The Scientific World Journal

Volume 2013 (2013), Article ID 813249, 5 pages

http://dx.doi.org/10.1155/2013/813249

Research Article

Rovibrational Interaction and Vibrational Constants of the Symmetric Top Molecule ¹⁴NF₃

Hamid Najib

Laboratoire de Physique de la Matière Condensée, Équipe de Spectrométrie Physique, Département de Physique, Université Ibn Tofaïl, Faculté des Sciences, BP 133, 14000 Kénitra, Morocco

Received 8 April 2013; Accepted 8 May 2013

Academic Editors: A. F. Borghesani and A. Kochur

Copyright © 2013 Hamid Najib. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

Several accurate experimental values of the and rotation-vibration interaction parameters and , , and vibrational constants have been extracted from the most recent high-resolution Fourier transform infrared, millimeter wave, and centimeter wave investigations in the spectra of the oblate symmetric top molecule ¹⁴NF₃. The band-centres used are those of the four fundamental, the overtones, the combination, and hot bands identified in the region between 400 cm⁻¹ and 2000 cm⁻¹. Comparison of our constants with the ones measured previously, by infrared spectroscopy at low resolution, reveals orders of magnitude higher accuracy of the new values. The agreement between our values and those determined by ab initio calculations employing the TZ2Pf basis is excellent.

1. Introduction

Nitrogen trifluoride NF₃ is a pyramidal symmetric top molecule belonging to point group. It has four vibrational normal modes:

(i)two totally symmetric ( type): and ;(ii)two doubly degenerate ( type): and .

Today, NF₃ is employed in the cleaning of the PECVD chambers in the high volume production of liquid crystal displays and silicon-based thin film solar cells. It has been considered as an environmentally preferable substitute for sulphur hexafluoride or perfluorocarbons such as hexafluoroethane [1]. But, recent publications [2–7] reported that NF₃ is 17,000 times more potent a greenhouse gas than CO₂ and recommended to include it in the basket of gases controlled by Kyoto protocol and to monitor its environmental levels.

Nitrogen trifluoride is also used in hydrogen fluoride and deuterium fluoride lasers, which are types of chemical lasers.

In spite of these interesting properties and important applications, the spectra of this molecule have not yet been much studied in the past, because of difficulties to obtain high quality spectra and to interpret its perturbed bands. Many of these difficulties have now been overcome through the advent of high-resolution spectrometers and the development of computers.

This is within the framework of this research orientation and the Moroccan/European collaboration that several bands of NF₃ gas were recently analysed [8–14]. We used independent and complementary methods, Fourier transform infrared (FTIR), millimetre wave (MMW), and centimetre wave (CMW) spectroscopies. All studied IR spectra were recorded at Wuppertal (Germany) with the Bruker 120 HR interferometer, except for the region around 1032 cm⁻¹, which was recorded at the University of Giessen (Germany). The rotational spectra were measured in Lille (France) with a computer-controlled MMW spectrometer. The measurements in the CMW range were performed at Kiel (Germany) by means of wave-guide microwave Fourier transform spectroscopy.

The subject of this work is to extract accurate experimental rotation-vibration interaction parameters and anharmonicity constants of the potential function of ¹⁴NF₃ from our recent studies by high-resolution spectroscopy and the latest results available in the literature.

2. Relationships Linking Vibrational Constants

More recently, we have established the following relationships linking band-centres, harmonic wavenumbers, and anharmonicity constants of a symmetric top molecule [15].

2.1. Fundamental Bands

is the normal wavenumber of the th mode; is its vibrational quantum number; refers to a totally symmetric or to a degenerate vibration; and are the anharmonicity constants; and is the vibrational angular momentum: , or 0 only exists for a doubly degenerate vibration.

2.2. Harmonic Bands (Integer > 1)

2.3. Combination Bands and (Integer),

For the oblate symmetric top NF₃, we count , , and ; .

3. The Ground State Constants of

The experimental ground state (GS) axial rotational parameters for the symmetric top molecule ¹⁴NF₃ employed in the present study and reported in Table 1 come from different sources.

Table 1: Ground state constants (cm⁻¹) of  ¹⁴NF₃.

