THE JOURNAL OF CHEMICAL PHYSICS 134, 194302 (2011)

Rovibrational eigenenergy structure of the [H,C,N] molecular systemGeorg Ch. Mellaua)

Physikalisch-Chemisches Institut, Justus-Liebig-Universität Giessen, Heinrich-Buff-Ring 58,D-35392 Giessen, Germany

(Received 17 March 2011; accepted 21 April 2011; published online 17 May 2011; corrected 23May 2011)

The vibrational-rotational eigenenergy structure of the [H,N,C] molecular system is one of the keyfeatures needed for a quantum mechanical understanding of the HCN⇀↽HNC model reaction. Therotationless vibrational structure corresponding to the multidimensional double well potential energysurface is well established. The rotational structure of the bending vibrational states up to the iso-merisation barrier is still unknown. In this work the structure of the rotational states for low and highvibrational angular momentum is described from the ground state up to the isomerisation barrierusing hot gas molecular high resolution spectroscopy and rotationally assigned ab initio rovibronicstates. For low vibrational angular momentum the rotational structure of the bending excitationssplits in three regions. For J < 40 the structure corresponds to that of a typical linear molecule, for40 < J < 60 has an approximate double degenerate structure and for J > 60 the splitting of the eand f components begins to decrease and the rotational constant increases. For states with high an-gular momentum, the rotational structure evolves into a limiting structure for v2 > 7 – the moleculeis locked to the molecular axis. For states with v2 > 11 the rotational structure already begins toaccommodate to the lower rotational constants of the isomerisation states. The vibrational energybegins to accommodate to the levels above the barrier only at high vibrational excitations of v2 > 22just above the barrier whereas this work shows that the rotational structure is much more sensitiveto the double well structure of the potential energy surface. The rotational structure already experi-ences the influence of the barrier at much lower energies than the vibrational one. © 2011 AmericanInstitute of Physics. [doi:10.1063/1.3590026]

I. INTRODUCTION

Fundamental understanding of the structure and dy-namical evolution of molecules can be extracted from highresolution spectra. The list of possible rovibrational eigenen-ergies is the main result obtained from these experiments.In principle, these eigenenergies could be determined toany precision by theoretical calculations if the molecularSchrödinger equation, which describes the correlated motionsof the electrons and nuclei could be solved exactly. This is,however, not possible, because while this multi-dimensionaleigenvalue differential equation is extremely simple to for-mulate, it is impossible to solve. For polyatomic moleculeswe can obtain theoretical eigenenergies for the molecularmotion of the nuclei only within the Born-Oppenheimer ap-proximation using a highly accurate potential energy surface(PES). But even using such an exact PES the eigenenergiesobserved do not reach the accuracy of the high resolutionexperiments. In fact in high resolution spectroscopy we re-verse the situation described: we use experiments to solve themolecular Schrödinger equation. The analysis of the observedline positions reveals the eigenenergy structure; the analysisof the line intensities gives direct information about the wavefunctions. From a theoretical point of view they are stronglycorrelated through the assigned quantum numbers.

a)Electronic mail: georg@mellau.de. URL:http://www.georg.mellau.de.

Molecular vibrations and rotations are well understood atlow excitation energies around the equilibrium structure butif the molecule gains energy in a quantity relevant to chem-ical reactions there are still many open questions. H2O, H+

3Acetylene, HCP, and HCN/HNC are the model molecules forwhich experimental and theoretical studies have been done atthe most basic level. The HCN and HNC isomers correspondto two global minima of the [H,C,N] molecular system withthe two stable linear isomers HCN and HNC. This system isimportant because there is an overlap between the two basicscientific tools that we can use to gain a fundamental under-standing of molecular physics on a full quantum mechanicalbasis. It is possible to do high-level ab initio theoretical calcu-lations (only 17 particles) and high resolution spectroscopicdata can be obtained for highly excited rovibrational states.The isomerisation reaction HCN⇀↽HNC is one of the impor-tant model systems for the study of unimolecular reactions.Figure 1 shows the one dimensional PES of the molecularsystem along the isomerisation path as the hydrogen atombends from one side of the CN core to the other. To de-scribe the relative positions of the nuclei in HCN and HNCthe Jacobi coordinates (R,r ,γ ) are used: R = rH−CN is thedistance between the H atom and the center-of-mass of themolecule CN part, r = rCN is the distance between the Nand C atoms and γ the angle between R and the CN bondaxis. On the HCN–HNC potential curve, the γ coordinatevaries linearly between the HCN (γ = 0) and HNC (γ = π )structures.

