Fermion excited states in one-dimensional molecular aggregates with site disorder: Nonlinear optical response

It is well known that Frenkel excitons are not true bosons or fermions. I show that the fundamental electronic excitations in a linear (noncyclic) one-dimensional molecular aggregate consisting of N coupled two-level absorbers with site disorder are in fact fermions, allowing one to calculate IallR of the $2^{\mathit{N}}$ excited-state eigenfunctions and eigenenergies with a single N×N matrix diagonalization. As an application, the third-order nonlinear absorption coefficient for a molecular aggregate with site disorder is calculated.