Knowledge Bank

Using a formalism appropriate for the electronic states and optical properties of disordered $systems1$, we have investigated the behavior of resonance pair (dimer) states at low concentrations in naphthalene isotopically mixed crystals. An exact calculation shows that quasi-resonance corrections ranging from $1cm-1$ to $4cm-1$ are necessary in order to extract interactions from the resonance pair data. As a matter of fact, due to the large interchange equivalent interaction term, $M12$, translationally equivalent dimers along the a and b axes could exhibit a splitting as large as $4cm-1$ even if the direct coupling terms ($Ma$, $Mb$) were exactly zero. We call this `exciton superexchange’. Using a trial and error method to fit data now $available2$, we have obtained three sets of parameters which agree with the density of states function of the neat crystal and with the dimer and monomer energies of mixed crystals. They are, corresponding to $Ma$, $Mb$, $Mc$, and $Ma+c$, $M12$ and $M121:(1)-0.6,-3.9,-3.7,6.1,18.0,2.0.(2)-1.2,1.6,-8.9,6.0,18.0,1.0.(3)-4.1,1.9,-6.1,6.0,18.0,1.0$, all in $cm-1$. ($M121$ is the next-nearest-neighbor interchange equivalent interaction). It was also found that the first set can be fitted with octupole parameters of $Q1e3=7$\AA$\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$, $Q3e3=72$\AA$\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$ provided $M12$ and $M121$ are excluded.