We extend the application
of our multilayer molecules-in-molecules
(MIM) fragmentation-based method to the study of open-shell systems,
particularly organic radicals. A test set of organic mono-, di- and
polyradicals with a wide range in size, containing up to 360 atoms,
was investigated. Total energies computed with MIM using density functional
theory (DFT) were compared with full, unfragmented energies to assess
the performance of MIM and to develop a systematic protocol for the
treatment of large radical systems. More specifically, a two-layer
(MIM2) model with a fragmentation scheme along the backbone involving
covalently bonded dimers, trimers, or tetramers was considered, with
DFT at a smaller basis set serving as the low level of theory. The
MIM method was evaluated on the high-spin state and several possible
broken-symmetry (BS) states for di- and polyradicals. When relevant
spin–spin interactions were considered, the errors in total
energies were less than 1 kcal mol–1. In addition,
the applicability of MIM2 was extended to predict the intersite magnetic
exchange coupling constants (J), which were compared
with reference values. Further, since the energy levels derived from
Hamiltonian diagonalization are physically more meaningful, the calculated J values estimated from the BS-DFT methodology were used
to obtain the lower spin state energies of the polyradicals. The difference
in calculated total energies of the lower spin state between full
and MIM2 lie within 1 kcal mol–1 in the majority
of these cases. Our rigorous, quantum chemical study demonstrates
that MIM can be successfully applied to the study of large organic
radicals reliably and accurately within the framework of BS-DFT.