Exploring organic semiconductors in solution: The effects of solvation, alkylization, and doping

Abstract

The first-principles simulation of the electronic structure of organic semiconductors in solution poses a number of challenges that are not trivial to address simultaneously. In this work, we investigate the effects and the mutual interplay of alkylization, solvation, and doping on the structural, electronic, and optical properties of sexithiophene, a representative organic semiconductor molecule. To this end, we employ (time-dependent) density functional theory in conjunction with the polarizable-continuum model. We find that the torsion between adjacent monomer units plays a key role, as it strongly influences the electronic structure of the molecule, including energy gap, ionization potential, and band widths. Alkylization promotes delocalization of the molecular orbitals up to the first methyl unit, regardless of the chain length, leading to an overall shift of the energy levels. The altered electronic structure is reflected in the optical absorption, which is additionally affected by dynamical solute-solvent interactions. Taking all these effects into account, solvents decrease the optical gap by an amount that depends on its polarity, and concomitantly increase the oscillator strength of the first excitation. The interaction with a dopant molecule promotes planarization. In such scenario, solvation and alkylization enhance charge transfer both in the ground state and in the excited state.

Full text

Exploring organic semiconductors in solution: The effects of solvation, alkylization,
and doping
Jannis Krumland
Humboldt-Universit¨at zu Berlin, Physics Department and IRIS Adlershof, 12489 Berlin, Germany and
Helmholtz-Zentrum Berlin, 12489, Berlin, Germany
Ana M. Valencia and Caterina Cocchi
Humboldt-Universit¨at zu Berlin, Physics Department and IRIS Adlershof, 12489 Berlin, Germany and
Carl von Ossietzky Universit¨at Oldenburg, Institute of Physics, 26129 Oldenburg, Germany
(Dated: March 8, 2021)
The first-principles simulation of the electronic structure of organic semiconductors in solution
poses a number of challenges that are not trivial to address simultaneously. In this work, we
investigate the effects and the mutual interplay of solvation, alkylization, and doping on the struc-
tural, electronic, and optical properties of sexithiophene, a representative organic semiconductor
molecule. To this end, we employ (time-dependent) density functional theory in conjunction with
the polarizable-continuum model. We find that the torsion between adjacent monomer units plays a
key role, as it strongly influences the electronic structure of the molecule, including energy gap, ion-
ization potential, and band widths. Alkylization promotes delocalization of the molecular orbitals
up to the first methyl unit, regardless of the chain length, leading to an overall shift of the energy
levels. The alterations in the electronic structure are reflected in the optical absorption, which is
additionally affected by dynamical solute-solvent interactions. Taking all these effects into account,
solvents decrease the optical gap by an amount that depends on its polarity, and concomitantly
increase the oscillator strength of the first excitation. The interaction with a dopant molecule pro-
motes planarization. In such scenario, solvation and alkylization enhance charge transfer both in
the ground state and in the excited state.
I. INTRODUCTION
Organic semiconductors are key components of ad-
vanced materials due to their efficiency in absorbing and
emitting light [1, 2]. Their chemical versatility can be
exploited to enhance these characteristics and, more gen-
erally, their physico-chemical properties, including their
solubility and their ability to be doped, that can further
tailor their functionalities [3–7]. Such great variability
brings about a formidable structural and electronic com-
plexity that is non-trivial to control experimentally nor to
model theoretically. This is a challenging task especially
for ab initio quantum-mechanical simulations, where the
chemical composition and the initial geometry of the sys-
tem are the only input. In spite of the proven success of
first-principles methods in unraveling the electronic and
optical properties of a variety of organic compounds or
composite systems thereof [8–20], the simplified models
that are often adopted hinder the possibility to achieve a
comprehensive picture, in which all (or at least most of)
the involved degrees of freedom are taken into account.
