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Journal of Quantitative Spectroscopy &Radiative Transfer

Journal of Quantitative Spectroscopy & Radiative Transfer 148 (2014) 13–17

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Extended analysis of the B2Σþ–X2Σþ and A2Π–X2Σþ

systems of ZrN

Soumen Bhattacharyya a, Sheo Mukund a,b,Suresh Yarlagadda b, S.G. Nakhate a,b,n

a Atomic and Molecular Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, Indiab Homi Bhabha National Institute, Bhabha Atomic Research Centre, Mumbai 400 085, India

a r t i c l e i n f o

Article history:Received 10 February 2014Received in revised form14 June 2014Accepted 16 June 2014Available online 23 June 2014

Keywords:ZrNElectronic spectraJet-cooled molecular beamLIF spectroscopyRotationalVibrational constants

x.doi.org/10.1016/j.jqsrt.2014.06.00973/& 2014 Elsevier Ltd. All rights reserved.

esponding author at: Atomic and MolecularAtomic Research Centre, Mumbai 400 085,1 22 25592362; fax: þ91 22 25505151.ail address: nakhate@barc.gov.in (S.G. Nakha

a b s t r a c t

Rotationally resolved spectra of (1,0), (1,1), (2,0), (2,1) and (2,3) bands of B2Σþ–X2Σþ and(3,3) band of A2Π–X2Σþ systems have been measured in a laser-induced fluorescencespectra of jet cooled ZrN molecule. Rotational analysis have been extended to include thelevels ν¼3 of X2Σþ , ν¼1,2 of B2Σþ and ν¼3 of A2Π states. The vibrational constants ofthe X2Σþ state have been determined. Perturbations were observed in all the rotationalbranches of the B–X system and A2Π1/2f–X

2Σþ subband.& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Using conventional emission spectroscopy, Bates and Dunn[1] first recorded the spectra of ZrN molecule, the (0,0) bandof B2Σþ–X2Σþ system in violet and (0,0), (1,1), and (2,2)bands of A2Π–X2Σþ system in yellow spectral range. Theydetermined the molecular constants for v¼0 of X2Σþ andB2Σþ and v¼0–2 of A2Π states. In the yellow system, theyreported severe perturbations in A2Π3/2–X

2Σþ subband andtheir spectral analysis in the violet system was hampered bylimited observations, especially absence of low-J rotationallines. Bates and Gruen [2] confirmed the X2Σþ as the groundstate of ZrN by matrix isolation spectroscopy. Later, Cheungand co-workers revisited the yellow and violet band systemsof ZrN [3–9] using laser-induced fluorescence (LIF)

Physics Division,India.

te).

spectroscopy. They studied the previously observed (0,0),(1,1), and (2,2) bands [4,5,7] of A2Π–X2Σþ system for thevarious isotopomer of ZrN and determined the magnetichyperfine structure of the X2Σþ state of 91ZrN [3,9]. Recently,Moskvitina and Kuzyako [10] investigated A–X system. Morerecently, Farhat et al. [11] computed the potential energycurves for 21 low-lying electronic states of the ZrN molecule.

The motivation for this work was to extend the analysisof the B2Σþ–X2Σþ and A2Π–X2Σþ systems to highervibrational levels. Because this molecule is of astrophysicalinterest, it is important to gather as much spectroscopicinformation as possible for a meaningful search of itsexistence in the stellar atmosphere.

2. Experiment

The ZrN molecules were produced in a pulsed free-jetapparatus, which was discussed in detail in our previouspublication [12]. In brief, a rotating and translating zirco-nium metal rod was ablated with the third harmonic beam

