Laboratory for theoretical studies of electronic structure and spectroscopy of open-shell and electronically excited species.

## What we can learn from the norms of one-particle density matrices, and what we can't: Some results for interstate properties in model singlet fission systems
The utility of the norms of one-particle density matrices, ||gamma||,
for understanding the trends in electronic properties is discussed. Using several
model systems that are relevant in the context of singlet fission (butadiene,
octatetraene, ethylene dimer), the dependence of interstate properties
(such as transition
dipole moments and nonadiabatic couplings, NACs) on molecular geometries is
investigated. ||gamma|| contains all the information about
the changes in electronic states involved,
such as varying degree of one-electron character of the transition; thus,
it captures leading trends in one-electron interstate properties (i.e., when
||gamma|| is small, the respective interstate matrix elements are also small).
However, finer variations in properties that arise due to the dependence of
the matrix elements of the respective operators may not be reproduced.
Analysis of NACs in ethylene dimer
reveals that intermolecular components of NACs follow the
trends in ||gamma|| well, as they are
determined primarily by the characters of the two wave functions,
however, intramolecular components depend on the relative orientation of
the two moieties via the dependence in the derivative of the electron-nuclear
Coulomb operator. Therefore, intramolecular NACs may exhibit large variations
even when the changes in ||gamma|| are small.
We observe large NACs at perfectly stacked
geometry, however, larger values (by a factor of 1.6) are observed at
slip-stacked (along the long axis) geometries. Larger values of NACs at
slip-stacked configurations are due to the breaking of symmetry of the local
environment of the heavy atoms and not due to the wave function composition.
We found that the variations in ||gamma|| for ethylene dimer are due to a
varying admixture of the charge-resonance configurations in the S ## Related Research |