observed in theX 3F(3d2) state. The spin-orbit components of theA 3D(v50) andthe X 3F(v51) states revealed interaction leading to homogeneous and heterogeneousperturbations. A set of deperturbed parameters has been determined with the help of a fullmatrix-based handling of theA 3D(v50) and theX 3F(v50,1) states. Study of the contributionsof the basis functions to the eigenvectors of the diagonalized matrix displayed evidence of a reversalof the leading character of theV53 spin-orbit components of theA 3D(v50) and theX 3F(v51) states. A remarkable example of avoided crossing has been observed between theA 3D1(v50!and the X 3F2(v51) spin-orbit components. ©1997 American Institute of Physics.@S0021-9606~97!02748-7#

I. INTRODUCTION

The spectroscopic study of diatomic radicals and ionshas been the subject of numerous papers in the past becausestrong emission spectra were observed from the visible to theUV range. However, it is rather limited in the case of ionscontaining heavy atoms, like metals, due to the technicaldifficulties associated with the generation and detection ofthese species. Very few high-resolution experimental dataare available, and most of them consist of emission spectrarecorded from electrical discharges.1–6 With the develop-ment of sensitive and selective detection schemes, the studyof heavy diatomic and polyatomic molecular ions producedin appropriate sources has been made possible.7,8 The experi-mental setup that we are developing in Lille aims to studysuch species by means of laser velocity modulation spectros-copy.

As a first stage, we recently published8 the analysis ofthe @17.8# 3D –X 3F(v50) transition of TiCl1 which hadbeen observed and tentatively assigned as a3P –3D transi-tion by Balfour and Chandrasekhar,6 while a theoreticalstudy by Kaledinet al.9 suggested the ground state to bea 3F state. Our study confirmed the3F symmetry of the

ground state of TiCl1. Moreover the observation of inter-combinationDV50 transitions between the@17.8# 3D andthe X 3F(v50) states allowed the first experimental deter-mination of the spin orbit constants of the two states. In thatpaper we noted that theX 3F(v50) state was affected by aperturbation which prevented the description of this state bya full matrix-based representation.

Using the same experimental velocity modulationtechnique10,11 as in our first paper on TiCl1 we have re-corded new spectral regions and congested ones in order toidentify weak remaining bands.12 No less than 16 new bandshave been identified, all of them sharing the same upper@17.8# 3D(v50,1,2) state.

In the present paper we report the observation of a new@17.8# 3D(3d4s)2A 3D(3d2) system of TiCl1. TheA 3D(3d2) state has been identified and fully characterizedin its ground vibrational level, which is located only350 cm21 above theX 3F(v50) state. In addition the~0,1!and ~1,1! vibrational bands of the @17.8# 3D(3d4s)2X 3F(3d2) system were observed. The newly observedlines combined with our previous results8 have been fitted inorder to determine a consistent set of deperturbed parametersfor the A 3D(v50) andX 3F(v50,1) states.

The present work is the first experimental study leadinga!Author to whom correspondence should be addressed. Electronic mail:therese.huet@univ-lille1.fr

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to a fully comprehensive energy diagram of TiCl1 below1000 cm21.

II. EXPERIMENT

The experimental apparatus has been described in detailin our previous paper.8 Only the main characteristics are re-minded. A Coherent 899-29 ring cw dye laser pumped by anAr1 laser~Coherent CR20! was employed to record a spec-trum of TiCl1. The ions were produced in the positive col-umn of an ac glow discharge driven at 30 kHz with typicalsinusoidal current of 300 mA peak-to-peak and voltage of 1kV peak-to-peak, and in a gas mixture ofHe/TiCl457/0.1 Torr. The velocity modulation detectiontechnique10,11 and a noise subtraction technique13 were usedin order to eliminate signals from the neutral species and toreduce the noise fluctuations from the lasers and the dis-charge, respectively. The spectra were recorded using theCoherent Autoscan software and were calibrated against io-dine lines14 with an accuracy of 0.005 cm21.

Revisitation of the 17 100– 18 600 cm21 region has beenperformed in order to record weak features of the spectrumand to identify bands overlapped by intense and alreadyknown transitions.8 Therefore most spectra were recordedwith a time constant of 300 ms and a sensitivity of 500mV.In addition we have scanned the 14 700– 17 100 cm21 spec-tral region, in which no signal has been observed.