Parameter
Value [12, 17]
Value [11, 18]
Value [11, 19]

0.1949980 (10)
0.19499250 (44)
0.19499250 (44)

0.3562828965 (40)
0.3562827950 (15)
0.3562828891 (21)

Numbers in parentheses represent one standard deviation in units of the last digit quoted.

For the -dependent constant, we used in our high-resolution studies the following values:

(i) = 0.1949980 (10): a preliminary value obtained in the course of our work on the overtone band of ¹⁴NF₃,(ii) = 0.19499250 (44): the definitive value adopted in the study of the = 2 state of ¹⁴NF₃. In the two cases, we used the “loop method” as described in [16].

For the -dependent constant, the values adopted were determined by Höhe et al. [17], Breidung et al. [18], and Cazzoli and Puzzarini [19].

4. The Rovibrational Bands of Observed below 2000 cm⁻¹

4.1. The Fundamental Band [17]

The = 1 excited state of ¹⁴NF₃ was investigated by FTIR spectroscopy and with saturation technique using CO₂ side bands as a tunable infrared source. This level was considered unperturbed, and the fit gave the band-centre: = 1032.00123750 (47) cm⁻¹. For the excited rotational constants, the values were determined relative to the GS.

4.2. The Fundamental Band [14]

The lowest fundamental band of the nitrogen trifluoride ¹⁴NF₃ was studied by high-resolution FTIR, MMW, and CMW spectroscopies near 493 cm⁻¹. The analysis of the = 1 state included , and intravibrational interactions and gave the band-centre: = 493.4227759 (89) cm⁻¹.

4.3. The Fundamental, Hot, Overtone, and Combination Bands [13]

They were analysed by FTIR and MMW spectroscopies. The corresponding excited states were treated as isolated levels, and the following band-centres were determined:

Because of the low intensity of the overtone, the = 2 state constants were determined from the hot and fundamental bands.

We point out that any explanation was offered for a severe intensity perturbation observed in the spectra of and bands (see [13]).

4.4. The Fundamental Band [12]

The perpendicular band of the symmetric top ¹⁴NF₃ was analysed by high-resolution FTIR and MMW spectroscopies. The = 1 excited state was considered vibrationally isolated, but several intravibrational interactions were included in the final fit. The band-centre obtained is = 907.5413300 (72) cm⁻¹.

4.5. The Overtone Band [11]

The = 2 excited state of the oblate molecule ¹⁴NF₃, lying near 985 cm⁻¹, was successfully studied by high-resolution FTIR and MMW spectroscopies. Assumed to be isolated, the treatment of this level gave the following band-centres for the parallel and perpendicular components:

4.6. The Overtone and Combination Bands [10]

In the analysis of these bands, we used spectra recorded by Fourier transform spectrometer. The same models applied to the and excited states were applied to treat the 2 and + bands. We obtained the following results:

4.7. The Combination Band [8, 9]

The perpendicular band of ¹⁴NF₃ was studied by high-resolution infrared spectroscopy. It was treated by a model taking into account - and -type intervibrational interactions. The band-centre obtained in the -reduction of the rovibrational Hamiltonian is = 1523.040783 (34) cm⁻¹.

5. Results and Discussion

In Table 2, we gather the recent measurements, at high-resolution, of the centres of the all studied bands between 400 cm⁻¹ and 2000 cm⁻¹ and the corresponding experimental rotation-vibration interaction constants: and and and being the constants of the upper level.

Table 2: Band-centres and rovibrational interaction constants of  ¹⁴NF₃ molecule (in cm⁻¹).

Band or component
Experimental band-centre, this work
Experimental   × 10³, this work
Ab  initio   × 10³, [18]
Experimental   × 10³, this work
Ab  initio   × 10³, [18]

