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Journal of Quantitative Spectroscopy &Radiative Transfer

Journal of Quantitative Spectroscopy & Radiative Transfer 119 (2013) 1–11

0022-40

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Infrared spectroscopy of 15ND3: The n2 and n4 bendingfundamental bands

Elisabetta Can�e, Gianfranco Di Lonardo, Luciano Fusina n, GiandomenicoNivellini, Filippo Tamassia, Mattia Villa

Dipartimento di Chimica Fisica e Inorganica, Universit �a di Bologna, Viale del Risorgimento 4, 40136 Bologna, Italy

a r t i c l e i n f o

Article history:

Received 8 November 2012

Accepted 29 January 2013Available online 4 February 2013

Keywords:

Ammonia15ND3

High resolution infrared spectra

Bending vibrations

Rovibration analysis

Fully deuterated ammonia

73/$ - see front matter & 2013 Elsevier Ltd.

x.doi.org/10.1016/j.jqsrt.2013.01.019

esponding author. Tel.: þ39 051 209 3707;

9 051 209 3690.

ail address: luciano.fusina@unibo.it (L. Fusin

a b s t r a c t

The infrared spectrum of the ammonia isotopologue 15ND3 has been investigated by high

resolution Fourier transform spectroscopy in the region from 450 to 1600 cm�1. In total,

2217 transitions involving the (s) and (a) inversion–rotation–vibration levels have been

identified and assigned to the n2 and n4 bending fundamentals. The assigned transitions

have been fitted simultaneously using an inversion–rotation–vibration effective Hamil-

tonian which includes all symmetry allowed interactions between and within the excited

state levels. The adopted model has been successful in rationalizing the complicated

energy level pattern. Accurate values for the vibration and rotation spectroscopic

constants, including 11 interaction coefficients, have been obtained for both inversion

levels of the v2¼1 and v4¼1 states. The standard deviation of the fit, 0.00071 cm�1, is

about two times the estimated measurement precision.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Among the light and small molecules, ammonia is oneof the most extensively studied since it collects theinterest of spectroscopists, astrophysicists and theoreticalscientists. As a prototype molecule for the study of thehindered inversion motion at the pyramidal nitrogenatom, ammonia and its isotopologues have been studiedfor many years ([1–3] and References therein). Neverthe-less, the interpretation of its spectroscopic behaviour stillposes a difficult challenge to both experimental and theo-retical approaches.

Ammonia is abundant in a wide variety of objectsthroughout the Universe. It has been detected in the inter-stellar medium [4], in remote stars [5], and in the atmo-spheres of the giant planets of the solar system and of their

All rights reserved.

a).

moons. The 14N/15N isotopic ratio in Jupiter’s atmospherefrom observation of NH3 transitions has been recentlyreported [6]. It has been detected also in low mass browndwarfs [7–9] and it is expected to be present in extrasolarplanets [10,11]. Since ammonia is present in so manycelestial objects, its ro-vibration spectrum has to be wellcharacterized for extended frequency and temperature inter-vals. Experimental studies have been devoted to implementthe spectroscopic data-bases of 14NH3 and 15NH3 [12–20],also by the addition of line lists with intensities, recorded attemperature higher [21–23] and lower [24] than 300 K.

Moreover, in the last 10 years the interest in thecomputation of the energies of vibration and ro-vibrationlevels up to high excitations has increased, fostered by theimprovement of the computational methodologies [25–33].An accurate reproduction of the observed transitions allowsreliable predictions at room and higher temperatures[31–33]. Also, it can help the interpretation of data collectedby astronomical missions [34–36]. In particular, in the latestcalculation of the vibrational energies characterized byunprecedented accuracy [32,33], it has been highlighted

E. Can�e et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 119 (2013) 1–112

the need of precise spectroscopic data for the less abundantammonia isotopologues. They are essential to evaluate if theaccuracy in the reproduction of the transitions and energypatterns of 14NH3 from the calculated potential energysurfaces (PES) can also be achieved for the other isotopolo-gues of the same symmetry. In fact, Huang et al. [33]evidenced that in the case of 15NH3 the agreement betweenpredicted and experimental energy levels was excellent butseveral deficiencies were noticed in the HITRAN database.For 14ND3 it was not possible to reproduce all four inversionpairs of vibration fundamentals with good accuracy [33].A re-analysis of the spectra was suggested, since the J¼0origins of the bending and stretching bands [2,37] resultednot to be consistent. Such inconsistency was ascribed to then2 mode, corresponding to the inversion motion.

Up to now the spectroscopic investigations of fullydeuterated ammonia have been limited to the fundamen-tals [2,37] and to the ground state (GS) ([38] and refer-ences therein) for 14ND3 while they are restricted to theanalysis of the pure inversion transitions in the GS and inv2¼1 in case of 15ND3 ([39,40] and references therein).We plan to complete the study of all vibration funda-mentals of 15ND3, thus providing precise spectroscopic datato test the PES of ammonia and contributing to thedetermination of its complete anharmonic potential surface.