For example, assuming hydrogenated oligomers in vacuo
to describe polymers in solution not only fails to include
solvation effects but also neglects the role of alkyl chains
that enhance the solubility of extended segments [21–
23]. Moreover, ab initio electronic structure calculations
usually rely on force minimization procedures to obtain
relaxed geometries which are ranked solely based on their
energetics [24]. In this way, it is not uncommon to find
local minima that are energetically very close to each
other and that can be alternatively accessed depending
on the initial conditions. For example, it is known that
adjacent monomers in oligo- and polythiophenes can oc-
cur in an aligned (cis) or an opposing orientation (trans),
representing two local minima. [25, 26] However, ordered
thiophenes are usually associated with the trans vari-
ant, [27, 28] which is energetically more favorable. [29]
Further complexity is added by doping, which is rou-
tinely exploited in organic semiconductors to improve
their electronic performance [28, 30–36]. The interaction
with dopant species leads to supramolecular compounds
with unique characteristics that are determined by the
hybridization between the donor and the acceptor and by
the charge transfer between them [33, 35, 37–41]. Also in
this scenario, ab initio simulations in vacuo have success-
fully led to the understanding of the basic mechanisms
driving the electronic and optical activity of these com-
plexes [13, 18, 19, 39, 40, 42]. However, open questions
concerning the role of solvents and functional chains have
not found an answer yet.
In this paper, we present a systematic analysis of
the effects of solvation, functionalization, and doping of
organic semiconductors in solution, carried out within
the quantum-mechanical ab initio framework of time-
dependent density-functional theory. We examine how
these parameters and their interplay influence structural,
electronic, and optical properties and, in turn, how these
characteristics affect each other. For this purpose, we
consider a sexithiophene oligomer in the trans conforma-
tion, a representative organic semiconductor, and inves-
tigate how the presence of alkyl chains, the interaction
with solvents of increasing polarity, as well as p-doping
arXiv:2103.03581v1 [cond-mat.mtrl-sci] 5 Mar 2021

2
perturbs its intrinsic properties. We discuss which initial
conditions have to be fulfilled to capture these effects
in the adopted theoretical scheme, and which degrees of
freedom influence the accuracy of the results.
II. THEORETICAL BACKGROUND AND
COMPUTATIONAL DETAILS
The electronic properties of the molecules investi-
gated in this work are determined using density func-
tional theory[43] (DFT) within the generalized Kohn-
Sham (KS) framework[44, 45]. In this formalism, the
nonlinear single-particle KS equation,
ˆ
HKS[ρ]ψ=Eψ, (1)
where the electron density is defined as
ρ=
occ
X
k
|ψk|2,(2)
is solved iteratively until self-consistency is achieved,
yielding the KS orbitals, ψk, and the corresponding KS
eigenvalues Ek. In atomic units, the electronic KS Hamil-
tonian is given by
ˆ
HKS[ρ](r) = −∇2
2+vnuc(r) + vR[ρ](r) + vH[ρ](r) + vxc [ρ](r),
(3)
where vnuc is the electrostatic potential due to the nuclei,
vRis the reaction potential caused by surrounding solvent
molecules (see below), vHis the Hartree potential, i.e.
the electrostatic potential created by the electron density
ρ, and vxc comprises the residual quantum-mechanical as-
pects of the electron-electron interactions. The last term
must be approximated, as its exact form is unknown.
In the original Kohn-Sham theory, an explicitly density-
dependent local potential is assumed [44]. Thanks to
its excellent trade-off between computational efficiency
and overall accuracy, this recipe was widely adopted for
decades. However, for almost thirty years, it has proven
of value, especially in the context of (doped) organic ma-
terials, to give up on this restriction of locality and to
mix in a portion of exact exchange, calculated from the
Hartree-Fock theory [46]. For these hybrid functionals,
vxc is no longer a universal local potential, but instead a
non-local operator, depending on the density ρas well as
on the set of (occupied) orbitals {ψk}[47]. For organic
materials, hybrid functionals usually yield more accurate
electronic and optical properties in comparison to their
(semi)local counterparts [48, 49]. Going one step further,
great popularity has been gained in the last decade by
range-separated hybrid functionals [50, 51], in which the
Coulomb interaction entering the exact-exchange energy
is separated into short- and long-range parts[52]:
1
r=α+βerf(µr)
r+1−[α+βerf(µr)]
r,(4)
where α,β, and µare adjustable parameters. In this
way, the exact-exchange energy becomes the sum of two
terms, the first of which, dominant in the short range, is
replaced by an approximate DFT functional. In contrast
to their semilocal and global hybrid counterparts, these
functionals are able to correctly describe excited states
involving significant charge transfer [53, 54].
To account for solvation effects, we employ the
integral-equation formalism [55] of the polarizable contin-
uum model [56]. In this framework, the solvent is mod-
elled as a bulk dielectric enclosing the solute molecule.
The solvent is characterized by its dielectric constant .