III. OBSERVED BANDS

Two systems of new bands have been identified~Fig. 1!,and all of them reach the well-known upper@17.8# 3D state.8

The first system is concerned with thev51 vibrational level

of the X 3F as lower state. Both main and intercombinationbands are observed. We can notice that the distances betweenthe v50 andv51 vibrational levels of theX 3F state donot lead to a commonDG1/2 value for the three spin-orbitcomponents, suggesting the presence of perturbations insome of the spin-orbit components of this state. Obviously,we can notice that the Pekeris and Kratzer15 expressions,linking the vibrationalve andvexe parameters to theB andD rotational parameters, are best accounted for in the3F4

v50 andv51 substates which can be assumed to be free ofperturbations in absence of anyV54 level of a close lyingelectronic state.9,16 The second system is located between17 400 and 17 500 cm21 for the Dv50 sequence and be-tween 17 950 and 18 000 cm21 for the Dv511 sequence.In the absence ofQ branches, these bands fairly equallyspaced are characteristic ofDV50 transitions involvinga 3D state. In addition, very weak intercombinationDV521 bands linking the@17.8# 3D state to the newly ob-served3D state, which will be now labeledA 3D, have beenobserved around 17 300 cm21 and 17 850 cm21. These redshaded bands are mostly headless up toJ560 in our spectra.The presence of intercombination bands allows each vibra-tional level of the three electronic states~except thev52level of the@17.8# 3D1 state! to be involved in two to fourtransitions. This leads to a confident energy level diagram~Fig. 1!. Due to the close lying positions of theA 3D(v50) andX 3F(v51) states, it obviously appeared that per-turbations could be expected between the two states. Themost striking feature is the closeness of the twoV53 spin-orbit components of theA 3D(v50) and X 3F(v51)states. Neither the intensity of the main and intercombinationbands nor the shape of these bands which all share a lower

FIG. 1. The energy level diagram and the observed transitions of the@17.8# 3D(3d4s)2X 3F(3d2) and the@17.8# 3D(3d4s)2A 3D(3d2) visible systemsof TiCl1. The states are located at their effective positions in agreement with Table I.

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V53 spin-orbit component can help to identify the two lev-els observed at 635 cm21 and 700 cm21 as the A 3D3(v50) or theX 3F3(v51) state. The same observation can bedone on theV52 spin-orbit components which are locatedat 474 cm21 and 559 cm21.

The presence of perturbations was confirmed by rota-tional analysis based on a polynomial effective model usedto describe each of the spin-orbit vibrational levels of thethreeX 3F, A 3D and @17.8# 3D states. This has been doneonly on the most abundant isotopomer48Ti35Cl1 because ofthe weakness of the observed bands. Table I summarizes theparameters derived from this fit which allows an easy re-building of the experimental data. Numerous values listed inthis table indicate that the lower statesA 3D(v50),X 3F(v51) and evenX 3F(v50) cannot be considered asisolated states following the Born–Oppenheimerapproximation15 to the contrary of what it is observed for the@17.8# 3D state. We can see, for example, that large and evennegativeD values are derived from the fit; moreover, chaoticevolution of theB rotational parameters is noted in the twostates 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 givenV53 spin-orbit com-ponent of theA 3D(v50) or theX 3F(v51) states basedon the effective rotational parameters stays meaningless atthis state of the work.

The above considerations sustain the idea that theX 3F(v50,1) and theA 3D(v50) states must be treated bya full direct approach matrix-based method17 which will givean useful insight on the assignment of theV53 andV52spin-orbit components. It is noticeable that no local pertur-bation has been observed nor any fine structure in the studiedbands.

IV. THEORETICAL MODEL AND LEAST-SQUARESPROCEDURE

Many authors have dealt with diatomic Hamiltonians,including spin-orbit and rotational structure, and other higherorder effects.17–21 Particularly, the diagrammatic methodshown in Ref. 18 has been successfully used in order to

localize theV53 spin-component of theA 3D(v50) level.The observation of the other components of this level and ofthe three components of theX 3F(v51) level, and moreprecisely the effective values of the parameters, suggested astrong perturbation between theX 3F(v51) and A 3D(v50) levels. A preliminary deperturbation procedure, takinginto account perturbation contributions up to the fourth or-der, allowed us to predict the effective parameters of theA 3D3(v50) component: the energy origin was estimated tolie between 626 and 654 cm21, the effective rotational con-stantBeff between 0.1766 and 0.1779 cm21, and the effectivecentrifugal stretchingDeff about 431027 cm21 ~that is anexceptionally large value in the present case!. The observedvalues were finally 635.187 cm21, 0.178793 cm21, and3.7331027 cm21, respectively~see Table I!.