In this paper the analysis of the high resolutioninfrared bands of the bending modes, n2 and n4, for15ND3, is presented for the first time. The experimentaldata will be analyzed using an effective Hamiltonianwhich considers simultaneously all the transitionsbetween levels with the same or different inversionsymmetry, taking into account all symmetry-allowedinteractions between vibration–inversion–rotation levels([41] and references therein). The analysis of the n1 and n3

stretching fundamental bands is in progress.The paper is structured as follows. The experimental

details are given in Section 2; the description of thespectra and the procedure adopted for the assignmentsare given in Section 3; the theoretical model and the

Fig. 1. Overview of the high resolution spectrum in the 600–1600 cm�1 reg

and 15NH2D are indicated. Experimental conditions: sample pressure 80.0 Pa;

results of the fits are described in Section 4 while theconclusions are drawn in Section 5.

2. Experimental details

The spectra of 15ND3 were recorded with a BOMEMDA3.002 Fourier transform interferometer. The instrumentwas equipped with a Globar source, KBr beam splitter anda HgCdTe detector. The spectrum was recorded in therange from 450 to 1600 cm�1 using a 0.18 m long glass cellequipped with KBr windows. The sample pressure was80.0 Pa and 1333.2 Pa and 1000 and 1200 scans were co-added, respectively. The achieved unapodized resolutionwas 0.004 and 0.006 cm�1, respectively.

Using a white type cell with optical path of 10 m and asample pressure of 360.0 Pa a spectrum was recorded from800 to 2300 cm�1, co-adding 300 scans. The achievedresolution was 0.006 cm�1. The isotopically pure (99 atom% D, 98 atom % 15N) sample of 15ND3 was purchased fromSigma Aldrich. The cell was flushed with pure 14ND3 severaltimes before the final filling to reduce as much as possiblethe H/D exchange. Nevertheless, many lines belonging tothe n2, n4a and n4b bands of 15ND2H and 15NH2D werepresent in the spectra. The assignment of the absorptionlines to the asymmetric species was based on the results ofthe analysis of n2 of 15ND2H and 15NH2D [42] while thelocation of the origins of the n4a and n4b bands for 15ND2Hwas deduced from the corresponding values for 14ND2H [3](see Fig. 1). Absorption lines of residual CO2 [43,44] or H2O[45] in the spectrometer were used for calibration. Both thewavenumber precision and accuracy of the absorption linesare estimated to be 0.3�10�3 cm�1.

3. Description of the spectrum and assignments

Fig. 1 illustrates the survey spectrum in the range 450–1600 cm�1 which is dominated by the n2 bands. In 15ND3

the n2 parallel band is centred at 743 cm�1, while the n4

perpendicular band, weaker than n2, is at 1190 cm�1.

ion. The band centres of the bending fundamentals of 15ND3, 15ND2H

path length 0.18 m.

E. Can�e et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 119 (2013) 1–11 3

The bands of the bending motions for the asymmetricspecies, 15ND2H and 15NH2D are also evident in Fig. 1.They have been labelled with the simpler notation, notrecommended by IUPAC, for analogy with ammonia [3].We presume that their remarkable intensity indicates thatsome D/H exchange took place on the inner surface of thestainless steel lecture bottle.

The shape of n2 for 15ND3 is, as expected, very similarto that of 14ND3 [37] and it is constituted by two s’a anda’s sub-bands, centred at 739.5 and 742.8 cm�1, respec-tively. The central Q-branch region extends for about9 cm�1 and is rather crowded, being formed by two seriesof Q branches, whose K-structures degrade to low wave-numbers with increasing K ( see Fig. 2). The spacingbetween adjacent K lines for a given J is larger in thes’a branch than in the a’s one. The separation betweenthe s and a components with the same J value is about3 cm�1, almost equal to the inversion splitting in v2¼1since the corresponding value in the ground state is rathersmall, 0.047 cm�1.

The qP and qR branches appear as groups of lines withresolved K structures. The adjacent J manifolds in bothbranches are separated by about 10 cm�1 (E2B). TheqP(J) branches have red–degrading K structure withincreasing K, in both the a’s and s’a components (seeFig. 3a), while the K structure is red-degraded in the s’a

but blue-degraded in the a’s qR(J) branches (see Fig. 3b).By inspection of Fig. 3 it can be appreciated that the ratio

of the intensities of absorption lines with K¼0 is 10 to 1 for J00

even and 1 to 10 for J00 odd in transitions from the s/a levels ofthe GS. Moreover, the 8, 8, 11 intensity alternation oftransitions for K 00 ¼3pþ1, 3pþ2 and 3pþ3, with p¼0, 1,2,y is clearly seen. These effects result from the nuclear spinstatistical weights of the GS levels in ND3 [2].

