New Investigation of Millimeter-Wave Rotational Spectrum of CCl 3 CN in Ground , v 7 = 1 and v 8 = 1 States

The millimeter-wave rotational spectra of the ground and excited vibrational states v7 =1 and v8 =1 of the symmetric top molecule, CCl3CN, have been analyzed again. The B0 = 1666.80894(13) MHz, DJ = 0.135023 (23) kHz, DJK = 0.60596 (45) kHz, HJ = -0.0192 (10) mHz, HJK = 1.188 (34) mHz and HKJ = -1.60 (21) mHz have been determined for ground state. The 𝓁 = ±1 series have been assigned and the rotational parameters including B7 =1667.96659(25) MHz, (q


Introduction
Trichloroacetonitrile , CCl 3 CN is a symmetric top molecule and belong to the C 3v point group.This molecule has the same symmetry as that of CF 3 CN.Selection rules show that there should be 4A 1 and 4E vibrations, all of which should be active both in the infrared and the Raman spectra of CCl 3 CN.Several authors have studied the rotational spectra of the ground state and some excited states [1][2][3][4][5] .The lowest doubly degenerate vibrational level,v 8 = 1, is approximately a N C C ≡ − − bending mode and lies 6 at 157 cm -1 , and occurs at slightly lower wave number than the corresponding vibration 7 in CF 3 CN.The next highest frequency, v 7 , is found at 268 cm -1 (CCl 3 rocking mode).It is still lower than the lowest A 1 fundamental, v 4 , which is found 6 at 318 cm -1 .There is no doubt about the assignment of the series of lines which lie to high frequency of the ground state rotational transitions.Owing to the large dipole moment and the large thermal population, the spectra are intense.The aim of this work is study and determination of rotational parameters for the low and high J values in ground and v 7 =1 and v 8 = 1 states, which are more accurate and reliable.

v 7 = 1and v 8 = 1states
Rotational frequencies for transitions J → J + 1 in the excited degenerate vibrational state v t = 1, l t = ± 1 of molecules with axial symmetry were calculated by Nielsen 8 .Although the theory was fairly satisfactory for the rotation spectrum of these types of molecules, some of the calculated frequencies by this method were different from the observed frequencies.This formula was extended to the case of higher J values by Gordy et al 9 .The frequency of transition J → J + 1 for molecules belonging to the point group C 3v in singly excited vibrational state v t = 1 is given by the approximate perturbation expression, Eq (3).ν = 2B(J + 1) -4D J (J + 1) 3 -2D Jk (J + 1)k 2 + 2η J (J + 1)kl + ∆ν where ∆ν has the value ± q t + (J + 1) if (kl -1) = 0 (l -type doubling) or 1) Aζ and η J which gives the J and k dependence of Aζ, are necessary to determine the frequency of spectra.l is the vibrational angular momentum quantum number and can accept the value l = ± 1; therefore, there are two different series in the spectrum.+ t q is the l -type doubling constant, B and A are rotational constants, and ζ is the z-coriolis constant for the vibrational state v t .The degree of l-resonance thus largely depends on the ratio of + t q to the resonance denominator . With low to moderate values of this denominator, the spectrum usually found consists of two extreme outer lines for (kl-1) = 0 (the ldoublets) and a center group of lines for (kl-1) ≠ 0 whose structure depends very strongly on other parameters such as the centrifugal distortion constants.As the strength of the resonance increase, the lines of the center group spread out until the low |kl-1| transitions approach the positions of the l-doublets.So for large + t q and small value it is possible to observe direct l-resonance transitions in the microwave range.This is a typical pattern for C 3v doubly degenerate states and is predominantly due to the combinations of the splitting of the positive and negative (kl-1) series by l-type resonance [which is inversely proportional to (kl-1)] and the shift to low frequency due to D Jk [which is proportional to (kl-1) 2 ].Eq (3) shows a pattern for doubly degenerate states of a C 3v molecule that is predominately due to the splitting of the positive and negative series by l-type resonance.As can be seen in Eq (4), this resonance is inversely proportional to (kl-1).Thus, one series goes from high frequency at low k to low frequency at high k, while the other is at low frequency.
In order to obtain more accuracy in rotational energies for singly excited vibrational states than can be obtained from perturbation theory, it is necessary to set up a rotational Hamiltonian as a matrix (H) in equation Hψ = Eψ and diagonalise to obtain the energy [10][11][12][13][14][15][16] .The Hamiltonian was set up for a symmetric top molecule like CCl 3 CN.This rotationvibrational Hamiltonian has two different blocks that belong to the different l = + 1 and l = -1 series.k and l are no longer good quantum numbers, but (kl) or (kl -1) may be used to distinguish between the symmetry species.Those levels with (kl -1) = 3n, where n is an integer, are of species A 1 or A 2 .If (kl -1) ≠ 3n the species are E.The q t + produces a first order splitting of the (kl -1) = 0, A 1 A 2 pair, which are the familiar l-doublets, as shown by Grenier-Besson and Amat 10 .The main difference from the ground state spectra is the splitting of the |k -l| = 0 into two widely separate l-doublets and the splitting due to l-resonance.
The diagonal matrix elements are given by: <v t , l t , J, k (5) In addition, there are off-diagonal terms that arise from the transformation.The major one of these gives rise to the l doubling: ) and hence, the lines can be assigned.The results of refinement of v 7 = 1 and v 8 = 1 states are listed in Tables 3 and 4 respectively.The values of the constants obtained are shown in Table 5.