1032.00123750 (47)
0.593526 (40)
0.643
−1.4496825 (43)
−1.227

647.1340617 (73)
0.4346 (10)
0.404
1.289844 (18)
1.300

907.5413300 (72)
0.7374 (11)
0.857
2.628451 (22)
2.758

493.4227759 (89)
0.5566 (10)
0.544
0.150021 (23)
0.164

645.121943 (14)
0.8777 (10)
—
2.592650 (37)
—

1292.25004 (21)a
0.8777 (10)
—
2.592650 (37)
—

+
1138.276629 (10)
0.9922 (10)
—
1.447060 (43)
—

983.701767 (34)
1.10135 (63)
—
0.192090 (23)
—

986.622364 (18)
1.10101 (56)
—
0.302179 (50)
—

1803.130213 (57)
1.47497 (80)
—
4.84308 (22)
—

1810.423993 (21)
1.49747 (50)
—
5.24715 (12)
—

+
1931.577516 (19)
1.30958 (56)
—
1.460127 (78)
—

+
1523.040783 (34)
1.37339 (84)
—
−1.13109 (44)
—

+
1546.30b
—
—
—
—

Numbers in parentheses represent one standard deviation in units of the last digit quoted.

aValue extracted from the values of ()⁰ and (Tables 2 and 3). bValue estimated from our FTIR spectrum which is in course of study.

The values of the rovibrational interaction constants were determined by ab initio calculations (Table 2) for only the fundamental bands. The agreement with our values is excellent.

Equation (2) leads to = −2.280208 (11) cm⁻¹.

For the harmonic band, we obtain the system of equations:

We derive = −0.841743 (22) cm⁻¹ and = 0.730149 (21) cm⁻¹.

As for , we deduce = −4.15278 (18) cm⁻¹ and = 1.82344 (18) cm⁻¹.

Using the band-centres of and , we obtain = −2.383248 (49) cm⁻¹. We can also derive, from the band-centres of and , the anharmonic constant: = −7.965051 (26) cm⁻¹.

All experimental anharmonicity constants determined in this work for the nitrogen trifluoride ¹⁴NF₃ are given in Table 3.

Table 3: Anharmonicity constants of  ¹⁴NF₃ (in cm⁻¹).

Anharmonicity constant
Experimental value, this work
Ab initio TZ2Pf [18]
Experimental value [20, 21]

—
−3.15
−2.9

—
−3.56
−4

−7.965051 (26)
−8.14
−9.9

−2.383248 (49)
−2.08
−1.5

−1.006059 (11)
−0.88
—

−8.53a
−6.46
−7.6

−2.280208 (11)
−1.98
−2.5

−4.15278 (18)
−4.19
—

—
−5.12
—

−0.841743 (22)
−0.79
−0.820

1.82344 (18)
1.96
—

—
−0.10
—

0.730149 (22)
0.72
0.729

—
—
−1

Numbers in parentheses are one standard deviation in units of the last digit quoted.

aValue deduced from the ( + )⁰ given in Table 2.

The experimental centre of the band was estimated from the branches edge at 1292.26 cm⁻¹. But a precise value can be obtained combining the values of the experimental centres of and (Table 2). From the relationships:

we can indeed deduce that = 1292.25004 (21) cm⁻¹ and = −1.006059 (11).

The values obtained for , , and are small suggesting that the corresponding levels and are not significantly affected by the anharmonic perturbations, whereas the vibrational dependence is extremely important for the and levels.

It is worth noting that our values of the anharmonicity constants of ¹⁴NF₃ are in good agreement with previous medium experimental studies (column 4 of Table 3), but significantly more accurate by at least three orders of magnitude.

One can notice the fair agreement between our values and those obtained by ab initio methods [18] employing the TZ2Pf basis.

We can also extract accurate values of the harmonic wavenumbers of the oblate symmetric top molecule ¹⁴NF₃. The results are gathered in Table 4.

Table 4: Harmonic wavenumber constants of  ¹⁴NF₃ (in cm⁻¹).

Harmonic wavenumber
Experimental value, this work
Ab initio unscaled value, [22]
Ab initio value TZ2Pf, [18]

—
1042.8
1053.8

648.140120 (18)
659.3
660.7

909.84264 (43)
905.0
935.7

493.534359 (52)
500.6
502.8

Numbers in parentheses represent one standard deviation in units of the last digit quoted.

The agreement between our values and those determined by the theoretical ab initio calculations is significantly worse. We think that it is necessary to give much more credibility to our values which were deduced from experimental constants.

6. Conclusion

Using the recent accurate results obtained for the bands below 2000 cm⁻¹, of the symmetric top molecule ¹⁴NF₃, several rovibrational interaction and anharmonicity constants have been deduced.

Our results contribute incontestably to the experimental knowledge of the molecular potential of this molecule which helps to test and improve theoretical models.

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