0021-9606/2011/134(19)/194302/10/$30.00 © 2011 American Institute of Physics134, 194302-1

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194302-2 Georg Ch. Mellau J. Chem. Phys. 134, 194302 (2011)

FIG. 1. Schematic one-dimensional solutions for the asymmetric double minimum potential. Left: for the one dimensional square double well (Ref. 1). Theblue and red wavefunctions are localized in one of the two wells, the orange ones correspond to both minima. Right: the [H,C,N] molecular system, only thedimension along the isomerisation path is shown (Ref. 2). The red area marks the eigenenergy regions where all 3822 and 1191 eigenenergies, respectively,have been measured.

To understand how the HCN and HNC molecules be-have when they become highly excited, we need to determinethe complete vibrational-rotational eigenenergy level struc-ture of the [H,C,N] molecular system. Figure 1 shows theeigenenergies and wavefunctions for the simplest model wecan define for the [H,C,N] molecular system: the asymmet-ric infinite square double well potential. The wavefunctionsbelow the barrier are localized in one of the two wells, andthe wavefunctions above the barrier correspond to both min-ima. We have a similar situation for the [H,C,N] system. Theeigenenergies and wavefunctions below the barrier are local-ized in one of the two wells and correspond to the two separatemolecules HCN and HNC; the ones above the barrier belongto a single “combined”H0.5–CN–H0.5 molecule.3 Our simplemodel in Fig. 1 reveals the basic feature of such a double wellpotential: the lower eigenenergies on both sides are indepen-dent of one another, but that already begins to change beforethe energy reaches the barrier height. For the [H,C,N] molec-ular system we have a similar multidimensional problem; theone dimensional double well PES shown in Fig. 1 is only anapproximation even for pure bending vibrations.

II. HOTGAME SPECTROSCOPY OF THE [H,C,N]MOLECULAR SYSTEM

In hot gas molecular emission (HOTGAME) spec-troscopy a molecular gas is heated to high temperatures, andthe infrared emission is collected with a high resolution spec-trometer. HOTGAME spectroscopy was pioneered by PeterBernath4 mainly to record the high resolution spectra of short-lived diatomic molecules. HOTGAME spectroscopy can beused to detect the highly excited rovibrational bending statesof small molecules with a very high sensitivity. There are tworeasons for the high sensitivity of this often ignored experi-mental scheme: one is due to the physics of transitions in ahot molecular gas5 and the other to the sensitivity of the FTIRspectrometers used to record the spectra. Using HOTGAME,highly excited states of H2O,6–8 HCN,9–13 and HNC (Refs. 5,14, and 15) isotopologues have been successfully measuredand analyzed.

To cover all eigenenergies of the molecular system, notonly highly excited vibrational states, but also rotationally ex-cited states have to be determined. Using HOTGAME spec-troscopy it may be possible to cover all of the approximately

45 000 states of the [H,C,N] system up to the isomerisationbarrier. In two recent papers such a complete eigenenergystudy for the HNC isotopomer has been reported5, 15 for thelower rovibrational excitation energy range where the theoret-ical description of the eigenstates through perturbation meth-ods still holds. In this paper we report the results for low andhigh angular momentum states from a similar analysis donefor HCN and compare the results to the ones obtained forHNC. The results for all detected l sublevels are published intwo separate papers.16, 17 For HNC and HCN we extended theanalysis to higher excited states than reported in the previouspapers. The experimental results are given as supplementarymaterial to this paper;18 the list of the vibrational states andthe determined spectroscopic constants are listed in Table I.Eigenenergy values are given as term values in cm−1.

