Supplementary Information
Electronic couplings for molecular charge transfer:
benchmarking CDFT, FODFT and FODFTB against high-level ab
initio calculations
Adam Kubas,1 Felix Hoffmann,1,2 Alexander Heck,3 Harald Oberhofer,4 Marcus Elstner,3
Jochen Blumberger1*
1
University College London, Department of Physics and Astronomy, Gower Street, London
WC1E 6BT, United Kingdom
2
Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, Universitätsstr. 150, 44801
Bochum, Germany
3
Institute of Physical Chemistry, Karlsruhe Institute of Technology, Fritz-Haber-Weg 6,
76131 Karlsruhe, Germany
4
Department of Chemistry, Technical University of Munich, Lichtenbergstr. 4, 85747
Garching, Germany
*Corresponding author
j.blumberger@ucl.ac.uk
1
See next page for continuation…
2
Continued
Figure S1. Comparison of spin densities obtained in reference calculations (MRCI+Q for
ethylene, acetylene, cyclopropene, cyclobutadiene, cyclopentadiene, furane, pyrrole; CASSCF
for thiophene, imidazole, phenol, benzene; UHF for naphthalene, anthracene, tetracene and
pentacene) with superimposed spin densities of donor and acceptor from CDFT calculations
with pure PBE functional.
3
The value of integrated spin density as a diagnostic tool in CDFT calculations
In contrast to spin-unpolarized DFT calculations, where pairs of electrons with unlike spin
share the same spatial orbital, our CDFT calculations employ a spin-polarized scheme. As a
consequence, spin orbitals in the α and β-manifold are allowed to differ spatially. However, in
the present case one would expect only very slight spatial differences for all, but the HOMOs
in the β and the LUMOs in α-manifold. Accordingly, the total absolute integrated value of
spin density (IVSD) is expected to be 1. For some of the investigated systems this is not the
case and IVSDs much larger than 1 are observed. This behaviour is usually referred to as
symmetry breaking, which becomes, in the present case, the more pronounced the larger the
admixture of HF exchange is in the exchange-correlation functional. Since this effect is
supposed to lead to deviating interactions between donor and acceptor fragments than in the
symmetric case, we report in addition to absolute Hab-values IVSDs in Table S1. We observed
particular high IVSDs for the cyclobutadiene dimer. This value was with 1.7 already high for
CDFT/0 and increased up to 3.6 for CDFT/100. This trend is in line with the behaviour of
hybrid functionals familiar in conventional DFT. Due to Fermi correlation, exact HartreeFock exchange tends to favour high-spin states, whereas GGA functionals prefer low spin
configurations. One characteristic of the present problem is a sudden flip of IVSDs and
therefore of electronic states during the diabat optimizations. Figure S2 illustrates this flipping
schematically based on involved orbitals for the α and β-manifold. The optimization starts
with an electronic configuration, where all occupied orbitals feature the same spatial part.
Consequently, the IVSD of this state is 1. At some point, the external potential due to the
charge constraint induces one occupied orbital (red bar in Figure S2) to raise in energy such
that it becomes part of the virtual manifold. On the other hand, an unoccupied orbital
decreases in energy (red occupied energy level), whereas at the same time, the energy of those
orbitals highlighted in blue will be decreased. Interestingly, absolute Hab-values and decay
constants seem not to suffer severely from this effect.
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Table S1. Total integrated absolute values of spin densities for the investigated dimers at an
intermolecular distance of 5 Å. Values for other distances are found to be very similar.
Dimer
Ethylene
Acetylene
Cyclopropene
Cyclobutadiene
Cyclopentadiene
Furane
Pyrrole
Thiophene
Imidazole
Phenol
Benzene
Naphthalene
Anthracene
Tetracene
Pentacene
0
1.10
1.08
1.10
1.74
1.15
1.19
1.21
1.23
1.24
1.19
1.13
1.24
1.28
1.33
1.38
25
1.10
1.08
1.11
2.40
1.17
1.21
1.25
1.26
1.30
1.31
1.17
-
CDFT/PBE % HFX
50
60
1.10
1.10
1.09
1.09
1.14
1.15
2.98
3.11
1.23
1.25
1.25
1.27
1.30
1.32
1.31
1.33
1.39
1.43
1.50
1.59
1.59
1.64
1.47
1.63
1.80
1.97
-
75
1.11
1.09
1.16
3.33
1.29
1.29
1.35
1.36
1.49
1.75
1.73
-
100
1.11
1.09
1.19
3.60
1.36
1.33
1.40
1.41
1.58
2.64
1.59
-
Figure S2. Flipping of electronic states during the optimization of diabatic states for the
cyclobutadiene hole transfer. The optimization starts in an electronic configuration, where all
but the highest occupied β-orbital feature the same spatial orbitals. During the optimization
procedure the constraint potential causes one level of the occupied α-manifold (red bar at
HOMO-4) to rise in energy, so that it becomes unoccupied. Conversely, an orbital from the
virtual manifold is lowered in energy and occupied (highlighted in red).
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