In the following, we shall use the notation of Brownet al.19 and Lefebvre-Brion and Field.17 The effective Hamil-tonian used for the analysis of the spin-orbit and rotationalstructures is given by the following expression:

H5HEV1HSO1HSS1HROT, ~1!

whereHEV is the vibronic part of the Hamiltonian, and thespin-orbit, spin-spin~or second-order spin-orbit22!, and rota-tional parts are defined respectively by the forms

HSO5A~r !L zSz11

2A~r !~L1S21L2S1!

11

2AD@~J2L2S!2,L•S#1 , ~2!

HSS5Fl1lD~J2L2S!2,Sz22

1

3S2G

1

, ~3!

HROT51

2mr 2 @~J22Jz2!1~L22L z

2!1~S22Sz2!#

11

2mr 2 @~L1S21L2S1!2~J1S21J2S1!

2~J1L21J2L1!#2D~J2L2S!4. ~4!

TABLE I. Effective parameters~in cm21! for the spin-orbit components of theX 3F(v50,1), A 3D(v50), and@17.8#3D(v50,1,2) states of48Ti35Cl1 ~alluncertainties are 1s!.

@17.8# 3D(v50) @17.8# 3D(v51) @17.8# 3D(v52)

V51 V52 V53 V51 V52 V53 V51

Tv 17 873.181~1! 17 984.744~1! 18 104.657~1! 18 381.064~1! 18 492.433~1! 18 612.183~1! 18 884.354~1!Bv 0.177 953~3! 0.178 532~3! 0.179 005~3! 0.177 102~3! 0.177 673~3! 0.178 150~3! 0.176 244~4!107Dv 0.796~7! 0.881~5! 0.916~6! 0.860~6! 0.878~5! 0.938~7! 0.892~10!

X 3F(v50) X 3F(v51) A 3D(v50)

V52 V53 V54 V52 V53 V54 V51 V52 V53

Tv 0 188.555~1! 382.727~1! 473.910~1! 700.136~1! 868.089~1! 431.261~1! 558.613~1! 635.187~1!Bv 0.173 912~3! 0.174 111~3! 0.174 029~3! 0.174 621~4! 0.176 412~3! 0.173 614~3! 0.180 479~5! 0.179 692~4! 0.178 793~4!107Dv 0.888~6! 0.882~5! 0.831~6! 2.04~1! 21.78(1) 0.796~7! 0.80~3! 0.10~1! 3.73~1!1011H 1.55~2! 20.49(1) 21.12(5) 20.50(1) 0.27~2!

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For an unperturbed3D or 3F state described in theHund’s case~a!, one obtains a 333 matrix as used in ourprevious paper.8 In these expressions the 1/2mr 2 factor ~r isthe internuclear distance andm the reduced mass of the mol-ecule! originates the well-known rotationalBv parameter.When two vibronic states are close enough to perturb eachother it is necessary to take into account these interactions byadding to the 333 matrices of the isolated states the cou-pling elements arising from the presence of the(1/2mr 2)L6S7, 2(1/2mr 2)J6L7 andA(r )L6S7 operatorsin the Hamiltonian. These terms, which are usually neglectedin the Born–Oppenheimer approximation,15 link bases func-tions which differ by at least one of theL or V quantumnumbers. According to Lefebvre-Brion and Field,17 we con-sider the three coupling operators and the derived off-diagonal elements as follows:

~1! 12A(r )L6S7 giving rise to homogeneous (DV50)

spin-orbit perturbations between states withDL561:

K v,L,S,VU12 A~r !L7S6Uv8,L61,S71,V L5avv8AS~S11!2S~S71!, ~5!

where avv85^v,Lu 12A~r !uv8L7,L61&, ~6!

