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 (
References
[1]
S. Inoue, T. Jigami, H. Nozoe, T. Otsubo, and F. Ogura, “2, -Bitellurophene and 2, : , -tertellurophene as novel high homologues of tellurophene,” Tetrahedron Letters, vol. 35, no. 43, pp. 8009–8012, 1994.
[2]
Q. Lei, X. H. Yin, K. Kobayashi, T. Kawai, M. Ozaki, and K. Yoshino, “Electrical properties of polymer composties: conducting polymer-polyacene quinone radical polymer,” Synthetic Metals, vol. 69, no. 1–3, pp. 357–358, 1995.
[3]
S. Millefiori and A. Alparone, “(Hyper)polarizability of chalcogenophenes C4H4X (X = O, S, Se, Te) conventional ab initio and density functional theory study,” Journal of Molecular Structure: THEOCHEM, vol. 431, no. 1-2, pp. 59–78, 1998.
[4]
K. Kamada, T. Sugino, M. Ueda, K. Tawa, Y. Shimizu, and K. Ohta, “Femtosecond optical Kerr study of heavy-atom effects on the third-order optical non-linearity of thiophene homologues: electronic hyperpolarizability of tellurophene,” Chemical Physics Letters, vol. 302, no. 5-6, pp. 615–620, 1999.
[5]
S. Millefiori and A. Alparone, “Second hyperpolarisability of furan homologues C4H4X (X=O, S, Se, Te): Ab initio HF and DFT study,” Chemical Physics Letters, vol. 332, no. 1-2, pp. 175–180, 2000.
[6]
K. Kamada, M. Ueda, H. Nagao et al., “Molecular design for organic nonlinear optics: polarizability and hyperpolarizabilities of furan homologues investigated by ab initio molecular orbital method,” Journal of Physical Chemistry A, vol. 104, no. 20, pp. 4723–4734, 2000.
[7]
S. Millefiori and A. Alparone, “Theoretical determination of the vibrational and electronic (hyper)polarizabilities of C4H4X (X = O, S, Se, Te) heterocycles,” Physical Chemistry Chemical Physics, vol. 2, no. 11, pp. 2495–2501, 2000.
[8]
B. Jansik, B. Schimmelpfennig, P. Norman, P. Macak, H. ?gren, and K. Ohta, “Relativistic effects on linear and non-linear polarizabilities of the furan homologues,” Journal of Molecular Structure: THEOCHEM, vol. 633, no. 2-3, pp. 237–246, 2003.
[9]
V. K. Yadav, A. Yadav, and R. A. Poirier, “Some periodic trends in organic compounds containing O, S, Se, and Te: an ab initio study,” Journal of Molecular Structure: THEOCHEM, vol. 186, no. C, pp. 101–116, 1989.
[10]
A. Poletti, R. Cataliotti, and G. Paliani, “Infrared crystal spectra of heterocyclic compounds. II. IR spectrum of selenophene in the solid state,” Chemical Physics, vol. 5, no. 2, pp. 291–297, 1974.
[11]
R. Cataliotti and G. Paliani, “Infrared study of the C-H stretching region of five-membered heterocyclic compounds,” Canadian Journal of Chemistry, vol. 54, pp. 2451–2457, 1976.
[12]
G. Paliani, R. Cataliotti, A. Poletti, F. Fringuelli, A. Taticchi, and M. G. Giorgini, “Vibrational analysis of tellurophene and its deuterated derivatives,” Spectrochimica Acta Part A, vol. 32, no. 5, pp. 1089–1104, 1976.
[13]
A. Santucci, G. Paliani, and R. S. Cataliotti, “Force field calculation of the in-plane fundamental motions of tellurophene and selenophene,” Spectrochimica Acta Part A, vol. 41, no. 5, pp. 679–685, 1985.
[14]
A. Santucci, G. Paliani, and R. S. Cataliotti, “Force field calculation of the out-of-plane fundamental modes of tellurophene and selenophene,” Chemical Physics Letters, vol. 138, no. 2-3, pp. 244–249, 1987.
[15]
A. A. El-Azhary and A. A. Al-Kahtani, “Force field scale factors of effective core potential basis sets of some selenium and tellurium heterocyclic molecules, selenophene, 1,2,5-selenadiazole, tellurophene and 1,2,5-telluradiazole,” Journal of Molecular Structure: THEOCHEM, vol. 572, pp. 81–87, 2001.
[16]
W. J. Hehre, L. Random, P. V. R. Schleyer, and J. A. Pople, Ab Initio Molecular Orbital Theory, Wiley, New York, NY, USA, 1986.
