Journal of Quantum Chemistry

Volume 2014 (2014), Article ID 860179, 8 pages

http://dx.doi.org/10.1155/2014/860179

Research Article

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

Andrea Alparone

Department of Chemistry, University of Catania, Viale A. Doria 6, 95125 Catania, Italy

Received 15 July 2013; Revised 25 September 2013; Accepted 25 September 2013; Published 2 January 2014

Academic Editor: Daniel Glossman-Mitnik

Copyright © 2014 Andrea Alparone. 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.

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⁻¹). For the C–H/C–D stretches, the harmonic H→D isotopic frequency red-shifts overestimate the observed data by 47–63 cm⁻¹ (5.9–8.1%), whereas the PT2 computations exhibit significantly better performances, predicting the experimental data within 1–19 cm⁻¹ (0.1–2.4%).

1. Introduction

Tellurophene is a five-membered heterocycle (C₄H₄Te, Figure 1) homologue of the furan molecule. Tellurophene-based compounds have received great attention for the development and fabrication of promising polymeric conductors [1, 2] and nonlinear optical materials [3–8]. The experimental structure of C₄H₄Te is available from microwave measurements [9], whereas the infrared and Raman spectra of C₄H₄Te and of its perdeuterated isotopomer (C₄D₄Te) were recorded in various phases [10–14]. On the theoretical side, the vibrational spectra of C₄H₄Te were previously calculated in vacuum under the harmonic approximation by using Hartree-Fock [7] and Density Functional Theory (DFT) computations [15]. However, as well-known in the literature, the harmonic treatment often overestimates experimental wavenumbers of fundamentals and overtones, in particular, of the highest-energy spectral regions [16]. To partially circumvent this deficiency, harmonic frequencies can be corrected through scaling procedures [17, 18] or direct anharmonic calculations [19–21]. Anharmonic terms are usually calculated by means of variational [19] or perturbative [20, 21] treatments. As established in the literature [22], the perturbative methods are less accurate than the variational ones. Nevertheless, many recent results attest satisfactory performances of the perturbative methodologies, especially for the prediction of anharmonic contributions to fundamentals and overtones of cyclic compounds [22–30].

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].

In this work we investigate the effects of the anharmonic corrections on the vibrational wavenumbers of fundamental and overtone transitions of C₄H₄Te and C₄D₄Te. 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.

2. Computational Details

The current computations were exclusively performed with the GAUSSIAN 09 package [35]. The structure of C₄H₄Te were fully optimized under the point group symmetry using the B3LYP functional with the LANL2DZ(d,p) basis set. The vibrational wavenumbers of C₄H₄Te and C₄D₄Te 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 [22–30]. 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, and , are respectively, the third- and fourth-order force constants. The and values are obtained through a finite difference scheme using quadratic normal coordinate force constants () 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 off-diagonal () anharmonic constants [20]:

3. Result and Discussion

Figure 1 displays the bond lengths and angles of C₄H₄Te 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 C₄H₄Te by 0.001–0.003 Å, whereas the bond angles vary within 0.2° (C–Te–C).

The experimental infrared and Raman spectra of C₄H₄Te and C₄D₄Te were obtained in vapour, liquid, CCl₄ solution, and solid phase [10–14]. Theoretically, some calculations on the C₄H₄Te 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 () and Raman activities () of C₄H₄Te and C₄D₄Te, 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 symmetry point group with the 21 normal modes categorized as 8A₁ + 3A₂ + 7B₁ + 3B₂. All the modes with the exception of the A₂ 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 C₄H₄Te were also detected in gas [11].

Table 1: Vibrational harmonic, , and anharmonic, , wavenumbers (cm⁻¹), infrared intensities, (km/mol), and Raman activities (Å⁴/amu) of C₄H₄Te.

Descriptiona
Calc.b
Exp.c

A₁
1
C–H
3
317
3237
3089
3084 (3106)

2
C–H
12
259
3191
3052
3045 (3064)

3
C=C + C–C + C–H
25
54
1465
1430
1432

4
ring + C–H
12
3
1341
1311
1316

5
C–H
2
5
1103
1083
1079

6
Ring breathing + C–H
1
22
1010
986
984

7
ring
18
22
702
692
687

8
C–Te–C
0
9
385
380
380

A₂
9
C–H
0
1
911
894
912

10
C–H
0
0
684
663
690

11
ring
0
0
512
503
507

B₁
12
C–H
3
2
3234
3085
3084

13
C–H
4
118
3176
3037
3030 (3047)

14
C=C + C–H
3
0
1548
1516
1516

15
C–H
31
3
1255
1220
1246

16
C–H
0
4
1099
1077
1079

17
ring
3
0
805
794
797

18
C–Te
2
8
557
547
552

B₂
19
C–H
0
0
876
859
884

20
C–H
132
0
683
667
674

21
ring
5
0
358
355
354

rms deviationd

66
11

rms deviatione

144
6

rms deviationf

21
12

 : stretching; : in-plane bending; : torsion; : out-of-plane bending.

bCalculations were carried out in vacuum at the B3LYP/LANL2DZ(d,p) level.

cLiquid phase [12]. The values in parentheses refer to the gas phase [11].

dAll vibrational modes.

eC–H modes.

fAll vibrational modes excluding C–H modes.