The charge densities associated with the electrons and
nuclei of the molecule polarize the continuum solvent,
creating interfacial polarization charges that generate the
reaction potential vR[ρ](r) acting back onto the molecule.
The quantum-mechanical equations for the molecule are
solved self-consistently in combination with the electro-
static ones for the environment. The adopted approach
neglects dispersion and chemical interactions between so-
lute and solvent, which can become significant in some
cases. To capture these effects, more sophisticated mod-
elling would be in order, entailing increased computa-
tional complexity. However, for the scope of this work,
which is determining polarity-dependent trends, it is suf-
ficient to account for electrostatic interactions only.
Optical absorption spectra are calculated within
linear-response time-dependent DFT (TDDFT) [57],
which implies solving the matrix equation
A B
B∗A∗X
Y=ω1 0
0 -1X
Y(5)
for the excitation energies ωkand (de-)excitation coef-
ficients Xk(Yk). For hybrid functionals, the coupling
matrices Aand Bare suitable interpolations[58] between
those from TDDFT and time-dependent Hartree-Fock
theory [59].
For time-dependent calculations including a solvent, a
term corresponding to vRis added to the matrix elements
of Aand B, accounting for the solvent polarization due to
the excited non-stationary electron density[60, 61]. These
excitation dynamics are so fast that the solvent molecules
cannot adapt to it by reorienting themselves, and thus
they are merely polarized. This effect is taken into ac-
count in non-equilibrium solvation models, in which the
solvent is characterized not only by its static dielectric
constant , but also its high-frequency limit, ∞. The
latter is connected to the usual refractive index nvia
the well-known relation ∞=n2. The static value 
corresponds to full solvent equilibration to the solute
state, whereas ∞, describes the mere electronic po-
larization. Hence, ground-state calculations assume a
surrounding continuum environment with dielectric con-
stant , whereas the time-dependent excitation-induced
charge density interacts with an effective solvent of di-
electric constant ∞.
In addition to linear-response TDDFT for solvated sys-
tems, we make use of the complementary state-specific

3
approach[62]. In this framework, the stationary excited-
state electron density and the corresponding solvent
polarization are determined self-consistently. This ap-
proach is different from the linear-response method de-
scribed above, in which absorption spectra are the main
output. Within the state-specific approach, excitation
energies are obtained as ω=Gneq
e−Gg, where Ggand Gneq
e
are the ground-state and the non-equilibrium excited-
state free energies resulting from a ground-state and a
state-specific-TDDFT calculation respectively. In the
latter, only the fast degrees of freedom of the solvent
are allowed to adapt to the variation of electron density
(non-equilibrium solvation). We will explore the comple-
mentary nature of the linear-response and state-specific
approaches by applying them to different types of exci-
tations.
We make use of the natural population analysis [63],
which has been devised to correct the major deficien-
cies of the well-known Mulliken charge analysis [64].
In the spirit of other “natural orbital” methods (e.g.,
natural transition orbitals in the context of optical
excitations[65]), the idea behind the natural population
analysis is the construction of minimal sets of atomic or-
bitals harboring the majority of the molecular electronic
density around those atoms.
All calculations are performed using the Gaussian16
package[66]. The CAM-B3LYP range-separated hybrid
functional [52, 67, 68] is employed in conjunction with
the double-ζcc-pVDZ and the triple-ζcc-pVTZ ba-
sis sets [69, 70]. We employ the polarized double-zeta
(double-ζ) basis set, cc-pVDZ, for geometry optimiza-
tions and TDDFT calculations. For electronic properties
such as orbital energies and partial charges, we use the
triple-ζpendant, cc-pVTZ. This choice enables quanti-
tative comparisons to previous results obtained for re-
lated materials [18, 19, 27]. We checked that cc-pVDZ
gives almost identical results to the 6-31G(d,p) basis
set [71] in TDDFT calculations. For the excited-state
calculations, we also considered the effect of adding dif-
fuse functions, using the 6-31+G(d,p) and 6-31++G(d,p)
basis sets, finding only minor improvements in accu-
racy (see Section III B 2 and S4.5 in the Supplementary
Material). Similar to the ground-state case, also the
self-consistent excited-state density obtained from state-
specific TDDFT can be used to analyze partial charges.