The overall shape of the n4 perpendicular band ischaracterized by the strong central feature constitutedby the pQK(J) and rQK(J) branches, located at the blue and

Fig. 2. Detail of the Q-branch of n2 near the band centre. Several qQK(J) branc

at lower wavenumbers. The J and K assignments are given. Experimental cond

the red side, respectively, with respect to rQ0(J) at theband centre (see Fig. 4).

The effect of the nuclear spin statistical weights isevident also in the rQ0(J) branch: only the strong linescorresponding to transitions from alternatively the a and s

GS levels are observed for J¼1,2,3,y. The J structure ofthe QK branches degrades to the blue with increasing J.

The strong pPK(J) and rRK(J) branches are red-degradedand blue-degraded, for increasing J, respectively, while fora given J value they degrade to high or low wavenumberswith increasing K. A striking difference of this band withrespect to n2 is that almost every transition shows a closedoublet structure (see Figs. 4 and 5). In fact, since theselection rules allow the s’s and a’a transitions, thewavenumber difference within each a–s doublet is equalto the difference between the inversion splittings in v4¼1and the ground states whose values are very similar. Theseparation of the a and s component of each doublet inthe pPK(7) branch, illustrated in Fig. 5, decreases fromK 00 ¼1 to K 00 ¼5. For K 00 ¼6 the two absorption lines areoverlapping. For K 00 ¼7 two lines are observed but the a

component of the doublet is at higher wavenumbers.Moreover, in case of K 00 ¼3, the a and s transitions aresplit in two doublets with intensity ratio 10:1. Both thestrong and the weak components of the quartet, rarelyobserved in the spectrum, are visible in Fig. 5.

Lines which have not been assigned either as n2 or n4

transitions of 15ND3 are scattered all over the investigatedspectral region. The most intense ones belong to n2 of15ND2H and 15NH2D and have been already analysed [42].The hot band 2n2’n2 of 15ND3 is clearly observed in themore dense spectrum, with the s’a and a’s band originsat about 606 and 676 cm�1, respectively. The results of itsanalysis will be presented in the near future.

The assignment procedure, restricted to transitions ofthe 15ND3 bending fundamentals, began from the strongestlines in the less dense spectrum. The first tentative

hes of both the a’s and s’a components are shown, the latter being

itions: sample pressure 80.0 Pa; path length 0.18 m.

Fig. 3. Details of the P- and R-branches of n2. In (a) the qPK(7) branches while in (b) the qRK(8) branches of both the a’s and s’a components are shown.

The K assignments are given. Note also that the intensities of the K¼0 lines change from 10 to 1 depending on the parity of the J00 quantum number and

the a/s inversion symmetry. Experimental conditions: sample pressure 80.0 Pa; path length 0.18 m.

Fig. 4. Detail of the n4 fundamental of 15ND3 illustrating the J progression of the rQ0(J) and rQ1(J) branches. The J assignment and the a/s symmetry are

given. Note also the alternation of the a, s labels for the J00 ¼odd or even transitions of rQ0(J). Due to the nuclear spin statistical weights of the K¼0 levels

only the strong lines are visible. Experimental conditions: sample pressure 80.0 Pa; path length 0.18 m.

E. Can�e et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 119 (2013) 1–114

assignments were guided by our experience on the analysisof the corresponding bands of 14ND3 [37] and by the methodof ground state combinations differences (GSCD) calculatedfrom the very precise GS molecular parameters [39]. Therelative intensity of the lines, governed by the nuclear spin

statistic weights, and the very low intensity or the absenceof K 00 ¼0 lines for odd J00(s) or even J00(a) in various branchesprovided further supports to the assignments. Initially,about 100 transitions were assigned and fitted by meansof a least-squares procedure. Plausible starting values of the

Fig. 5. Details of the n4 fundamental of 15ND3 illustrating the K progression of the pPK(7) branch for both the a’a and s’s components. The K

assignment and the a/s symmetry are given (See the text for a detailed description). Experimental conditions: sample pressure 80.0 Pa; path length

0.18 m.

E. Can�e et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 119 (2013) 1–11 5

spectroscopic constants of v2¼1 and v4¼1 were calculatedfrom the corresponding parameters of 14ND3 [37]. Theywere adjusted in the fit and the assignments were progres-sively extended to higher values of J and K quantumnumbers by means of their predicted positions and theextensive use of GSCD. In total, 2217 transitions withJ0max ¼ K 0max ¼ 20 were assigned; of these, 876 belong to n2,436 and 440 to the s’a and the a’s components,respectively, while 1341 belong to n4, 668 to the s’s and673 to the a’a component. We searched for forbiddentransitions in the nu4 band but none was identified even inthe high pressure spectrum.

