# Polyacetylene: Myth and Reality

## Abstract

**:**

^{1}A

_{g}ground electronic state with the 2

^{1}A

_{g}excited electronic singlet state. This excitation is diradical (two electron) in character. The polyacetylene limit is an equal admixture of these two

^{1}A

_{g}states making theory intractable for long chains. A method is outlined for preparation of high molecular weight polyacetylene with fully extended chains that are prevented from reacting with neighboring chains.

## 1. Introduction/Background History

^{−1}) [4]. A more extensive 1997 treatment [5] used multiple linear conjugated polyenes of increasing length, for which optimized structures were compared with equal bond structures or with structures that had one of several variations of bond alternation with optimized bond lengths at the molecular ends changing to equal bonds in the middle of the chain. The resulting dimerization energy extrapolated to 1/N = 0 at the MP2/6-31G* level was 0.4 ± 0.1 kJ/mol depending on the method of structure variation used. The low end of this range is 0.3 kJ/mol or 105 cm

^{−1}. The point that has never before been considered in this context is that the harmonic vibrational motion at the bond alternation geometry has a frequency known since at least 1958 to be in the 1500–1600 cm

^{−1}range corresponding to a double bond stretching motion [6,7,8]. The harmonic zero-point energy is higher than the estimated barrier height.

^{−1}. This corresponds to the strongest Raman active mode at a similar wavenumber. (2) The best estimate of the height of the Peierls barrier via extrapolations discussed above is 100–300 cm

^{−1}[5]. The harmonic zero point level is thus 2–7 times larger than this barrier height. Use of the harmonic approximation is clearly not justified.

## 2. Summary of This Review

^{1}A

_{g}excited state with the ground 1

^{1}A

_{g}state is the origin of the double minimum barrier for polyacetylene in its ground electronic state. It is also the basis of the difficulty in dealing theoretically with the ground state of polyacetylene with current periodic quantum chemical computational methods, since it requires inclusion of at least all doubly excited configurations at a non-perturbative level. This is followed by a brief review in Section 7 of the experimental electronic and vibrational Raman spectra of finite linear polyenes facilitated by the recent availability of such materials in homologous series. In Section 8, it is shown how these Raman spectra are relevant to our ongoing experimental Raman and vibrational inelastic neutron scattering studies of a molecular crystal for which photochemical elimination polymerization has been demonstrated to occur that leads to polyacetylene constrained to be fully extended in parallel channels formed by an inert lattice that also prevents cross-linking reactions. The iodine atoms that are photochemically cleaved are able to leave the host crystal as iodine vapor. In Section 9, the salient features gleaned from the literature are reviewed and an outlook is presented.

## 3. Double Minimum Potential Vibrational Energy Levels: Ammonia and [18]-Annulene

^{−1}. A potential that fits the precise vibrational data is shown in Figure 1 [9,10,11,12,13]. A potential that has the form V(x) = C

_{2}x

^{2}+ C

_{4}x

^{4}with C

_{2}= −9000 cm

^{−1}A

^{−2}and C

_{4}= 10,000 cm

^{−1}A

^{−4}and a reduced mass of 1.008 amu has a tunneling splitting of 0.45 cm

^{−1}(vs. 0.79 cm

^{−1}of Figure 1). The 0 to 1 transitions of 932.5 and 968.3 cm

^{−1}are computed to be at 940.3 and 969.8 cm

^{−1}. The barrier height of 2031 cm

^{−1}is 2025 cm

^{−1}in this simple treatment using the efficient FGH (Fourier Grid Hamiltonian) method [14,15]. The reduced mass for ammonia varies along the out-of-plane umbrella coordinate. For the equilibrium pyramidal geometry, the value is 1.18 amu, while at the trigonal D

_{3h}maximum it is 1.20 amu. This increase relative to the mass of H reflects the small geometry-dependent contribution of the N atom to the inversion normal mode. The zero-point level tunneling splitting of ammonia corresponds to an inversion time for the pyramidal superposition state of about 11 ps. This follows from the tunneling splitting 0.45 cm

^{−1}for NH

_{3}in the simplest model treatment. This same model gives 792 ps for the tunneling splitting for ND

_{3}.

_{18}H

_{18}compound is the 4n + 2 analog of benzene (n = 1) with n = 4, and is thus expected to be aromatic. To make a complicated story short, this conclusion is consistent with the observation of six-fold equivalent bonds in the X-ray diffraction structure but not with the computed NMR spectrum (for which the inside and outside protons are not shifted in opposite directions by the same amount as is the case for the D

_{6h}symmetry). It has been proposed that [18]-annulene has a D

_{3h}bond-alternate structure. A method of computation is found that results in a D

_{3h}bond-alternate structure that results in agreement with the NMR spectrum [16]. This proposed geometry is either one of the structures corresponding to the minima of the potential in Figure 3. The zero-point level and probability distribution are shown. This proposed geometry is either one of the structures corresponding to the minima of the potential in Figure 3. The zero-point level and probability distribution are shown. A vibrational normal mode analysis at the symmetry point maximum and also at the minima gives in each case a reduced mass of 9.315 amu. The proton NMR spectrum computed for 200 points along bond order displacement coordinate weighted by the probability of Figure 3 gives a value in reasonable agreement with experiment. Other details of this density functional theory (DFT) and FGH treatment for [18]-annulene are in [17]. A classical MD (Molecular Dynamics) treatment for NMR averaging that includes this case is in [18]. An important factor for this case is that one of the normal modes of this molecule converts the structure from the maximum of the potential to either one of the minima and back. This example provides a demonstration that zero-point heavy atom averaging is expected in such cases because of the very stiff nature of the bonds prohibits localization into one of the minimum energy wells. The general point to keep in mind is that even with heavy atom motion, it is impossible to localize a carbon-based structure into a localized bond-alternate structure for a period of time that is significant on an experimental time scale. Benzene is the obvious example.

## 4. Double Minimum Potential Vibrational Energy Levels: Polyacetylene

^{−1}.