~2! (1/2mr 2)L6S7 giving rise to homogeneous spin-electronic perturbations between states withDL561:

K v,L,S,VU 1

2mr 2 L7S6Uv8,L61,S71,V L5bvv8AS~S11!2S~S71!, ~7!

where bvv85 K v,LU 1

2mr 2 L7Uv8,L61L ; ~8!

~3! 2(1/2mr 2)J6L7 giving rise to heterogeneous (DV561) electronic-rotational perturbations~L -uncoupling!:

K v,L,S,VU2 1

2mr 2 L7J6Uv8,L61,S,V61L52bvv8AJ~J11!2V~V61!. ~9!

In our previous paper8 we observed that it was not pos-sible to fit the data with a fully matrix-based representationdirectly derived from the Hamiltonian for theX 3F(v50)state and we noticed that it was necessary to introduce aneffective model by sharing the matrix of theX 3F(v50)state in two parts and that it was not out of question that thisstate was perturbed. As a consequence we decided to includethe X 3F(v50) state in the interaction matrix even if thisstate is 350 cm21 away from theA 3D(v50) state. On ac-count of these considerations, one obtains a 939 matrixmade of theA 3D(v50), X 3F(v50), and X 3F(v51)333 matrices and of the twentyDLÞ0 off-diagonal cou-pling elements. Let us remember that the unperturbed upper@17.8# 3D state is described by a 333 matrix for each of thev50 andv51 vibronic levels.

For the main isotopomer48Ti35Cl1, twenty-four bands~Fig. 1! including 3009 rotational lines have been simulta-

neously fitted in order to derive the deperturbed molecularconstants of the involved states. 1740 lines are newly ob-served~the set of assigned lines has been placed in PhysicsAuxiliary Publication Service~PAPS!23!, while the 1269 re-maining ones were already published in our previouspaper.8,24 All the lines were weighted to an experimentaluncertainty equal to60.005 cm21.

Numerous studies are devoted to transitions involvingperturbed electronic states.25–31 Usually, the observation fora given electronic state of perturbed and unperturbed vibra-tional levels allows an extrapolation from the parameters ofthe unperturbed vibrational levels to predict the expectedvalues of the constants of the perturbed levels. Even more,these extrapolated values are often held fixed in the fittingprocedure in order to reduce the number of freedom degreesof the system.26 Such an opportunity does not occur in thecase of TiCl1 where it appears that all the studied vibrationallevels of theA 3D andX 3F states are perturbed.

In the fitting procedure all the parameters were allowedto vary freely. As explained in our previous paper,8 each ofthe 333 matrices accounting for a given vibronic state in-cludes seven parameters to be calculated:Tv is the vibronicterm value,B is the rotational constant,A andl are the first-and second-order spin-orbit constants; to each of the threelast parameters is associated a centrifugal distortion constant,respectively namedD, AD andlD . A unique set of param-etersl andlD has been used for thev50 andv51 vibra-tional levels of theX 3F state. Wickeet al.30 showed thatthese two parameters are essentially independent ofv. Thisis effectively observed in the upper@17.8# 3D state.

Following the previously described model, four couplingparameters appear in the twenty off-diagonal terms account-ing for the perturbations:a00 and b00 for the X 3F(v50)2A 3D(v50) interaction and the correspondinga10 andb10 for the X 3F(v51)2A 3D(v50) interaction. The de-rived molecular parameters for theX 3F(v50,1), A 3D(v50) and@17.8# 3D states and the coupling parametersavv8andbvv8 are respectively listed in Tables II and III. In orderto compare Table I and Table II, it should be noted that theorigin of the energies in the effective polynomial fit has beenfixed to T0(X 3F2(v50))50, when it has been fixed toT0(X 3F(v50))50 for the fully deperturbed model. Theconversion factor between these two values isT0(X 3F(v50))5T0(X 3F2(v50))1194.501 cm21. The overallstandard deviation is 0.0056 cm21 for the deperturbedmatrix-based model. This value is quite close to the esti-mated experimental accuracy (0.005 cm21). The comparisonwith the overall standard deviation of the polynomial fit(0.0054 cm21) suggests that the matrix-based model used tofit the experimental data is satisfying. Equilibrium constantsof the @17.8# 3D and theX 3F states are listed in Table IVfor the main isotopomer48Ti35Cl1.