4. Discussion

4.1. Details of the analysis

As expected, the assignment of the spectrum evi-denced that the overall shape and the detailed patternof the n2 and n4 bands for 15ND3 were very similar tothose of 14ND3. Thus, the ro-vibration analysis was per-formed using the same theoretical model adopted in Ref.[37] which successfully reproduced the anomalies of therotation-inversion structure in the vibrational states. Fourlevels, namely the s and a components of v2¼1 and v4¼1,were considered simultaneously taking into accountexplicitly all symmetry allowed interactions betweenand within them. The theoretical model includes theDl¼ 0, Dk¼ 73 interaction terms, which connect levelswith opposite inversion symmetry in the same vibrationalstate and resulted to be effective also in the GS [38,39].Differently from 14NH3 [46,47] and 15NH3 [48], the v2¼2,

v2¼v4¼1 and v2¼3 states were not considered in theanalysis, because the interaction between the statesclosest in energy, an4 and s2n2, was demonstrated to beineffective in 14ND3 [37].

An upgraded version [49] of the programme described indetails in [37] has been used for the analysis of theexperimental dataset. For each value of J the programmebuilds two Hamiltonian matrices of dimensions 4� (2Jþ1):one for the A01, A02 and A001, A002 symmetry levels, and theother for one of the two (degenerate) blocks of E0 andE00symmetry. The two blocks are numerically diagonalisedto obtain the energy levels. The diagonal matrix elements,containing the usual contributions up to the 6th power inthe angular momentum operators, were given by:

ðiÞEvðJ,k,‘Þ=hc¼ ðiÞE0vþðiÞBv½JðJþ1Þ�k2

�þðiÞCvk2

�2ðiÞðCzÞvk‘

�ðiÞDvJ½JðJþ1Þ�2�ðiÞDvJK ½JðJþ1Þ�k2

�ðiÞDvK k4

þðiÞZvJ½JðJþ1Þ�k‘þðiÞZvK k3‘

þðiÞHvJ ½JðJþ1Þ�3þðiÞHvJK ½JðJþ1Þ�2k2

þðiÞHvKJ ½JðJþ1Þ�k4

þðiÞHvK k6

þðiÞtvJ½JðJþ1Þ�2k‘þðiÞtvJK ½JðJþ1Þ�k3‘

þðiÞtvK k5‘þðiÞtnvK k3‘3 ð1Þ

where (i) refers to the parity of the level with respect to theinversion, s or a; k¼ 7K; v¼2 or 4; l¼ l4. All termscontaining l vanish for the v2¼1 levels. The off-diagonalmatrix elements are reported in Appendix A, where Hmn

represents a group of terms in the Hamiltonian containingm vibrational operators qr and/or pr, and n rotationaloperators Ja [50]. We remind that the subscript of the

E. Can�e et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 119 (2013) 1–116

interaction constants represents the Dk and Dl selectionrules for the levels connected by the interaction term in theHamiltonian. Moreover, a constant without the left super-script (i) corresponds to an s2a resonance, while an (s) or(a) superscript represents interaction between levels of thesame parity where there is no ambiguity, i.e. ðsÞq22, ðsÞf K

22 ,ðsÞf J

22 , ðsÞCð2Þ21 , etc. For the Coriolis constants ðiÞCð1Þ11 , ðiÞCð2Þ11 ,ðiÞCð3aÞ

11 and ðiÞCð3bÞ11 the superscript (i) refers to the parity of

the interacting v4¼1 level.A weighted least-squares analysis was performed simul-

taneously on all the assigned transitions to derive theparameters of the excited states. In the least-squares fits aunitary statistical weight has been attributed to each isolatedline, while the weight has been reduced to 1/n if n transitionsare assigned to the same wavenumber. The GS term valuesused to calculate the transition wavenumbers were obtainedas eigenvalues from the appropriate energy matrices, usingthe parameters from [39] and listed in Table 1 of this paper.The diagonal elements were calculated from the followingexpression which includes the octic distortion constants

ðiÞEðJ,kÞ=hc¼ ðiÞE0þðiÞB0½JðJþ1Þ�k2

�þðiÞC0k2

�ðiÞD0J½JðJþ1Þ�2

�ðiÞD0JK ½JðJþ1Þ�k2

�ðiÞD0K k4

þðiÞH0J ½JðJþ1Þ�3

þðiÞH0JK ½JðJþ1Þ�2k2

þðiÞH0KJ ½JðJþ1Þ�k4

þðiÞH0K k6

þðiÞL0J½JðJþ1Þ�4þðiÞL0JJK ½JðJþ1Þ�3k2

þðiÞL0JK ½JðJþ1Þ�2k4

þðiÞL0JKK ½JðJþ1Þ�k6

þðiÞL0K k8

ð2Þ

Table 1Spectroscopic parameters (in cm�1) for the ground state of 15ND3.