^{−1}. In their treatment, a series of computational methods are applied to three structures for each member in a series of a finite polyene chains with an even number of carbon atoms. The structures are (1) the optimized bond-alternate structure, (2) the equal bond length (barrier) structure, and (3) the bond order reversed structure corresponding to the other minimum in the infinite chain case. These energies values relative to the optimized structure are plotted against 1/N, where N is the number of C=C bonds. The values of this energy difference for the bond reversed and bond optimized cases must, of course, extrapolate to zero as 1/N goes to zero. The plot for the barrier height when extrapolated linearly gives a finite value of about 100 cm

^{−1}. Figure 5 uses a barrier of 200 cm

^{−1}. This value comes from the observation that for chain lengths that are sufficiently long, the computed values before extrapolation are below that value, so this value is an upper limit. The harmonic force constant for the model of Figure 5 is chosen to match the value of the force constant for C–C single bonds based on harmonic normal mode analyses for simple molecules like ethane. This is the lowest reasonable value. Higher values of this force constant parameter will result in a higher zero-point energy. The reduced mass for both cases is 4.33 amu. This is derived from a Gaussian computation for finite polyenes which uses the Wilson, Decius & Cross prescription [21]. This value depends on the C–C–C bond 120° C–C–C angle but is not crucially dependent on this value.

^{−1}for the DFT computed potential and at 1460 cm

^{−1}for the variable parameter treatment. At the time of this work, it was thought that the strongest Raman active mode of what was thought to be polyacetylene was at 1459 cm

^{−1}. The 1460 cm

^{−1}value was chosen as a target value in adjusting the barrier width of this analytic empirical model of Figure 5.

^{−1}the ground state zero-point level has a double maximum. Because of the symmetry, the probability of being in one well is the same as being in the other in this and every other state. If the barrier height is raised to 20,000 cm

^{−1}, then the energy levels occur in pairs with a splitting for the lowest level of 20 cm

^{−1}corresponding to femtosecond time scale tunneling. Bond-order alternation states will be exceedingly ephemeral.

## 5. Review of Experimental Observations on Polyacetylene with Emphasis on Bond Alternation

#### 5.1. X-ray Diffraction

_{1}/a and P2

_{1}/n corresponding to the case of in-phase bond alternation or out-of-phase, respectively. For the former P2

_{1}/a in-phase case, the (001) reflection is expected to be strong; for P2

_{1}/n, it is forbidden. In this experiment [22], the (001) reflection is observed very weakly. The information in [22] as to bond alternation stems from an analysis of the shape of this (001) reflection with a two-parameter least squares fit of the alteration parameter u

_{0}and the monoclinic angle β to data with an intensity of unspecified physical origin, that depends on sample preparation, that clearly consists of more than one reflection and for which the statistics of the fit are not reported. The data presented in [22] are critically analyzed in [23] and in particular, the two parameter fit was repeated. No distinct minimum was observed for the least squared fit. The newer 1992 experimental study with new data of [24] took a global look at the full data set. It was decisively determined that the structure is P2

_{1}/n with expectation of a forbidden (001) but again, observed weakly. The authors note, “A possible explanation of the (001) intensity might be the coexistence of a small, variable fraction of bulk P21/a second phase. However, in our sample the (00L) intensities imply 20% P2

_{1}/a while the ratio of I(021)/I(011) gives an upper limit of only 4%. This inconsistency between on-axis and off-axis measures rule out the phase separation argument.” They continue, “An alternative explanation is that local defects are responsible for the (001) intensity. For example, since the energy difference between the two structures is small, one might envision defects such as short chain segments which correlate in-phase with the surrounding long chains. Such defects would be a natural consequence of small molecular weight fragments, and could easily be quenched in from the polymerization. They would contribute to the (001) but not to general (HKL) intensities as is observed.” Or they could be low molecular weight interstitial oligopolyenes. In the analysis of this data [24], the bond alternation parameter was not adjusted to fit the data. Instead, a value determined by NMR was used. This removes this X-ray study from having an impact on the bond-alternation issue. The validity of this NMR determination is discussed below.

#### 5.2. Infrared Dichroism

^{−1}C–H stretch absorption will be, by symmetry, perpendicular to the chain (and thus perpendicular to the stretch direction for a stretched film). The absorption will be zero when the electric field lies along the orientation axis. It is found that this is not the case. The out-of-plane bending mode exhibits significant dichroism in the direction expected, indicating that the chain is well oriented. It was concluded that the local symmetry is C

_{s}, not C

_{2v}, permitting a dipole derivative with a component along the chain axis. However, a DFT calculation for the finite polyene chain C

_{60}H

_{62}gives the dipole derivative for the IR-active CH mode at an angle of only about 25 degrees with the extended chain. This is presumably due to the very large axial polarizability. This axial component, however, vanishes in the postulated symmetric structure. It is expected that longer oligopolyene chains will have a larger axial/transverse ratio, and it is quite possible that the long-chain part of the distribution may dominate the IR spectrum, even if they are not the predominant species in the sample. The interpretation of this experiment depends on whether the signal is dominated by finite chains in the sample or by polyacetylene. This depends on both the amounts of these components and their relative intensities.

#### 5.3. NMR Spectroscopy

^{13}C NMR that ≈5% of the carbon atoms have sp

^{3}hybridization instead of the predominant sp

^{2}hybridization. The sp3 features “can probably be ascribed to chain terminations, cross-links, or hydrogenated double bonds” [27]. This corresponds to one atom in 20. If we ascribe the putative sp

^{3}carbons to cyclobutane ring formation then this corresponds to two cyclobutane defects in 200 carbons or 50 C=C double bonds from one to the next in two chains connected by four sp

^{3}carbons in cyclobutane rings at each end. This is, of course, only the average structure in a distribution.

^{13}C–

^{13}C dipolar coupling constant of polyacetylene prepared with low levels of acetylene–

^{13}C

_{2}[28,29]. In this case, the observation of two coupling constants for trans-polyacetylene indicates two distinct bond lengths. This work has led to the prevailing bond alternation value and the individual C–C bond lengths for polyacetylene. For example, [30] compares a computed value to the bond lengths in [28]. There are, however, a few areas of concern in this work. The cis-polyacetylene isomer shows, as expected, only one coupling constant corresponding to a double bond length, 1.37 Å. Converting the sample of cis-polyacetyene to trans-polyacetylene is done by heating in vacuum at 160 °C for one hour. The resulting solid state nutation NMR spectra at 77 K show two coupling constants corresponding to 1.36 and 1.44 Å bond lengths. It is noted [28] that “The generation of approximately equal populations of singly and doubly bonded labeled carbon pairs in trans-(CH)

_{x}starting with only doubly bonded pairs in cis-(CH)

_{x}is intriguing.” No explanation is given for this observation. The only obvious explanation is that half of the

^{13}C=

^{13}C double bonds react with nearby predominantly

^{12}C=

^{12}C double bonds to make

^{13}C–

^{13}C single bonds from the original

^{13}C=

^{13}C double bonds in cyclobutane rings. This is the kind of unambiguous experiment that is not done often enough. Presumably this also happens with half of the

^{12}C=

^{12}C bonds. The result is best called poly(“ladderane”). Performing a CP-MAS

^{13}C determination of random

^{13}C labeled polyacetylene treated in the same fashion. Both before and after thermal conversion to the trans form would be interesting.

