Structure of PPVBased Systems
Based on molecular mechanics energy minimization in a vacuum, a single MEHPPV or CNPPV molecule containing tetrahedral defects has a lower total potential energy when folded into cofacialstacked chain segments (see Figure 14.5) than in an extended chain configuration: on the order of tens of kcal/mol determined from the MM3 model for the all transanticonfiguration. For MEHPPV, an all transsynconfiguration lies at ~3 kcal/mol higher in potential energy than the anti'configuration due to steric interactions of the side groups. For CNPPV, the synconfiguration is ~4 kcal/mol lower in potential energy mainly due to the strong intermolecular interactions of the CN groups. The synconfiguration is also lower in energy for PPV, ~2 kcal/mol relative to anti. Similar results can be found for various isomeric forms, ranging from having the vinyl linkages all cis to random amounts of cistrans. For molecules with shorter oligomer segments between tetrahedral defects, steric repulsion can become significant and folding is not energetically favorable for less than 4 monomers.
The intermolecular interactions in all of the PPVbased systems are strong enough to lead to efficient nucleation of multiple oligomer chains into aggregates with varying degrees of crystalline order. For a PPV system consisting of 7 chains with 8 monomers, based on molecular mechanics optimization using the MM3 model (converged to a root mean square gradient of 10~5), a herringbonetype packing arrangement is found with identifiable crystallographic parameters of a = 5.2, b = 8.0, c = 6.4 A, and a setting angle of 58°. This is in good agreement with experimental determination and with recent molecular mechanics simulations [60]. For a MEHPPV system of the same size, aggregate formation occurs but the packing does not conform to a herringbonetype arrangement but instead more to a cofacial staking of the oligomers with an average interchain separation of ~3.7 A. CNPPV behaves quite similar to MEHPPV except with a closer interchain separation of 3.4 A and a greater degree of helical twisting (the phenyl rings remain cofacial). This type of pstacking of the conjugated oligomers leads to increased chargecarrier mobility by generating large valence or conduction bandwidths proportional to the orbital overlap of adjacent oligomers. Quantum chemistry computations show increased transport properties and indicate decreased luminescence quenching for pstaked structures [61] as well as substantial selfsolvation effects that lead to greater enhancement of orbital overlap
(see below). A herringbone packing arrangement destroys the orbital overlap between oligomers (see discussion below on electronic spectra), and due to the two symmetry inequivalent oligomers in a unit cell, leads to a splitting of the bands (Davydov splitting), which subsequently can cause luminescent quenching. Thus, it is desirable to generate PPVbased systems with a pstacked arrangement [62]. The single molecule nanoparticles generated by our experimental procedure provide this unique capability by using a combination of threedimensional confinement and solventinduced morphologies in the absence of an interacting substrate.
We have also carried out extensive semiempirical quantum mechanics calculations to determine single molecule structures. For these calculations the initial geometry was taken from a MM3optimized structure. The results obtained from the AMI calculations (PM3 results were very similar) show larger interchain separation for both MEHPPV and CNPPV molecules with a fold (as much as 0.5 A). The optimized AMI structures for folded 14monomer MEHPPV and CNPPV molecules have larger torsional rotations about the bonds adjacent to the vinyl C=C, which tends to force the oligomer chains farther apart (see Figure 14.6).
On the other hand, for just PPV (no side groups), the structures for small oligomers (up to 4 monomers) and even multiple cofacial oligomers are reasonably similar to the MM3 results. However, as the number of monomers increase, deviations from planarity occur even for PPV. Again, the result is a significantly different structure than that obtained from classical MM3 molecular mechanics. Either the enhanced intermolecular interactions caused by the cofacial arrangements of the substituted PPV oligomer chains (dispersive van der Waals forces) cause considerable changes that are not accounted for in the MM3 model or the semiempirical AMI parameterization or model (perhaps inadequate electron correlation) is not appropriate for this type of conjugated system. As the MM3generated multioligomer aggregate structure is particularly accurate compared to experimental determinations for PPV, the source of the difference in structures would appear to be in the semiempirical models. In addition, the AMloptimized geometric structures for MEHPPV do not give electronic structure results for the vertical transitions that agree with experiment, whereas the vertical transitions computed based on the MM3optimized structures conform quite closely to experimental results. Full quantum calculations using wave function or DFT also give approximately planar structures with interchain distance on the order of 3.5 A for both PPV and MEHPPV (see below). As such, geometry
optimizations of multioligomer PPVbased systems using the semiempirical AM1 and PM3 models should be questioned. We recommend using the much faster, and apparently for this particular case, accurate, classical molecular mechanics minimization of the MM3 force field for the PPVbased systems. In addition, structural differences between semiempirical AM1, DFT, and HF calculations have also been previously observed for small oligomers of PPV [63].