[17]
P. Pulay, G. Fogarasi, G. Pongor, J. E. Boggs, and A. Vargha, “Combination of theoretical ab initio and experimental information to obtain reliable harmonic force constants. Scaled quantum mechanical (SQM) force fields for glyoxal, acrolein, butadiene, formaldehyde, and ethylene,” Journal of the American Chemical Society, vol. 105, no. 24, pp. 7037–7047, 1983.
[18]
G. Rauhut and P. Pulay, “Transferable scaling factors for density functional derived vibrational force fields,” Journal of Physical Chemistry, vol. 99, no. 10, pp. 3093–3100, 1995.
[19]
J. M. Bowman, “Self-consistent field energies and wavefunctions for coupled oscillators,” The Journal of Chemical Physics, vol. 68, no. 2, pp. 608–610, 1978.
[20]
V. Barone, “Anharmonic vibrational properties by a fully automated second-order perturbative approach,” Journal of Chemical Physics, vol. 122, no. 1, Article ID 014108, 2005.
[21]
D. A. Clabo Jr., W. D. Allen, R. B. Remington, Y. Yamaguchi, and H. F. Schaefer III, “A systematic study of molecular vibrational anharmonicity and vibration-rotation interaction by self-consistent-field higher-derivative methods. Asymmetric top molecules,” Chemical Physics, vol. 123, no. 2, pp. 187–239, 1988.
[22]
R. Burcl, N. C. Handy, and S. Carter, “Vibrational spectra of furan, pyrrole, and thiophene from a density functional theory anharmonic force field,” Spectrochimica Acta Part A, vol. 59, no. 8, pp. 1881–1893, 2003.
[23]
N. C. Handy and A. Willetts, “Anharmonic constants for benzene,” Spectrochimica Acta Part A, vol. 53, no. 8, pp. 1169–1177, 1997.
[24]
V. Barone, “Accurate vibrational spectra of large molecules by density functional computations beyond the harmonic approximation: the case of azabenzenes,” Journal of Physical Chemistry A, vol. 108, no. 18, pp. 4146–4150, 2004.
[25]
V. Barone, “Vibrational spectra of large molecules by density functional computations beyond the harmonic approximation: the case of pyrrole and furan,” Chemical Physics Letters, vol. 383, no. 5-6, pp. 528–532, 2004.
[26]
V. Barone, G. Festa, A. Grandi, N. Rega, and N. Sanna, “Accurate vibrational spectra of large molecules by density functional computations beyond the harmonic approximation: the case of uracil and 2-thiouracil,” Chemical Physics Letters, vol. 388, no. 4-6, pp. 279–283, 2004.
[27]
A. D. Boese and J. M. L. Martin, “Vibrational spectra of the azabenzenes revisited: anharmonic force fields,” Journal of Physical Chemistry A, vol. 108, no. 15, pp. 3085–3096, 2004.
[28]
V. Librando, A. Alparone, and Z. Minniti, “Computational note on anharmonic infrared spectrum of naphthalene,” Journal of Molecular Structure: THEOCHEM, vol. 847, no. 1-3, pp. 23–24, 2007.
[29]
A. Alparone, “Ab initio and DFT anharmonic spectroscopic investigation of 1,3-cyclopentadiene,” Chemical Physics, vol. 327, pp. 127–136, 2006.
[30]
A. Alparone, “Infrared and Raman spectra of C4H4Se and C4D4Se isotopomers: a DFT-PT2 anharmonic study,” Journal of Chemistry, vol. 2013, Article ID 741472, 8 pages, 2013.
[31]
A. D. Becke, “A new mixing of Hartree-Fock and local density-functional theories,” The Journal of Chemical Physics, vol. 98, no. 2, pp. 1372–1377, 1993.
[32]
C. Lee, W. Yang, and R. G. Parr, “Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density,” Physical Review B, vol. 37, no. 2, pp. 785–789, 1988.
[33]
T. H. Dunning Jr. and P. J. Hay, in Modern Theoretical Chemistry, H. F. Schaefer III, Ed., vol. 3, pp. 1–28, Plenum, New York, NY, USA, 1976.
[34]
W. R. Wadt and P. J. Hay, “Ab initio effective core potentials for molecular calculations. Potentials for main group elements Na to Bi,” The Journal of Chemical Physics, vol. 82, no. 1, pp. 284–298, 1985.
[35]
M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., GAUSSIAN 09, Revision A.02, Gaussian, Inc., Wallingford, Conn, USA, 2009.
[36]
G. A. Zhurko and D. A. Zhurko, “Chemcraft,” http://www.chemcraftprog.com/.