^{13}C–

^{13}C splitting up to 300 K and did not see an expected coalescence of the features from defect migration along long chains. They speculated that the signals that they were observing came from chains that did not contain mobile defects necessary for thermal averaging, i.e., locked-in bond alternation due to cross-linking. In another work [29], it was concluded that “nuclear spin-lattice relaxation rates for

^{1}H and

^{13}C in polyacetylene cannot be adequately explained in terms of either nuclear spin diffusion to a static paramagnetic defect or rapid one-dimensional diffusion of the defect itself. A model in which only a small fraction of the molecular chains contain defects was proposed. Nuclei on these chains are rapidly relaxed, whereas the remainder achieve equilibrium by nuclear spin diffusion. The dependence of the measured relaxation rates upon frequency and isotopic concentration agreed with the predictions of the model.” As indicated by the above, an alternative hypothesis for this signal is that it comes from finite polyene chains.

#### 5.4. Resonance Raman Spectroscopy

^{−1}with a smaller contribution from another mode around 1100 cm

^{−1}. The details of this are discussed in Section 6 below. Here, we concentrate on “polyacetylene” in the context of its anticipated Raman scattering. This issue was noted in [44] in the context of periodic solids and in a way relevant to this review in [45,46]. In these publications, it is noted that the Condon mechanism for Raman scattering (also called A-term scattering) due to geometry changes in excited electronic states vanishes for periodic solids and for polyacetylene as we have defined it. This is because the one-electron excitation involved does not result in a significant geometry change for a system of effectively infinite size. The most argumentative statement of the issue is in [46], in which it is claimed that (a) since “polyacetylene” has a well-known Raman spectrum, it must be the case that something is missing that is beyond the Condon scattering mechanism; (b) a vibronic activity term is added (called B-term scattering), which (c) explains (“solving polyacetylene”) by addition of the next term albeit with an unknown magnitude, and (d) that this refinement also removes the need to consider polyacetylene as a heterogeneous mixture of finite chains [31,32,33,34,35,36,37,38,39,40,41,42]. Specifically, quoting from [46], “In ref. 24 (of [46]), three samples of nearly monodisperse polyacetylene with lengths of about 200, 400, and 3800 unit cells were synthesized and their Raman spectra were obtained. The sidebands remained, and many of the earlier “polydisperse” explanations for the line shape quickly evaporated.” The relevant ref. [24] is here ref. [35].

#### 5.5. A Cautionary Note on Doping

_{3}

^{−}and I

_{5}

^{−}in the material. In [47], the conduction is claimed to be electronic.

## 6. Electronic Spectroscopy of Finite Linear Conjugated Polyenes

_{g}symmetry in C

_{2h}as the ground state. The observation of a strongly allowed electronic excitation contradicted this view. For linear conjugated polyenes with an even number of carbons in the C

_{2h}point group, the symmetries of the non-degenerate molecular orbitals alternate in symmetry with increasing energy with a behavior similar to that of a particle in a box. Because of this, the HOMO-to-LUMO excitation is thus necessarily from an A

_{g}ground state to an excited state of B

_{u}electronic symmetry. This seemed to be in agreement with experiment in respect to a low-energy, strongly allowed transition that increased in intensity and decreased in energy as the polyene chain increased in length. There were, however, several aspects of linear conjugated polyene electronic spectroscopy and, especially, of the corresponding photophysics that attracted our attention that all was not right. The main things that we found of interest was the observation [49,50] that the intrinsic fluorescence (or radiative) lifetime of linear polyenes is much longer than expected on the basis of the integration of the absorption spectrum. The other items of interest were the series of spectroscopic papers on linear polyenes by Hauser and co-workers [51,52,53,54,55,56] and the discussion of that work by Mulliken [57]. In this discussion, Mulliken said:“A puzzling phenomenon reported by Kuhn, Hausser, and co-workers in their comparative study of absorption and fluorescence in polyene derivatives is the existence of a gap between the longest wave-length absorption band in the vibrational structure of N to V

_{1}and the shortest wave-length band the corresponding V

_{1}to N fluorescence spectrum. It is worth noting, however, that there seems to be still a small amount of absorption and emission at the middle of the gap. The width of the gap increases with increase in the number of conjugated double bonds. The absorption and fluorescence spectra are roughly mirror images of each other on a frequency scale. There seems to be no reason, especially in view of our theoretical analysis, to doubt that the fluorescence spectrum really is V

_{1}to N. According to the theory, no other excited singlet level should be below V

_{1}.” This is followed by an attempt to explain the observed spectral pattern in terms of an in-plane bending deformation of large amplitude. A similar explanation was posed for the long intrinsic lifetime [49,50].

^{−1}and the first fluorescence feature near 29,000 cm

^{−1}. This is not anticipated if there is only one low-energy excited electronic state. On the other hand, if there is another low-lying state, this absorption should begin where the fluorescence begins near 29,000 cm

^{−1}.

^{1}A

_{g}to 1

^{1}B

_{u}electronic transition near 310 nm (32200 cm

^{−1}in Figure 7), (b) the first absorption transition to the new low-energy, low-intensity transition near 348 nm (Figure 8) (28,730 cm

^{−1}in Figure 7), and (c) the first emission transition from the as of yet unknown excited electronic state to the ground electronic state of 1

^{1}A

_{g}symmetry near 352 nm in Figure 8. The line shapes reflect phonon side-band structure.