Parameter sa aa

ðiÞE0b 0.0 0.047793490(323)

ðiÞB 5.123657150(665) 5.123494406(665)

ðiÞC 3.124569c 3.124648945(154)

ðiÞDJ�104 1.975535(127) 1.972658(127)

ðiÞDJK�104 �3.513534(502) �3.505049(502)

ðiÞDK�104 0.0c�0.00612448(816)

ðiÞHJ�108 2.36008(615) 2.33397(617)

ðiÞHJK�108 �7.6191(242) �7.4926(242)

ðiÞHKJ�108 8.6593(308) 8.4655(308)

ðiÞHK�108 0.0c 0.096091(447)

ðiÞLJ�1011 �4.1972(902) �10.199(742)

ðiÞLJJK�1011 1.4289(411) 1.4356(411)

ðiÞLJK�1011 �1.3240(498) �1.3240(498)

ðiÞLKKJ0.0c 0.0c

ðiÞLK0.0c 0.0c

Interaction parameters

e0�105 3.7486(100)

eJ0�108 �0.9542(413)

eK0�108 2.3055(351)

Number of fitted lines 406

St. dev. of an obs. of unit

weight

1.39

a From Ref. [39]. The uncertainties as 1s given in parentheses refer to

the last significant digits.b ðaÞE0 is the inversion splitting in the GS for J¼K¼0.c Fixed at the 14ND3 value or zero.

and the off-diagonal ones from the Dk¼ 73 essentialresonance element in Appendix A with vs¼vt¼0.

4.2. The v2¼1 and v4¼1 spectroscopic parameters

Once all the transitions that could be unambiguouslyassigned were identified, a systematic investigation toderive the set of parameters that best reproduces theexperimental data was carried out. All the constants up tothe third order of approximation, E0, B, C, Cz, Cð1Þ11 , Cð2Þ11 , Cð2Þ21 ,q22, q12, Cð3aÞ

11 , Cð3bÞ11 , Cð3Þ21 , ZJ, and ZK were refined keeping the

other parameters and the distortion constants D and H

constrained to zero or to their ground state values. Next,higher order parameters were included in the modelaccording to the following criteria. Both the J and K

dependences and, if present, the s and a components ofa lower order coefficient, determined in the fit, i.e. f J

12 andf K

12, were added simultaneously in the refinement.The significant fourth order interaction parameters weredetermined together with the distortion constants D,while the sextic distortion constants H were kept con-strained. The results of each fit were checked to verifythat the newly, as well as the previously refined para-meters, were statistically determined, that they improvedthe standard deviation of the fit and that anomalouscorrelations between the parameters were absent. Onlythe parameters fulfilling these requirements were main-tained in the following fits constraining the others eitherto zero or to their corresponding ground state values.The sextic distortion constants H could be significantlydetermined after the inclusion in the experimental data-set of transitions with J and K quantum numbers Z15.

In total, 1930 transitions were retained in the last cycleof the refinement with a standard deviation of thefit¼0.00071 cm�1. Two hundred and eighty seven transi-tions, about 13% of the assigned lines, were excluded fromthe dataset in the final cycle of the refinement, since thedifference between the experimental and calculated wave-numbers exceeded a chosen limit, set at 0.002 cm�1, as inthe corresponding analysis of 14ND3. The discarded transi-tions are in general poorly measured, weak or blendedlines and are randomly distributed in the dataset. Theoverall results collected in Table 2 comprise 20 spectro-scopic parameters of v2¼1, 26 of v4¼1, and 11 coefficientsof the off-diagonal terms. All the parameters in Eq. (1) andin Appendix A which are not reported in Table 2 wereconstrained to zero in the refinement. The standard devia-tion of the fit is about two times the experimentaluncertainty. This result indicates that the model adoptedin the analysis satisfactorily reproduces the energy patternof the v2¼1 and v4¼1 bending states.

All the derived parameters are statistically well deter-mined. The values of the refined s and a rotationalconstants are very similar in the two studied vibrationalstates apart from a few exceptions. Most of parametersare also close to the corresponding ones in the groundstate, both in sign and value. The DK and HK distortionconstants are effective, being constrained to 0.0 in the s

component of the GS. No significant correlations werefound among the spectroscopic constants with the excep-tion of tJK , whose values are 96% and 97% correlated to ZJ

Table 2Spectroscopic parameters (in cm�1) for the v2 ¼ 1 and v4 ¼ 1 excited states of 15ND3

a.

