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DFT Study and Heat Capacity of Polyaniline Pernigraniline Base Abhishek Kumar Mishra*,† and Poonam Tandon‡ Department of Physics, Amity School of Engineering and Technology, Amity UniVersity, Noida 201 301, India, and Department of Physics, UniVersity of Lucknow, Lucknow 226 007, India ReceiVed: February 7, 2009; ReVised Manuscript ReceiVed: June 12, 2009
Polyaniline (PANI) is a very important polymer owing to its diversified chemistry and interesting physical properties. To investigate the structural parameters of polyaniline pernigraniline base (PANI PNB), DFT geometry optimization using B3LYP/6-31G** basis set was carried out on its two well-known model compounds. Electrostatic potential surfaces have been mapped over the electron density isosurfaces to obtain information about size, shape, charge distribution, and chemical reactivity of these molecules. The heat capacity of PANI PNB in the temperature range 10-300 K is being reported for the first time. 1. Introduction Polyaniline (PANI) represents one of the most important conducting polymers and recently received much attention due to its controllable electrical conductivity,1 environmental stability,2 and interesting redox properties associated with the chain hetroatoms.3 The objective of this paper is to investigate the structural details of polyaniline pernigraniline base (PANI PNB) by DFT geometry optimization of its model compounds and to depict the size, shape, charge density, and the site of the chemical reactivity of these model compounds with the help of their electrostatic potential plots on the total density. PANI has not been studied so far for its thermal behavior, although a wide variety of other techniques have been employed for understanding its electronic properties,4 and one of the other objectives of this paper is to present the heat capacity values of PANI PNB. The PANI family of polymers has been recently recognized as an interesting and unusual member of the class of π-electroncontaining conducting polymers. Unlike many other members of this class such as polyacetylene, polypyrrole, and polythiopene, whose electronic properties are well understood solely on the basis of their conjugated carbon backbones, in PANI a nitrogen hetroatom is incorporated between constituent phenyl (C6H6) rings in the backbone. The chemical flexibility provided by the nitrogen hetroatom allows access to several insulating ground states that are distinguished by their oxidation state. PANI exists in a variety of forms which differ in their oxidation level. The general formula describing PANI chain is {[-(C6H6)sNHs(C6H6)sNH-]1-x[-(C6H6)sNd(C6H4)sNd N-]x}n, where x gives the average degree of oxidation. The three stable forms of PANI correspond to the values x ) 0 (leucoemeraldine base, LB), x ) 0.5 (emeraldine base, EB), and x ) 1 (pernigraniline base, PNB). The electronic properties of PANIs are controlled both by bond length dimerization, as in most conjugated polymers, and by torsional angle dimerization,5-7 since the phenylene rings leave the plane defined by the nitrogen atoms to reduce the strong sterical hindrance taking place between adjacent rings in the fully planar conformation. These torsions are found to influence the π delocalization, and hence the mobility of charge * Corresponding author. Tel.: +91-522-264-8064. E-mail: drabhishekkmishra@ yahoo.in. † Amity University. ‡ University of Lucknow.