V. DISCUSSION

A. Deperturbed parameters

In order to validate the theoretical model used in thefitting procedure, it is of interest to discuss the parameters

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listed in Table II. Among the various points that can bechecked, we can first observe that the chaotic evolution ofthe B and D parameters evidenced in the polynomial fit~Table I! for the perturbed states has been eliminated. Thisobservation is easier to do on theX 3F state where twovibrational levels are studied:D is now independent ofv andclose to theD values of the3F4(v50,1) substates whichwere supposed to be almost unaffected by the perturbation.On its side,B follows now a smooth evolution withv, whichis comparable to what is observed in the unperturbed@17.8# 3D state. The deperturbed positions of the vibronicstates can be compared with the expected vibrational con-stants ve and vexe derived from Kratzer and Pekeris’relations15 which were revealed to be satisfactorily ac-counted for in the upper@17.8# 3D state.8 These relationshipsgive respectivelyve5487.13 cm21 and vexe52.05 cm21

for the X 3F state leading to a value of 483.03 cm21 forve22vexe , which has to be compared15 to the distanceDG1/25484.56 cm21 between the energy origins of thev50 andv51 vibrational levels of theX 3F state. The dis-crepancy of 1.5 cm21 is fully comparable to the value2.3 cm21 observed in the unperturbed@17.8# 3D state.8 Onthe contrary, the evolution ofAD is less satisfactory, as it is5 times larger in theX 3F(v51) than in theX 3F(v50)state~Table II!. A similar observation has been already en-countered on small second-order parameters in the studies ofother perturbed states.25,27 This discrepancy can find its ori-gin in neglected terms in the Hamiltonian beyond secondorder. For example, centrifugal distortion is included in the333 diagonal3D(v50), 3F(v50,1) matrices, but not inthe DLÞ0 coupling termsavv8 and bvv8 . Moreover, we

can note that the possible influence of the unobserved highervibrational levels of the3D and3F states has not been con-sidered.

For theA 3D state where no more than one vibrationallevel is observed, we can only compare the order of magni-tude of the parameters with those of the other electronicstates. We observe that the chaotic evolution of theB andDparameters derived from the polynomial fit is now smoothed.

In most of the transition element containing diatomicmolecules, the molecular structures are strongly related tothe configuration of the involved transition-element atom orion32 and more precisely to the open 3d shell. According toBencheikh33 and Focsaet al.,16 TiCl1 can be reasonably welldescribed by the Ti21–Cl2 ionic structure, and the molecularconfigurations of theX 3F and theA 3D states are respec-tively ~...!5p1d and ~...!11s1d, where the valence 1d, 5p,and 11s molecular orbitals are essentially 3dTi atomic orbit-als. Comparison of spin-orbit constants of theLÞ0 molecu-lar electronic states and of the atomic ones can sustain thisassumption. If the 3d(d) and 3d(p) orbitals are not appre-ciably changed when the bond is formed, Lefebvre-Brionand Field17 ~pages 87 to 92! show that one can writeA(X 3F)'z3d/2 andA(A 3D)'z3d/2. In the case of TiCl1

these relationships are well fulfilled when considering theexperimental values of the molecular spin-orbit parametersA(X 3F)563.5 cm21 and A(A 3D)556.0 cm21 ~Table II!and the atomic valuez3d(3d2)5121 cm21 ~Shadmiet al.34!.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# 3D(3d4s) state (58 cm21) and the corre-

TABLE IV. Equilibrium parameters~in cm21 unless quoted! for the X 3Fand @17.8#3D electronic states~all uncertainties are 1s!.

Parameter @17.8#3D X 3F

ve 511.930~3! 488.66~1!a

vexe 2.114~3! 2.05~1!a

Ae 58.2672~5! 63.399~1!Be 0.178 927~6! 0.174 779~9!ae 0.000 860~6! 0.000 912~9!107De 0.878~10! 0.917~9!Re ~Å! 2.15 777~8! 2.1832~1!

avexe is derived from the Pekeris’ relation andve from DG1/212vexe

~experimentalDG1/25484.56 cm21, see Table I!.

TABLE II. Deperturbed parameters~in cm21! derived from the full matrix-based treatment for theX 3F(v50,1), A 3D(v50), and@17.8# 3D(v50,1) vibronic states of48Ti35Cl1 ~all uncertainties are 1s!.