_{u}vibrational symmetry in the upper or the ground state. The lower trace is the two-photon excitation spectrum showing the true 0-0 at 350 nm plus phonon side bands and the lowest molecular a

_{g}mode an in-plane bending vibration. These spectra present the classic pattern of Herzberg–Teller vibronic coupling, in which an electronic transition that is forbidden by symmetry is made allowed by a vibronic promoting mode that is non-totally symmetric and thus transiently reduces the molecular symmetry. The absence of the true origin transition in the one-photon excitation spectrum is a result of strict centrosymmetry in the n-octane crystal. The electronic symmetry of the ground electronic state is

^{1}A

_{g}and so the upper level must also be

^{1}A

_{g}. These are designated 1

^{1}A

_{g}and 2

^{1}A

_{g}respectively with the superscript 1 indicating single states. Use of n-nonane or n-heptane in place of n-octane induces significant intensity in the 0-0 transition due to the necessary loss of symmetry. The vibration-less origin transition is two-photon allowed as is observed. The strongly allowed one-photon transition at about 312 nm is ca. 10

^{5}times stronger than the first vibronic feature of the excitation spectrum in the 2

^{1}A

_{g}region. The vibronically active normal modes are expected to be of vibrational b

_{u}symmetry because of the proximity of the strong 1

^{1}B

_{u}excitation. The two-photon high resolution spectral feature when compared to the high resolution fluorescence spectrum permits determination of the frequency the promoting mode as 86 cm

^{−1}, which is an observed mode of this b

_{u}symmetry. All of the above were the contribution of Bryan E. Kohler and his students [59,60,61,62,63,64] following the present author’s initial contributions [65,66,67,68]. The above argument as to the presence of a low lying 2

^{1}A

_{g}state in octatetraene is airtight on experimental grounds. The development of the theoretical situation showed very early [69,70,71,72] that the low-lying 2

^{1}A

_{g}state is derived from doubly excited configurations that mix with singly excited configurations of the same symmetry to become the lowest excited state. It is now possible to compute the electronic excitations of octatetraene and get very good agreement with experiment using advanced ab initio methods [73].

^{−1}C=C and C–C stretching modes. This is the case for both the transitions to or from the upper 2

^{1}A

_{g}electronic state and the allowed electronic absorption transition to the 1

^{1}B

_{u}state. This means that these excited states differ from the ground electronic 1

^{1}A

_{g}state by displacement along the total symmetric double bond and single bond contraction/expansion vibrational modes. The direction of the displacement is to upper states that have a reversal in their bond alternation pattern. The relative intensity of a vibration in an electronic transition is related to this displacement, which leads to finite overlap between the vibrational modes of the two states involved. These overlap integrals are called Franck–Condon factors. This displacement is the major mechanism that results in the vibrational structure and overall width of electronic spectra and in Raman activity of totally symmetric modes. This is called the A-term or Condon contribution to Raman scattering. This depends on the displacement of the potential energy minimum for the low-energy, strongly allowed electronic excitations. In a more general treatment of Raman scattering, there can also be cases where the mechanism of Raman intensity is due to the fact that some displacements of the atoms result in a change in the intensity of the electric dipole transition moment rather than a change in the energy of the potential energy surface that is required for non-zero Franck–Condon factors. This is especially important in electronic transitions that are between states and have electronic symmetries that cause the electric dipole transition moment to vanish at the equilibrium geometry, as is the case for the 1

^{1}A

_{g}to 2

^{1}A

_{g}electronic transitions of linear polyenes giving rise to the pattern of features shown above.

^{1}A

_{g}state in finite polyenes to properties of polyacetylene, as pointed out by Torii and Tasumi, is that polyacetylene in its ground electronic state must necessarily be an admixture of structures that have the standard pattern of bond alternation with another structure that has its bond order pattern reversed from that of the optimized structure [74]. The result is a polyacetylene with equal bond lengths. This has been investigated by Torii and Tasumi using the CASSCF (Complete Active Space Self Consistent Field) method. Their results for N = 6, dodecahexaene with an STO-3G basis set give an energy difference per CH group for the optimized geometry and that of the bond-reversed geometry of 2000 cm

^{−1}. A slight inflection in the potential hints at the evolution toward a double minimum expected for longer chains.

^{1}A

_{g}state as a function of chain length and thus to the argument above concerning its ultimate admixture with the ground state. However, these are experimental studies and therefore the excitation energies of the 2

^{1}A

_{g}state from the 1

^{1}A

_{g}ground state already includes the mixing which will push the 2A

_{g}state up as it is repelled by the receding 1

^{1}A

_{g}ground state. It is, in fact, already known that in finite polyenes the two lowest

^{1}A

_{g}states are vibronically coupled [76,77,78,79,80].

## 7. Raman Vibrational Spectroscopy of Finite Polyenes

- synthesis of these compounds is limited by solubility to N =12, i.e., N > 12 are insoluble;
- there are two strong Raman features near 1100 cm
^{−1}and in the 1600–1500 cm^{−1}region; - the lower C–C mode is not very sensitive to chain length;
- the higher C=C mode moves to lower frequency as the chain elongates;
- when plotted vs. 1/N, this C=C mode extrapolates to a value of ca. 1440 cm
^{−1}; - the integrated intensity of the C–C mode increases relative the C=C mode as N increases.

- there is a loss of mass corresponding quantitatively to the loss of iodine;
- loss of Raman intensity due to the decreasing effect of a one-electron excitation on a large chain.

## 8. In Situ Synthesis of Oriented Insulated Polyacetylene

^{−1}. The strong tetragonal urea feature at 1010 cm

^{−1}is shifted to 1022 cm

^{−1}, the value observed for hexagonal urea. Irradiation with ultraviolet (UV) light results in new Raman modes near 1509 and 1125 cm

^{−1}[86] (Figure 10a), nearly identical to spectra of trans-(CH)

_{x}prepared in solution [87]. The 254 nm radiation used in this experiment has very limited penetration into the DIBD–urea complex due to the high optical density. The change in composition of the urea channels is expected to be as shown in Figure 11.

## 9. Summary of Lessons from the Literature on Polyacetylene

^{13}C labeling.