S. Bhattacharyya et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 148 (2014) 13–1714

(354.7 nm, �10–15 mJ/pulse) of a Nd:YAG laser (QuantaSystem, SYL 203) focused to an �1 mm2 spot. The laserproduced Zr metal plasma reacted with 2% ammonia seededin helium gas emerging from a pulse valve under a backingpressure of 275 kPa. The products of the reaction wereexpanded into vacuum, cooling the internal degrees offreedom of the molecules and were probed at right angleto the supersonic expansion axis about 50 mm downstreamthe nozzle by a XeCl excimer (Coherent, CompexPro 201)pumped pulse dye laser (Coherent, ScanmatePro). Theresulting laser-induced fluorescence was imaged on anentrance slit of a monochromator (Spex, 270M) equippedwith a Peltier cooled photomultiplier tube (Hamamatsu,R943-02). An output signal from the photomultiplier wasamplified by a 1 GHz bandwidth amplifier (Femto Messtech-nik, DUPVA-1-60), integrated by a gated integrator (StanfordResearch System, SR250), and stored on a computer. Excita-tion spectra were obtained by scanning the pulsed dye laserand recording the laser-induced fluorescence through themonochromator set at fixed wavelength corresponding tothe strongest fluorescence terminating either to a ground oran excited state. Here monochromator was used as a broadband filter by setting width of the entrance and exit slits to2.24 mm. The excitation spectra were obtained with atypical resolution of 0.08 cm�1. Transition wavenumberswere calibrated by using laser wavelength calibration facilityof the dye laser utilizing neon optogalvanic spectral lines aswell as by known atomic lines of Zr I [13] appeared inthe spectra with an absolute precision of �0.1 cm�1.The dispersed fluorescence (DF) spectra were recorded byscanning the monochromator. Lifetimes of the excited elec-tronic states were recorded by acquiring the fluorescencedecay curve on a 200MHz digital storage oscilloscope(Tektronics, TDS 2024) having sampling rate of 2 Giga-samples/s and rise time o2 ns. The decay curve was averagedfor 128 shots in order to obtain a good signal to noise ratio.

3. Data analysis and results

3.1. B2Σþ–X2Σþ system

Naturally abundant ammonia and zirconium was usedin this study. Naturally abundant Zr has five isotopes,90Zr (51.45%), 91Zr (11.23%), 92Zr (17.11%), 94Zr (17.40%)and 96Zr (2.80%). The spectral resolution employed in thepresent study does not permit to observe isolated rota-tional branches for each ZrN isotopic molecule. However,simulating B–X (0,0) band with the data from Ref. [8] witha resolution �0.1 cm�1, we could infer that the peakscorresponding to P1 and P2 branches of the main isotope90ZrN gets only slightly blended by P2 of other two 92ZrNand 94ZrN isotopes. The rotational branches of 91ZrN and96ZrN are expected to be weak because of their lowernatural abundance. This simulated spectra of ZrN isotopicmolecule in a given rotation N is in line with our experi-mental observations and in this work we report thespectral analysis of 90Zr14N molecule. First, Bates and Dunn[1] and later Chen et al. [8] observed and analyzed B–X(0,0) band. Bates and Dunn reported that their analysiswas hampered by the absence of low-J rotational lines andperturbations maximized at N¼44 caused by an

interacting excited vibrational level of A2Π substate. Chenet al. determined the rotational constants for three isotopicmolecules 90ZrN, 92ZrN and 94ZrN. They found that all therotational branches were perturbed and made efforts toidentify the perturbing state and concluded that furtherhigh-resolution studies were necessary for establishingthe identity of the perturbing state unambiguously. Theysearched for the (1,0) band of this transition but did notfind it and concluded a very unfavorable Franck–Condonfactor as the reason. However, we observed (1,0), (1,1),(2,0), (2,1), (2,3) bands with considerable intensity and aweak (3,4) band. All the bands other than (3,4) wereanalyzed by simulating the spectra with the Pgopherprogram [14]. The rotational constants for ν0 ¼1, 2 of Bstate were determined by fitting to the effective Hamilto-nian for 2Σþ state given in the Pgopher program [14].In the (1,0) band, clear rotational lines of N up to 16 in theP and N up to 14 in the R branch were observed, where itforms band head in R. Similarly, in the (2,0) band, P branchlines could be followed up to N¼25 and R branch formsband head at N¼12. After turning, R branch rotationallines merged with lower J members and could not beclearly identified because of limited resolution. Eventhough, P branch lines could be observed for a few moreN in the (1,0) band, they could not be identified forcertainty with lower state combination differencesbecause of band head formations in R. In the (1,0) band,a small local rotational perturbation was observed atJ0 ¼13.5 of F1 component. The (2,0) band was found to beperturbed at 15.5r Jr21.5 in P1- and at 12.5r Jr17.5 inP2-branch.The rotational constants were determined forboth bands by fitting the above mentioned lines of P and Rbranches and are listed in Table 1. The constants in Table 1were derived by fitting 60 lines (J¼1.5 to 16.5 in P1, J¼1.5to 15.5 in P2, J¼0.5 to 14.5 in R1and J¼0.5 to 13.5 R2) in(1,0) and 59 lines (J¼1.5 to 14.5; 22.5–24.5 in P1, J¼1.5 to11.5; 18.5–25.5 in P2, J¼0.5 to 11.5 in R1 and J¼0.5 to 9.5 inR2) in the (2,0) band. The output from Pgopher programincluding lower state combination difference fit is given inthe Supplementary information. The molecular constantsfor the ν″¼0 level of X2Σþ state were fixed in the fit to themore accurate values from Cheung et al. [7]. The centrifu-gal distortion constant Dν could not determined in thepresent work because of its small magnitude and observa-tions limited to low rotational levels populated in the jet-cooled source. The spin-splitting in the P branches werenot found to increase linearly with N because of rotationalperturbations and thus γv for the B2Σþ state could only beestimated and not accurately determined.