carriers, and to deeply affect the electronic properties of polyanilines, and in the present paper efforts are being made to find out information about the torsional angle between the benzoid and quinoid rings of PANI PNB through the quantum chemical study of its model compounds. Thermal properties such as thermal diffusivities, specific heat capacities, and thermal conductivities of PANI films are crucially important from the viewpoint not only of fundamental aspect for academia but also of various processing and applications of the polymer, especially the thermoelectric application.8,9 The physical properties of a polymer are strongly influenced by the conformation of the polymer. Vibrational spectroscopy, besides providing information about different conformational states, plays an important role in an understanding of the thermodynamical behavior of polymer chains. The presence of regions of high density of states, which appear in all techniques and play an important role in thermodynamical behavior, is also dependent on the profile of the dispersion curves. The evaluation of the normal mode of a polymeric system is in general an order of magnitude more difficult than molecular systems. However, the advent of lasers and fast computers has eased these problems to a large extent. In the present paper we have extended our earlier work10 to report for the first time the heat capacity of PANI PNB in the temperature range 10-300 K. The paper is organized as follows: first, a brief description of the computational details and methodology we adopted for the geometry optimization calculations and electrostatic potential surfaces is given in the Theoretical Details section. In the same section we will describe our method of calculating the heat capacity of PANI PNB from its frequency distribution function. Afterward, in the Results and Discussion section, we will discuss first our DFT geometry optimization results of its two model compounds namely B2Q1 and B3Q2 (B stands for benzoid ring and Q stands for quiniod ring). We will mainly focus on the torsional angle between the phenyl rings in these two model compounds. Then we will discuss the effect of electrostatic potential surface plot on the total density of these two model compounds in order to depict the size, shape, charge density, and site of chemical reactivity of the molecules. In the last subsection of the Results and Discussion we will discuss about the heat capacity of PANI PNB that we have calculated from our normal-mode calculations. No experimental data is available for the heat capacity and hence to support our results we will
10.1021/jp901143m CCC: $40.75 2009 American Chemical Society Published on Web 07/01/2009
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∫ g(νi) dνI ) 1
give a short discussion about our normal-mode assignments and their comparison with the earlier works. The last part of the paper discusses the conclusions of this work. 2. Theoretical Details 2.1. Geometry Optimization and Electrostatic Potential. The DFT calculations are being performed with the Gaussian03 program11 and are analyzed with the help of the GaussView program.12 The geometries of the model compounds are fully optimized, i.e., without any physical constraint or forced symmetry using the 6-31G** split-valence basis set, at the DFT level, and these calculations are mainly carried out in the framework of the Becke-Lee-Yang-Parr [B3LYP] functionals, in which the exchange functional is a local spin density exchange with Becke gradient correction13 and the correlation functional is that of Lee, Yang, and Parr with both local and nonlocal terms.14 Convergence criteria in which both the forces and displacement are smaller than the cutoff values of 0.000 45 and 0.0018 and rms force and displacement are less than 0.0003 and 0.0012 have been used in the calculations. Isoelectronic molecular electrostatic potential surfaces (EPS) are plotted by the computer program GaussView.12 2.2. Calculation of Specific Heat. Normal-mode calculation for PANI PNB chain has been carried out using Wilson’s GF matrix15,16 method as modified by Higgs17 for an infinite polymeric chain. The vibrational secular equation to be solved is
|G(δ)F(δ - λ(δ)I| ) 0,
(1)
0eδeπ
where δ is the phase difference between the modes of adjacent chemical units, G(δ) is the inverse kinetic energy matrix, and F(δ) is the force field matrix for a certain phase value. The frequencies νi (in cm-1) are related to eigenvalues by
λi(δ) ) 4π2c2νi2(δ)
(2)
A plot of νi (δ) versus δ gives the dispersion curve for the ith mode. Dispersion curves can be used to calculate the specific heat CV of a polymeric system. For a one-dimensional system, the density-of-states function or frequency distribution function expresses the way energy is distributed among the various braches of normal modes in the crystal and is calculated from the relation
g(ν) )
∑ (∂νj/∂δ)-1νj(δ))νj
(3)
j
The sum is over all the dispersion branches j. Considering a solid as an assembly of harmonic oscillators, frequency distribution g(ν) is equivalent to a partition function. The constantvolume heat capacity, CV can be calculated using Debye’s relation: CV )
with
∑ g(ν )KN (hν /KT) [exp(hν /KT)/{exp(hν /KT) - 1)} ] 2
j
A
j
2
j
j
(4)
(5)