## Acknowledgments

## Conflicts of Interest

## References

- Chiang, C.K.; Fincher, C.R.; Park, Y.W.; Heeger, A.J.; Shirakawa, H.; Louis, E.J.; Gau, S.C.; MacDiarmid, A.G. Electrical conductivity in doped polyacetylene. Phys. Rev. Lett.
**1977**, 39, 1098–1101. [Google Scholar] [CrossRef] - Swager, T.M. 50th Anniversary Perspective: Conducting/Semiconducting Conjugated Polymers; A Personal Perspective on the Macromolecules; ACS Publications: Washington, DC, USA, 2017; Volume 50, pp. 4867–4886. [Google Scholar] [CrossRef]
- Ovchinnikov, A.A.; Ukrainskii, I.I.; Kventsel, G.F. Theory of one-dimensional Mott semiconductors and the electronic structure of long molecules with conjugated bonds. Uspekhi Fiziceskih Nauk
**1972**, 108, 81–111. [Google Scholar] [CrossRef] - Suhai, S. Bond alternation in infinite polyene: Peierls distortion reduced by electron correlation. Chem. Phys. Lett.
**1983**, 96, 619–625. [Google Scholar] [CrossRef] - Guo, H.; Paldus, J. Estimates of the Structure and Dimerization Energy of Polyacetylene from Ab Initio Calculations on Finite Polyenes. Int. J. Quant. Chem.
**1997**, 63, 345–360. [Google Scholar] [CrossRef] - Lippincott, E.R.; White, C.E.; Siblia, J.P. Vibrational spectra and geometrical configuration of 1,3,5-hexatriene. J. Am. Chem. Soc.
**1958**, 80, 2926–2930. [Google Scholar] [CrossRef] - Lippincott, E.R.; Kenney, T.E. Vibrational spectra and geometric configuration of cis-1,3,5-hexatriene. J. Am. Chem. Soc.
**1962**, 84, 3641–3648, (includes updated data for trans form.). [Google Scholar] [CrossRef] - Guo, H.; Karplus, M. Ab initio studies of polyenes. I. 1,3-Butadiene. J. Chem. Phys.
**1991**, 94, 3679–3699. [Google Scholar] [CrossRef] - Laane, J. Eigenvalues of the Potential Function V = z
^{4}± Bz^{2}and the Effect of Sixth Power Terms. Appl. Spectrosc.**1970**, 24, 73–80. [Google Scholar] [CrossRef] - Bernath, P.F. Spectra of Atoms and Molecules; Oxford Univ. Press: New York, NY, USA, 1994; pp. 273–274. [Google Scholar]
- Dennison, D.M.; Uhlenbeck, G.E. The two-minima problem and the ammonia molecule. Phys. Rev.
**1932**, 41, 313–321. [Google Scholar] [CrossRef] - Dennison, D.M. The infrared spectra of polyatomic molecules. II. Rev. Mod. Phys.
**1940**, 12, 175–214. [Google Scholar] [CrossRef] - Aquino, N.; Campoy, G.; Yee-Madeira, H. The inversion potential for NH
_{3}using a DFT approach. Chem. Phys. Lett.**1998**, 296, 111–116. [Google Scholar] [CrossRef] - Marston, C.C.; Balin-Kurti, G.G. The Fourier grid Hamiltonian method for bound state eigenvalues and eigenfunctions. J. Chem. Phys
**1989**, 91, 3571–3576. [Google Scholar] [CrossRef] - Johnson III, R.D. Fourier Grid Hamiltonian (FGH) 1D Program. Available online: https://www.nist.gov/chemical-informatics-research-group/products-and-services/fourier-grid-hamiltonian-fgh-1d-program (accessed on 26 December 2017).
- Wannere, C.S.; Sattelmeyer, K.W.; Schaefer III, H.F.; Schleyer, P.V.R. Aromaticity: The alternating C–C bond length structures of [14]-, [18]-, and [22]annulene. Angew. Chem. Int. Ed.
**2004**, 43, 4200–4206. [Google Scholar] [CrossRef] [PubMed] - Hudson, B.S.; Allis, D.G. The Structure of [18]-annulene: Computed Raman Spectra, Zero-point Level and Proton NMR Chemical Shifts. J. Mol. Struct.
**2012**, 1023, 212–215. [Google Scholar] [CrossRef] - Kwan, E.E.; Liu, R.Y. Enhancing NMR Prediction for Organic Compounds Using Molecular Dynamics. J. Chem. Theory Comp.
**2015**, 11, 5083–5089. [Google Scholar] [CrossRef] [PubMed] - Hudson, B.S.; Allis, D.G. Bond alternation in infinite periodic polyacetylene: Dynamical treatment of the anharmonic potential. J. Mol. Struct.
**2013**, 1032, 78–82. [Google Scholar] [CrossRef] - Born, M.; Kármán, T.V. Vibrations in Space-gratings (Molecular Frequencies). Phys. Z.
**1912**, 13, 297–309. [Google Scholar] - Wilson, E.B., Jr.; Decius, J.C.; Cross, P.C. Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra (Dover Books on Chemistry); Courier Corporation: North Chelmsford, MA, USA, 1980. [Google Scholar]
- Fincher, C.R., Jr.; Chen, C.E.; Heeger, A.J.; MacDiarmid, A.G.; Hastings, J.B. Structural determination of the symmetry-breaking parameter in trans-polyacetylene (CH)x. Phys. Rev. Lett.
**1982**, 48, 100–104. [Google Scholar] [CrossRef] - Chien, J.C.W. Polyacetylene: Chemistry, Physics, and Materials Science; Academic Press: New York, NY, USA, 1984; pp. 112–117. ISBN 0-12-172460-3. [Google Scholar]
- Zhu, Q.; Fischer, J.E.; Zuzok, R.; Roth, S. Crystal structure of polyacetylene revisited: An X-ray study. Solid State Commun.
**1992**, 83, 179–183. [Google Scholar] [CrossRef] - Zicovich-Wilson, C.M.; Kirtman, B.; Civalleri, B.; Ramirez-Solis, A. Periodic density functional theory calculations for 3-dimensional polyacetylene with empirical dispersion terms. Phys. Chem. Chem. Phys.
**2010**, 1, 3289–3293. [Google Scholar] [CrossRef] [PubMed] - Castiglioni, C.; Zerbi, G.; Gussoni, M. Peierls distortion in trans-polyacetylene—Evidence from infrared intensities. Solid State Commun.
**1985**, 56, 863–866. [Google Scholar] [CrossRef] - Maricq, M.M.; Waugh, J.S.; MacDiarmid, A.G.; Shirakawa, H.; Heeger, A.J. Carbon-13 nuclear magnetic resonance of cis- and trans-polyacetylenes. J. Am. Chem. Soc.
**1978**, 100, 7729–7730. [Google Scholar] [CrossRef] - Yannoni, C.S.; Clarke, T.C. Molecular Geometry of cis- and trans-Polyacetylene by Nutation NMR Spectroscopy. Phys. Rev. Lett.
**1983**, 51, 1191–1193. [Google Scholar] [CrossRef] - Scott, J.C.; Clarke, T.C. Nuclear magnetic relaxation in polyacetylene. J. Phys. Colloq.
**1983**, 44, 365–368. [Google Scholar] [CrossRef] - Izmaylov, A.F.; Scuseria, G.E. Efficient evaluation of analytic vibrational frequencies in Hartree-Fock and density functional theory for periodic nonconducting systems. J. Chem. Phys.
