The fundamental steps are:

(1) Determining the PES of the stacked HAT6 molecules and extracting the corresponding equilibrium parameters in terms of co-facial separation (D) and twist angle (0) between the monomers,

(2) Calculating charge-transfer integrals (CTIs) by modelling a defined structural — disorder.

(3) Evaluating how these quantities vary with the imposed conformational fluctuations.

Three degrees of freedom can be modelled in practice at the ab initio level[4] to mimic structural fluctuations: the co-facial separation D, the twist angle 0, and the lateral slide or offset L. The three-dimensional PES highlights (Fig. 6.9) an energy minimum at 0 * 30° and D * 3.5 A, L being constrained to zero. This agrees well with previous work dedicated to similar systems with smaller aliphatic tails. Fol­lowing the estimation of the equilibrium parameters of stacked HAT6 molecules, the next step is to vary these parameters in order to mimic structural disorder, and to estimate how the HAT6-HAT6 interaction is affected. This is achieved by evaluating CTIs[5] which indicates the importance conformational fluctuations in the columnar phase. This is shown in Fig. 6.9 (middle left and right, and bottom). The dependence of the charge transfer J on the twist angle 0 between two stacked HAT6 molecules is evaluated at a fixed distance D =3.5 A, determined from PES calculations.[6] Due to the D3h point-group symmetry, the angular dependence of J is periodic.

When 0 A n f, there is a reduction in point-group symmetry from D3h to C3 and if 0 = n f then the symmetry is lowered from D3h to C3v. Increasing the twist angle from 0 to 60° results in a decrease of the interaction of individual HAT6 molecules. The dependence of the charge transfer J on the co-facial separation D between two stacked HAT6 molecules, with a fixed twist angle, 0 = 30°, is found to decreases exponentially. J increases rapidly with increase of the co-facial separation D until reaching the long-range interaction limit at higher D, which is the monomeric zero

Є

L — >

overlap limit. Therefore the charge-transport description, in terms of only the neighbouring electronic coupling, is adequate.

The third degree of freedom to be investigated is the lateral slide, or offset, L between the columnar stacked HAT6 molecules. Such a fluctuation can notice­ably perturb charge-transfer processes through symmetry breaking, and hence spatial overlap. The offset L is achieved by sliding one HAT6 molecule with respect to the other along a C2 axis. The complex nodal structure (nodes of the wave — function), which is perpendicular to the plane of the large HAT6 molecule, is well reflected through consecutive and damped oscillations of local maxima and minima, which correspond to a constructive/destructive character of the overlap between the individual HAT6 molecules. A higher offset results in a zero overlap, and hence zero charge-transfer. In the presence of dynamic and/or static structural fluctuations the mobility, and therefore the conductivity, should scale approximately quadrati — cally with the charge-transfer integral as has been reported for similar organic materials [19-21]. Thus, the above data can be used to quantitatively obtain charge — transport properties in triphenylene derivatives. It follows that this level of analysis can be extended to more realistic large-scale structural fluctuations, obtained from NPD measurements and MD simulations in the liquid crystalline phase.