where g(ν) is the density of states, K is Boltzmann’s constant, NA is the Avogadro number, T is absolute temperature, and h is Planck’s constant. 3. Results and Discussion A. Molecular Structure. One chemical repeat unit of PANI PNB is shown in Figure 1 and to investigate about its molecular structure, DFT geometry optimizations have been first carried out on diphenylamine (DPA) (Figure 2) which is the simplest model compound of the PANI family and whose limited size allows us to start our calculations; then we selected the two model compounds of PANI PNB, namely, B2Q1 and B3Q2. DFT-optimized molecular structures using the B3LYP/6-31G** basis set of these model compounds are given in Figures 3 and 4. In the fully oxidized polyaniline, PANI PNB, phenylene rings with benzoid-type sequence of bonds and rings of quinoid type of bonds are present in the ratio 1:1 and are separated by imine nitrogens. B2Q1 is the first model compound under study, in which terminal rings are benzoid while the central ring is of quinoid type. From our calculations, we found that torsional angle (sum of angles C2-C3-N22-C12 and C3-N22-C12C13, Figure 3) between the first terminal benzoid ring and the quinoid ring is 58.16° while the torsional angle between the quinoid ring and second terminal benzoid ring (C16-C15N34-C23, Figure 2) is found to be -58.16°. In the second model compound B3Q2, we have three benzoid and two quinoid rings,and the torsional angle between the first terminal benzoid ring and the next quinoid ring is +57.94° and that of second terminal ring and quinoid ring is -57.94°, while the torsional angles between the internal benzoid and quinoid rings are found to be +54.9° and -54.9°. Hence from DFT-optimized structure of both these model compounds we can finally conclude that in the PANI PNB chain the torsional angle between the internal benzoid and quinoid rings is approximately (55°, while the torsional angle between the terminal rings is approximately (58°. B. Molecular Electrostatic Potential. The molecular electrostatic potential (ESP) at a point r in the space around a molecule is (in atomic units)
V(r) )
Z
F(r) dr′ ∑ |RA -A r| - ∫ |r′ - r|
(6)
where ZA is the charge on nucleus A located at RA and F(r′)is the electronic density. The first term in the expression represents the effect of the nuclei and the second represents that of electrons. The terms have opposite signs and therefore opposite effects. V(r) is their resultant at each point r: it is an indication of the net electrostatic effect produced at the point r by the total charge distribution (electrons + nuclei) of the molecule. Electrostatic potential correlates with dipole moment, electronegativity, partial charges, and site of chemical reactivity of the molecule. It provides a visual method to understand the relative polarity of a molecule. While the negative electrostatic potential corresponds to an attraction of the proton by the concentrated electron density in the molecule (and is colored in shades of red on the ESP surface), the positive electrostatic potential corresponds to repulsion of the proton by atomic nuclei in regions where low electron density exists and the nuclear charge is incompletely shielded (and is colored in shades of blue). By
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Figure 1. One chemical repeat unit of PANI PNB.
Figure 2. B3LYP/6-31G** optimized geometry of DPA.
Figure 3. B3LYP/6-31G** optimized geometry of B2Q1.
Figure 4. B3LYP/6-31G** optimized geometry of B3Q2.
definition, electron density isosurface is a surface on which molecule’s electron density has a particular value and which encloses a specified fraction of the molecule’s electron probability density. The electrostatic potential at different points on the electron density isosurface is shown by coloring the isosurface with contours. The electron density isosurface on to which the electrostatic potential surface has been mapped is shown in Figure 5 for B2Q1 and in Figure 6 for B3Q2. Such surfaces depict the size, shape, charge density, and site of chemical reactivity of the molecules. The different values of the electrostatic potential at the surface are represented by different colors; red represents regions of most negative electrostatic potential, blue represents regions of most positive electrostatic potential, and green represents regions of zero potential. Potential increases in the order red < orange < yellow < green < blue. These molecules contains the polar atom nitrogen and the shape of the electrostatic potential surface is influenced by the charge density distributions in the molecules with sites close to the nitrogen atom, showing regions of most negative electrostatic potential. C. Heat Capacity of PANI PNB. PANI with 22 atoms in a chemical repeat unit (Figure 1) gives rise to 66 dispersion curves. Dispersion curves and frequency distribution function are important for an understanding of thermodynamical and elastic properties of solids. Besides providing knowledge of density of states, dispersion curves give information on the extent to the coupling of a mode along the chain in the ordered state. The regions of high density of states, which are observable in the IR and Raman spectra under suitable conditions, depend on the profile of the dispersion curves which play an important role in the thermodynamic behavior of the system.
