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

Abstract

Several accurate experimental values of the 𝛼^𝐶 and 𝛼^𝐵 rotation-vibration interaction parameters and 𝜔_𝑖, 𝑥_𝑖𝑗, and 𝑔_𝑖𝑗 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 C_3v point group. It has four vibrational normal modes:(i)two totally symmetric (𝐴₁ type): 𝜈₁ and 𝜈₂;(ii)two doubly degenerate (𝐸 type): 𝜈₃ and 𝜈₄.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 𝜈_𝑖=1

𝜈^ℓ𝑖_𝑖=𝜔⁰_𝑖+𝑥_𝑖𝑖+𝑔_𝑖𝑖ℓ_𝑖 (1)𝜔_𝑖 is the normal wavenumber of the 𝑖th mode; 𝜈_𝑖 is its vibrational quantum number; 𝑖 refers to a totally symmetric or to a degenerate vibration; 𝑥_𝑖𝑖 and 𝑔_𝑖𝑖 are the anharmonicity constants; and ℓ_𝑖 is the vibrational angular momentum: |ℓ_𝑖|=𝜈_𝑖,𝜈_𝑖−2,…,1, or 0 only exists for a doubly degenerate vibration.

2.2. Harmonic Bands 𝜈_𝑖=𝑛 (Integer > 1)

𝑛𝜈^ℓ𝑖_𝑖=𝑛𝜈_𝑖^±10+𝑛²−𝑛𝑥_𝑖𝑖+ℓ²_𝑖−𝑛𝑔_𝑖𝑖. (2)

2.3. Combination Bands 𝜈_𝑖=𝑛 and 𝜈_𝑖′=𝑚 (Integer), 𝑖≠𝑖^′

𝑛𝜈^ℓ𝑖_𝑖+𝑚𝜈^ℓ𝑖′_𝑖′⁰=𝑛𝜈^ℓ𝑖_𝑖⁰+𝑚𝜈^ℓ𝑖′_𝑖′⁰+𝑛𝑚𝑥_𝑖𝑖′+𝑔_𝑖𝑖′ℓ_𝑖ℓ_𝑖′. (3) For the oblate symmetric top NF₃, we count 4𝜔⁰_𝑖, 10𝑥_𝑖𝑗, and 3𝑔_𝑖𝑗; 𝑖≤𝑗.

3. The Ground State Constants of ¹⁴NF₃

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.

For the 𝐶₀𝐾-dependent constant, we used in our high-resolution studies the following values:(i)𝐶₀ = 0.1949980 (10): a preliminary value obtained in the course of our work on the 2𝜈₄ overtone band of ¹⁴NF₃,(ii)𝐶₀ = 0.19499250 (44): the definitive value adopted in the study of the 𝜈₄ = 2 state of ¹⁴NF₃. In the two cases, we used the “loop method” as described in [16].For the 𝐵₀𝐽-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 ¹⁴NF₃ Observed below 2000 cm⁻¹

4.1. The 𝜈₁ Fundamental Band [17]

The 𝜈₁ = 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: (𝜈₁)⁰ = 1032.00123750 (47) cm⁻¹. For the excited rotational constants, the values were determined relative to the GS.

4.2. The 𝜈₄ Fundamental Band [14]

The lowest fundamental band 𝜈₄ of the nitrogen trifluoride ¹⁴NF₃ was studied by high-resolution FTIR, MMW, and CMW spectroscopies near 493 cm⁻¹. The analysis of the 𝜈₄ = 1 state included ℓ(2,2),ℓ(2,−1),ℓ(2,−4), and 𝑘(0,6) intravibrational interactions and gave the band-centre: (𝜈₄)⁰ = 493.4227759 (89) cm⁻¹.

4.3. The 𝜈₂ Fundamental, 2𝜈₂−𝜈₂ Hot, 2𝜈₂ Overtone, and 𝜈₂+𝜈₄ 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: 𝜈₂⁰=647.1340617(73)cm⁻¹,2𝜈₂−𝜈₂⁰=645.121943(14)cm⁻¹,𝜈₂+𝜈₄⁰=1138.276629(10)cm⁻¹. (4) Because of the low intensity of the 2𝜈₂ overtone, the 𝜈₂ = 2 state constants were determined from the 2𝜈₂−𝜈₂ hot and 𝜈₂ fundamental bands.