The presence of severe perturbation in the rotationalspectra of (0,0) band was reported by earlier workers [1,8].Bates and Dunn [1] reported perturbations only at theexcited levels of F2 component at high N, maximum atN¼44. They suggested an excited vibrational state of A2Πas the perturbing state. Later Chen et al. [8] reportedperturbations at both the F1 and F2 component at differentJ values. From the shift of perturbations occurring atdifferent J values for different isotopes in F1, while at thesame J for F2, they concluded that at least two perturbingstates were involved and suggested A2Π or 4Σ� as possibleperturbing state. In a recent ab initio calculation, Farhat

Table 1

Molecular constants (cm�1) for X2Σþ (v¼3), A2Π (v¼3) and B2Σþ (v¼1,2) states and radiative lifetimes (ns) of the B2Σþ state of 90ZrN.

B2Σþ A2Π1/2,e A2Π3/2 X2Σþ

v¼0a v¼1 v¼2 v¼3 v¼3 v¼3

Tv 24,670.60(3)b 25,546.72(2)c 26,424.54(1) 20,232.92(3) 20,232.68(3) 2961.53(3)A – – – 566.01d 566.01d –

Bv 0.45870(8) 0.4507(2) 0.4490(1) 0.4704(3) 0.4728(5) 0.4749(5)107Dv 1.7(5) – – 196(7) – –

γv �0.098(10) �0.060(3) �0.077(2) – – –

τ 22.9(12) 23.5(10) 22.8(13) – – –

a Parameters from Ref [8] tabulated for completeness.b Typographical error in Ref. [8] corrected by the corresponding author (private communication).c Numbers in parentheses are one standard deviation in the last digits.d Fixed.

S. Bhattacharyya et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 148 (2014) 13–17 15

et al. [11] showed that the potential energy curves of anumber of electronic states (2)2Δ, (1)2Φ, (3)2Π, (2)2Φ,(4)2Π, (1)4Σþ , (2)4Δ, (1)4Π and (1)4Φ could cross thepotential energy curve of the B2Σþ (in notation of Ref. [11],(3)2Σþ) state and listed their crossing positions. The Teand ωe values of their calculation shows that v¼4 of(3)2Π, v¼3 of (4)2Π, v¼2 of (1)4Σþand v¼11 of (1)4Πstates are close in energy of v¼0 of B2Σþ state. Twoenergetically close lying vibrational states belonging totwo different electronic states can perturb each other if thelevels lie close to the intersection of their potential energycurves [15]. To locate the intersection of potential energycurves of the above mentioned states with the B2Σþ state,we reconstructed the potential energy curves of therelevant states shown in different figures in Ref. [11] in asingle potential energy plot and placed the vibrationallevels of those states from the predicted ωe values. Fromthe plot, we infer that v¼4 of (3)2Π, v¼3 of (4)2Π andv¼2 of (1)4Σþ levels lie close to the crossing point of theirrespective potential energy curves and could be thepotential perturbing states. The potential energy curvesof A2Π and B2Σþ states do not cross at all and thus thehigher vibrational levels of A2Π state cannot cause anyrotational perturbation in the (0,0) band as suggested inearlier references. Farhat et al. did not find the theoretical4Σ� state at 27,297 cm�1 reported by Chen et al. Eventhough the potential energy curves of (2)2Δ, (2)4Δ and(1)4Π states intersect that of B2Σþ state, the interactionbetween them should be weak and cannot cause pertur-bations of this magnitude. The predicted ωe values of(4)2Π and (1)4Σþ states being similar with that of B2Σþ