Although this excited-state analysis is not as commonly
employed as in the ground state, it contributes to under-
stand the character of the excitations. For a quantitative
comparison with the partial charges computed from the
ground-state density, we use the triple-ζbasis set also for
the corresponding state-specific TDDFT calculations.
Long-range dispersion interactions are included in the
geometry optimizations through Grimme’s empirical cor-
rection scheme with the original D3 damping func-
tion. [72] Having checked that these contributions play
no role in the TDDFT results, we did not include them in
those calculations. As implicit solvents, we consider ben-
zene (= 2.27, n= 1.50), chloroform (= 4.71, n= 1.45),
and nitromethane (= 36.5, n= 1.38), representing ap-
olar, semipolar, and polar solvents, respectively. We em-
phasize once more that the purely electrostatic treatment
of the PCM is not necessarily adequate for these partic-
ular solvents; [73] they are chosen solely based on the
values of their dielectric constants.
III. RESULTS
A. Structural and Electronic Properties
1. In Vacuo
We examine sexithiophene (6T) as a representa-
tive organic semiconductor, which is often adopted
to model extended polymeric poly(3-hexylthiophene)
(P3HT) chains [74–77]. Like all oligothiophenes, this
molecule is polymorphic both in the gas phase [78] and in
its crystalline form [15, 79–82]. Here, we consider 6T in
the trans conformation, in which the S atoms in consecu-
tive thiophene units (T) point to opposite directions [see
Figure 1a)]. This conformation represents the global en-
ergetic minimum, [25, 26] and is most commonly studied
also in the context of extended thiophene polymers [27–
29] due to its enhanced order compared to the cis con-
former.
It is known that 6T is not planar, neither in vacuo
nor in solution. Neighboring T units are twisted with re-
spect to each other, striking a balance between the pla-
narizing π-conjugation and the steric S· · · H repulsion,
which is partially relieved by torsion of the rings[25].
The torsion equips trans 6T with a large number of sub-
conformations. We find that adopting a planar geom-
etry as a starting point for the structure optimization
of 6T typically leads to an unstable planar conforma-
tion or to an irregular structure, in which the individual
rings are bent up- or downwards without a pattern. The
planar arrangement of two neighboring T units corre-
sponds to a saddle point of the torsional potential en-
ergy curve [25, 26, 83]; numerical noise tips the scales in
either direction at some point of the calculation, giving
rise to a random sign sequence of the torsion angles across
the overarching structure. This scenario is common when
the geometry optimization starts from a planar structure,
but ends in a non-planar one.
To remove this arbitrariness and avoid unrealistic ge-
ometries corresponding to unstable saddle points, calcu-
lations can be nudged towards a more regular structure
by assigning small starting torsion angles. This way, we
obtain two geometries, which can be considered as oppo-
site poles comprising all the intermediate irregular con-
figurations in between. In one extreme, the torsion angle
alternates from +θto -θfrom one T-T link to the next.
This gives rise to the structure sketched in Figure 1b),
characterized by an arc-shaped backbone. In the other
extreme, the torsion angle between subsequent T units
maintains a fixed sign, resulting in the helical structure

4
e)
y
x
a)
T1
T2
T3
T4
T5
T6
ϑ
1
2
33’
2’
b) arcb) arc
c) helix
d) locally planar
FIG. 1. a) Ball-and-stick representation of 6T, with the tor-
sion angle θand the alkyl chain docking sites indicated. In the
first ring (T1), the intra-monomeric numbering of the atoms is
shown. b-d) Schematic representation of polythiophene seg-
ments corresponding to different 6T conformations. Yellow
circles mark the positions of the S atoms. e) Equilibrium ge-
ometry of the propylated 6T/F4-TCNQ charge-transfer com-
plex.
shown in Figure 1c). The total energy difference between
the two conformations is almost negligible, amounting to
about 10 meV. The analysis of their vibrational frequen-
cies, which are all positive, confirms that they correspond
to energetic minima. In all cases, the average torsion an-
gle is about 20◦. The angles are slightly larger for the
b)
53.0°
13.8° 14.8°
5.6° 33.3°
a)
23.1°
21.0°
21.0°
21.0°
23.1°
FIG. 2. Isosurfaces of the HOMO of 6T in vacuo, a) in the
arc configuration without alkyl chains, and b) in the geom-
etry extracted from the CT complex (locally planar ), with
C3H7groups attached. The torsion angles between adjacent
T rings are specified. The isovalue for the orbitals is fixed at
±0.016 bohr−3/2.
outer rings, T1and T6[Figure 2a)], indicating that twists
are especially favorable at the edge. In the following, we
will consider these two limiting configurations in parallel,
in order to achieve a confidence interval that encompasses
all intermediate structures.
