Long-range corrected (range-separated hybrid) functionals represent a relatively new class of functionals for generalized Kohn-Sham theory that have proven to be very successful, for instance, when it comes to predicting ionization potentials and energy gaps for a wide range of molecules and solids. The results obtained from long-range corrected density functional theory approaches can be improved dramatically, if the range-separation parameter (ω) is optimized for each system separately. In this work, we have optimized ω for a series of π-conjugated molecular systems of increasing length by forcing the resulting functionals to obey the ionization potential-theorem, i.e., that their highest occupied eigenvalue be equal to the ΔSCF ionization potential. The optimized ω values are observed to vary substantially from their default values for the functionals. For highly conjugated chains such as oligoacenes and polyenes, we find that the characteristic length scale of the range-separation, i.e., 1/ω, grows almost linearly with the number of repeat units, for saturated alkane chains, however, 1/ω quickly saturates after 5-6 repeat units. For oligothiophenes, we find that 1/ω grows linearly for the shorter oligomers but then saturates at around 10 repeat units. Our results point to a close relation between the optimal range-separation parameter and the degree of conjugation in the system.
Noncovalent intermolecular interactions,
which can be tuned through
the toolbox of synthetic chemistry, determine not only the molecular
packing but also the resulting electronic, optical, and mechanical
properties of materials derived from π-conjugated molecules,
oligomers, and polymers. Here, we provide an overview of the theoretical
underpinnings of noncovalent intermolecular interactions and briefly
discuss the computational chemistry approaches used to understand
the magnitude of these interactions. These methodologies are then
exploited to illustrate how noncovalent intermolecular interactions
impact important electronic propertiessuch as the electronic
coupling between adjacent molecules, a key parameter for charge-carrier
transportthrough a comparison between the prototype organic
semiconductor pentacene with a series of N-substituted
heteropentacenes. Incorporating an understanding of these interactions
into the design of organic semiconductors can assist in developing
novel materials systems from this fascinating molecular class.
Correlations among the molecular
structure, crystal structure,
electronic structure, and charge-carrier transport phenomena have
been derived from six congeners (2–7) of rubrene (1). The congeners were synthesized via
a three-step route from known 6,11-dichloro-5,12-tetracenedione. After
crystallization, their packing structures were solved using single-crystal
X-ray diffraction. Rubrenes 5–7 maintain
the orthorhombic features of the parent rubrene (1) in
their solid-state packing structures. Control of the packing structure
in 5–7 provided the first series
of systematically manipulated rubrenes that preserve the π-stacking
motif of 1. Density functional theory calculations were
performed at the B3LYP/6-31G(d,p) level of theory to evaluate the
geometric and electronic structure of each derivative and reveal that
key properties of rubrene (1) have been maintained. Intermolecular
electronic couplings (transfer integrals) were calculated for each
derivative to determine the propensity for charge-carrier transport.
For rubrenes 5–7, evaluations of
the transfer integrals and periodic electronic structures suggest
these derivatives should exhibit transport characteristics equivalent
to, or in some cases improved on, those of the parent rubrene (1), as well as the potential for ambipolar behavior. Single-crystal
field-effect transistors were fabricated for 5–7, and these derivatives show ambipolar transport as predicted.
Although device architecture has yet to be fully optimized, maximum
hole (electron) mobilities of 1.54 (0.28) cm2 V–1 s–1 were measured for rubrene 5.
This work lays a foundation to improve our understanding of charge-carrier
transport phenomena in organic single-crystal semiconductors through
the correlation of designed molecular and crystallographic changes
to electronic and transport properties.
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