# Rovibrational Interaction and Vibrational Constants  of the Symmetric Top Molecule14NF3

Authors: Hamid Najib
Journal: The Scientific World Journal
 (2013)

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## Abstract

Several accurate experimental values of theαC and
αB rotation-vibration interaction parameters and ωi, xij, and gij 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.


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## Body

## 1. Introduction

Nitrogen trifluoride NF3 is a pyramidal symmetric top molecule belonging to C3v 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 of14NF3 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 Bandsνi=1

(1)
(
ν
i
ℓ
i
)
=
ω
i
0
+
x
i
i
+
g
i
i
ℓ
i
ω
i is the normal wavenumber of the ith mode; νi is its vibrational quantum number; i refers to a totally symmetric or to a degenerate vibration; xii and gii are the anharmonicity constants; and ℓi is the vibrational angular momentum: |ℓi|=νi,νi-2,…,1, or 0 only exists for a doubly degenerate vibration.


### 2.2. Harmonic Bandsνi=n (Integer > 1)

(2)
(
n
ν
i
ℓ
i
)
=
n
(
ν
i
±
1
)
0
+
(
n
2
-
n
)
x
i
i
+
(
ℓ
i
2
-
n
)
g
i
i
.


### 2.3. Combination Bandsνi=n and νi′=m (Integer), i≠i′

(3)
(
n
ν
i
ℓ
i
+
m
ν
i
′
ℓ
i
′
)
0
=
(
n
ν
i
ℓ
i
)
0
+
(
m
ν
i
′
ℓ
i
′
)
0
+
n
m
x
i
i
′
+
g
i
i
′
ℓ
i
ℓ
i
′
.
For the oblate symmetric top NF3, we count 4ωi0, 10xij, and 3gij; i≤j.


## 2.1. Fundamental Bandsνi=1

(1)
(
ν
i
ℓ
i
)
=
ω
i
0
+
x
i
i
+
g
i
i
ℓ
i
ω
i is the normal wavenumber of the ith mode; νi is its vibrational quantum number; i refers to a totally symmetric or to a degenerate vibration; xii and gii are the anharmonicity constants; and ℓi is the vibrational angular momentum: |ℓi|=νi,νi-2,…,1, or 0 only exists for a doubly degenerate vibration.


## 2.2. Harmonic Bandsνi=n (Integer > 1)

(2)
(
n
ν
i
ℓ
i
)
=
n
(
ν
i
±
1
)
0
+
(
n
2
-
n
)
x
i
i
+
(
ℓ
i
2
-
n
)
g
i
i
.


## 2.3. Combination Bandsνi=n and νi′=m (Integer), i≠i′

(3)
(
n
ν
i
ℓ
i
+
m
ν
i
′
ℓ
i
′
)
0
=
(
n
ν
i
ℓ
i
)
0
+
(
m
ν
i
′
ℓ
i
′
)
0
+
n
m
x
i
i
′
+
g
i
i
′
ℓ
i
ℓ
i
′
.
For the oblate symmetric top NF3, we count 4ωi0, 10xij, and 3gij; i≤j.


## 3. The Ground State Constants ofNF314

The experimental ground state (GS) axial rotational parameters for the symmetric top molecule14NF3 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]
C
0
0.1949980 (10)
0.19499250 (44)
0.19499250 (44)
B
0
0.3562828965 (40)
0.3562827950 (15)
0.3562828891 (21)
Numbers in parentheses represent one standard deviation in units of the last digit quoted.For theC0K-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 ofNF314 Observed below 2000 cm−1

### 4.1. Theν1 Fundamental Band [17]

Theν1 = 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. Theν4 Fundamental Band [14]

The lowest fundamental bandν4 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. Theν2 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:(4)(ν2)0=647.1340617(73)cm-1,(2ν2-ν2)0=645.121943(14)cm-1,(ν2+ν4)0=1138.276629(10)cm-1.
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 ofν2 and 2ν2 bands (see [13]).


### 4.4. Theν3 Fundamental Band [12]

The perpendicular bandν3 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. The2ν4 Overtone Band [11]

Theν4 = 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:
(5)(2ν40)0=983.701767(34)cm-1,(2ν4±2)0=986.622364(18)cm-1.


### 4.6. The2ν3 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 theν4=2 and ν3=1 excited states were applied to treat the 2ν3 and ν1 + ν3 bands. We obtained the following results:
(6)(2ν30)0=1803.130213(57)cm-1,(2ν3±2)0=1810.423993(21)cm-1,(ν1+ν3)0=1931.577516(19)cm-1.


### 4.7. Theν1+ν4 Combination Band [8, 9]

Theν1+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.


## 4.1. Theν1 Fundamental Band [17]

Theν1 = 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. Theν4 Fundamental Band [14]

The lowest fundamental bandν4 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. Theν2 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:(4)(ν2)0=647.1340617(73)cm-1,(2ν2-ν2)0=645.121943(14)cm-1,(ν2+ν4)0=1138.276629(10)cm-1.
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 ofν2 and 2ν2 bands (see [13]).