Before proceeding along these lines, we briefly discuss
the choice of the exchange-correlation functional in the
structural optimization. While semi-local generalized-
gradient approximations such as PBE [84] are very ef-
ficient for obtaining reasonable equilibrium geometries,
they are unsuitable for the considered systems, as they
generally predict a flat structure for 6T. This failure is
partially cured by employing a global hybrid functional
like B3LYP[46]. However, comparisons with higher-level
quantum-chemical methods, such as Møller-Plesset per-
turbation theory [85] and coupled cluster [86], reveal
that global hybrid functionals still overstabilize the pla-
nar configuration and overestimate the torsional bar-
rier [87, 88]. On the other hand, range-separated hybrids
like CAM-B3LYP [52], while mainly devised to improve
the description of charge-transfer excitations [53], appear
to perform better also for the structural properties of π-
conjugated oligomers[89–91].
In order to increase their solubility, oligo- and poly-
thiophenes are usually functionalized with alkyl side
chains [21–23, 27]. These groups exert an influence on
the structural and electronic properties of the backbone,
which we explore in the following. The arc and helix con-
figurations of 6T remain energetically equivalent upon re-
placing the H atoms highlighted in Figure 1a) by methyl

5
TABLE I. Torsion angle (in ◦) between T3and T4for 6T in
the arc,helix, and locally planar configurations a) in vacuo
with different groups attached and b) In different solvents
with CH3groups attached
a)
group arc helix planar
none 21.0 17.5 10.3
CH328.6 26.9 8.2
C2H530.0 28.4 7.6
C3H730.7 28.9 5.6
b)
solvent arc helix planar
none 28.6 26.9 8.2
C6H625.6 21.8 6.5
CHCl323.7 19.9 5.8
CH3NO220.8 12.8 5.0
(CH3), ethyl (C2H5), or propyl (C3H7) groups. Their ad-
dition leads to an increase of the torsion angle θ[Table
Ia)] due to the steric repulsion between the attached C
atom of the alkyl chain and the close-by S atom[92–94],
which is stronger than the S· · · H steric interaction, as
a consequence of the higher van-der-Waals radius of C
compared to the one of H. Since the innermost C atom
of the chain is the crucial one in this context, replacing
the H atoms by CH3groups causes an increase of 8-9◦in
the torsional angle, while extending the chains to C2H5
and C3H7only causes slight further changes (1-2◦).
The alkyl groups affect the electronic properties of the
6T in two different ways [Fig. 3a)]. The first one is
related to the aforementioned variability of the torsion
angles. These angles are key degrees of freedom, as they
can be manipulated at very small energetic costs and con-
comitantly exert great influence on the electronic struc-
ture of the molecule [95], which is a general feature of flex-
ible organic semiconductors [75]. The highest occupied
molecular orbital (HOMO) of 6T is the fully antibonding
superposition of the six HOMOs of the individual T rings.
The corresponding fully bonding superposition is not the
HOMO-5, as one might expect, but the HOMO-11, as
the HOMO-1 of the T units form an intermediate disper-
sionless band [96] (see Section S1 in the Supplementary
Material for detailed information about the frontier en-
ergy levels). The splitting between the KS energies of
the HOMO and the HOMO-11 (EHOMO −EHOMO-11),
which can be seen as the finite equivalent of the valence
bandwidth, gives an estimate of the electronic coupling
between the rings [97]. From the results shown in Fig-
ure 3b), it is evident that this quantity decreases dramat-
ically in the presence of covalently bonded alkyl groups
to the arc and helix 6T. This energy variation is par-
ticularly pronounced between H-terminated 6T and its
CH3-functionalized counterpart. Prolonging the chains
to C2H5and C3H7induces only slighter decrements, mir-
roring the trend of the torsion angles [Table Ia)]. The
correlation between these two parameters indicates that
increasing torsion is indeed responsible for the change
of the valence electronic structure. Additional influ-
ence of the alkyl chains is evident upon inspection of
the ionization potential (IP). This quantity, estimated
as −EHOMO, according to the Koopmans’ theorem for
DFT [98], decreases when alkyl groups are attached to
the 6T [Figure 3c)] [99]. This effect cannot be under-
stood in terms of the torsion-induced decoupling of the
T units, which conversely implies a decrease of EHOMO,
i.e., an increase of the IP: since the HOMO of 6T is the
fully antibonding linear combination of the HOMOs of
the T units, its energy is lowered when the coupling is
reduced. The reduction of the IP upon alkyl function-
alization is instead related to the partial delocalization
of the frontier orbitals, which extend into the covalently
bonded groups. However, as shown in Figure 2b) for the
HOMO, this spill-out charge does not extend beyond the
first unit of the alkyl chain.
