posted on 2019-10-23, 17:39authored byAlexandr Zaykov, Petr Felkel, Eric A. Buchanan, Milena Jovanovic, Remco W. A. Havenith, R. K. Kathir, Ria Broer, Zdeněk Havlas, Josef Michl
A procedure
is described for unbiased identification of all π-electron
chromophore pair geometry choices that locally maximize the rate of
conversion of a singlet exciton into a singlet biexciton (triplet
pair), using a simplified version of the diabatic frontier orbital
model of singlet fission (SF). The resulting approximate optimal geometries
provide insight and are expected to represent useful starting points
for searches by more advanced methods. The general procedure is illustrated
on a pair of ethylenes as the simplest model of a π-electron
system, but it is applicable to pairs of much larger molecules, with
dozens of non-hydrogen atoms, and not necessarily planar. We first
examine the value of |TA|2,
the square of the electronic matrix element for SF with initial excitation
fully localized on partner A, on a grid of several billion geometries
within the six-dimensional space of physically realizable possibilities.
Several of the optimized pair geometries are somewhat unexpected,
but all are found to follow the qualitative guidance proposed earlier.
In the neighborhood of each local maximum of |TA|2, consideration of mixing with charge-transfer
configurations and of excitonic interaction between partners A and
B determines the SF energy balance and yields squared matrix elements
|T*|2 and |T**|2 for the lower and upper excitonic
states S* and S**, respectively. Assuming Boltzmann populations of
these states, the geometry is further optimized to maximize k, the sum of the SF rates obtained from Marcus theory,
and this reorders the suitable geometries substantially. At 87 pair
geometries, the |T*|2 and |T**|2 values are compared with those obtained from high-level
ab initio nonorthogonal configuration interaction calculations and
found to follow the same trend. Finally, the biexciton binding energy
at the optimized geometries is calculated. Altogether, 13 significant
local maxima of SF rate for a pair of ethylenes are identified in
the physically relevant part of space that avoids molecular interpenetration
in the hard-sphere approximation. The three best geometries are twist-stacked,
slip-stacked, and L-shaped. The maxima occur at the (five-dimensional)
surfaces of seven six-dimensional “parent” regions of
space centered at physically inaccessible geometries at which the
calculated SF rate is very large but the two ethylenes interpenetrate.
The results are displayed in interactive graphics. The computer code
(“Simple”) written for these calculations is flexible
in that it permits a choice of performing the search for local maxima
in six dimensions on |TA|2,
|T*|2, or k. It is available
as freeware at https://cloud.uochb.cas.cz/simple.