The linear HCN and HNC molecules have three nor-mal modes v = v1, v2, v3 two stretching vibrations of �+

symmetry and a bending mode of � symmetry: ν1 is theHN stretch at 3311.47/3652.65 cm−1, ν3 is the CN stretchat 2096.84/2023.86 cm−1, and ν2 is the degenerate bendingmode at 711.97/462.72 cm−1. The rovibrational eigenstatesare labeled using the quantum numbers of the Wang sym-metrized basis functions |v, l, J, (e/ f )〉, where l is the vibra-tional angular momentum quantum number and J the end-over-end rotational quantum number. We use the symmetrylabels e and f as the possible values of a symbolic quantumnumber e/ f labeling the eigenvalues. For a linear moleculethe vibrational angular momentum l is the only contributionto the axial component of the angular momentum. The vi-brational angular momentum is equal to the absolute valueof the signed quantum number k in the symmetric top basisfunctions l = |k|.

To show the rotational effects described in this paper theexperimentally determined rovibrational eigenenergy corre-sponding to each vibrationally excited state is plotted usinga reduced energy value Er by subtracting two terms Ev,(J = 0)

and E0,J from each measured value

Er = Emeas − Ev,(J = 0) − E0,J . (1)

Ev,(J = 0) is the rotationless vibrational energy calculatedfor l �= 0 vibrational states by extrapolating the rotationalstates to the nonphysical J = 0 state. This term value is con-stant for the rotational manifold corresponding to a given(v1, v2, l, v3) vibrational substate and describes the basic

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194302-3 Rovibrational eigenenergy structure of the [H,C,N] molecular system J. Chem. Phys. 134, 194302 (2011)

contribution of the vibration to the rovibrational eigenener-gies. In an excited bending state, the rotating linear moleculehas an effective moment of inertia and a component of an-gular momentum about the figure axis. In an excited bendingmode, the linear molecule is therefore a symmetric top andthe rotational energy values are to the first approximation19

Bv J (J + 1) + (Av − Bv )l2. (2)

The eigenenergy due to the vibrational angular momen-tum is usually divided in two components, the Avl2 positivecomponent is treated as vibrational energy and the −Bvl2 neg-ative component is treated as rotational energy. This splittingis necessary for practical purposes: due to this splitting thevibrational dependence of the rotational constant is not in-cluded in the vibrational energy. If the analysis of the rovi-bronic eigenenergies is completed, it is possible to redefinethe vibrational energy and to include the −Bvl2 term. Alter-natively, we can use the experimental eigenenergy values for a(v1, v2, l, v3) vibrational substate and interpolate the eigenen-ergies to J = 0. The Ev,(J = 0) vibrational eigenenergies usedin this work have been calculated through such an interpola-tion of the parity component with the lower eigenenergy valueusing the eigenenergies up to J = 30. The Ev,(J = 0) vibra-tional eigenenergies are approximately equal to the eigenen-ergy values predicted for J = 0 by the physical model definedin Ref. 16 (sometimes denoted Gc or Tv,J = 0). For the statesreported here the difference between these two definitions isless than 0.01 cm−1. The Ev,(J = 0) vibrational eigenenergy al-lows us to visualize the vibrational, rotational, and rotation-vibration interaction effects with increasing rotational exci-tation relative to the zero order situation for a (v1, v2, l, v3)vibrational substate.

E0,J energy values correspond to the vibrationlessground state and describe the manifold of the rotational statesin the case where the molecule is not vibrating. This is notonly a visual scaling of the eigenenergy values but also aphysical one: We consider the difference between the rota-tional manifold in a vibrating state relative to all rotationaleffects that we observe at high rotational excitations in thevibrationless state. The reduced energy Er is plotted againstthe J quantum number for each e/ f symmetry label. We plotagainst J rather than J (J + 1) (which is equivalent to plotagainst rotational excitation energy) because the true indepen-dent variable of the problem is the J quantum number and notthe rotational energy value. With the definition of Ev,(J = 0)

used in this work the reduced energy plots are defined onlythrough the exact Schrödinger equation and are meaningfulfor the isomerisation states.

