Journal of Molecular Spectroscopy 265 (2011) 102–105

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Journal of Molecular Spectroscopy

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Rovibrational spectrum and potential energy surface of the N2–N2Ovan der Waals complex

Rui Zheng, Yu Zhu, Song Li, Min Fang, Chuanxi Duan ⇑College of Physical Science and Technology, HuaZhong Normal University, 152 Luoyu Road, Wuhan 430079, China

a r t i c l e i n f o

Article history:Received 10 November 2010In revised form 17 December 2010Available online 11 January 2011

Keywords:Rovibrational spectrumvan der Waals complexN2–N2O

0022-2852/$ - see front matter � 2011 Elsevier Inc. Adoi:10.1016/j.jms.2011.01.003

⇑ Corresponding author. Fax: +86 27 67866927.E-mail address: cxduan@phy.ccnu.edu.cn (C. Duan

a b s t r a c t

The rovibrational spectrum of the N2–N2O van der Waals complex has been recorded in the N2O m1 region(�1285 cm�1) using a tunable diode laser spectrometer to probe a pulsed supersonic slit jet. The observedtransitions together with the data observed previously in the N2O m3 region are analyzed using a WatsonS-reduced asymmetric rotor Hamiltonian. The rotational and centrifugal distortion constants for theground and excited vibrational states are accurately determined. The band-origin of the spectrum isdetermined to be 1285.73964(14) cm�1. A restricted two-dimensional intermolecular potential energysurface for a planar structure of N2–N2O has been calculated at the CCSD(T) level of theory with theaug-cc-pVDZ basis sets and a set of mid-bond functions. With the intermolecular distance fixed at theground state value R = 3.6926 Å, the potential has a global minimum with a well depth of 326.64 cm�1

at hN2 = 11.0� and hN2O = 84.3� and has a saddle point with a barrier height of 204.61 cm�1 athN2 = 97.4� and hN2O = 92.2�, where hN2 ðhN2OÞ is the enclosed angle between the N–N axis (N–N–O axis)and the intermolecular axis.

� 2011 Elsevier Inc. All rights reserved.

1. Introduction

In the past three decades more than thirty van der Waals com-plexes containing nitrous oxide (N2O) have been studied by highresolution infrared and/or microwave spectroscopy [1]. Thesestudies have provided a wealth of information on the structure,dynamics and intermolecular interactions in the N2O-containingcomplexes. Spectroscopic investigations of the N2–N2O and O2–N2O complexes are of atmospheric interest, because a precise char-acterization of the weak interactions between N2 or O2 and N2O isessential for accurate calculations of the N2 or O2 pressure-broad-ening coefficients of N2O [2]. The rotationally resolved infraredspectrum of the N2–N2O complex was first reported by Randallet al. [3] in the m3 asymmetric stretching mode region of N2Omonomer. A near T-shaped geometry was determined from therotational constants and rationalized by the construction of poten-tials using a distributed multipole and distributed dispersion mod-el. In order to gain a more detailed structure of this complex, Leung[4] studied the rotational spectrum of 15N2–14N2O using a pulsedmolecular beam Fourier transform microwave spectrometer. Withthe rotational constants and the nuclear quadrupole coupling con-stants, four possible structures of 15N2–14N2O were determined.These structures are all planar and approximately T-shaped, withN2 forming the leg of the T. The 15N2 axis and the 14N2O axis were

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).

found to make an angle of 13� and 81� with the intermolecularaxis, respectively [4]. The infrared spectrum of the O2–N2O com-plex was first investigated in the nitrogen matrix [5] and later inthe molecular beam [6]. The equilibrium structure of the O2–N2Ocomplex was experimentally determined to be planar but withan effective out-of-plane angle of 23� [6]. The angles between theO2/N2O axis and the intermolecular axis were determined to beeither hO2 = 58� and hN2O = 77�, or hO2 = 122� and hN2O = 100� [6].The band-origin of O2–N2O in the N2O m3 region has a small shiftof +0.36635 cm�1 from that of the N2O monomer [6], comparedwith a large shift of +2.2327 cm�1 for N2–N2O [3]. To our knowl-edge, no high-level ab initio intermolecular potential energy sur-faces (PES) have been reported for these two complexes.