**2007**, 127, 144106/1–144106/9. [Google Scholar] [CrossRef] [PubMed] - Lefrant, S.; Lichtmann, L.S.; Temkin, H.; Fitchen, D.B.; Miller, D.C.; Whitewell II, G.E.; Burlitch, J.M. Raman scattering in (polyacetylene) and (polyacetylene) treated with bromine and iodine. Solid State Commun.
**1979**, 29, 191–196. [Google Scholar] [CrossRef] - Brivio, P.; Mulazzi, E. Absorption and resonant Raman scattering from trans-polyacetylene. Chem. Phys. Lett.
**1983**, 95, 555–560. [Google Scholar] [CrossRef] - Mulazzi, E.; Brivio, P.; Falques, E.; Lefrant, S. Experimental and theoretical Raman results in transpolyacetylene. Solid State Commun.
**1983**, 46, 851–855. [Google Scholar] [CrossRef] - Brivio, P.; Mulazzi, E. Theoretical analysis of absorption and resonant Raman scattering spectra of trans-polyacetylene ((CH)x). Phys. Rev. B
**1984**, 30, 876–882. [Google Scholar] [CrossRef] - Schen, M.A.; Chien, J.C.W.; Perrin, E.; Lefrant, S.; Mulazzi, E. Resonant Raman scattering of controlled molecular weight polyacetylene. J. Chem. Phys.
**1988**, 89, 7615–7620. [Google Scholar] [CrossRef] - Masetti, G.; Campani, E.; Gorini, G.; Piseri, L.; Tubino, R.; Piaggio, R.P.; Dellepiane, G. Resonance Raman-spectra of highly oriented trans-polyacetylene. Solid State Commun.
**1985**, 55, 737–742. [Google Scholar] [CrossRef] - Kuzmany, H. Resonance Raman-Scattering from Neutral and Doped Polyacetylene. Phys. Status Soldi
**1980**, 97, 521–531. [Google Scholar] [CrossRef] - Schuegerl, F.B.; Kuzmany, H. Optical modes of trans-polyacetylene. J. Chem. Phys.
**1981**, 74, 953–958. [Google Scholar] [CrossRef] - Kuzmany, H.; Imhoff, E.A.; Fitchen, D.B.; Sarhangi, A. Franck-Condon approach for optical absorption and resonance Raman scattering in trans-polyacetylene. Phys. Rev. B
**1982**, 26, 7109–7112. [Google Scholar] [CrossRef] - Kuzmany, H. The particle in the box model for resonance Raman scattering in polyacetylene. Pure Appl. Chem.
**1985**, 57, 235–246. [Google Scholar] [CrossRef] - Kuzmany, H.; Knoll, P. Application of the particle in the box model for resonance Raman scattering to recent experimental results of polyacetylene. Mol. Cryst. Liq. Cryst.
**1985**, 117, 385–392. [Google Scholar] [CrossRef] - Kuzmany, H.; Knoll, P. The Dispersion effect of Resonance Raman Lines in Trans-Polyacetylene, Springer Series in Solid-State Sciences. Electron. Prop. Polym. Relat. Compd.
**1985**, 63, 114–121. [Google Scholar] - Eckhardt, H.; Steinhauser, S.W.; Chance, R.R.; Schott, M.; Silbey, R. Anti-Stokes Raman-scattering in trans polyacetylene. Solid State Commun.
**1985**, 55, 1075–1079. [Google Scholar] [CrossRef] - Martin, R.M.; Falicov, L.M. Resonance Raman Scattering in Light Scattering in Solids; Cardona, M., Guntherodt, G., Eds.; Springer: New York, NY, USA, 1975; pp. 79–145. ISBN 03034216. [Google Scholar]
- Jin, B.; Silbey, R. Theory of resonance Raman scattering for finite and infinite polyenes. J. Chem. Phys.
**1995**, 102, 4251–4260. [Google Scholar] [CrossRef] - Heller, E.J.; Yang, Y.; Kocia, L. Raman Scattering in Carbon Nanosystems: Solving Polyacetylene. ACS Cent. Sci.
**2015**, 1, 40–49. [Google Scholar] [CrossRef] [PubMed] - Thakur, M. A Class of Conducting Polymers Having Nonconjugated Backbones. Macromolecules
**1988**, 21, 661–664. [Google Scholar] [CrossRef] - Shang, Q.; Pramanick, S.; Hudson, B. Chemical nature of conduction in iodine-doped trans-1,4-poly(buta-1,3-diene) and some of its derivatives: The presence of I
_{3}^{−}and the effect of double-bond configuration. Macromolecules**1990**, 23, 1886–1889. [Google Scholar] [CrossRef] - Birks, J.B.; Dyson, D.J. The relations between the fluorescence and absorption properties of organic molecules. Proc. R. Soc. Lond. Ser. A
**1963**, 275, 135–148. [Google Scholar] [CrossRef] - Birks, J.B.; Birch, D.J.S. Fluorescence of diphenyl- and retinolpolyenes. Chem. Phys. Lett.
**1975**, 31, 608–610. [Google Scholar] [CrossRef] - Hausser, K.W.; Kuhn, R.; Smakula, A.; Kreuchen, K.H. Absorption of light and double bonds. I. Problem and methods. Z. Phys. Chem.
**1935**, B29, 363–370. [Google Scholar] - Hausser, K.W.; Kuhn, R.; Smakula, A.; Hoffer, M. Absorption of light and double bonds. II. Polyene aldehydes and polyene carboxylic acids. Z. Phys. Chem.
**1935**, B29, 371–377. [Google Scholar] - Hausser, K.W.; Kuhn, R.; Smakula, A.; Deutsch, A. Absorption of light and double bonds. III. Investigation in the furane series. Z. Phys. Chem.
**1935**, B29, 378–383. [Google Scholar] - Hausser, K.W.; Kuhn, R.; Smakula, A. Absorption of light and double bonds. IV. Diphenylpolyenes. Z. Phys. Chem.
**1935**, B29, 384–389. [Google Scholar] - Hausser, K.W.; Kuhn, R. Seitz, Absorption of light and double bonds. V. The absorption of compounds with conjugate double bonds of carbon at low temperature. Z. Phys. Chem.
**1935**, B29, 391–416. [Google Scholar] - Hausser, K.W.; Kuhn, R.; Kuhn, E. Absorption of light and double bonds. VI. The fluorescence of diphenylpolyenes. Z. Phys. Chem.
**1935**, B29, 417–454. [Google Scholar] - Mulliken, R.S. Intensities of electronic transitions in molecular spectra. VII. Conjugated polyenes and carotenoids. J. Chem. Phys.
**1939**, 7, 364–373. [Google Scholar] [CrossRef] - D’Amico, K.L.; Manos, C.; Christensen, R.L. Electronic energy levels in a homologous series of unsubstituted linear polyenes. J. Am. Chem. Soc.
**1980**, 102, 1777–1782. [Google Scholar] [CrossRef] - Granville, M.F.; Holtom, G.R.; Kohler, B.E.; Christensen, R.L.; D’Amico, K.L. Experimental confirmation of the dipole forbidden character of the lowest excited singlet state in 1,3,5,7-octatetraene. J. Chem. Phys.
**1979**, 70, 593–594. [Google Scholar] [CrossRef] - Granville, M.F.; Holtom, G.R.; Kohler, B.E. High-resolution one and two photon excitation spectra of trans, trans-1,3,5,7-octatetraene. J. Chem. Phys.
**1980**, 72, 4671–4675. [Google Scholar] [CrossRef] - Hudson, B.S.; Kohler, B.E. Polyene spectroscopy. Lowest energy excited singlet state of diphenyloctatetraene and other linear polyenes. J. Chem. Phys.
**1973**, 59, 4984–5002. [Google Scholar] [CrossRef] - Adamson, G.; Gradl, G.; Kohler, B.E. Photochemical hole burning for 1,3,5,7-octatetraene in n-hexane. J. Chem. Phys.
**1989**, 90, 3038–3042. [Google Scholar] [CrossRef] - Kohler, B.E. Electronic Properties of Linear Polyenes; Conjugated Polymers; Brédas, J.L., Silbey, R.J., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1991; pp. 405–434. [Google Scholar]
- Kohler, B.E. Octatetraene photoisomerization. Chem. Rev.