## 4.4. Theν3 Fundamental Band [12]

The perpendicular bandν3 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. The2ν4 Overtone Band [11]

Theν4 = 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:
(5)(2ν40)0=983.701767(34)cm-1,(2ν4±2)0=986.622364(18)cm-1.


## 4.6. The2ν3 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 theν4=2 and ν3=1 excited states were applied to treat the 2ν3 and ν1 + ν3 bands. We obtained the following results:
(6)(2ν30)0=1803.130213(57)cm-1,(2ν3±2)0=1810.423993(21)cm-1,(ν1+ν3)0=1931.577516(19)cm-1.


## 4.7. Theν1+ν4 Combination Band [8, 9]

Theν1+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 Table2, 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: αC=C0-C′ and αB=B0-B′ and C′ and B′ being the constants of the upper level.Table 2
Band-centres and rovibrational interaction constants of14NF3 molecule (in cm−1).
Band or component
Experimental band-centre, this work
ExperimentalαC  × 103, this work
Ab  initio
α
B  × 103, [18]
ExperimentalαB  × 103, this work
Ab  initio
α
B  × 103, [18]
ν
1
1032.00123750 (47)
0.593526 (40)
0.643
−1.4496825 (43)
−1.227
ν
2
647.1340617 (73)
0.4346 (10)
0.404
1.289844 (18)
1.300
ν
3
907.5413300 (72)
0.7374 (11)
0.857
2.628451 (22)
2.758
ν
4
493.4227759 (89)
0.5566 (10)
0.544
0.150021 (23)
0.164
2
ν
2
-
ν
2
645.121943 (14)
0.8777 (10)
—
2.592650 (37)
—
2
ν
2
1292.25004 (21)a
0.8777 (10)
—
2.592650 (37)
—
ν
2 + ν4
1138.276629 (10)
0.9922 (10)
—
1.447060 (43)
—
2
ν
4
0
983.701767 (34)
1.10135 (63)
—
0.192090 (23)
—
2
ν
4
±
2
986.622364 (18)
1.10101 (56)
—
0.302179 (50)
—
2
ν
3
0
1803.130213 (57)
1.47497 (80)
—
4.84308 (22)
—
2
ν
3
±
2
1810.423993 (21)
1.49747 (50)
—
5.24715 (12)
—
ν
1 + ν3
1931.577516 (19)
1.30958 (56)
—
1.460127 (78)
—
ν
1 + ν4
1523.040783 (34)
1.37339 (84)
—
−1.13109 (44)
—
ν
2 + ν3
1546.30b
—
—
—
—
Numbers in parentheses represent one standard deviation in units of the last digit quoted.
aValue extracted from the values of (ν2)0 and x22 (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 byab 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 the2ν4 harmonic band, we obtain the system of equations:
(7)(2ν40)0=2(ν4±1)0+2x44-2g44,(2ν4±2)0=2(ν4±1)0+2x44+2g44.
We derive x44 = −0.841743 (22) cm−1 and g44 = 0.730149 (21) cm−1.As for2ν4, we deduce x33 = −4.15278 (18) cm−1 and g33 = 1.82344 (18) cm−1.Using the band-centres ofν1 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 trifluoride14NF3 are given in Table 3.Table 3
Anharmonicity constants of14NF3 (in cm−1).
Anharmonicity constant
Experimental value, this work
Ab initio TZ2Pf [18]
Experimental value [20, 21]
x
11
—
−3.15
−2.9
x
12
—
−3.56
−4
x
13
−7.965051 (26)
−8.14
−9.9
x
14
−2.383248 (49)
−2.08
−1.5
x
22
−1.006059 (11)
−0.88
—
x
23
−8.53a
−6.46
−7.6
x
24
−2.280208 (11)
−1.98
−2.5
x
33
−4.15278 (18)
−4.19
—
x
34
—
−5.12
—
x
44
−0.841743 (22)
−0.79
−0.820
g
33
1.82344 (18)
1.96
—
g
34
—
−0.10
—
g
44
0.730149 (22)
0.72
0.729
x
34
+
g
34
—
—
−1
Numbers in parentheses are one standard deviation in units of the last digit quoted.
aValue deduced from the (ν2 + ν3)0 given in Table 2.The experimental centre of the2ν2 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:
(8)(2ν2)0=2(ν2)0+2x22,(2ν2-ν2)0=(ν2)0+2x22,
we can indeed deduce that (2ν2)0 = 1292.25004 (21) cm−1 and x22 = −1.006059 (11).The values obtained forx22, 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 of14NF3 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 byab initio methods [18] employing the TZ2Pf basis.We can also extract accurate values of the harmonic wavenumbers of the oblate symmetric top molecule14NF3. The results are gathered in Table 4.Table 4
Harmonic wavenumber constants of14NF3 (in cm−1).
Harmonic  wavenumber
Experimental value, this work
Ab initio  unscaled value, [22]
Ab initiovalue TZ2Pf, [18]
ω
1
0
—
1042.8
1053.8
ω
2
0
648.140120 (18)
659.3
660.7
ω
3
0
909.84264 (43)
905.0
935.7
ω
4
0
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 theoreticalab initio calculations is significantly worse. We think that it is necessary to give much more credibility to our ωi0 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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*Source: 813249-2013-05-23.xml*