The present paper reports the observation and analysis of therovibrational spectrum of N2–N2O in the m1 symmetric stretchingmode region of N2O monomer. A set of improved molecular con-stants for the ground and excited vibrational states has been deter-mined from a global analysis of our observed spectrum and thedata observed previously in the N2O m3 region [3]. An ab initiotwo-dimensional intermolecular potential energy surface for N2–N2O is used to determine the orientation of the monomers in thecomplex.

2. Experimental

The rovibrational spectrum of N2–N2O was measured with atunable infrared diode laser spectrometer which has been

Fig. 1. The observed and simulated spectrum of the N2–N2O complex. (a) Observedspectrum. Lines marked with an asterisk are due to absorption of N2O monomer inthe jet. (b) Simulated spectrum. The spectrum was simulated with a rotationaltemperature Trot = 8 K and a Gaussian line-width of 0.002 cm�1.

R. Zheng et al. / Journal of Molecular Spectroscopy 265 (2011) 102–105 103

described in detail elsewhere [7,8]. A Pb-salt infrared diode laserwas operated in a rapid scan mode [9]. The laser current wasramped by a laser controller (Laser Components, L5830) at a fre-quency of 1 kHz. The laser beam was reflected 120 times througha pulsed supersonic jet expansion by a pair of astigmatic mirrors.A home-made 30 mm � 200 lm slit nozzle was attached to a0.8 mm pin-hole pulsed valve (General Valve series 9). An air-spaced internally coupled confocal Fabry–Perot interferometer(ic-FBI) [10] with a free spectral range of about 0.01 cm�1 was usedfor relative frequency calibration. The strong absorption lines ofthe N2O monomer in the slit jet and their accurate frequency posi-tions in HITRAN [11] were used for absolute frequency calibration.The absolute accuracy of the frequency calibration was estimatedto be about 0.0005 cm�1. The direct absorption signal from thejet and the interferometer fringes were digitized by a two-channel14-bit 50 MHz A/D card (NI PXI-5122) and transferred to anembedded controller (NI PXI-8186). A LabView program wasdeveloped to acquire and process the data. A software line-lockingscheme with a strong absorption line of N2O in the slit jet as thewavelength reference was used to correct the laser frequency driftduring signal averaging [12].

The N2–N2O complexes were generated in the supersonicexpansion using about 0.3% N2O and 3% N2 diluted in helium.The gases were pre-mixed in a gas cylinder before use. The optimalstagnation pressure was about 14 atmospheres. The opening timeof the nozzle was about 1500 ms with a repetition rate of 5 Hz. Theaverage pressure during valve operation in the vacuum chamberwas 8.0 � 10�3 mbar.

Table 1Molecular parameters (1r in parentheses) for N2–N2O.

Parameters Ground state

This work Ref. [3]

A (MHz) 12797.4 (15) 12801.2 (17)B (MHz) 2100.73 (30) 2101.81 (55)C (MHz) 1791.87 (27) 1791.80 (39)DJ (kHz) 6.4 (12) 21.7 (74)DJK (kHz) 348 (17) 573.0 (50)d1 (kHz) �1.64 (18) �5.5 (19)d2 (kHz) �0.797 (74) –m0 (cm�1) – –R (Å) 3.6926 (3) 3.6926 (4)D (amuÅ2) 1.98 (8) 2.12 (13)

a These values were constrained to their ground state values in the fit.

