Study of tetrathiafulvalene (TTF) dimers and trimers in eclipsed and slipped geometries

Self-consistent-field-$X\alpha$-scattered-wave molecular-orbital (MO) calculations have been performed on dimers of tetrathiafulvalene (TTF) in eclipsed ($D_{2h}$) and slipped ($C_{2h}$) geometries. In both cases the MO's of the dimer are formed to a good approximation simply by taking bonding and antibonding combinations of the MO's of the monomer. The interaction leads to a splitting of about 0.5 eV for the $D_{2h}$ dimer. Owing to the slipped geometry the corresponding splitting is only 0.12 eV for the $C_{2h}$ dimer. These splittings provide estimates of the "bandwidths" for infinite TTF stacks in the conducting salts TTF ${\mathrm{Br}}_{0.71-0.76}$ and TTF-TCNQ (tetracyanoquinodimethane), respectively. Extended Hückel (EH) calculations for the TTF molecule and both dimers are in good agreement with the $X\alpha$ results; the EH splittings being 0.67 and 0.15 eV for the $D_{2h}$ and $C_{2h}$ dimers, respectively. EH calculations on TTF trimers yield "bandwidths" of 0.99 and 0.20 eV for the eclipsed and slipped geometries, respectively, and also indicate that for qualitative considerations results obtained for the dimers are sufficient. It is suggested that eclipsed stacks of TTF molecules can be treated by normal band-structure techniques using the monomer MO's as fixed ($k$-independent) basis functions to generate Bloch functions. For the slipped geometry found in TTF-TCNQ, however, the small "bandwidth" found here and also in previous studies makes it doubtful whether band theory is appropriate.