We point out that any explanation was offered for a severe intensity perturbation observed in the spectra of 𝜈₂ and 2𝜈₂ bands (see [13]).

4.4. The 𝜈₃ Fundamental Band [12]

The perpendicular band 𝜈₃ of the symmetric top ¹⁴NF₃ was analysed by high-resolution FTIR and MMW spectroscopies. The 𝜈₃ = 1 excited state was considered vibrationally isolated, but several intravibrational interactions were included in the final fit. The band-centre obtained is (𝜈₃)⁰ = 907.5413300 (72) cm⁻¹.

4.5. The 2𝜈₄ Overtone Band [11]

The 𝜈₄ = 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: 2𝜈⁰₄⁰=983.701767(34)cm⁻¹,2𝜈₄^±20=986.622364(18)cm⁻¹. (5)

4.6. The 2𝜈₃ Overtone and 𝜈₁+𝜈₃ Combination Bands [10]

In the analysis of these bands, we used spectra recorded by Fourier transform spectrometer. The same models applied to the 𝜈₄=2 and 𝜈₃=1 excited states were applied to treat the 2𝜈₃ and 𝜈₁ + 𝜈₃ bands. We obtained the following results: 2𝜈⁰₃⁰=1803.130213(57)cm⁻¹,2𝜈₃^±20=1810.423993(21)cm⁻¹,𝜈₁+𝜈₃⁰=1931.577516(19)cm⁻¹. (6)

4.7. The 𝜈₁+𝜈₄ Combination Band [8, 9]

The 𝜈₁+𝜈₄ perpendicular band of ¹⁴NF₃ was studied by high-resolution infrared spectroscopy. It was treated by a model taking into account ℓ- and 𝑘-type intervibrational interactions. The band-centre obtained in the 𝐷-reduction of the rovibrational Hamiltonian is (𝜈₁+𝜈₄)⁰ = 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: 𝛼^𝐶=𝐶₀−𝐶^′ and 𝛼^𝐵=𝐵₀−𝐵^′ and 𝐶^′ and 𝐵^′ being the constants of the upper level.

Table 2 

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

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 𝑥₂₄=(𝜈₂+𝜈₄)⁰−(𝜈₂)⁰−(𝜈₄)⁰ = −2.280208 (11) cm⁻¹.

For the 2𝜈₄ harmonic band, we obtain the system of equations: 2𝜈⁰₄⁰=2𝜈₄^±10+2𝑥₄₄−2𝑔₄₄,2𝜈₄^±20=2𝜈₄^±10+2𝑥₄₄+2𝑔₄₄. (7) We derive 𝑥₄₄ = −0.841743 (22) cm⁻¹ and 𝑔₄₄ = 0.730149 (21) cm⁻¹.

As for 2𝜈₄, we deduce 𝑥₃₃ = −4.15278 (18) cm⁻¹ and 𝑔₃₃ = 1.82344 (18) cm⁻¹.

Using the band-centres of 𝜈₁ and 𝜈₄, we obtain 𝑥₁₄ = −2.383248 (49) cm⁻¹. We can also derive, from the band-centres of 𝜈₁ and 𝜈₃, the anharmonic constant: 𝑥₁₃ = −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).

The experimental centre of the 2𝜈₂ band was estimated from the ^𝑄𝑄 branches edge at 1292.26 cm⁻¹. But a precise value can be obtained combining the values of the experimental centres of 𝜈₂ and 2𝜈₂−𝜈₂ (Table 2). From the relationships: 2𝜈₂⁰=2𝜈₂⁰+2𝑥₂₂,2𝜈₂−𝜈₂⁰=𝜈₂⁰+2𝑥₂₂, (8) we can indeed deduce that (2𝜈₂)⁰ = 1292.25004 (21) cm⁻¹ and 𝑥₂₂ = −1.006059 (11).

The values obtained for 𝑥₂₂, 𝑥₄₄, and 𝑔₄₄ are small suggesting that the corresponding levels 𝜈₂=2 and 𝜈₄=2 are not significantly affected by the anharmonic perturbations, whereas the vibrational dependence is extremely important for the 𝜈₁=𝜈₃=1 and 𝜈₂=𝜈₃=1 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).

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 𝜔⁰_𝑖 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.