@17.8#3D A 3D X 3F

v51 v50 v50 v51 v50

T 18 301.314~4! 17 793.615~4! 348.243~8! 484.560~3! 0~fixed!A 58.1368~3! 58.2271~2! 55.977~2! 63.7906~2! 63.5298~9!104AD 20.142(2) 20.135(2) 20.87(1) 20.802(2) 20.163(6)l 2.2751~3! 2.2674~2! 0.6939~5! 0.368~2! 0.368~2!105lD 0.27~2! 0.26~2! 7.39~5! 1.69~2! 1.69~2!B 0.177 637~3! 0.178 497~3! 0.180 823~6! 0.173 411~3! 0.174 323~6!107D 0.871~5! 0.876~5! 0.972~5! 0.895~6! 0.910~5!

TABLE III. The DLÞ0 coupling parameters~in cm21! accounting for theinteractions in theA 3D(v50) –X3F(v50,1) complex~all uncertaintiesare 1s!.

Interacting states

X 3F(v51) –A 3D(v850) X 3F(v50) –A 3D(v850)

avv8 21.8615~6!a 31.01~2!a

avv8 27.40~1!b 55.86~1!b

bvv8 0.1400~2!a 0.340~3!a

aExperimental values.bTheoretical values.

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sponding atomic value34 z3d(3d4s)5114 cm21.The off-diagonalavv8 andbvv8 parameters can be writ-

ten as a product of vibrational and electronic matrix elementsin which the electronic part is independent from the vibra-tional quantum numbersv andv8 and is used as a test of thecorrectness of the experimental values ofavv8 and bvv8 .17

The model used to fit the perturbed levels of TiCl1 is nec-essarily somewhat arbitrary in the absence of experimentalinformation about the upper vibrational levels of theA 3DandX 3F states and one may be surprised by the numericalresults obtained for the off-diagonalavv8 and bvv8 param-eters~Table III!. Using a simple harmonic oscillator modelfor the vibrational levels~Fig. 42, p. 77 of Ref. 15!, theoverlapping of the wave-functions is generally expected tobe large between twov50 and small between av50 and av51 vibrational levels. However, the magnitudes of the vi-brational overlap integrals are strongly related to an evenslight difference of the equilibrium distances of the interact-ing electronic states.

In the case of TiCl1, the rotational parametersBe of theX 3F state (0.17 478 cm21) andA 3D state~estimated value0.18 127 cm21! are close. They lead to equilibrium distancesrespectively 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 thevariation of the internuclear distance of the lowest (v50)vibrational levels of these states. Despite this, the derivedvibrational overlap integrals are equal to 0.887 betweenX 3F(v50) and A 3D(v50) and to 0.435 betweenX 3F(v51) andA 3D(v50). Furthermore, in order to de-termine the theoretical values ofavv8 parameters, it is nec-essary to estimate the contribution of the electronic matrixelements. This can be derived from ligand fieldcalculations16 which show that theX 3F state is almost ex-clusively related to the 3d2Ti11 atomic configuration, whiletheA 3D state is a mixing of 3d2 and 3d4s atomic configu-rations of Ti11. The derived theoreticalavv8 parameters tak-ing into account vibrational overlap and electronic mixingare listed in Table III.

Even though a remaining discrepancy is observed, thiscalculation sustains particularly the fact that the interactionbetween theX 3F(v51) and A 3D(v50) states is madepossible and of course enhanced by the proximity of thesetwo states, while the interaction between theX 3F(v50)and A 3D(v50) is reduced by vibrational overlap. This fi-nally leads to comparable values of bothavv8 parameters,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 isof peculiar interest in the case of TiCl1 where two spin-orbitcomponents~V52 andV53! of each of theA 3D(v50)andX 3F(v51) states cannot be clearly assigned. Figure 2shows theJ-evolution of the fractional character of the basisfunctions’ contribution to the eigenvector associated witheach of the six spin-orbit components of theA 3D(v50)

FIG. 2. The squared eigenvector coefficients associated with the nine basisfunctions are displayed againstJ, for the following states:~a! X 3F4(v51), ~b! X 3F3(v51), ~c! A 3D3(v50), ~d! A 3D2(v50), ~e! X 3F2(v51), and ~f! A 3D1(v50). For the mixed states the denomination of agiven state refers to the leading character at lowJ values. The basis func-tions contributing for less than 5% to the eigenvectors have not been la-beled.