III. APPROXIMATE TWOFOLD ROTATIONALDEGENERACY OF THE HCN AND HNCROVIBRATIONAL STATES WITH LOW ANGULARMOMENTUM

Figures 2 and 3 show the evolution of the rovibrationaleigenenergy for HCN and HNC with increasing rotationalquantum numbers for low angular momentum excitations.The eigenenergies shown fit the classical expressions usedto describe the rotational-vibrational eigenenergies of a linear

molecule extremely accurately. The curves shown in Figs. 2and 3 reveal interesting molecular physics behind the inter-play of the high order spectroscopic constants.

For the bending vibrational states with l = 0 and1 angular momentum we report here an approximatetwofold rotational degeneracy at high rotational excitation(60 > J > 40). For which of the two vibrational states therotational eigenenergy becomes approximately the same isdifferent between HCN and HNC. Such difference is notsurprising since the curvature of the bending potentials isquite different for the two molecules (with considerablydifferent bending frequencies). The two (e, f ) componentsof the rovibrational eigenenergy are the two degeneratecomponents of the bending vibrational excitation in the har-monic approximation of a nonrotating linear molecule. Thedegeneracy is lifted in a rotating molecule by l = k = ±2Coriolis matrix elements connecting substates with differentangular momentum, the separation between the levels in-creases with the rotational excitation.20, 21 The matrix elementis proportional to v2 and J , the splitting in the e and fcomponents should increase with bending excitation for thesame rotational quantum number. This is what we observeexperimentally for low (J < 40) vibrational excitation.

At high rotational excitation (J > 40) the evolution ofthe eigenenergies is determined by several effects. Thereis a distinguished plane formed by two spatial directions:the molecule axis and the direction of rotational angularmomentum. We expect that the two degenerate componentsof the bending vibration will be separated into two nondegen-erate vibrations: one vibration in the distinguished plane andone perpendicular to it. The corresponding classical picturecorrelates with the two different rotational structures. TheCoriolis force depends on the angle between the axis ofrotation and the vibrational velocity of the molecules in anaxis frame fixed to the molecule. The Coriolis force for thevibration in the spatially distinguished plane is zero, and forthe vibration perpendicular to it, it has a maximum value.If for a linear molecule the bending mode is excited, therovibrationally averaged angle γ in these bound states γ=〈γ 〉= 〈 |γ | 〉 is not 0. 〈γ 〉 is increasing substantially withthe bending excitation so that at high excitation of thebending vibration, the linear molecule can be considered as aslightly asymmetric rotor.23 The rotational energy levels for aslightly asymmetric rotor22 for Ka = 0 and 1 show a similarevolution at high J as observed here for HCN and HNC.With rotational excitation, the off-diagonal matrix elementsconnecting the sublevels with different vibrational angularmomentum increase continuously and l loses its significanceas quantum number.

For HCN the e states with zero or one vibrational angularmomentum the rotational eigenenergy in the excited bendingstates corresponds approximately to the rotational structureof the non-vibrating molecule plus a constant energy factor,which increases approximately with E = 3.6(7) cm−1 asthe bending excitation increases

Ev,J = Ev,J=0 + E0,J + m × E for 40 < J < 60. (3)

This may be interpreted as a decoupling of the rota-tion from the vibration. The separations between the flat

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194302-4 Georg Ch. Mellau J. Chem. Phys. 134, 194302 (2011)

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194302-5 Rovibrational eigenenergy structure of the [H,C,N] molecular system J. Chem. Phys. 134, 194302 (2011)

FIG. 2. The evolution of the reduced rovibrational eigenenergy for the HCN and HNC ν2 states with zero or single vibrational angular momentum excitationwith increasing bending excitation.

FIG. 3. The evolution of the reduced rovibrational eigenenergy for the HCN and HNC ν1 + ν2 states with zero or single vibrational angular momentumexcitation with increasing bending excitation.