state, the successive vibrational levels of these states, i.e.,v¼4 of (4)2Π and v¼3 of (1)4Σþ with v¼1 of B2Σþ andv¼5 of (4)2Π and v¼4 of (1)4Σþ with v¼2 of B2Σþ willbe close in energy. However, the levels being away fromcrossing point of their potential energy curves, a smallrotational perturbation is expected in the (1,0) and (2,0)bands. The predicted ωe¼1408.5 cm�1 of (3)2Π statebrings v¼5 energetically closer to v¼2 of B2Σþ state butagain being away from the crossing point may cause asmall rotational perturbation. The intersection of potentialenergy curves of (1)4Π with B2Σþ state lie higher inenergy compared to the relevant vibrational levels ofB2Σþ state and thus no perturbation is expected from this

state. We observed 8–10 groups of doublet like peaks ofintensity �1/4 of the main P-branch appearing approxi-mately at the middle of F1 and F2 component from N¼12–19 in the (2,0) band. These features could be presentNo12 also, but could not be identified from the main P-branches. Similarly, a few extra weak lines are observed inthe P-branch of (1,0) band as well. But these features arenot as regular and prominent as observed in the (2,0)band. However, our best efforts did not yield any resulttowards the identification of these peaks. In view of this, itwas not possible at this stage to conclude confidently theexact nature of the perturbing states and deperturbthe rotational spectra. These additional lines are listed in theSupplementary information. The radiative lifetimes of theexcited state B2Σþ were also determined. No systematicvariation in radiative lifetime of the rotational levels withindifferent vibrational levels was observed.

The DF spectra were recorded in the wavelength region360–900 nm by exciting a single rotational level withinν0 ¼0–2 of the B state via various observed excitationbands of the B–X system. A typical DF spectrum fromP2(6.5) rotational line of the B2Σþ–X2Σþ (2,0) transitionshowing the vibrational progression up to ν″¼0–5 of theX2Σþ ground state, is shown in Fig. 1. The DF linesterminating to the ground state split into PR-doubletswhen either P- or R-lines were excited, the lower levelswere confirmed as the vibrations of the ground electronicstate. The equilibrium vibrational constants for the groundstate were obtained by fitting the vibrational term valuesusing least squares method to an anharmonic oscillatorformula,

ΔG¼ GðνÞ�Gð0Þ ¼ωeν�ωexeνðνþ1Þ; ð1Þwhere ν is a vibrational quantum number, G(ν) is termvalue of νth vibrational level and ωe andωexe are harmonicand anharmonic vibrational constants. To determine ωe

and ωexe, term values of six vibrational levels (ν¼0–5)were included in the fit in which term values for ν¼1, 3were taken from band origin. Previously, the equilibriumvibrational constants for X2Σþ were determined from alimited set of dispersed fluorescence data ν¼0–2 [6].The vibration term values and the equilibrium constantsωe and ωexe are listed in Table 2 and compared with theprevious results.

0 1000 2000 3000 4000 5000 6000Displacement(cm−1)

3x

Χ 2Σ+ ν = 0 1 2 3 4 5

Fig. 1. Dispersed fluorescence (DF) spectra of 90ZrN observed from ν0 ¼2,J0 ¼5.5 of B2Σþ state; the x-axis shows the displacement in cm�1 fromthe excitation line.