Mishra and Tandon The study of dispersion curves enables the calculation of the frequency distribution function. This function shows how the energy is distributed among the various branches of normal modes. The flat region in the frequency distribution curves correspond to regions of high density of state. The density of states can also be used to calculate thermodynamical parameters such as heat capacity, enthalpy, etc. Heat capacity has been calculated as a function of temperature in the range 10-300 K using eq 4. The results obtained from this equation are given in Figure 7. As we have calculated the heat capacity of PANI PNB from our normal-mode calculations and no experimental data is available for the heat capacity results, as a support of our heat capacity results we will discuss here normal-mode assignments of PANI PNB. The observed18,19 and calculated frequencies along with their assignments and a comparison with earlier works18-20 are presented in Table 1. Many authors have examined benzene derivatives21-28 and made assignments that have been used in this work to assign the modes of PANI PNB form. One of the most comprehensive discussions is that of Varsanyi.21 For purposes of assigning fundamental modes, PANI is considered to be “di-light”, since it is para-disubstituted by nitrogen atom whose atomic weight is below 14. In the frequency range around 1600 cm-1, we can notice the presence of two well-resolved bands in the Raman spectra at 1612 and 1579 cm-1. The band at 1612 cm-1 frequency (assigned to normal mode calculated at 1623 cm-1) is due to the CC stretching vibration of the benzoid ring (8a), while the band at 1579 cm-1 (assigned to calculated normal mode at 1580 cm-1) is associated with CC stretching vibration of the quinoid ring (8a). In this frequency range, the infrared spectra is characterized by an intense absorption at 1570 cm-1 and is assigned to the calculated normal mode at 1562 cm-1. This absorption has its origin in a vibrational mode involving the benzoid ring C-C stretching partially mixed with C-H bending (8b). In the Raman spectra we can also notice some weak bands around 1555 cm-1 which are found to be associated with CC stretching vibrations of the benzoid ring. The IR band29 at 1495 cm1 and weak Raman band at 1418 cm-1 are assigned to the normal mode calculated at 1496 and 1415 cm-1, respectively, and are related with CC stretch of the quinoid ring (Wilson no. 19a and 19b). Raman and infrared active mode due to CN stretchings (vibrations 7a and 13) are observed at 1215 and 1211 cm-1, respectively, and are assigned to the calculated mode at 1217 and 1214 cm-1. C-H in-plane bending vibrations are also expected to appear in this range for the para-disubstituted benzene derivatives. In PANI PNB form the calculated normal mode at 1324 and 1317 cm-1 are assigned to the IR band at 1315 cm-1 and can be seen as C-H in-plane bending vibration of quinoid and benzoid rings, respectively (Wilson no. 3). In the IR spectra, bands29 at 1164 and 1006 cm-1 are found to be associated with C-H in-plane bending vibrations of the benzoid ring (Wilson no. 9a and 18a). while the bands at 1157 and 1098 cm-1 are associated with quinoid ring C-H bending vibrations (Wilson no. 9a and 18b). The C-H out-of-plane vibrations of para-disubstituted benzenes lies in the range below 1000 cm-1 and in Wilson’s notations they are referred as no. 17a, 10b, 10a, and 11. In the IR spectra29 of PANI PNB form the band at 965 cm-1 is assigned to the calculated modes at 978 and 966 cm-1 and can be seen as 17a Wilson vibration of the benzoid and quinoid rings, respectively. Similarly, the IR bands29 at 953 and 931 cm-1 (assigned to calculated modes at 948 and 938 cm-1, respectively) correspond to 10b vibrations of the quinoid and benzoid rings, respectively; IR bands at 844, 775, and 751 cm-1 and Raman
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Figure 5. Molecular electrostatic potential mapped on the isodensity surface for model compound B2Q1 in the range from -4.129 × 10-2 (red) to +4.129 × 102 (blue).
