Hexatrienes calculated

The most easily obtained information from such calculations is the relative orderings of the eneigy levels and the atomic coefficients. Solutions are readily available for a number of frequently encountered delocalized systems, which we will illustrate by referring to some typical examples. Consider, first, linear polyenes of formula C H 2 such as 1,3-butadiene, 1,3,5-hexatriene, and so forth. The energy levels for such compounds are given by the expression... 

An excellent agreement with the X-ray photoionization spectra of ethylene, butadiene and hexatriene (7) is obtained (12) (Figure 3) when including in our calculations the Gelius (36) photoionization cross sections for an Alka photon beam, by means of Eqs. (4) and (5). Such a direct comparison is impossible for octatetraene, a compound for which there is no available XPS data. 

These compounds have been the subject of several theoretical [7,11,13,20)] and experimental[21] studies. Ward and Elliott [20] measured the dynamic y hyperpolarizability of butadiene and hexatriene in the vapour phase by means of the dc-SHG technique. Waite and Papadopoulos[7,ll] computed static y values, using a Mac Weeny type Coupled Hartree-Fock Perturbation Theory (CHFPT) in the CNDO approximation, and an extended basis set. Kurtz [15] evaluated by means of a finite perturbation technique at the MNDO level [17] and using the AMI [22] and PM3[23] parametrizations, the mean y values of a series of polyenes containing from 2 to 11 unit cells. At the ab initio level, Hurst et al. [13] and Chopra et al. [20] studied basis sets effects on and y. It appeared that diffuse orbitals must be included in the basis set in order to describe correctly the external part of the molecules which is the most sensitive to the electrical perturbation and to ensure the obtention of accurate values of the calculated properties. 

In a series of calculations on ethylene, butadiene and hexatriene, Deleuze and co-workers [105] showed that the ADC(3) method can provide a very accurate picture of the electronic processes associated with ionisation in the valence region. Poly(acetylene) has a large feature above 21 eV, which was previously assigned to shake up. The theoretical work showed conclusively that in fact even the band at around 17eV, which had previously been assigned to a C 2s excitation could not be explained by a single particle picture but was due to satellite excitations. 

Forster (1968) points out that R0 is independent of donor radiative lifetime it only depends on the quantum efficiency of its emission. Thus, transfer from the donor triplet state is not forbidden. The slow rate of transfer is partially offset by its long lifetime. The importance of Eq. (4.4) is that it allows calculation in terms of experimentally measured quantities. For a large class of donor-acceptor pairs in inert solvents, Forster reports Rg values in the range 50-100 A. On the other hand, for scintillators such as PPO (diphenyl-2,5-oxazole), pT (p-terphenyl), and DPH (diphenyl hexatriene) in the solvents benzene, toluene, and p-xylene, Voltz et al. (1966) have reported Rg values in the range 15-20 A. Whatever the value of R0 is, it is clear that a moderate red shift of the acceptor spectrum with respect to that of the donor is favorable for resonant energy transfer. 

TABLE 4. Selected geometrical parameters" (A) of all-trans-hexatriene computed at several levels of calculation ... 

Vibrational frequencies of hexatriene and octatetraene have been reported by several authors21,24-26,36. The increase in the size of these molecules with respect to butadiene limits the use of highly accurate levels of calculation, so that a good choice of scaling factors is necessary to obtain useful results. Kofraneck and coworkers21 have shown that employing scale factors determined from vibrational data for trans structures alone does not give a balanced description of cis and trans structures. 

Liu and Zhou29 have computed the quadratic force field of cis-hexatriene by a systematic scaling of ah initio force constants calculated at the planar C2V structure. Their results reproduce satisfactorily the observed spectral features of this molecule. 

Kofraneck and coworkers24 have used the geometries and harmonic force constants calculated for tram- and gauche-butadiene and for traws-hexatriene, using the ACPF (Average Coupled Pair Functional) method to include electron correlation, to compute scaled force fields and vibrational frequencies for trans-polyenes up to 18 carbon atoms and for the infinite chain. 

TABLE 2. Geometrical parameters for 1,3-butadiene (C4H6), 1,3,5-hexatriene (CcIIx), 1,3,5,7-octatetraene (CgHio) and 1,3,5,7,9-decapentaene (C10H12) from n-CAS-MCSCF calculations with 6-31G basis set17... 

The amount of high precision experimental structural data on conjugated polyenes is limited. Some structure results are presented in Table 5. In gas electron diffraction studies it is difficult to determine closely spaced bond distances accurately, because these parameters are highly correlated with the corresponding vibrational amplitudes. Today it is possible to calculate the vibrational amplitudes accurately, if the vibrational frequencies are known. This was, however, not the case when the GED studies presented in Table 5 were carried out. The observed differences between the terminal and central C=C bonds in the GED studies of traw.s-l,3,5-hexatriene and c/s-l,3,5-hexatricne are probably too large29. A very accurate X-ray study of traw.s-l,3,5-hexatriene has, however, been carried out also in connection with the preparation of this chapter4. Figure 4 shows the molecular structures of trans-1,3-butadiene and trans-l,3,5-hexatriene as found in the crystal lattice. 

TABLE 8. Observed and calculated vibrational frequencies (cm 1) of trans-X,3,5-hexatriene ... 

A, respectively. The infrared and Raman spectra of m-hexatriene84- 86,96 and its deuterated analogs87,88 have been reported. The structures and vibrational frequencies have been calculated by means of MO methods87,88,91,93,94. According to ab initio MO calculations91,93,94 (HF/6-31G, HF/6-31G and MP2/6-31G levels), cis-hexatriene has a planar structure. The observed vibrational spectra have been reasonably explained by the... 

Unstable conformers of trans- and cis-hexatriene have been detected by means of the combination of matrix-isolation infrared spectroscopy and photoexcitation (or the high-temperature nozzle technique)84. Ab initio MO calculations at the HF/6-31G level have been performed for several conformers of 1,3,5-hexatriene93. The observed infrared bands of unstable conformers have been attributed to the gTt (major species) and gTg (minor species) conformers of /raw.s -hexalricne and the gCt conformer of cw-hexatriene93. It is noted that, in the previous paper93, the notation c is used for twisted structures for the sake of simplicity. The calculated torsional angles around C—C bonds for the gTt, gTg and gCt conformers are in the range between 32° and 45°. The observed and calculated vibrational frequencies of gTt and gCt are reported in Reference 93. 

In a recent comprehensive study at the CASSCF level of ab initio theory, Cave and lohnson have carried out calculations for all six rotamers of the hexatriene radical cation. In agreement with experiment they found that the first excited state is hardly affected by the additional interactions which prevail in partially cA-configurated rotamers, whereas the energy of the second excited states decreases as the number of those cA-interactions increases. On this basis, they were able to confirm some of the original assignments of the observed spectra305 but proposed revisions for some of the others. 

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