Parameter v2 ¼ 1 v4 ¼ 1

s a s a

ðiÞE0v

739.530096(126) 742.775007(134) 1186.910962(110) 1186.9731061(113)

ðiÞB 5.20781378(548) 5.19946251(545) 5.15566714(464) 5.15545837(480)

ðiÞC 3.08910256(450) 3.09396727(477) 3.10548954(404) 3.10561845(405)

ðiÞDJ�104 2.317821(358) 2.200535(371) 2.088482(414) 2.087342(435)

ðiÞDJK�104 �4.193453(689) �3.813474(708) �3.888549(943) �3.863991(959)

ðiÞDK�104 0.380027(500) 0.085189(518) 0.247095(680) 0.225438(660)

ðiÞHJ�108 2.97521(579) 2.05253(583) 2.7053(107) 2.7150(117)

ðiÞHJK�108 �9.2994(286) �5.1063(265) �9.4808(398) �9.3440(400)

ðiÞHKJ�108 10.8400(448) 4.4913(414) 10.8345(516) 10.7014(506)

ðiÞHK�108 �1.3363(224) 1.8239(203) �0.8338(231) �0.8283(212)

ðiÞCz �0.927345(264) �0.959500(132)

ðiÞZJ�103 �0.927427(335) �0.927444(272)

ðiÞtJK�106 �0.182577(697) �0.180181(730)

Interaction parametersðsÞCð1Þ11

3.3777073(685) ðaÞCð1Þ113.3913751(647)

ðsÞCð3aÞ11 �103 �0.383697(397) ðaÞCð3aÞ

11 �103 �0.398221(404)

ðsÞCð2Þ11�103 4.6221(109) ðaÞCð2Þ11�103 4.2430(109)

ðsÞCð3Þ21�103 0.28725(201) ðaÞCð3Þ21�103 0.25232(201)

q12 �0.02029849(768)

e2�105 2.4593(253)

e4�105 4.5720(163)

Number of fitted/assigned lines 1930/2217

Standard deviation of the fit 0.000714

a The uncertainties as 1s given in parentheses refer to the last significant digits.

E. Can�e et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 119 (2013) 1–11 7

of v4¼1, s, and a, respectively. In many aspects theseresults are very similar to those of 14ND3 [37]. With theexception of eJ

2, eK2 , eJ

4 and eK4 which in 15ND3 were kept

fixed to zero, the same spectroscopic parameters wererefined for the two isotopologues due to the strikingsimilarities of the energy patterns in the v2¼1 andv4¼1 states. The vibration constants follow the expecteddecreasing trend due to the 15N isotopic substitution.The K dependent parameters C and Cz have nearlyidentical values. Also the D and H distortion constantsare very similar both in value and sign. The uncertaintiesof corresponding parameters in the two sets are verysimilar and the number of significant digits is identical.Overall, the quality of the fit for 15ND3 is comparable withthe one obtained for 14ND3. The standard deviation of thefit is 0.00071 cm�1 compared to 0.00057 cm�1, and 13%of the lines are discarded, instead of 11% for 14ND3. A tablewith the list of the transition wavenumbers, assignmentsand residuals from the simultaneous fit of all the analysedbands in 15ND3 has been deposited to the Editor asSupplementary Material.

4.3. Ground state spectroscopic parameters

A total of 1168 s–s and a–a GSCD, with J0max ¼

18 and K 0max ¼ 17, were calculated from the 2217 tran-sitions assigned to the n2 and n4 bands of 15ND3. Theywere added to the experimental dataset used to derivethe precise GS spectroscopic parameters in [39]. They

included 51 DJ¼DK ¼ 0, a’s pure inversion transitionsmeasured in the millimetre wave (MMW), with 1rJ¼ Kr18, and 372 DJ¼ þ1, DK ¼ 0, a’s, and s’a

inversion–rotation transitions, with 0r J00r19, from thefar-infrared (FIR) spectrum and from [51,52]. In total,1591 transitions were analysed simultaneously on thebasis of the inversion–rotation Hamiltonian reported in[39] adopting the same weighting scheme and rejectionlimit. The uncertainties for the GSCD were set equal to0.00141 cm�1. Nine hundred and thirty five data wereretained in the final fit and the standard deviation for anobservation of unit weight was 0.91. The values of therefined constants overlap the corresponding ones of set IIIin Table III of [39] within less than 1s and the uncertain-ties are slightly smaller. Thus, the addition of GSCD doesnot improve the values of the parameters nor significantlyreduces the errors on the higher order distortion con-stants. In fact, only 4.7% of the n2 and n4 transitions haveJ0 and K 0Z18. Therefore, the spectroscopic parametersderived in [39] were used in the analysis of the excitedstates. They are listed in Table 1 to facilitate the compar-ison with those of v2¼1 and v4¼1.