**1993**, 93, 41–54. [Google Scholar] [CrossRef] - Hudson, B.S.; Kohler, B.E. Low-lying weak transition in the polyene α,ω-diphenyl-octatetraene. Chem. Phys. Lett.
**1972**, 14, 299–304. [Google Scholar] [CrossRef] - Hudson, B.; Kohler, B. Linear polyene electronic structure and spectroscopy. Annu. Rev. Phys. Chem.
**1974**, 25, 437–460. [Google Scholar] [CrossRef] - Hudson, B.S.; Kohler, B.E.; Schulten, K. Linear polyene electronic structure and potential surfaces. Excit. States
**1982**, 6, 1–95. [Google Scholar] - Hudson, B.; Kohler, B. Electronic structure and spectra of finite linear polyenes. Synth. Met.
**1984**, 9, 241–253. [Google Scholar] [CrossRef] - Schulten, K.; Karplus, M. Origin of a low-lying forbidden transition in polyenes and related molecules. Chem. Phys. Lett.
**1972**, 14, 305–309. [Google Scholar] [CrossRef] - Schulten, K.; Ohmine, I.; Karplus, M. Correlation effects in the spectra of polyenes. J. Chem. Phys.
**1976**, 64, 4422. [Google Scholar] [CrossRef] - Tavan, P.; Schulten, K. The low-lying electronic excitations in long polyenes: A PPP-MRD-CI study. J. Chem. Phys.
**1986**, 85, 6602–6609. [Google Scholar] [CrossRef] - Tavan, P.; Schulten, K. Electronic excitations in finite and infinite polyenes. Phys. Rev. B
**1987**, 36, 4337–4358. [Google Scholar] [CrossRef] - Angeli, C.; Pastore, M. The lowest singlet states of octatetraene revisited. J. Chem. Phys.
**2011**, 134, 184302. [Google Scholar] [CrossRef] [PubMed] - Torii, H.; Tasumi, M. Changes in the electronic structures of trans-polyenes in the 1
^{1}A_{g}and 2^{1}A_{g}states induced by molecular vibrations. Chem. Phys. Lett.**1996**, 260, 195–200. [Google Scholar] [CrossRef] - Christensen, R.L.; Enriquez, M.M.; Wagner, N.L.; Peacock-Villada, A.Y.; Scriban, C.; Schrock, R.R.; Polivka, T.; Frank, H.A.; Birge, R.R. Energetics and Dynamics of the Low-Lying Electronic States of Constrained Polyenes: Implications for Infinite Polyenes. J. Phys. Chem. A
**2013**, 117, 1449–1465. [Google Scholar] [CrossRef] [PubMed] - Orlandi, G.; Zerbetto, F. Vibronic coupling in polyenes: The frequency increase of the active C = C a
_{g}stretching mode in the absorption spectra. Chem. Phys.**1986**, 108, 187–195. [Google Scholar] [CrossRef] - Zerbetto, F.; Zgierski, M.Z.; Orlandi, G. Correlation between the frequency of the Franck-Condon active carbon:carbon a
_{g}stretch vibration and the excitation energy of the 1B_{u}electronic state in polyenes. Chem. Phys. Lett.**1987**, 141, 138–142. [Google Scholar] [CrossRef] - Buma, W.J.; Zerbetto, F. The large 1
^{1}A_{g}^{−}-2^{1}A_{g}^{−}C=C and C–C stretch vibronic interaction in all-trans polyenes. Chem. Phys. Lett.**1998**, 289, 118–124. [Google Scholar] [CrossRef] - Buma, W.J.; Zerbetto, F. Modeling the Spectroscopy of the Lowest Excited Singlet State of cis,trans-1,3,5,7-Octatetraene: The Role of Symmetry Breaking and Vibronic Interactions. J. Phys. Chem. A
**1999**, 103, 2220–2226. [Google Scholar] [CrossRef] - Fuss, W.; Haas, Y.; Zilberg, S. Twin states and conical intersections in linear polyenes. Chem. Phys.
**2000**, 259, 273–295. [Google Scholar] [CrossRef] - Schaffer, H.E.; Chance, R.R.; Silbey, R.J.; Knoll, K.; Schrock, R.R. Conjugation length dependence of Raman scattering in a series of linear polyenes: Implications for polyacetylene. J. Chem. Phys.
**1991**, 94, 4161–4170. [Google Scholar] [CrossRef] - Hollingsworth, M.D.; Harris, K.D.M. Urea, Thiourea, and Selenourea. In Comprehensive Supramolecular Chemistry; Solid State Supramolecular Chemistry: Crystal Engineering; Atwood, J.L., Davies, J.E.D., MacNicol, D.D., Vogtle, F., Eds.; Elsevier: Oxford, UK, 1996; Volume 6, pp. 177–237. [Google Scholar]
- Harris, K.D.M. Fundamental and applied aspects of urea and thiourea inclusion compounds. Supramol. Chem.
**2007**, 19, 47–53. [Google Scholar] [CrossRef] - Harris, K.D.M.; Palmer, B.A.; Edwards-Gau, G.R. Reactions in Solid-State Inclusion Compounds. In Supramolecular Chemistry: From Molecules to Nanomaterials; Gale, P., Steed, J., Eds.; John Wiley & Sons, Ltd.: Chichester, UK, 2012; Volume 4, pp. 1589–1612. ISBN 978-0-470-74640-0. [Google Scholar]
- Lashua, A.F.; Smith, T.M.; Hu, H.; Wei, L.; Allis, D.G.; Sponsler, M.B.; Hudson, B.S. Commensurate urea inclusion crystals with the guest (E,E)-1,4-diiodo-1,3-butadiene. Cryst. Growth Des.
**2013**, 13, 3852–3855. [Google Scholar] [CrossRef] - Dincă, S.A.; Allis, D.G.; Lashua, A.F.; Sponsler, M.B.; Hudson, B.S. Insulated polyacetylene chains in an inclusion compound by photopolymerization. MRS Online Proc. Libr. Arch.
**2015**, 1799, 1–6. [Google Scholar] [CrossRef] - Schuehler, D.E.; Williams, J.E.; Sponsler, M.B. Polymerization of acetylene with a ruthenium olefin metathesis catalyst. Macromolecules
**2004**, 37, 6255–6257. [Google Scholar] [CrossRef] - Marti-Rujas, J.; Desmedt, A.; Harris, K.D.M.; Guillaume, F. Kinetics of molecular transport in a nanoporous crystal studied by confocal raman microspectrometry: Single-file diffusion in a densely filled tunnel. J. Phys. Chem. B
**2007**, 111, 12339–12344. [Google Scholar] [CrossRef] [PubMed] - Marti-Rujas, J.; Desmedt, A.; Harris, K.D.M.; Guillaume, F. Bidirectional transport of guest molecules through the nanoporous tunnel structure of a solid inclusion compound. J. Phys. Chem. C
**2009**, 113, 736–743. [Google Scholar] [CrossRef]