The relation between torsion angle and low-lying vir-
tual orbitals is essentially reversed with respect to the
scenario delineated above for the occupied states. De-
creasing the coupling between the rings by increasing
the torsion raises the energy of the lowest unoccupied
moleular orbital (LUMO), as it corresponds to the fully
bonding superposition of the LUMOs of the T units[96].
This increase adds up to the influence of the alkyl chains,
which increase the energy of all levels (occupied and vir-
tual), resulting in a significantly expanded electronic gap
∆Eelec =ELUMO −EHOMO [Figure 3d)]. Arc and he-
lix configurations differ significantly with respect to each
other in terms of ∆Eelec, due to differences between their
respective torsion angles, which, while small, entail size-
able variations of the electronic levels. Since the main
change in torsion is observed upon replacing H by CH3,
and since the frontier orbitals do no extend further than
on the first unit of the chains, the effect of covalently at-
tached alkyl groups on the electronic structure of 6T is
essentially captured by the addition of CH3groups (see
also Section S1 of the Supplementary Material).
2. In solution
For the analysis of the structural properties of 6T in
solution, we focus only on CH3-functionalized 6T. We
choose this variant over the H-terminated one, since sol-
vated P3HT is usually alkylized. We examine three
scenarios corresponding to three solvents with increas-
ing polarity: benzene (C6H6), which is an apolar sol-
vent, chloroform (CHCl3), which can be considered a
semipolar solvent, and the strongly polar nitromethane
(CH3NO2). Assuming purely electrostatic coupling, ap-
olar solvents interact with the solute through (local)
dipole· · · induced dipole interactions, whereas polar ones
couple by stronger dipole· · · dipole forces. Computation-
ally, they are treated on equal footing.
The presence of a solvent reverses the increase of tor-

6
a)
orbital energies
anti-bonding
bonding
anti-bonding
bonding
FIG. 3. a) Schematic representation of the indirect torsion-
related and direct effects of alkyl chains on the valence and
conduction bands of 6T. b) HOMO (H) splitting (EHOMO −
EHOMO-11), c) ionization potential −EHOMO, and d) energy
gap, ∆Eelec, computed as ELUMO −EHOMO , of 6T in the arc,
helix and locally planar configurations, with different alkyl
chains.
sion angles upon alkyl functionalization [Table Ib)]. Tor-
sion angles decrease monotonically with the polarity of
the solvent; the smallest angles are thus found in 6T in
CH3NO2, the polar solvent. Sizeable differences in this
reduction exist between arc and helix conformations: In
the former, the torsion is reduced by approximately 30%,
while in the latter by about 50%, when comparing the
corresponding values in vacuo and in CH3NO2. The an-
gle of 12.8◦assumed by helix -6T in the polar solvent
corresponds to an almost planar structure. We conjec-
ture that the underlying cause for the planarization is the
direct electrostatic solute-solvent interaction. While the
solvent also causes a redistribution of electronic charge
within the solute that potentially gives rise to planariz-
ing forces on the nuclei, we find this redistribution to
be so small that this effect is likely negligible. This is
supported by the fact that the bond lengths along the
conjugation path remain essentially unaffected by solva-
tion, indicating that the electronic structure of the con-
jugated network is not perturbed by the solvent[74]. The
S atom and the alkyl chain exchange a very small frac-
tion of charge upon solvation (∼0.01 e), and the local
dipole moments of neighboring T units remain so small
that inter-ring dipole-dipole forces are weak and likely
negligible here.