4.4. Bending fundamentals of 14ND3

We reconsidered the analysis of the n2 and n4 bands of14ND3, using the spectra and the assignments previouslyreported [37], following the suggestion of Huang et al.[33]. These authors failed to reproduce the J¼0 vibration

E. Can�e et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 119 (2013) 1–118

fundamentals of 14ND3 with the accuracy expected usingthe calculated PES and ascribed the discrepancy to the n2

band origins. In fact, they found relatively more difficultto reproduce the values of its inversion splitting com-pared with other fundamentals. Our re-examination ofthe assignments and of the analysis in [37] did notevidence systematic errors or pitfalls which could beresponsible of the claimed inconsistency. The modelHamiltonian used in the analysis reproduces satisfactorilythe experimental data. However, unlike the analysis of thestretching fundamentals [2], the term values of the GSlevels were calculated using the GS parameters of Table IIIin [37] instead of the more precise ones reported subse-quently [38]. Therefore, the n2 and n4 wavenumbertransitions were fitted using the more recent GS valuesin [38]. The number of lines retained in the last cycle ofthe refinement and the standard deviation of the fit arealmost the same as in [37]. The obtained parameters,listed in Table 3, agree within 2s with the correspondingones in Tables IV and V of [37], thus confirming theirreliability and the validity of the previous analysis. There-fore, we believe that the discrepancy pointed out byHuang et al. is not to be attributed to n2 or n4. On theother hand, the spectroscopic parameters resulting from

Table 3Spectroscopic parameters (in cm�1) for the v2 ¼ 1 and v4 ¼ 1 excited states of

Parameter v2 ¼ 1

s a

ðiÞE0v

745.5974458(932) 749.145288(122

ðiÞB 5.22459865(445) 5.21583649(416

ðiÞC 3.08867357(298) 3.09393767(343

ðiÞDJ�104 2.305975(313) 2.186555(262)

ðiÞDJK�104 �4.160341(577) �3.771089(445

ðiÞDK�104 0.374391(324) 0.071188(293)

ðiÞHJ�108 2.93566(583) 1.99685(306)

ðiÞHJK�108 �9.2312(227) �5.0325(137)

ðiÞHKJ�108 10.9030(318) 4.6300(224)

ðiÞHK�108 �1.4893(148) 1.6141(112)

ðiÞCzðiÞZJ�103

ðiÞtJK�106

Interaction parametersðsÞCð1Þ11

3.3645326(564)

ðsÞCð3aÞ11 �103 �0.376990(322)

ðsÞCð2Þ11�103 4.63645(870)

ðsÞCð3Þ21�103 0.27871(174)

q12 �0.02029034(628)

e2�105 2.6638(118)

eJ2�108 �0.96399b

eK2�108 2.09337b

e4�105 4.7654(127)

eJ4�108 �0.96399b

eK4�108 2.09337b

Number of fitted/assigned lines 2215/2511

Standard deviation of the fit 0.000561

a The uncertainties as 1s given in parentheses refer to the last significantb Fixed to the corresponding GS value.

the analysis of the stretching fundamentals should beconsidered with less confidence. In fact, they were derivedfrom a fit restricted to v1¼1 and v3¼1 levels, without theinclusion of the interactions with the v2¼4, s, and v4¼2excited states [2]. Snels et al. pointed out this limit of theirmodel, which could not reproduce adequately a largenumber of perturbed lines [2]. An improved interactionmodel was adopted for the analysis of the stretchingfundamental bands of 14NH3 and 15NH3, considering simul-taneously the Fermi and Coriolis interactions affecting thelevels of the v1¼1, v3¼1, v4 ¼ 20 and v4 ¼ 282 excitedstates [49,53].

5. Conclusions

The high resolution infrared absorptions of 15ND3 from450 to 1600 cm�1, corresponding to the v2¼1’GS andv4¼1’GS transitions, have been analysed. The adoptedinversion–rotation–vibration Hamiltonian model has beensuccessful in rationalizing the complicated pattern ofvibration–rotation–inversion levels in the interacting stateswith a limited number of spectroscopic parameters. As anexample of that complexity the inversion splitting in a few J

levels of v4¼1 with K¼2 and l¼�1 is depicted in Fig. 6.

14ND3a.

v4 ¼ 1

s a

) 1190.4896280(897) 1190.5585310(869)

) 5.17520922(371) 5.17497807(378)

) 3.10573374(298) 3.10583346(293)

2.083503(338) 2.081856(324)

) �3.864488(711) �3.843683(697)

0.245626(457) 0.224255(469)

2.59033(892) 2.56540(833)

�9.2884(316) �8.9779(317)

11.3408(402) 10.3362(409)

�1.4655(171) �73.94(168)

�0.98929759(771) �0.98941390(779)

�0.921445(162) �0.922926(170)

�0.182643(368) �0.173961(386)

ðaÞCð1Þ113.3788939(521)

ðaÞCð3aÞ11 �103 �0.392785(319)

ðaÞCð2Þ11�103 4.23105(842)

ðaÞCð3Þ21�103 0.25950(187)

digits.