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194302-6 Georg Ch. Mellau J. Chem. Phys. 134, 194302 (2011)

FIG. 4. The evolution of the reduced rovibrational eigenenergy for the HCN and HNC ν2 states with highly excited vibrational angular momentum withincreasing bending excitation.

eigenenergy regions match the g22 = 3.76(1) cm−1 parame-ter for Ev,J = 0 vibrational energies calculated for pure bend-ing states. The f states with l = 1, 2 also have an equidistantstructure, but it is less pronounced than for the e states. Theeigenenergy structure described is valid only for rotational ex-citations in the range of 40 < J < 60, for higher excitationsthe effects corresponding to the double well potential changethis structure. The eigenenergy lists determined experimen-

tally in this work reach up to J = 85, and there is a cleartrend for rotational excitations with J > 60, the effective e/ fsplitting is decreasing with rotational excitation.

The experimental study presented here does not reach upto the barrier of isomerisation. To understand the eigenenergystructure it is necessary to use values from ab initio calcu-lations. In fact all 45 000 eigenvalues up to the isomerisa-tion barrier have already been calculated.24, 25 For the [H,C,N]

FIG. 5. Typical variation of the l-doubling for HCN and HNC up to the isomerisation barrier. Upper left figure: The evolution of the reduced rovibrationaleigenenergy for the HCN states with highly excited vibrational angular momentum.

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194302-7 Rovibrational eigenenergy structure of the [H,C,N] molecular system J. Chem. Phys. 134, 194302 (2011)

10 20 30 40 50 60

0

5

10

15

20

25

0110

10 20 30 40 50 60

0

10

20

30

40

0310

10 20 30 40 50 60

0

20

40

60

0420

10 20 30 40 50 60

0

10

20

30

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0510

10 20 30 40 50 60

0

20

40

60

80

0620

10 20 30 40 50 60

0

10

20

30

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0710

10 20 30 40 50 60

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0820

10 20 30 40 50 60

0

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0910

10 20 30 40 50 60

0

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01020

10 20 30 40 50 60

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01110

10 20 30 40 50 60

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01220

10 20 30 40 50 60

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01310

10 20 30 40 50 60

0

50

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01420

10 20 30 40 50 60

0

25

50

75

100

125

150

175

01510

B=1.564

01620 B=1.588

B=1.495

B=1.506

B=1.518

B=1.533

B=1.548

B=1.500

B=1.508

B=1.516

B=1.525

B=1.535

B=1.1.548

10 20 30 40 50 60

0

10

20

30

40

0220 B=1.486B=1.483

B=1.491

-1/c

m

JJ 10 20 30 40 50 60

0

50

100

150

200

FIG. 6. The evolution of the reduced rovibrational eigenenergy for the HCN bending states up to the isomerisation barrier. The Ev,(J = 0) vibrational energyused to calculate the reduced energy was calculated from the ab initio data. (blue: e states; red: f states; green: experimental eigenenergies relative to theexperimental Ev,(J = 0) vibrational energy; first vertical line: barrier height mark; second vertical line: barrier height plus 2000 cm−1).

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194302-8 Georg Ch. Mellau J. Chem. Phys. 134, 194302 (2011)

10 20 30 40 50 60

0

50

100

150

200

250

01710 B=1.552

10 20 30 40 50 60

0

100

200

300

400

01820 B=1.619

10 20 30 40 50 60

0

100

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300

01910 B=1.554

10 20 30 40 50 60

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400

02020 B=1.634

10 20 30 40 50 60

0

100

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400

02110 B=1.578

10 20 30 40 50 60

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100

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02310 B=1.661023 0-022 01 0

10 20 30 40 50 60

20

30

40

50

60

70

80

02420

02220 B=1.640

B=4.690

10 20 30 40 50 60

0

10

20

30

40

50

60

02400 B=3.059

J

J

/cm

-1

10 20 30 40 50 60

0

50

100

150

200

FIG. 7. The evolution of the reduced rovibrational eigenenergy for the HCN bending states up to the isomerisation barrier; the inset represents a simulatedemission spectrum for 2000 K (blue: e states; red: f states; first vertical line: barrier height mark; second vertical line: barrier height plus 2000 cm−1)