Figure 6. Molecular electrostatic potential mapped on the isodensity surface for model compound B2Q2 in the range from -3.984 × 10-2 (red) to +3.984 × 102 (blue).
band at 790 cm-1 are also characteristic bands of C-H out-ofplane vibrations (Wilson no. 10a and 11) and are assigned to calculated modes at 842, 761, 752, and 807 cm-1, respectively. Radial skeletal vibrations of para-disubstituted benzenes are completely mixed modes and are expected to lie in this range. Calculated normal modes at 776 cm-1 (assigned to observed IR band at 775 cm-1) and 708 cm-1 are completely mixed modes and can be seen as Wilson vibrations 1 and 12 of benzoid and quinoid ring, respectively. Mode calculated at 614 cm-1 corresponding to 6b normal mode having C-C-C bend as major component in PED is assigned to IR band29 at 624 cm-1. A weak IR band at 542 cm-1 is assigned to the calculated normal modes at 544 and 543 cm-1 and is found to be associated with CN out-of-plane bend vibration of the rings. IR dip at 498 cm-1
Figure 7. Variation of heat capacity of PANI PNB form as a function of temperature.
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TABLE 1: Comparison of the Present Assignments of PANI PNB Form with Earlier Worksa our study obsd bands
calcd modes
1612R 1579R 1570IR 1555R 1495IR 1418R 1411IR 1377IR
1623 1580 1562 1558 1496 1415 1398 1381
CdC CdC C-C C-C CdC C-C C-C C-C
1315IR 1315IR 1164IR 1157R 1098IR 1006IR
1324 1317 1176 1154 1087 1008
1480R,IR 1215R 1211IR
1487 1217 1214
previous studies
assignments
calcd modes
C-C Stretching Vibrations + C-C stretch (B) (8a) + C-C stretch (Q) (8a) + CdC stretch (Q) (8b) + CdC stretch (B) (8b) + C-C stretch (Q) (19a) stretch (Q) (19b) stretch (B) + C-H bend (B) (19b) stretch (Q) + C-H bend (Q) (14)
assignments
1613b 1572b -
C-C stretch (B) (8a) CdC stretch (Q) -
1416b 1433b 1367b
C-C stretch (Q) (19b) C-H bend (B) + C-C stretch (B) C-C stretch (Q)
C-H Bending Vibrations C-H bending (Q) (3) C-H bending (B) (3) C-H bending (B) + C-C stretch (B) (9a) C-H bending (Q) (9a) C-H bending (Q) + CdC stretch (Q) (18b) ring deformn (B) + C-H bend (18a)
1308b 1308b 1160b 1025b
C-H bending (Q)(3) C-H bending(B) (3) C-H bending (Q) (9a) ring deformn (B) (18a)
C-N Stretching Vibrations NdC + C-C stretch (Q) + C-H bending (Q) C-N stretch (7a) C-N stretch (13)
1488c 1208b 1234b
NdC stretch + C-H bending (B)b C-N stretch (14) C-N stretch (14)
C-H Out-of-Plane Vibrations (B) + wag (C-H) (Q) (17a) (Q) + wag (C-H)(B) (17a) (Q) (10b) (B) (10b) (B) + wag (C-H) (Q) (10a)
965IR 965IR 950IR 931IR 845IR
978 966 948 938 842
wag wag wag wag wag
790R
807
wag (C-H) (Q) + wag (C-H) (B) (10a)
775IR 750IR
761 752
wag (C-H) (B) (11) wag (C-H) (Q) (11)
775IR
776
624IR 518R
(C-H) (C-H) (C-H) (C-H) (C-H)
945d
ring deformn in-plane (Q) (17b)
824d 843d 904d 796d 788d
C-H wag (11) C-H wag (10a) ring deformn i.p. (B) (1) ring deformn i.p. C-H bend o.p. (Q)
760b 752d 742c
ring bend o.p. (Q) ring deformn (Q)
901c
-
708 614 519
Radial Skeletal Vibrations C-H wag + CsCdC bend (B) + CsCdC bend (B) + C-N stretch (1) CsCdC + C-C-C bend (Q) + CsNdC bend (12) CsCdC bend (B) (6b) ring deformn i.p. (Q) (6a)
690b 611b 506d
CsNdC bend (6b) ring deformn B (6b) ring deformn i.p. (Q)
498IR 410IR
718 482 406
Out-of-Plane Skeletal Vibrations C-N stretch + CsCdC bend o.p. (B) (4) CsCdC bend o.p. (B) + C-C-C bend o.p. (Q) (16b) ring deformn o.p. (B) + ring deformn o.p. (Q) (16a)
466d 387d
C-H wag (16b) C-CdC bend o.p.