Table 2Term values and equilibrium vibrational constants (cm�1) of the X2Σþ

ground state of 90ZrN.

v Tv ωe ωexe

0 0.0 1002.5 (16)a 4.01 (30)1 994.69 (2) 1002.6b 3.8b

995.0 (9)b

2 1980 (5)1982.4 (13)b

3 2961.53 (3)4 3930 (4)5 4891 (3)

a Numbers in parentheses are one standard deviation in the lastdigits.

b Ref. [6].

17530 17540 17550 17560 17570 17580

17.516.5

11.5

13.5

Experimental

Simulated

Portion of (2

,2)

A2 Π 3/2

-X2 Σ

+1.5Q2(J) [P21(J+1)]

Wavenumber (cm-1)

5.5P2(J)

2.5

R 21(J)0.5

Q21(J+1) [R2(J)]

Fig. 2. The excitation and simulated spectra of the (3,3) band of A2Π3/2–

X2Σþ transition.

S. Bhattacharyya et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 148 (2014) 13–1716

3.2. A2Π–X2Σþ (3,3) system

We have observed (3,3) band of A2Π–X2Σþ systemalong with the previously reported [1,4,5,7] (0,0), (1,1), and(2,2) bands. The two subbands of A2Π–X2Σþ (3,3) wereidentified with band origins at 16,988 and 17,554 cm�1

which corresponds to A2Π1/2–X2Σþ and A2Π3/2–X

2Σþ

subband transitions respectively. Six branches P2, Q2, R2and P21, Q21 and R21 expected from 2Π3/2 (a) –X2Σþ (b)transition was identified (Fig. 2). However, the branches Q2

from P21 and R2 from Q21 were not resolved. The branchesof 2Π3/2–

2Σþ subband were found to be normal and noperturbations were observed with at least our spectralresolution of �0.1 cm�1, whereas 2Π1/2f–

2Σþ subbandwas found to be perturbed. In the least squares fit, Bconstants 0.47281(53) and 0.47489(48) cm�1 respectivelyfor 2Π3/2 and 2Σ state and T3¼20,232.7(1) cm�1 weredetermined with A-constant fixed to 566.01 cm�1.This fixed value for A-constant was determined from thedifference in band origins of the two subbands of A–Xsystem. The line position fitting was carried out by fitting53 line positions of P2 (J¼5.5–17.5), Q2 (2.5–17.5), R2 (0.5–11.5) and R21 (2.5–13.5) to an effective Hamiltonian opera-tor for a 2Π and 2Σ state in the Pgopher program [12]. Themeaningful value of Dν¼3 for both the states, γν″ and

Λ-doubling parameter qν0 could not be determined inthe fit.

Six branches P1, Q1, R1 and P12, Q12 and R12 expectedfrom 2Π1/2 (a) –X2Σþ (b) transition were identified. How-ever, the branches Q1 from R12 and P1 from Q12 were notresolved. Since the 2Π1/2 (v¼3) spin component of theexcited A2Π state is affected by perturbation, our attemptto fit both the subbands of A–X (3,3) together wasunsuccessful. Our attempt to fit 2Π1/2e and 2Π1/2f compo-nents of A2Π1/2–X

2Σþ together also did not providesatisfactory results. The e-parity levels were found to befree from perturbation and the rotational constants weredetermined by fitting only e levels from R1(2.5)–R1(19.5),P1(1.5) [Q12(0.5)]–P1(16.5) [Q12(15.5)]. However, a mean-ingful rotational analysis of f levels was not possible for thereasons explained below. The isolated rotational lines inQ1(R12) branch corresponding to the excited f-parity levelswere observed from J0 ¼0.5–7.5. Beyond this, the rotationallines could not be separated from each other and a bandhead like structure appeared at 16,992.2 cm�1 (Fig. 3). Inthe P12 branch, isolated lines from the f-parity levels wereobserved from J0 ¼5.5–13.5. Below J0o5.5, P12 lines couldnot be resolved from the P1(Q12) lines and an unambiguousassignment was not possible. We could fit the abovementioned rotational lines of Q1(R12) and P12 togetherbut this produced the band head position at16,992.7 cm�1, which is 0.5 cm�1 higher in energy thanthe observed one. The similar values of rotational con-stants and simulated band head position were obtainedwhile fitting only P12 lines. However, while fitting onlyQ1(R12) lines, the simulated band head appeared at16,991.6 cm�1 and the line positions of P12 were notreproduced as well. The assignments of rotational linescould not be confirmed from the lower state combinationdifferences. In lower J, while isolated Q1(R12) lines wereobserved, the corresponding P12 lines could not be assignedunambiguously as it was blended with the P1(Q12) branchlines. Similarly, in higher J, while isolated P12 lines wereobserved, the corresponding Q1(R12) lines could not beresolved and assigned unambiguously. In view of this,conclusive rotational analysis of A2Π1/2f–X