Table 2: Vibrational harmonic, , and anharmonic, , frequencies (cm⁻¹), infrared intensities, (km/mol), and Raman activities (Å⁴/amu) of C₄D₄Te.

Descriptiona
Calc.b
Exp.c

A₁
1
C–D
2
143
2400
2294
2308

2
C–D
3
104
2355
2270
2262

3
C=C + C–C + C–D
31
57
1443
1409
1405

4
ring + C–D
11
7
1208
1169
1180

5
C–D
2
23
839
828
824

6
Ring breathing + C–D
0
10
782
770
768

7
ring
14
12
640
632
630

8
C–Te–C
0
9
374
371
370

A₂
9
C–D
0
1
753
742
741

10
C–D
0
0
533
520
548

11
ring
0
0
438
432
437

B₁
12
C–D
1
4
2395
2313
2308

13
C–D
1
55
2339
2249
2240

14
C=C + C–D
7
0
1493
1458
1455

15
C–D
12
2
1002
986
995

16
C–D
2
4
853
840
811

17
ring
1
0
706
697
704

18
C–Te
3
7
524
517
522

B₂
19
C–D
0
0
683
673
696

20
C–D
77
0
506
497
502

21
ring
3
0
329
325
326

rms deviationd

43
12

rms deviatione

91
10

rms deviationf

18
12

 : stretching; : in-plane bending; : torsion; : out-of-plane bending.

bCalculations were carried out in vacuum at the B3LYP/LANL2DZ(d,p) level.

cLiquid phase [12].

dAll vibrational modes.

eC–H modes.

fAll vibrational modes excluding C–H modes.

The harmonic frequencies systematically overestimate the experimental data with the notable exception of the modes numbers 9, 10, and 19 for C₄H₄Te and of the modes numbers 10 and 19 for C₄D₄Te. 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 for all the modes, the C–H/C–D stretching vibrations (νC–H/νC–D), and all the modes except for the νC–H and νC–D vibrations. When considering all the vibrational transitions, the rms deviations between the harmonic and observed data are 66 cm⁻¹ for C₄H₄Te and 43 cm⁻¹ for C₄D₄Te. These rms deviations are noticeably reduced if we exclude the νC–H and νC–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 C₄H₄Te (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), 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 calculations were performed in vacuum, the introduction of the PT2 anharmonic corrections generally improves the agreement between the observed and computed data; for all the vibrational transitions the rms deviations are 11 cm⁻¹ for C₄H₄Te and 12 cm⁻¹ for C₄D₄Te. As should be expected, the calculated harmonic wavenumbers overestimate the anharmonic figures, the zero-point energy (ZPE) correction, a physicochemical property of fundamental importance for an accurate determination of thermochemical and kinetic parameters, being influenced by the anharmonic corrections. Indeed, when passing from the harmonic to the PT2 anharmonic treatment, the ZPE for C₄H₄Te (C₄D₄Te) decreases from 40.22 (32.30) to 39.72 (31.44) kcal/mol.

As can be appreciated from the data reported in Tables 1 and 2, the largest anharmonic contributions are found for the νC–H and νC–D transitions (modes. numbers 1, 2, 12, and 13), decreasing the harmonic frequency values of C₄H₄Te by 140–150 cm⁻¹ (ca. 4%) and of C₄D₄Te 80–110 cm⁻¹ (ca. 3-4%), in agreement with previous PT2 computations on other cyclic compounds [22–30]. As a consequence, the agreement between the experimental and calculated wavenumbers for the νC–H and νC–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 νC–H fundamentals of C₄H₄Te (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 νC–H modes numbers 1 and 2 of C₄H₄Te (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 and , 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 and , are given by the , (ca. −30 cm⁻¹ for both the couplings), and (−12 cm⁻¹) terms.

Figure 2: B3LYP/LANL2DZ(d,p) anharmonic vibrational constants for the C–H stretching modes numbers 1 and 2 with the vibrational modes = 1–21 of C₄H₄Te. For the mode numbering, see Table 1.

For the νC–H/νC–D modes, we evaluated the H→D isotopic wavenumber downward shifts ( = νC–H − νC–D) obtained by the harmonic and anharmonic calculations. The deviations of the calculated data from the observed values are reported in Figure 3, together with the percentage 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.

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

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 (C₄H₄Te) and five (C₄D₄Te) vibrational modes. Confirming the above results of the fundamentals, the greatest anharmonic corrections for the overtones occur for the νC–H (νC–D) transitions, which reduce the harmonic values by ca. 5-6% (4-5%).

