Anharmonic Spectroscopic Investigation of Tellurophene and Its Perdeuterated Isotopomer : Application of Second-Order Perturbation Theory

Vibrational spectra of tellurophene and of its perdeuterated isotopomer were computed using the DFT-B3LYP functional with the LANL2DZ(d,p) basis set. The frequencies of fundamental and overtone transitions were obtained in vacuum under the harmonic approximation and anharmonic second-order perturbation theory (PT2). On the whole the anharmonic corrections reduce the harmonic wavenumber values, in many cases better reproducing the observed fundamental frequencies. The largest anharmonic effects are found for the C–H and C–D stretching vibrations, characterized by relatively high anharmonic coupling constants (up to ca. 120 cm). For the C–H/C–D stretches, the harmonic H→D isotopic frequency red-shifts overestimate the observed data by 47–63 cm (5.9–8.1%), whereas the PT2 computations exhibit significantly better performances, predicting the experimental data within 1–19 cm (0.1–2.4%).

In this work we investigate the effects of the anharmonic corrections on the vibrational wavenumbers of fundamental and overtone transitions of C 4 H 4 Te and C 4 D 4 Te.The anharmonic terms were predicted in the gas phase using the second-order perturbation theory (PT2) as described in detail by Barone [20].The calculations were performed using the hybrid three-parameters B3LYP DFT method [31,32] with the LANL2DZ(d,p) basis set [33,34].Anharmonic PT2-DFT spectra have been previously reported for the congeners furan [22,25], thiophene [22], and more recently selenophene [30].To the best of our knowledge, anharmonic theoretical wavenumbers of fundamental and overtone transitions of tellurophene and its perdeuterated isotopomer have been computed here for the first time.

Computational Details
The current computations were exclusively performed with the GAUSSIAN 09 package [35].The structure of C 4 H 4 Te were fully optimized under the C 2v point group symmetry using the B3LYP functional with the LANL2DZ(d,p) basis set.The vibrational wavenumbers of C 4 H 4 Te and C 4 D 4 Te were determined at the B3LYP/LANL2DZ(d,p) level under the harmonic approximation through analytical computations.Anharmonic terms were calculated numerically using the PT2 procedure implemented in the GAUSSIAN 09 program (option: Freq (VibRot, Anharmonic)) [20].There are many reports in the literature confirming that the PT2 treatment in combination with DFT methods provides satisfactory performances, especially for computing anharmonic vibrational frequencies of cyclic structures [22][23][24][25][26][27][28][29][30].In particular, the PT2 method and the B3LYP functional have been employed with success to obtain the vibrational spectra of the homologues furan [22,25], thiophene [22], and more recently selenophene [30].The used PT2 scheme computes the third and fourth energy derivatives with respect to the normal coordinates through a numerical differentiation procedure described in detail in [20].The potential energy surface () can be expanded including anharmonic contributions up to the quartic term as where   are the harmonic wavenumbers,   are the dimensionless normal coordinates, Φ  and Φ  , are respectively, the third-and fourth-order force constants.The Φ  and Φ  values are obtained through a finite difference scheme using quadratic normal coordinate force constants (Φ  ) calculated analytically and performing displacements along each normal coordinate (   ): ] . ( As commonly adopted in the literature [24-26, 29, 30], step size displacements of 0.025 Å along the normal coordinates were used in the present work.The fundamental frequencies (]  ) were determined from the   , diagonal (  ) and offdiagonal (  ) anharmonic constants [20]:

Result and Discussion
Figure 1 displays the bond lengths and angles of C 4 H 4 Te calculated at the B3LYP/LANL2DZ(d,p) level.In addition, the figure reports the available experimental data obtained by microwave measurements [9].The B3LYP/LANL2DZ(d,p) geometry is in good agreement with the observed one, especially for the bond lengths C-Te (within 0.005 Å), C=C (within 0.003 Å), and C-H (the calculated and experimental values are identical), as well as for the bond angles (within 0.2-0.5 ∘ ). Figure 1 also presents the vibrationally averaged geometries (  structure) calculated by the vibration-rotation interaction constant values [20].In line with previous studies on cyclic compounds [29,30], the vibrational averaging corrections lengthen the bond lengths of C 4 H 4 Te by 0.001-0.003Å, whereas the bond angles vary within 0.2 ∘ (C-Te-C).
The experimental infrared and Raman spectra of C 4 H 4 Te and C 4 D 4 Te were obtained in vapour, liquid, CCl 4 solution, and solid phase [10][11][12][13][14]. Theoretically, some calculations on the C 4 H 4 Te isotopomer were previously performed using the harmonic treatment [7,15].In Tables 1 and 2 we present the B3LYP/LANL2DZ(d,p) harmonic () and anharmonic wavenumbers (]), infrared intensities ( IR ) and Raman activities ( Raman ) of C 4 H 4 Te and C 4 D 4 Te, together with the available observed data for comparison [12].The assignments of the vibrations were performed using normal modes as displacements in redundant internal coordinates (in the GAUSSIAN 09, the option: Freq = IntModes) and also through the graphical program Chemcraft [36].The title compounds belong to the C 2v symmetry point group with the 21 normal modes categorized as 8A 1 + 3A 2 + 7B 1 + 3B 2 .All the modes with the exception of the A 2 vibrations are infrared active.It is worth noting that, the current assignments of the transitions reasonably agree with those previously determined by experimental [12] and computational [7,15] studies.
The complete sets of experimental fundamentals of both the investigated isotopomers are available from measurements in liquid phase [12], whereas three C-H stretching transitions (modes numbers 1, 2, and 13) of C 4 H 4 Te were also detected in gas [11].
The harmonic frequencies systematically overestimate the experimental data with the notable exception of the modes numbers 9, 10, and 19 for C 4 H 4 Te and of the modes numbers 10 and 19 for C 4 D 4 Te.In the present study, we determined the root mean square (rms) deviation between the experimental and calculated wavenumbers which is defined as follows: where ]  is a vibrational frequency value.The rms deviations are included in Tables 1 and 2  ), but worsened for the remaining modes (rms deviation of 23 versus 21 cm −1 ).Therefore, for the anharmonic computations the use of the smaller LANL2DZ(d,p) basis set for all the atoms can be considered a reasonable choice.Although the experimental wavenumber values of the 21 fundamentals were obtained in liquid phase [12] and the present As can be appreciated from the data reported in Tables 1 and 2, the largest anharmonic contributions are found for the ]C-H and ]C-D transitions (modes.numbers 1, 2, 12, and 13), decreasing the harmonic frequency values of C 4 H 4 Te by 140-150 cm −1 (ca.4%) and of C 4 D 4 Te 80-110 cm −1 (ca.3-4%), in agreement with previous PT2 computations on other cyclic compounds [22][23][24][25][26][27][28][29][30].As a consequence, the agreement between the experimental and calculated wavenumbers for the ]C-H and ]C-D stretches is significantly improved by the anharmonic treatment (within 1-14 cm −1 , 0.03-0.61%).Note that when we consider the gas phase experimental ]C-H fundamentals of C 4 H 4 Te (modes numbers 1, 2, and 13, Table 1), the experimental/calculation deviations are slightly augmented (up to 17 cm −1 ).To elucidate the origin of the above large anharmonic effects, as a case test, we analysed the contributions of the anharmonic constant values ( , ) for the ]C-H modes numbers 1 and 2 of C 4 H 4 Te (Figure 2).The most significant  , corrections are produced by the diagonal term ( , ) as well as by the coupling with the remaining C-H stretching modes.In the specific case of the modes numbers 1 and 2, the largest anharmonic coupling are  1,12 and  2,13 , which are predicted to be ca.−120 cm −1 and recover about 80% of the total anharmonic corrections ( − ], (3)).Other nonnegligible anharmonic contributions, although less substantial than  1,12 and  2,13 , are given by the  1,1 ,  2,2 (ca.−30 cm −1 for both the couplings), and  1,2 (−12 cm −1 ) terms.
For the ]C-H/]C-D modes, we evaluated the H→D isotopic wavenumber downward shifts (Δ] H/D = ]C-H -]C-D) obtained by the harmonic and anharmonic calculations.The deviations of the calculated Δ] H/D data from the observed values are reported in Figure 3, together with the percentage a See Tables 1 and 2 for the mode description.b Calculations were carried out in vacuum at the B3LYP/LANL2DZ(d,p) level.c Liquid phase, [12].
errors.The harmonic approximation overestimates the experimental shifts by 47-63 cm −1 (5.9-8.1%),whereas the anharmonic computations, with the exception of mode number 1, underestimate the isotopic shifts showing smaller errors (1-19 cm −1 , 0.1-2.4%).The results are particularly excellent for the mode number 2. Table 3 collects the frequencies of the overtone bands of title compounds obtained using the harmonic and anharmonic approaches, together with the available experimental data which are only limited to eleven (C 4 H 4 Te) and five (C 4 D 4 Te) vibrational modes.Confirming the above results of the fundamentals, the greatest anharmonic corrections for the overtones occur for the ]C-H (]C-D) transitions, which reduce the harmonic values by ca.5-6% (4-5%).
In Figures 4 and 5 we plot the infrared and Raman spectra obtained by the anharmonic calculations using pure Lorentzian band-shapes with a full width at half maximum of 10 cm −1 .The C-H and C-D stretching transitions are placed in the highest-wavenumber regions of the vibrations spectra.The lowest-energy region of the infrared spectra of C 4 H 4 Te and C 4 D 4 Te is mainly characterized by an isolated and strong absorption located at 667 cm −1 ( IR = 132 km/mol) and 497 cm −1 ( IR = 77 km/mol), respectively, to be compared with the experimental values of 674 cm −1 (−1%) and 502 cm −1 (−1%), respectively.The vibrational analysis ascribes this  1 and 2).From the present calculations, an almost isolated and relatively intense peak ( Raman ∼ 50 Å4 /amu) located near 1400 cm −1 appears in the Raman spectra of both tellurophene and its perdeuterated isotopomer.This transition (mode number 3) also visible in the infrared spectra is assigned to the C=C + C-C bonds stretchings with