molecular system only parity and total angular momentumare exact quantum numbers and the eigenenergies have to belabeled with vibrational quantum numbers in an assignmentprocedure. This work presents the results from the rotationalassignment of all rovibrational eigenenergies up to the iso-merisation barrier. The eigenenergies published in Ref. 25have been used for this analysis. When the assignment workwas started there was no reason to try to construct a betterPES and to recalculate the rovibrational eigenenergies. For theHNC part of the potential the HOTGAME results show thatthe eigenenergies and the conclusions that we get from such astudy may differ for a more accurate PES. For the HCN partof the potential and for the main features of the eigenenergystructure around the isomerisation barrier the eigenenergy listshould give us definitive results. The vibrational assignment

can be done using either the wave functions26 or the rotationalstructure of the eigenenergies as assignment information. Theassignment reported here is based on the rotational structure.The assignment was done by assuming that the eigenenergiesare described by spectroscopic constants up to the isomeri-sation and that the eigenenergy structure is not disturbed byquantum monodromy,27 details of the assignment procedurecan be found in Ref. 16.

For the low l states the inset in Fig. 2 shows approxi-mately the same rotational structure as detected in the exper-iment. Figure 5 shows some typical rotational structures forlow l states up to the isomerisation barrier: the e and f com-ponents of the doublets begin to move closer together and justbefore the barrier the slope of the eigenenergy curve increasessubstantially. Figures 6 and 7 show the step by step evolution

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194302-9 Rovibrational eigenenergy structure of the [H,C,N] molecular system J. Chem. Phys. 134, 194302 (2011)

11420 B=1.565

11620 B=1.581

1420 B=1.486

1620 B=1.498

1820 B=1.511

11020 B=1.525

11220 B=1.543

1510 B=1.491

1710 B=1.499

1910 B=1.507

11110 B=1.519

11310 B=1.538

11510 B=1.535

1220 B=1.4761110 B=1.473

1310 B=1.482

-1/c

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FIG. 8. The evolution of the reduced rovibrational eigenenergy for the HCN 1v20 bending states up to the isomerisation barrier. The Ev,(J = 0) vi-brational energy used to calculate the reduced energy was calculated from the ab initio data. (blue: e states; red: f states; green: experimentaleigenenergies relative to the experimental Ev,(J = 0) vibrational energy; first vertical line: barrier height mark; second vertical line: barrier height plus3300 cm−1).

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194302-10 Georg Ch. Mellau J. Chem. Phys. 134, 194302 (2011)

of the rotational structure with increasing bending excitation(for the vibrational assignment see Refs. 16). Figure 8 showsthe step by step evolution of the rotational structure withincreasing bending excitation for the 1v20 states. The rota-tional structure of the experimental and the ab initio datamatch perfectly within the resolution of the data plots.

IV. SATURATION OF THE HCN AND HNCROVIBRATIONAL STATES WITH HIGH ANGULARMOMENTUM

Figure 4 shows the evolution of the rovibrationaleigenenergy with maximum angular momentum l = v2.Classically, the l = v2 case corresponds to the situation of nu-clei rotating around the molecule axis. The HCN eigenenergystructure reaches a limit for v2 = 8. For the vibrational stateswith v2 > 8 the rotational eigenenergy structure does notchange any more, the molecule is “locked”on the molecularaxis. For HNC there is a change in the eigenenergy structurefor v2 ≥ 7 to lower eigenenergy values. This happens due tothe slope change in the potential surface as shown in the insetin Fig. 4.

For the high l states the ab initio data insets in Fig. 4perfectly reproduce the measured eigenenergy structure up tov2 = 11. Figure 5 shows the evolution of the l = v2 bend-ing states for v2 > 11. From the ab initio data we can seethat a structure change begins to take place at approximatelyhalf the barrier height (v2 = 11). The vibrational energy be-gins to accommodate to the levels above the barrier mainly athigh vibrational excitations of v2 > 22 just above the barrier16

first only for low l states, the high l states remain linear HCNstates.27 It is possible to argue that the rotational structure al-ready experiences the influence of the barrier at much lowerenergies than the vibrational one. To understand the observedstructural change at high l it is necessary to repeat the anal-ysis presented here for similar isomerising linear moleculeswith different barrier heights and compare the obtainedresults.