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and X 3F(v51) states for which the interactions are themost sensitive. Three points can be emphasized: First~Fig.2~a!!, the 3F4(v51) level is free of any mixing as it isexpected from a spin-orbit componentV54 which cannotsuffer any DV50 interaction and which is far from anyother vibronic state. Second, Figs. 2~b! and 2~c! are a goodillustration of the strong mixing between theV53 spin-orbitcomponents of theA 3D(v50) and X 3F(v51) states.They provide the key to the labelling of these components aseither theA 3D3(v50) or theX 3F3(v51) states which isdetermined by the leading character which itself depends onthe predominant basis function’s contribution to the eigen-vector of the studied state. An impressive evolution of thefractional characters withJ is observed inducing a reversal inthe characters of the two states atJ550. The labelling of theV53 spin-orbit components in both Table I and Fig. 1 re-flects the leading character of the spin-orbit components atlow J values. A less important mixing is observed for theV52 spin-orbit components which does not lead to a rever-sal of the leading character if we consider Fig. 2~d!. Third,Fig. 2~e! should be expected to be symmetrical to Fig. 2~d!.However, a strong mixing of the3F2(v51) and 3D1(v50) is observed forJ values higher than 70. This is due tothe action of theL-uncoupling operator characteristic of aDL561, DV561 interaction. This mixing induces a re-versal of the leading character of the two states atJ582where the term values of the two states are closer than10 cm21. The symmetrical behavior is observed for the3D1(v50) state on Fig. 2~f!. Figure 3 shows a textbookexample of avoided crossing of theA 3D1(v50) andX 3F2(v51) states. This figure displays the evolution ofTv(J)2Tv2BJ(J11)1D@J(J11)#2 againstJ(J11); Tv ,B and D are respectively the averages of the vibronic termvalues, and of the rotational and centrifugal distortion param-eters of the two levels. As for the reversal of the leadingcharacter observed in Figs. 2~e! and 2~f!, the maximum ofthe effect is observed atJ'80.

VI. CONCLUSION

Absorption through an ac glow discharge associatedwith a velocity modulation detection technique was revealed

to be quite efficient to record spectra of heavy atom-containing molecules such as TiCl1. Owing to the high sen-sitivity of this technique it has been possible to analyze weakand/or overlapped transitions, the study of which allowed theidentification of the A 3D(v50) state located 350 cm21

above theX 3F(v50) state. The closeness of theA 3D(v50) andX 3F(v51) states induces a strong interaction be-tween the two states evidenced by abnormal effective param-eters. A full matrix-based handling of the threeA 3D(v50), X 3F(v50,1) levels, including DLÞ0 couplingterms, has been carried out in order to determine a set ofdeperturbed parameters. Only four coupling parameters havebeen necessary to perform a fit as accurate as the effectiveone. From the study of the contributions of the basis func-tions to the eigenvectors of the diagonalized matrix it hasbeen possible to determine the mixing ratio of theV53components of theA 3D(v50) andX 3F(v51) states andto evidence a reversal of the leading character of these com-ponents. All these considerations explain the experimentalobservation of many intercombination bands involving lowerstates the symmetry of which is not strictly characterized.

It turns out that for the 3d2Ti21 atomic configuration, towhich both theX 3F andA 3D states can be associated,9,16

when considering the closeness of the atomic and molecularspin-orbit constants, the well-known Hund rule is fulfilled atleast by the two first electronic states. In a very recent work,Focsaet al.16 have shown that the lowering of theA 3D statefrom Kaledin et al.’s9 predicted location is made possibleonly by taking into account the interaction between the 3d2

and 3d4s configurations.The various works carried out these last years on TiCl1

are a good illustration of the benefits resulting from the con-frontation between theory9,16 and experiment,6,8 both of thembringing 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, thiswork reinforces the conviction that the velocity modulationtechnique has been revealed to be one of the good ways inorder to observe weak ions signals.

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-plications is supported by the Ministe`re charge´ de laRecherche, the Re´gion Nord-Pas de Calais and the FondsEuropeen de De´veloppement Economique des Re´gions.

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