Table 3: Wavenumbers of first overtones (cm⁻¹) of tellurophene isotopomers.

Symm.
Mode no.a
C₄H₄Te
C₄D₄Te

Calc.b
Exp.c
Calc.b
Exp.c

A₁
1
6474
6144

4801
4575

2
6382
6047

4711
4516

3
2931
2848
2851
2886
2810

4
2683
2617
2627
2415
2343

5
2205
2167
2160
1678
1652

6
2019
1968
1966
1563
1541

7
1404
1382

1279
1263
1254

8
769
759
758
748
740

A₂
9
1823
1788
1822
1505
1485

10
1369
1322
1385
1067
1039

11
1024
1009
1014
877
864
872

B₁
12
6469
6083

4789
4598

13
6351
6013

4679
4478

14
3096
3019
3015
2986
2921
2916

15
2510
2451

2004
1969

16
2199
2154

1706
1680

17
1611
1588

1412
1393

18
1114
1093
1111
1049
1031
1049

B₂
19
1753
1717
1768
1367
1347
1383

20
1367
1331

1013
993

21
716
709

657
650

See Tables 1 and 2 for the mode description.

bCalculations were carried out in vacuum at the B3LYP/LANL2DZ(d,p) level.

cLiquid phase, [12].

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 C₄H₄Te and C₄D₄Te is mainly characterized by an isolated and strong absorption located at 667 cm⁻¹ ( km/mol) and 497 cm⁻¹ ( 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 transition (mode number 20) to a pure out-of-plane C–H (and C–D) bending deformation, γC–H (γC–D). A graphical representation of the atomic displacement vectors involved in this vibration is depicted in Figure 6(a).

Figure 4: Anharmonic infrared spectra of C₄H₄Te (bottom) and C₄D₄Te (top). Lorentz line-shapes with half-width of 10 cm⁻¹ are used. B3LYP/LANL2DZ(d,p) results.

Figure 5: Anharmonic Raman spectra of C₄H₄Te (bottom) and C₄D₄Te (top). Lorentz line-shapes with half-width of 10 cm⁻¹ are used. B3LYP/LANL2DZ(d,p) results.

(a)

(b)

Figure 6: Atom vector displacements for the normal modes of C₄H₄Te: (a) γC–H (mode number 20); (b) νC=C + νC–C + δC–H (mode number 3). B3LYP/LANL2DZ(d,p) results.

The most active transitions in the Raman spectra of C₄H₄Te and C₄D₄Te involve the C–H and C–D stretches (Tables 1 and 2). From the present calculations, an almost isolated and relatively intense peak ( 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 the nonnegligible contribution from the in-plane C–H (C–D) bending motion (Figure 6(b)). The present harmonic computations place this band at 1465 cm⁻¹ (C₄H₄Te) and 1443 cm⁻¹ (C₄D₄Te), overestimating the observed wavenumbers of 1432 cm⁻¹ (+2.3%) and 1405 cm⁻¹ (+2.7%), respectively. Note that the corresponding PT2 anharmonic frequencies here calculated at 1430 cm⁻¹ (C₄H₄Te) and 1409 cm⁻¹ (C₄D₄Te), give a noticeably better agreement with experiment (within 0.1–0.3%).

4. Conclusions

In this work we computed harmonic and PT2 anharmonic vibrational frequencies of fundamentals and overtone bands of C₄H₄Te and C₄D₄Te. The computations were performed in vacuum at the B3LYP/LANL2DZ(d,p) level of theory. The infrared and Raman spectral profiles were simulated using Lorentzian band-shapes and the most informative transitions were discussed. In general, the calculated harmonic frequencies deviate from the observed ones, with rms deviations of 66 and 43 cm⁻¹ for C₄H₄Te and C₄D₄Te, respectively. The introduction of the PT2 anharmonic contributions in several cases significantly reduces the calculation/experiment discrepancy, giving rms deviations of 11 cm⁻¹ (C₄H₄Te) and 12 cm⁻¹ (C₄D₄Te). A vibrational analysis reveals that the anharmonic corrections are especially conspicuous for the νC–H and νC–D transitions, decreasing the harmonic wavenumber values, respectively, by 140–150 cm⁻¹ (ca. 4%) and 80–110 cm⁻¹ (ca. 3-4%), and noticeably improving the agreement with the experimental data. As a consequence, in comparison to the harmonic approximation, the observed H→D isotopic frequency red-shifts for the C–H and C–D stretches are better reproduced by the PT2 scheme with deviation up to 1–19 cm⁻¹ (0.1–2.4%). Important anharmonic effects (ca. 35 cm⁻¹, 2.3%) are also found for the mode number 3 (νC=C + νC–C + δC–H, νC=C + νC–C + δC–D), characterized by a relatively intense peak in the Raman spectra. 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.

Conflict of Interests

The author declares that there is no conflict of interests regarding the publication of this paper.

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