2Σþ band was

16970 16980 16990 17000 17010

*

Experimental

Simulated

14.5 6.5P12(J)

0.55.5 Q1(J) [R12(J−1)]

Wavenumber (cm-1)

R1(J)2.5 19.5Q12(J) [P1(J+1)]0.515.5

*

Fig. 3. The excitation spectrum of the (3,3) band of A2Π1/2–X2Σþ

transition. The simulated spectrum is shown for unperturbed A2Π1/2e–

X2Σþ transition.

S. Bhattacharyya et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 148 (2014) 13–17 17

not possible. Moreover, the Q1(R12) band head was observedat 17,009.81 cm�1 by Moskvitina and Kuzyako [10]. Never-theless, the details of fit of the A2Π1/2f–X

2Σþ band areincluded in the Supplementary information. Our efforts toanalyze the band head like structure (Fig. 3) further byobtaining high resolution dispersed fluorescence (DF) spec-tra did not yield any result as it fluoresced back only to theexcitation line. The DF obtained from different isolatedrotational lines in various branches of this A–X subbandalso fluoresced back to the excitation line only. The mole-cular constants for v¼3 of X2Σþ , A2Π3/2 and A2Π1/2e statesare given in Table 1.

Our rotational analysis indicates the presence of pertur-bation in A2Π1/2f–X

2Σþ (3,3) band. However, neither theexact location nor the nature of perturber in the excitedstate could be established. Severe rotational perturbations inthe A2Π3/2–X subbands of (0,0), (1,1) and (2,2) of A–X systemwere reported by previous authors [1,4,5,7]. They suggestedthe perturbing states as 2Δ and 4Π. Farhat et al. [11] hadshown that the theoretical potential energy curves of A2Π[in notation of Ref. [11], (1)2Π] has avoided crossing withthe (2)2Π state at r¼1.83 Å and the crossing with the (1)2Φstate at r¼1.84 Å. They concluded that this crossing andavoided crossing might be responsible for the experimentalvibrational perturbations occurring in the spectra of the A2Πelectronic state.

4. Conclusion

In revisiting ZrN, B2Σþ–X2Σþ and A2Π–2ΣþX bands,rotational constants were obtained for ν¼1, 2 of the B2Σþ

state. In view of perturbations, these constants weredetermined by fitting a limited number of rotational linesin the P1 and P2 branches, and a few R-branch lines of (1,0)and (2,0) bands of B–X system. Earlier authors also

reported perturbations in the ν¼0 of B2Σþ state. Theyproposed these perturbations could be due to A2Π or a4Σ� state from the similarities of isoelectronic TiN mole-cule. However, in view of the recent theoretical work ofFarhat et al. [11], the plausible perturbing states could be(3)2Π, (4)2Π and (1)4Σþ . Term energies determined fromthe band origin data of ν¼1,3 and DF data for ν¼2,4,5were used to determine vibrational constants of theground state. In the A2Π–X2Σþ system, degenerate andnon-degenerate rotational perturbations were identified atseveral places in the (0,0), (1,1) and (2,2) A2Π3/2–X

2Σþ

subband in the previous works [1,4,5,7]. The A2Π3/2–X2Σþ

subband was found to be unperturbed in the present workand rotational constants and term energies of both stateswere determined. However, rotational perturbations wereobserved in A2Π1/2f–X

2Σþ subband.

Appendix A. Supporting information

Supplementary data associated with this article can befound in the online version at http://dx.doi.org/10.1016/j.jqsrt.2014.06.009.

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