**Figure 3.**Computed potential energy as a function of displacement from 6-fold symmetry for [18]-annulene (black line) showing the two lowest vibrational energy levels (red) and the probability distribution for the ground state (blue) [17].

**Figure 4.**Computed potential energy of polyacetylene using periodic boundary conditions-density functional theory (PBC-DFT) with B3LYP 6-311G(2d,2p) at 240 points (black points) along one displacement direction with subsequent generation of the symmetric potential shown as blue dotted trace [19]. The horizontal red lines are the two lowest energy levels; the light blue line is the probability distribution.

**Figure 6.**Fluorescence and absorption spectra of all trans-1,3,5,7-octatetraene in 3-methylpentane at 77K. Left, fluorescence on an arbitrary emission scale; right, absorption on an arbitrary absorbance scale [58].

**Figure 7.**(

**a**) The one-photon fluorescence excitation spectrum of octatetraene in n-octane matrix at 4.2 K. The arrows mark the vibronically induced transitions to the forbidden 2

^{1}A

_{g}excited state. The intense broad feature at 32,200 cm

^{−1}is the vibration-less origin of the allowed electronic transition to the 1

^{1}B

_{u}excited state; (

**b**) Two-photon fluorescence excitation spectrum of the same sample. All of the features are due to transitions to the 2

^{1}A

_{g}excited state. [59,67,68].

**Figure 8.**The upper trace left is the beginning of the fluorescence spectrum; the upper trace right is the beginning of the one-photon fluorescence excitation spectrum; the lower trace is the beginning of the two-photon fluorescence excitation spectrum. The two traces on the right are the same as the extreme left of Figure 7. [59,67,68].

**Figure 9.**Representations of the commensurate, fully-ordered single-crystal DIBD–urea inclusion compound (UIC) complex as obtained by X-ray diffraction at 90 K viewed along the c (left panel) and b (right panel) crystal axes. Redrawn from structure Crystallographic Information File, cif of [85].

**Figure 10.**Raman spectra with 532 nm excitation of (

**a**) DIBD–UIC after irradiation at 254 nm; (

**b**) trans –(CH)

_{x}; (

**c**) crystalline DIBD; and (

**d**) tetragonal urea [86]. The ν

_{n}values at the top are the mode frequencies for polyacetylene fundamental transitions and their overtones.

**Figure 11.**Schematic figure showing progress of the photochemical reaction from diiodobutadiene to polyacetylene with an intermediate stage showing a dimer and a trimer. The picture is to scale showing the large loss of channel filling with loss of iodine. There is a 2:1 ratio in the number of carbons in the bottom/top panels. Dimers and trimers have been shown by UV-vis of the extracted material. Longer chains have been shown by Raman.

**Figure 12.**Irreversible sequential second order kinetics. The blue decreasing curve is for the monomer. The dimer peaks at p = 1 where f

_{2}= f

_{1}, the trimer peaks at p = 2 where f

_{3}= f

_{2}, etc. The number of carbons in the most frequent species is C

_{N}= 4(p + 1). The line colors differentiate the time dependence of the sequentially larger oligomers with their increasing delay.

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Hudson, B.S.
Polyacetylene: Myth and Reality. *Materials* **2018**, *11*, 242.
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Hudson BS.
Polyacetylene: Myth and Reality. *Materials*. 2018; 11(2):242.
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2018. "Polyacetylene: Myth and Reality" *Materials* 11, no. 2: 242.
https://doi.org/10.3390/ma11020242