Electronic Couplings for Charge Transfer across Molecule/Metal and Molecule/Semiconductor Interfaces: Performance of the Projector Operator-Based Diabatization Approach

One
principal parameter determining charge transfer rates between
molecules and metals is the electronic coupling strength between the
discrete electronic states of the molecule and the band states of
the metal. Their calculation with computational chemistry methods
remains challenging, both conceptually and in practice. Here, we report
the implementation of the projection-operator diabatization (POD)
approach of Kondov et al. (J. Phys. Chem. C 2007, 111, 11970–11981) in the CP2K program package,
which extends the range of applications to charge transfer at infinite
periodic surfaces. In the POD approach the self-consistent Kohn–Sham
Hamiltonian of the full system is partitioned in donor (e.g., molecule)
and acceptor (e.g., metal) blocks which are block-diagonalized. The
coupling matrix elements between donor and acceptor states are simply
identified with the matrix elements of the off-diagonal block. We
find that the POD method performs similarly well as constrained DFT
(CDFT) on the HAB11 database for excess hole transfer between simple
organic dimers, with a mean relative unsigned error of 9.3 %, compared
to 5.3 % in CDFT. By studying two case examples, electron injection
from a dye molecule to TiO2 and electron transfer from
a molecule, that forms self-assembled monolayers, to metallic Au(111),
we demonstrate that the POD method is a useful and cost-effective
tool for estimation of electronic coupling across heterogeneous interfaces.