Results and Discussion
The 255 different measurements of CCl 3 CN for ground state were fitted to the Eq (2) by weighted least-squares method 17 in which the weights were taken to be w = 1/(observed error) 2 = 1/(0.02) 2 , where 0.02 in MHz is estimated uncertainty in an observation for each unblended line.Some of the lines have an observed error of 0.03 to 0.2 MHz to allow for overlapping or broadening.The results of refinement is listed in Table 1, and correlation coefficients of parameters are shown in Table 2.These Tables show that the frequencies of low and high values of CCl 3 CN were fitted very well and correlation coefficients of parameters are reasonable.The structural parameters of this compound as shown in Table 5 were obtained with higher accuracy and compared with previous works.
The spectra in this state is simple, so the different k values (k = 0,1,2,3,4...) for each J transition are assigned easily.The centrifugal distortion produces a band head to high frequency at k = 0, with a spread to lower frequency with higher k.
If |k| values are plotted against frequency for this state, the Fortrat diagram is produced which is shown in (Fig1).In this diagram the splitting increase as k increases and this is due to the D Jk parameter.In other words the term -2D Jk (J + 1)k 2 has the effect of separating the (J + 1) components of each (J + 1) -J transition.This diagram indicates the splitting k = 3 lines about 5 MHz for transition 113 112 J → = . .The sextic splitting constant h 3 is very small and normally is less than values of sextic parameters.Cazzoli 18 and colleagues have found a strong correlation between h  (8), the h 3 = 0.02714 mHz is obtained for CCl 3 CN.while this value has been determined 0.02209 (20) mHz 4 .The  For the v 7 = 1 state the important parameters in determining form of the spectrum are the type − l doubling constant + 7 q and the value of 7 Aζ .As Table 5 shows, the B 7 is slightly larger than the B 8 value and this means that the spectrum lies amongst the transitions due to v 8 = 2.The parameter η J , which is to be regarded as a type of centrifugal distortion constant, has a negative value.As can be seen from Eq (3) this results in the positive series being displaced to lower frequency and the negative series to higher frequency (Fig 4).
In this work, all of the frequencies selected from Ref (4) and refined them by least square method 12 .If all the sextic constants were included in the fit, these were not only strongly correlated but also had standard deviations which were of about the same absolute magnitudes as the quantities themselves.This means that actual values are not significant, hence H kJ was set to zero.In this case H Jk and H J were determined with reasonable standard deviations.The results of fitting are given in Table 3 and obtained results are shown in Table 5.
For v 8 = state a least-squares refinement of the 172 observations was carried out using the programme 17 .The results of fitting are given in Table 4 and obtained results are shown in Table 5.For this state the sextic parameters are not determinable by this data.The Fortrat-like diagram in this state is shown in (Fig 4).This diagram shows that the 'l' doublet splitting is smaller than this term in the v 7 = 1 state (Fig 3).η J can be determined precisely from the mm-wave spectrum, while η k is not determined.In this molecule, the term MHz 854 ) A B (A = − − ζ and -1269 MHz for v 8 = 1 and v 7 = 1 states respectively, so the l-resonance is observable and Aζ can be determined from mm-wave spectrum which has positive and negative values for these two states (Table 5).JJ ζ parameter was obtained with negative value for v 7 = 1 and with positive value for v 8 = 1 states but this parameter has different signs in these two states 5 .

Figure 1 .
Figure 1.Fortrat diagram of CCl 3 CN in ground state.113 112 J → = The K = 3 lines of a C 3v symmetric top should be split because the rotational Hamiltonian has a nonvanishing off-diagonal matrix element 6 k H k ±

Figure 2 .Figure 2 .
Figure 2. Variation of K = 3 splitting with J is shifted to high frequency from band origin (Fig 2).The value of D Jk for CCl 3 CN is low and separations of the low-k lines do not exceed their half width very much.For this reason the close doublet seen for 64 63 J → = disappears with increasing J, as the k = 3 components move into the neighboring lines.

Table 1 .
Results of refinement of observed frequencies for CCl 3 CN in ground state.

Table 3 .
Results of refinement of observed frequencies for CCl 3 CN in v 7 = 1 state

Table 5 .
Comparison of rotation-vibration parameters for CCl 3 CN in ground , v *constrained at this value.