Fig. 6. Energy level diagram of the first few inversion–rotation levels for K ¼ 2, l¼�1, in the v4¼1 state of 15ND3. Going from J0 ¼5 to J0 ¼9 the value of

the inversion splitting decreases, changes sign at J0 ¼8 and increases again. In addition, the A1/A2 splitting increases regularly with J and becomes larger

than the corresponding inversion splitting for J046. Values in parentheses after the symbol of the symmetry species represent the relative nuclear spin

statistical weights.

E. Can�e et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 119 (2013) 1–11 9

Accurate values for the spectroscopic constants and forthe interaction coefficients have been obtained, togetherwith accurate vibration tunnelling energies for v2¼1 andv4¼1. The analysis of the same dyad in 14ND3 has beenreconsidered, confirming the validity of former results[37]. We plan to complete the analysis of the stretchingfundamental bands of 15ND3, recording new spectra withlonger path length, in order to enhance the intensity ofthese bands and of the overtone and combination bandsof the bending modes present in the same region. Thisstudy will complete the spectroscopic characterization ofall fundamental bands of the fully hydrogenated anddeuterated ammonia. New accurate results will be avail-able to test if the PES recently calculated [33], whichprovides accurate results for 14NH3, can be extended tothe other isotopologues.

1 F 7n ¼ ½JðJþ1Þ�kðk71Þ�1=2½JðJþ1Þ�ðk71Þðk72Þ�1=2. . .::fJðJþ1Þ� ½k

7 ðn�1Þ�ðk 7nÞg1=2

Acknowledgements

The authors acknowledge the financial support fromthe Universit�a di Bologna and from the Ministero dellaRicerca e dell’Universit�a, PRIN 2009 ‘‘Spettroscopia

molecolare per la Ricerca Atmosferica e Astrochimica:Esperimento, Teoria ed Applicazioni’’.

Appendix A

Off�diagonal matrix elements of the vibration–rotation–

inversion Hamiltonian1

The basis functions ares

a9ns, nt , lt , J, kS¼ s

a9n2, n4,l4, J, kS

Coriolis type resonancess

ans, nt , lt , J, k9ðH21þH23Þ=hc9ns�1, ntþ1, lt 71, J, k71,� �a

s

¼ 7ffiffiffi2pfðiÞCð1Þ11 þ

ðiÞCð3aÞ11 JðJþ1ÞþðiÞCð3bÞ

11 ½k2þðk71Þ2�gF 71

s

a ns, nt , lt , J, k9H22=hc9ns�1, ntþ1, lt 71,J, k71� �a

s¼

ffiffiffi2pðiÞCð2Þ11 ð2k71ÞF 71

s

a ns, nt , lt , J, k9ðH22þH24Þ=hc9ns�1, ntþ1, lt 81, J, k72� �s

a

¼ffiffiffi2pfðiÞCð2Þ21 þ

ðiÞCð4aÞ21 JðJþ1ÞþðiÞCð4bÞ

21 ½k2þðk72Þ2�gF 72

s

a ns, nt , lt , J, k9H23=hc9ns�1, ntþ1, lt 81, J, k72,� �s

a

¼ 7ffiffiffi2pðiÞCð3Þ21 ð2k72ÞF 72

E. Can�e et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 119 (2013) 1–1110

Essential resonancesa

s nt , lt , J, k9ðH22þH24Þ=hc9nt , lt 82, J,�

k71�s

a¼ 2f½q12þ f J

12JðJþ1Þ�ð2k71Þ

þ f K12½k

3þðk71Þ3�gF 71

a

s nt , lt , J, k9ðH22þH24Þ=hc9nt , lt 72, J,�

k72�a

s¼ 2fðiÞq22þ

ðiÞf J22 JðJþ1ÞþðiÞf K

22 ½k2þðk72Þ2�gF 72

a

s ns, J, k9ðH04þH24þH26Þ=hc9ns, J,�

k73�s

a¼ f½e2þe2J JðJþ1Þ�ð2k73Þþe2K ½k

3þðk73Þ3�gF 73

a

s nt , lt , J, k9ðH04þH24þH26Þ=hc9nt , lt , J,�

k73�s

a¼ f½e4þe4J JðJþ1Þ�ð2k73Þþe4K ½k

3þðk73Þ3�gF 73

Appendix B. Supporting information

Supplementary data associated with this article can befound in the online version at http://dx.doi.org/10.1016/j.jqsrt.2013.01.019.

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