542IR 374R 374R 212R
543 379 374 200
C-N C-N C-N C-N
548d -
CdN bend o.p. -
359R
358 190
C-N bend i.p. (9b) C-N bend i.p. (15)
-
-
99INS 67INS 55INS
91 66 60
Torsional Modes torsion (C-N) + torsion (CdN) torsion C-C (Q and B) + torsion C-N torsion C-N
-
-
C-N Out-of-Plane Vibrations + CdN bend o.p. bend o.p. (5) bend o.p. out of phase (5) bend o.p. in phase (17b) C-N In-Plane Bending Vibrations
b
a All frequencies are in cm-1. Wilson numbers are given in parentheses. B and Q stand for benzoid and quinoid ring, respectively. Reference 18. c Reference 20. d Reference 19.
(assigned to calculated mode at 482 cm-1) is related to the outof-plane skeletal vibrations of the benzoid and quinoid ring (Wilson no. 16b). Observed IR band at 410 cm-1 is related to out-of-plane skeletal vibration (16a and 16b in Wilson notation) and is assigned to the calculated mode at 406 cm-1 at the zone
center. C-N in-plane bending vibrations in para-disubstituted benzene appear in the range 260-490 cm-1 (Wilson no. 9b) and 190-350 cm-1 (Wilson no. 15), and in our calculation we find them at 358 cm-1 (assigned to Raman peak at 359 cm-1) and at 190 cm-1; as the value of the phase factor is increased,
Polyaniline Pernigraniline Base both these start dispersing but in opposite direction. While the former mode decreases and reaches 286 cm-1, the latter increases and reaches 263 cm-1 at the zone boundary. In-phase C-N out-of-plane vibration (17b in Wilson notation) in paradisubstituted benzene is expected in the frequency interval 150-220 cm-1 and in our calculation we found it at 200 cm-1 and is assigned to Raman peak at 212 cm-1; this mode is also highly dispersive in nature and shows a dispersion of 59 wavenumbers. Below 100 wavenumbers we can observe some INS peaks30 at 99, 67, and 55 cm-1, these peaks are associated with torsional motion of the rings and are assigned to the calculated modes at 91, 66, and 65 cm-1, respectively (Table 1). 4. Conclusion The structural details of the polyaniline fully oxidized base form can be successfully interpreted from the DFT calculations of its two model compounds B2Q1 and B3Q2. Electrostatic potential surfaces mapped over the electron density isosurfaces provides information about size, shape, charge distribution, and chemical reactivity of these molecules. For the first time, the heat capacities of PANI PNB as a function of temperature in the region 10-300 K have been calculated and this paper provides a better understanding of the PANI PNB spectra by assigning bands based on para-disubstituted benzene derivatives. Supporting Information Available: Details of force constants, complete normal-mode assignments, and dispersion curves along with density of states of all the dispersive and nondispersive modes and crossing between different modes. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Ray, A.; Asturias, G. E.; Kershner, D. L.; Richer, A. F.; MacDiarmid, A. G.; Epstein, A. J. Synth. Met. 1989, 29, E141. (2) Neoh, K. G.; Kang, E. T.; Khor, S. H.; Tan, K. L. Polym. Degrad. Stab. 1990, 27, 107. (3) Tan, K. L.; Tan, B. T. G.; Kang, E. T.; Neoh, K. G. J. Chem. Phys. 1991, 94, 5382. (4) Skotheim, T. A.; Elsenbaumer, R. L.; Reynolds, J. R. Handbook of Conducting Polymers; Marcel Dekker: New York, 1998. (5) Ginder, J. M.; Epstein, A. J. Phys. ReV. B 1990, 41, 10674.