V. CONCLUSION AND OUTLOOK

In this work we have shown that the rotational structureof HCN and HNC has an approximate twofold rotationaldegeneracy for low vibrational angular momentum and highrotational excitation until effects due to the isomerisationbarrier spoil it. We have demonstrated using rotationally andvibrationally assigned ab initio calculations that the rotationstates are much more sensitive to the isomerisation barrierthan the vibrational states. The high vibrational angularmomentum states begin to accommodate the eigenenergystructure already at rovibrational energies correspondingapproximately to half the barrier height. For HNC the

experimental data demonstrates that the rotational eigenen-ergy structure is extremely sensitive to changes in thepotential energy surface. Using the complete vibrational androtational analysis for a triatomic molecule as an example itmay now be much easier to search for alternative methods insolving the Schrödinger equation for polyatomic molecules.Using the findings of this work it will be possible to assign ex-perimental HOTGAME spectra with even higher vibrationaland rotational excitation and give an exact quantum mechan-ical picture in the frequency domain for a basic chemicalmodel reaction, the HCN⇀↽HNC isomerisation reaction.

1K. S. Exner and G. Ch. Mellau, Visualization of the asymmetric infinitesquare double well energy eigenstates, Poster L13, 21st Conference onH.R.M.S., Poznan (2010).

2T. van Mourik, G. J. Harris, O. L. Polyanski, J. Tennyson, A. G. Császár,and P. J. Knowles, J. Chem. Phys. 115, 3706 (2001).

3J. M. Bowman, Science 290, 724 (2000).4P. F. Bernath, Chem. Soc. Rev. 25, 111 (1996).5G. Ch. Mellau, J. Chem. Phys. 133, 164303 (2010).6S. N. Mikhailenko, Vl. G. Tyuterev, and G. Ch. Mellau, J. Mol. Spectrosc.217, 195 (2003).

7G. Ch. Mellau, S. N. Mikhailenko, E. N. Starikova, S. A. Tashkun, H. Over,and Vl. G. Tyuterev, gion, J. Mol. Spectrosc. 224, 32 (2004).

8S. N. Mikhailenko, G. Ch. Mellau, E. N. Starikova, S. A. Tashkun, and Vl.G. Tyuterev, Actra, J. Mol. Spectrosc. 233, 32 (2005).

9W. Quapp, M. Hirsch, G. Ch. Mellau, S. Klee, M. Winnewisser, andA. Maki, Cli J. Mol. Spectrosc. 195, 284 (1999).

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13J. P. Hofmann, B. Eifert, and G. Ch. Mellau, J. Mol. Spectrosc. 262, 75(2010).

14A. Maki and G. Ch. Mellau, J. Mol. Spectrosc. 206, 47 (2001).15G. Ch. Mellau, J. Mol. Spectrosc. 264, 2 (2010).16G. Ch. Mellau, “Complete experimental rovibrational eigenenergies of

HCN up to 6880 cm−1 above the ground state,” J. Chem. Phys.(submitted).

17G. C. Mellau, “The ν1 band system of HCN,” J. Mol. Spectrosc. (2011)(submitted).

18See supplementary material at http://dx.doi.org/10.1063/1.3590026 for theexperimental and calculated rovibrational eigenenergies of HCN and HNCreported for the first time in this work.

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20J. K. G. Watson, High-ordelecules, J. Mol. Spectrosc. 1983, 83 (1983).21J. K. G. Watson, Can. J. Phys. 79, 521 (2001).22J. K. G. Watson, M. Herman, J. C. Van Craen, and R. Colin, J. Mol. Spec-

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(2002).25G. J. Harris, J. Tennyson, B. M. Kaminsky, Y. V. Pavlenko, and H. R. A.

Jones, Mon. Not. R. Astron. Soc. 367, 400 (2006).26J. M. Bowman, S. Irle, K. Morokuma, and A. Wodtke, J. Chem. Phys. 114,

7923 (2001).27K. Efstathiou, M. Joyeux, and D. A. Sadovskii, Phys. Rev. A 69, 032504

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