It is tempting to analyze the electronic structure of the
solvated molecule in terms of KS eigenvalues, as we did
for the systems in vacuo. However, this type of analysis
is based on the assumption that the KS energies repre-
sent reasonable estimates for IPs and electron affinities,
i.e., that they approximate well the energy required to
add or remove an electron to the system. The resulting
charged systems evoke strong solvent responses: With a
charged solute, the polarization charge densities at the
interface between solute and solvent carry a total charge
with opposite sign [55], which is not the case for neutral
species. The stabilizing solute-solvent interaction is thus
of monopol-monopol type and much stronger than the
dominant dipole-dipole interactions encountered in neu-
tral solutes. KS eigenvalues, however, implicitly assume
a frozen solvent. Thus, they represent the unphysical
situation in which the charged solute interacts with the
reaction field of the neutral species, grossly underesti-
mating the degree of stabilization. Indeed, KS electronic
gaps remain nearly unchanged, while the stabilization
should lead to a sizeable bandgap decrease on the or-
der of ∼1 eV [100]. In vertical ionization processes, the
solvent does not instantaneously equilibrate in full with
the freshly ionized species; only the fast degrees of free-
dom are able to do so. Thus, vertical ionization energies
should be calculated with a total free energy-based non-
equilibrium solvation approach similar to the one com-
monly employed for optical excitations[101, 102]. We do
not follow this path here. The strong level renormaliza-
tion is not mirrored in the optical spectra, since optical
excitations are charge-neutral; shifts in excitation ener-
gies are on the order of 100 meV, as we will see in Sec-
tion III B. The decrease of the electronic bandgap is, to
a large extent, compensated by a corresponding decrease
of the exciton binding energy due to the screening effect
of the continuum solvent.
3. 6T/F4-TCNQ charge-transfer complex
The electronic structure and in particular the con-
ductivity of organic semiconductors can be effectively
enhanced by molecular doping. In oligo- and polythio-
phenes, the strong electron acceptor 2,3,5,6-tetrafluoro-
7,7,8,8-tetracyanoquinodimethane (F4-TCNQ) has
shown to be a particularly efficient p-dopant [31, 39, 103–
106]. However, numerous studies have shown that such
interactions are far from trivial; both oligothiophenes

7
and P3HT form charge transfer (CT) complexes with
F4-TCNQ, although in the polymer, integer CT can
occur as well [27, 34, 35, 39, 107–112]. The prevalence
of either form of CT is mainly determined by the degree
of order in the P3HT [34]. Highly-ordered regioregular
P3HT has a tendency to aggregate and thus form large
planar domains, enabling polaron delocalization and
charge separation [107]. However, there is increasing
evidence for the coexistence of both types of CT also
in the ordered thiophene polymer, with the relative
occurrence depending on doping concentration and
processing parameters [108–110]. Disordered polymers,
like the regiorandom variant of P3HT, aggregate and
planarize to a much smaller degree than ordered poly-
mers. Without extended planar regions, CT complex
formation prevails over ion pair formation [27]. While
integer CT enhances the conductivity of polymers much
more than partial CT, oligomeric crystals as well exhibit
a significant increase in conductivity upon F4-TCNQ
admixture, in spite of the exclusive formation of CT
complexes [39].
We simulate CT complexes by combining 6T with F4-
TCNQ molecules to form π-πstacked structures. Re-
gardless of the presence of alkyl chains bound to the 6T,
in the optimized geometry of the complex, the tetrafluo-
robenzene ring of the acceptor is situated above the link
between T3and T4[13, 18, 19] [see Figure 1e)]. The
four T rings underneath the F4-TCNQ are almost flat.
On the other hand, the outermost rings, T1and T6, are
bent upwards. We term this 6T configuration as locally
planar, bearing in mind that it exists only as part of
the CT complex. Without alkyl chains attached and in
vacuo, the torsion angle of the outer rings amounts to
23.9◦. Inclusion of CH3groups increases this value to
34.0◦on average. Prolonging the chain length increases
the torsion, from 36.9◦with C2H5up to 41.9◦with C3H7
groups. Notably, the last value (41.9◦) is the average
between 53.0◦, obtained between T1and T2, and 33.3◦,
between T5and T6. Thus, the twist is much stronger
for T1, where the C3H7is situated close to the accep-
tor, than for T6, where the chain is bound to the ex-
ternal site [Figure 1e)]. The pronounced torsion is a
consequence of attractive N· · · CH interactions between
the F4-TCNQ and the alkyl chain. Longer chains like
C3H7can close in on the acceptor molecule and reduce
the CH-N distance to 2.6 ˚
A, which is the corresponding
equilibrium value [113]. Hence, the bonding site of the
alkyl chain [position 3 versus 3’ within the rings, see Fig-
ure 1a) and e)] selectively affects the interaction with the
dopant. The presence of direct coupling between alkyl
chains and doping molecules demands the explicit inclu-
sion of longer chains in the simulations of CT complex
in order to obtain an accurate description of the system.