Conclusions
In this work we computed harmonic and PT2 anharmonic vibrational frequencies of fundamentals and overtone bands of In line with the recent literature, the present results on tellurophene isotopomers confirm that the anharmonic PT2-DFT approach can be employed to accurately predict the infrared and Raman spectra of heterocyclic compounds.

Figure 1 :
Figure 1: B3LYP/LANL2DZ(d,p) geometrical parameters (  structure) of tellurophene.The data reported in the round brackets refer to the B3LYP/LANL2DZ(d,p) vibrationally averaged geometry (  structure).The data reported in the square brackets refer to the experimental geometry [9].

4 H 4
for all the modes, the C-H/C-D stretching vibrations (]C-H/]C-D), and all the modes except for the ]C-H and ]C-D vibrations.When considering all the vibrational transitions, the rms deviations between the harmonic and observed data are 66 cm −1 for C Te and 43 cm −1 for C 4 D 4 Te.These rms deviations are noticeably reduced if we exclude the ]C-H and ]C-D modes, becoming 21 cm −1 and 18 cm −1 , respectively.On the whole, the modification of the basis set for the C and H atoms [LANL2DZ(d,p) → 6-311G(d,p)] does not produce significant effects on the harmonic wavenumber values of C 4 H 4 Te (the data are available on request from the author), giving a rms deviation of 63 cm −1 with respect to the experimental data.Specifically, the performances of the 6-311G(d,p) in comparison to the LANL2DZ(d,p) basis set are slightly improved for the C-H stretches (rms deviation of 135 versus 144 cm−1

1 )Figure 3 :Figure 4 :
Figure 3: Deviation of the B3LYP/LANL2DZ(d,p) H→D isotopic wavenumber shifts (Δ] H/D ) for the C-H and C-D stretching modes from experiment[12].The reported values refer to the percentage deviations.