3. Results and analysis

3.1. Rotational analysis

The absorption spectrum of N2–N2O has been measured in thespectral region between 1284.1 and 1285.9 cm�1. Fig. 1 shows aportion of our observed spectrum. The spectrum was synthesizedby several individual frequency scans. Each scan was averagedfor more than 2000 gas pulses. The line-width of most isolatedlines is about 0.002 cm�1. Lines marked with an asterisk are dueto absorption of N2O monomer in the slit jet.

The spectrum observed in the N2O m1 region was very similar tothat observed in the N2O m3 region [3]. The assignment wasstraightforward using a conventional Watson S-reduction Hamilto-nian [13] and molecular constants reported in Ref. [3]. A total of152 b-type transitions were assigned, with J up to 20 and Ka upto 4, while no a-type transitions were found under the present sen-sitivity. Due to the limited spectral coverage of our diode lasers,most of these transitions belong to the Q- or P-branch. A globalanalysis of these transitions and 65 transitions assigned previouslyin the N2O m3 region [3] were performed to determine molecularconstants for both ground and excited vibrational states usingthe SPFIT/SPCAT program [14]. In the final fit, the band-origin m0,three rotational constants (A, B, C) and two centrifugal distortionconstants (DJ, DJK) for all three vibrational states were floated.The centrifugal distortion constants d1 and d2 for two excitedvibrational states were constrained to their values in the groundstate. Even with a largely expanded dataset, the centrifugal distor-tion constant DK could not be well determined and so was fixed atzero. The resulting molecular constants are listed in Table 1 andthe observed transitions and their residues are given in Table SIof the supplementary material. The standard deviation of the fitis 0.00037 cm�1, which is within the experimental uncertainty.

A simulated spectrum with molecular constants in Table 1 and arotational temperature of 8 K is shown in Fig. 1b. The simulatedspectrum of N2–N2O reproduces the observed spectrum very well.However, there are several lines whose observed intensities aresignificantly weaker than their predicted intensities, for example,the lines near 1284.573 and 1284.822 cm�1. This discrepancy isstill not understood. Other van der Waals complexes or clustersformed in the supersonic expansion of He/N2/N2O, such as He–N2O [7], (N2O)2 [15] and (N2O)3 [16], are also possible to be de-tected in the N2O m1 region. No transitions of He–N2O were identi-fied due to the relatively high rotational temperature in our jet.Some lines could be readily assigned to the transitions of the non-polar isomer of (N2O)2 with high values of J and Ka [15]. But manyweak lines and even several strong lines remain unassigned. Forexample, two strong lines which are partially overlapped by the111–220 and 110–221 K-doublets around 1284.39 cm�1 were notable to be assigned to any of the above-mentioned complexes.

N2O m1 N2O m3

This work This work Ref. [3]

12734.8 (25) 12705.5 (17) 12706.6 (14)2100.93 (29) 2097.30 (40) 2097.90 (60)1790.53 (27) 1787.46 (37) 1787.73 (49)6.4 (12) 8.2 (29) 21.7a

337 (17) 511 (59) 573.0a

�1.64a �1.64a �5.5a

�0.797a �0.797a –1285.73964 (14) 2225.98936 (17) 2225.9896 (1)3.6929 (3) 3.6954 (4) 3.6951 (5)2.02 (9) 1.99 (12) 2.02 (15)

104 R. Zheng et al. / Journal of Molecular Spectroscopy 265 (2011) 102–105

The newly determined molecular constants for the ground andN2O m3-excited vibrational states are in good agreement with thosereported in Ref. [3] except DJK in the ground state. In previous study[3], DJ and DJK for the N2O m3-excited vibrational state were con-strained to their ground state values. Our results show DJK for theground state, 348(17) kHz, is slightly smaller than that for the N2Om3-excited excited vibrational state, 511(59) kHz. The determinedcentrifugal distortion constants for N2–N2O are very similar to thosefor its isoelectronic complex CO–N2O [17–19]. The band-origin of ourobserved spectrum is determined to be m0 = 1285.73964(14) cm�1,with a blue-shift of +0.8363 cm�1 from that of N2O monomer, com-pared with +2.2325 cm�1 in the N2O m3 region [3].