J. Phys. Chem. B, Vol. 113, No. 29, 2009 9707 (6) Ginder, J. M.; Epstein, A. J.; MacDiarmid, A. G. Solid State Commun. 1989, 72, 987. (7) Bredas, J. L.; Quattrocchi, C.; Libert, J.; MacDiarmid, A. G.; Ginder, J. M.; Epstein, A. J. Phys. ReV. B 1991, 44, 6002. (8) Yan, H.; Toshima, N. Chem. Lett. 1999, 1217. (9) Semiconductors and Thermoelements and Thermoelectric Cooling; Loffe, A. F., Ed.; Infosearch Limited: London, 1957. (10) Mishra, A. K.; Tandon, P.; Gupta, V. D. Macromol. Symp. 2008, 265, 111. (11) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Cheeseman, J. R.; Montgomery, J.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Mennucci, B.; Cossi, M.; Scalmani, G.; Nakajima, H.; Honda, Y.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Morokuma, K.; Voth, G. A., Salvadorm, P.; Jannenberg, J.; Dapprich, S. ; Daniels, A. D.; Strain, M. C.; Malick, D. K.; Rabuck, A. D.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Nanayakkara, A.; Challacombe, M.; Gill, M. W.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, ReVision C.02; Gaussian Inc.: Pittsburgh, PA, 2003. (12) Computer Program GaussView Ver. 2; Gaussian Inc.: Pittsburgh, PA. (13) Becke, A. D. Phys. ReV. A 1988, 38, 3098. (14) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (15) Wilson, E. B., Jr. J. Chem. Phys. 1939, 7, 1047. (16) Wilson, E. B., Jr. J. Chem. Phys. 1941, 9, 76. (17) Higgs, P. W. Proc. R. Soc. London 1953, A 220, 472. (18) Boyer, M. I.; Quillard, S.; Rebourt, E.; Louarn, G.; Buisson, J. P.; Monkman, A.; Lefrant, S. J. Phys. Chem. B 1998, 102, 782. (19) Cochet, M.; Louarn, G.; Quillard, S.; Boyer, M. I.; Buisson, J. P.; Lefrant, S. J. Raman Spectrosc. 2000, 31, 1029. (20) Quillard, S.; Louarn, G.; Lefrant, S.; Macdiarmid, A. G. Phys. ReV B 1994, 50:17, 12496. (21) Varsanyi, G. Vibrational spectra of Benzene DeriVatiVes; Academic Press: New York, 1969; Chapter 3. (22) Dollish, F. R.; Fateley, W. G.; Bentley, F. F. Characteristic Raman Frequencies of Organic Compounds; Wiley: New York, 1974. (23) Colthup, N. B.; Daly, L. H.; Wiberley, S. E. Introduction to Infrared and Raman Spectroscopy; Acedemic Press: Boston, 1990; Chapter 8. (24) Stojiljkovic, A.; Whiffen, D. H. Spectrochim. Acta 1958, 12, 47. (25) Stojiljkovic, A.; Whiffen, D. H. Spectrochim. Acta 1958, 12, 57. (26) Garrigou-Lagrange, C.; Lebas, J. M.; Josien, M. L. Spectrochim. Acta 1958, 12, 305. (27) Whiffen, D. H. Spectrochim. Acta 1955, 7, 253. (28) Randle R. R.; Whiffen D. H. Molecular Spectroscopy; Institute of Petroleum: London, 1955; p 111. (29) Neugebauer, H.; Neckel, A.; Sariciftci, N. S.; Kuzmany, H. Synth. Met. 1989, 29, E185. (30) EL Khalki, A.; Colomban, Ph.; Hennion, B. Macromolecules 2002, 35, 5203.
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