Correlation effects in the magnetism of small aggregates and in polyenes

Abstract

First, we apply a Gutzwiller technique developed in other papers to the problem of the appearance of magnetism in small aggregates. We show that the intra-atomic correlation energy ${U}_{\mathrm{crit}}$, for which magnetism appears, varies with the number of atoms $N$ in the clusters considered ($N=55 \mathrm{and} 147$) and with the band filling $n (n=\frac{1}{4},\frac{5}{8}, \mathrm{and} \frac{1}{2})$. This behavior can be understood by the first-order (in $U$) Stoner criterion. However, our results are more precise and include higher orders of $U$; i.e., they include the rearrangements of electrons due to correlations. Second, we apply the technique to the study of the triplet-singlet separation in various six-atom polyenes. Our model reproduces the results of a precise calculation for almost all the shapes considered, except for the shapes where ${m}_{\ensuremath{\uparrow}}\ensuremath{\ne}{m}_{\ensuremath{\downarrow}}$. We also apply the model to the study of the ionization energy of relatively large polyenes (up to $N=34$ carbon atoms). Many features of the experimental results are reproduced.