Charge transfer and ionic bonding in organic solids with segregated stacks

In ionic charge-transfer salts which have segregated stacks of organic donor ($D$) and acceptor ($A$) molecules, the major feature of the classical electrostatic interactions is the strong repulsion between like charges along the stacks. Two ways are described by which the magnitude of this repulsion may be decreased: (i) by the formation of a complex salt (i.e., one whose ratio $D:A\ne 1:1$); and (ii) by incomplete transfer of charge from $D$ to $A$. In both cases, some of the molecules in the stack are neutral, giving rise to a mixed-valence, partly ionic ground state. The first effect is quantitatively investigated by a Madelung energy calculation of tetrathiafulvalene-${\mathrm{Br}}_{0.79}$ as a function of (theoretical) bromine concentration. The results of this calculation show that the unusual composition of this salt occurs in order to reduce the Coulomb repulsion along the stacks. As an example of the second effect, a similar calculation is described for TTF-TCNQ (tetrathiafulvalene-tetracyanoquinodimethane), as a function of the amount of charge transferred from TTF to TCNQ. Although electrostatic interactions do not give a complete description in this case, they are clearly an important factor in determining the degree of charge transfer in such salts. In fact, in cases where the net electrostatic binding energy is small, incomplete charge transfer may be energetically favored. In this case, the charge distribution is shown to be modulated along the stack and charge density waves are formed, with wave vector "$4k_F$". These results are compared to the case of Rb-TCNQ, where the Madelung energy is shown to favor complete charge transfer.