Fig. 3. Contour plots of the potential energy surface for N2–N2O with R fixed at3.6926 Å. Contours are labeled in cm�1.

3.2. Structural analysis

The effective structure of N2–N2O was derived from the rota-tional constants using a similar approach which was applied toCO–N2O by Qian and Howard [18]. Assuming the geometries ofthe monomers remain unchanged upon complexation, the struc-ture of N2–N2O is defined by four Jacobi coordinates as shown inFig. 2, where R is the intermolecular distance between the N2

and N2O centers of mass, hN2 is the enclosed angle between theN–N axis and R, hN2O is the enclosed angle between the N–N–O axisand R, and u is the dihedral angle between the two subunits. Thecalculated inertial defects (D = Ic � Ib � Ia) for three vibrationalstates are 1.98(8), 2.02(9) and 1.99(12) amu Å2, respectively. Thesmall positive values of the inertial defect indicate the complexis planar (u = 0). For a planar structure, R can be determined fromC constant by the following formula:

R ¼ kl

1C� 1

bN2O� 1

bN2

� �� �1=2

;

where l is the reduced mass of the complex, bN2O, bN2 are the rota-tional constants of N2O [20] and N2 [21], k is a conversion factor(505 379 MHz amu Å2). The distance R in the ground state,3.6926(3) Å, increases slightly to 3.6929(3) and 3.6954(4) Å in theN2O m1 and m3-excited vibrational states, respectively, indicatingthe complex is slightly expanded upon vibrational excitation.

For a planar molecule, only two out of the three rotational con-stants are independent because the moments of inertia have a pla-nar relationship: Ic � Ia + Ib. The C constant has been used todetermine R, so only one more constant, A or B, remains to deter-mine the angles hN2 and hN2O. Obviously their values cannot bedetermined separately. In the absence of isotopic substitution datait is impossible to determine the orientation of the subunits withinthe complex from the rotational constants. In order to get some

Fig. 2. The Jacobi coordinates used to define the structure of N2–N2O. R is theintermolecular distance between the N2 and N2O centers of mass, hN2 (hN2 O) is theenclosed angle between the N–N axis (N–N–O axis) and R, and u is the dihedralangle between the two subunits. The z axis is chosen to be coincident with theintermolecular axis. The N2O monomer lies in the x–z plane and the y axis is out ofthe plane.

indications about the structural angles, Randall et al. calculatedthe intermolecular potential energy curves for N2–N2O in the T-shaped form (hN2 þ hN2O ¼ 90�) and the slipped parallel form(hN2 ¼ hN2O) using a distributed multipole and distributed disper-sion model [3]. Considering the rough approximations of this mod-el and constrains used in the calculation, it is necessary toconstruct a more precise intermolecular potential energy surfacefor N2–N2O. For this purpose, an ab initio two-dimensional inter-molecular potential energy surface will be calculated and used todetermine the possible structure in the next section.

4. Intermolecular potential

The N2 and N2O monomers were assumed to be rigid and werefrozen at their equilibrium structures: r(N–N) = 1.0977 Å for N2

[21], r(N–N) = 1.1273 Å and r(N–O) = 1.1851 Å for N2O [22], respec-tively. The intermolecular potential energy of N2–N2O for a givengeometry was calculated at the coupled-cluster singles anddoubles with perturbative triples [CCSD(T)] level [23], using aug-cc-pVDZ basis sets [24] for all atoms supplemented with bondfunctions (3s3p2d) [25] placed at the midpoint of R. The supermo-lecular approach was used, where the intermolecular interactionenergy was the difference between the dimer energy and the en-ergy of the N2 and N2O monomers. The full counterpoise correction[26] was used to account for the basis set superposition error. Allthe calculations were carried out with the Molpro 2009.1 package[27].