One consistent structural observation obtained from the various optimizations using the MM3 and AM1 models is that when small oligomers of PPV with no substitution tend to form cofacialplanar geometries with a shift along the chain axis, MEHPPV and CNPPV tend to have some helical twisting of the PPV backbone (see Figure 14.7), with a larger angle for CNPPV. The phenyl rings in these structures are rotated about the backbone by about +6° for MEHPPV and +10° for CNPPV but maintain an approximate cofacial orientation with respect to the phenyl rings on the neighboring chain. Addition of a fold and larger oligomers causes the twist angle to decrease (depending on the oligomer length between the folds). For example, a twist is present in structures determined from MM3 calculations with folds and longer oligomer segments but not for those with less than 4 monomers. Quantum calculations based on SCFHF theory using a modest basis set (631G*) give a structure for MEHPPV consisting of 8 monomers and one tetrahedral defect that has an interchain separation of dIC = 3.53 A and has very little helical twisting. The intermolecular interactions of a multiple folded MEHPPV molecule will tend to decrease any backbone twisting as well as decrease the interchain separation. This influence, often referred to as selfsolvation, is discussed in more detail below.
The values for interchain separations are probably not as accurate as the general trend of decreasing interchain separation for CNPPV as compared to MEHPPV. The interchain distance reported from xray diffraction studies of MEHPPV thin films [64] is dIC = 3.56 A and is in good accord with our results from MM3 (discussed above) and full ab initio quantum calculations carried out for short oligomer chains of PPV (no side chains) as well as folded MEHPPV molecules at the MP2/321++G level of theory. For short bioligomer PPV systems, the synconformation is of lower energy than the anf¿conformation by ~0.96 kcal/mol (side chains change this result as noted earlier). An optimized structure for a 4monomer PPV systems has an interchain distance of dIC = 3.5 A and there is a shift of 0.98 A along the chain backbone axis and one of 0.7 A along the remaining axis. Addition of side groups to produce MEHPPV or CNPPV leads to geometries that do not show the shifts and dIC = 3.53 A for MEHPPV and dIC = 3.4 A for CNPPV. Whether the interchain distance and the shifts (for PPV) about the remaining axes depend on the number of monomers in the oligomer segments or to chain folds is clearly of interest. Unfortunately, the only way the shifts can be quantified is through full quantum calculations using manybody perturbation theory, which scales like N5. The largest system that we have been able to treat at this level of theory and get converged results is for 2 oligomers consisting of 4 monomers, which does maintain the shifts for PPV. Whereas we believe the shift gives a true structural
FIGURE 14.7 Structures of MEHPPV (left) and CNPPV (right) obtained from AMI semiempirical calculations. The systems consist of 24 monomer oligomers without a fold. The twist is more pronounced in these types of nonfolded oligomer systems.
FIGURE 14.7 Structures of MEHPPV (left) and CNPPV (right) obtained from AMI semiempirical calculations. The systems consist of 24 monomer oligomers without a fold. The twist is more pronounced in these types of nonfolded oligomer systems.
minimum, the values we obtain are significantly smaller than those typically used for stacked PPV molecules (generally half a unit cell length, ~3.3 A). As will be shown below, the degree of orbital overlap is strongly dependent on both the interchain distance and the shifts along the other axes and it is therefore important to obtain an accurate initial structure. The degree the shifts along the two axes change as the system is taken from the very small isolated cluster to the bulk can be examined reasonably effectively by using periodic DFTLDA (local density approximation) calculations. Here, we have carefully calibrated the particular implementation (plane wave normconserving pseudopotentials) of the DFTLDA method to the geometry of the MP2 study to ensure consistency. We emphasize the importance of doing this calibration as many geometry optimizations for short oligomers (from 3 to 4 monomers per oligomer) based on either DFT or SCFHF theory can generate optimal (lowest energy) geometries that are Tshaped. Inclusions of electron correlation and dispersion appear to be crucial in obtaining the cofacial geometries for a given basis set ranging from STO3G* to ccaugpVTZ. We mention this in passing only to point out some of the many problems with electronic structure geometry optimization when used in the black box context. Errors from the incompleteness of the basis sets and from electron correlation tend to cause significant variation in the optimized geometries and likewise for the vertical transitions. On the other hand, a planewave basis function representation is a complete one (there is no BSSE) and with careful selection of the representation of the core through pseudopotentials, these calculations are considerably quicker yet often provide very accurate results. From the periodic DFTLDA calculations of 4 monomer PPV oligomers, we find that interchain separation decreases somewhat but the shifts about the two other axes are not significantly altered. The decreased interchain distance going toward a more bulklike phase is assignable to a selfsolvation effect that we discuss in more detail below and the persistence of the shift about the other axes means these structural details should be noted in any excited state calculation for these types of stacked PPV oligomers.
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Klaudia Bauer3 years ago
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