The intermolecular potential was calculated for geometrieswith R fixed at its averaged ground state value, 3.6926 Å, with an-gles hN2 and hN2O varied from 0 to 360� in steps of 10�, and with ufixed at 0. A total of 1369 data points for the intermolecular poten-tial energy were obtained (Table S2 in the supplemental material).The PES was constructed using the cubic spline interpolation meth-od. The global minimum occurs at hN2 = 11.0� and hN2O = 84.3�, witha well depth of 326.64 cm�1. Saddle point between the two equiv-alent minima (hN2 = 11.0� or 191.0�) occurs at hN2 = 97.4� andhN2O = 92.2�, with a barrier height of 204.61 cm�1, which impliesa hindered in-plane bending motion of the N2 subunit. Fig. 3 showsconstant energy contours of the two-dimensional PES with R and ufixed at 3.6926 Å and 0, respectively.

5. Discussion and conclusion

The equilibrium structural angles of the complex, predictedfrom the restricted two-dimensional intermolecular potential, are

R. Zheng et al. / Journal of Molecular Spectroscopy 265 (2011) 102–105 105

hN2 = 11.0� and hN2O = 84.3�. This equilibrium structure is in goodagreement with the third possible structure of 15N2–14N2O(Fig. 6iii in Ref. [4]) determined from the nuclear quadrupole cou-pling constants, in which the N2 axis is pointing towards the termi-nal N nuclei of N2O and the O end of N2O is closer to the N2

monomer than the N end. From the intermolecular PES of CO–N2O estimated with the model of Muenter [28], the global mini-mum was found at R = 3.87 Å, hCO = 15� and hN2O = 86�, with a welldepth of 322 cm�1 [18]. Obviously, the structural angles and welldepth of N2–N2O are very similar to those of CO–N2O. The effectiveintermolecular distance of N2–N2O (R = 3.6926 Å) is slightly shorterthan that of CO–N2O (R = 3.87 Å). The band-origin of CO–N2O in theN2O m3 region was observed to shift +2.9054 cm�1 from that of theN2O monomer [18], compared with +2.2325 cm�1 for N2–N2O. Ablue-shift of the band-origin means the intermolecular interactionbecomes weaker upon vibrational excitation. From this point ofview, the intermolecular interaction between CO and N2O mightbe slightly weaker than that between N2 and N2O even thoughCO has a permanent electric dipole moment. A more quantitativecomparison need to calculate the intermolecular PES of CO–N2Oat the same level of computational method and basis sets for N2–N2O.

Two internal motion states due to the internal motion of the15N2 subunit have been observed in the pure rotational spectrumof 15N2–14N2O [4]. Transitions between these two internal motionstates are unobservable due to the forbidden of spin flip. In ourinfrared spectrum as well as that observed by Randall et al. [3],no evidence of tunneling splitting was observed. The change ofthe barrier height upon the m1 vibrational excitation of N2O is prob-ably too small to be resolved under our experimental conditions.

In conclusion, the high resolution spectrum of the N2–N2O vander Waals complex has been recorded in the N2O m1 region. Therotational and centrifugal distortion constants for the ground andexcited vibrational states are accurately determined from a globalanalysis of the available data in both the N2O m1 and m3 regions. Theaveraged intermolecular distance in the ground state is determinedto be R = 3.6926 Å. The equilibrium structure of the complex, pre-dicted from the restricted two-dimensional intermolecular poten-tial energy, are hN2 = 11.0� and hN2O = 84.3�. This structure shows aremarkable similarity to that of the isoelectronic complex CO–N2O.

Acknowledgments

This work has been supported by the National Natural ScienceFoundation of China (Grant No. 10604019) and self-determinedresearch funds of CCNU from the colleges’ basic research and oper-

ation of MOE (Grant No. CCNU09A02012). The authors thank Dr.Minghui Yang for his help on theoretical calculations.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.jms.2011.01.003.

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