However, already attached methyl groups provide a good
estimate of the overall trend.
We now proceed to analyzing the electronic properties
of the CT complex. Its frontier orbitals are dominated by
the hybridization between the HOMO of the donor and
the LUMO of the acceptor, which give rise to an occu-
pied bonding and an unoccupied antibonding orbital su-
perposition [13, 18, 19, 114]. Also other valence orbitals
show signs of hybridization, i.e. they are delocalized over
the whole complex and occur in bonding-antibonding
pairs[13]. As we will discuss in Section III B 2 in the
context of optical excitations, this does not necessarily
mean that the electron densities associated with these
hybrid orbitals are equally distributed between the two
constituent molecules.
The natural population analysis[63] allows us to pin-
point the interaction-induced charge relocalization asso-
ciated with the hybridization. The ground-state CT be-
tween the H-terminated 6T and F4-TCNQ amounts to
0.28 ein vacuo. Upon closer inspection of the charge dis-
tribution within the 6T [Table IIa)], it is evident that the
outer thiophene rings, T1and T6, give only minor contri-
butions to the charge transferred to the F4-TCNQ. The
electron depletion is thus mainly restricted to the four T
rings directly underneath the acceptor, as observed ex-
perimentally [112]. The corresponding positive charge is
uniformly distributed among those four rings.
The addition of alkyl chains of increasing length to
6T leads to a systematic enhancement of the CT in the
ground state (see Figure 4; values specified in Section S2
of the Supplementary Material). Upon inclusion of CH3
groups, the CT goes up to 0.38 e; extending the chain
length increases this value, saturating at 0.45 e. This re-
sult is consistent with the behavior of the IP of 6T, which
decreases upon addition of alkyl groups [Figure 3b)]: The
lower the IP with respect to the electron affinity of the
acceptor, the stronger the CT driving force [115]. We
recall that the reduction of the IP is mainly a direct con-
sequence of the presence of the alkyl chains, although
the chain-length dependent decrease of the torsion un-
derneath the F4-TCNQ [Table Ia)] also raises EHOMO.
In contrast to the uniform distribution discussed pre-
viously, upon alkylization the excess positive charge is
increasingly localized on the center rings, T3and T4[Ta-
ble IIa)]. Furthermore, the CT complex acquires a dipole
moment of 1.2 – 1.6 D (depending on the alkyl chain
length) in the xy-plane [see coordinate system in Fig-
ure 1e)], due to the breaking of its C2symmetry upon
alkyl substitution. This dipole moment, induced by in-
tramolecular CT, is non-negligible compared to the in-
terfacial z-directed dipole moment of 3.3 - 3.6 D, which
is related to the intermolecular CT. The emergence of a
dipole moment parallel to the 6T axis can be rational-
ized by appreciating the asymmetric distances between
the electronegative atoms (N and F) of the acceptor and
the alkyl chains of 6T on the left- and right-hand sides
of the complex, which cause an overall in-plane charge
imbalance.
Solvents as well increase significantly the ground-state
CT in the complex, with the degree of solvent polarity
playing a crucial role (Figure 4). In the H-passivated 6T,
the ground-state CT increases from 0.28 ein vacuo to
0.36 ein CH3NO2. With covalently bonded CH3groups,

8
TABLE II. Partial charges in the donor of the charge-transfer
complex in the ground state (in e) on the outer (T1and T6),
intermediate (T2and T5), and inner (T3and T4) thiophene
rings [see Figure 1a)] (a) in vacuo with different alkyl groups,
(b) in different solvents (increasing polarity), with CH3groups
attached
a)
group outer interm. inner total
none 0.05 0.10 0.12 0.28
CH30.06 0.13 0.20 0.39
C2H50.06 0.15 0.24 0.44
C3H70.05 0.15 0.25 0.45
b)
solvent outer interm. inner total
none 0.06 0.13 0.20 0.39
C6H60.06 0.14 0.24 0.45
CHCl30.07 0.14 0.27 0.48
CH3NO20.07 0.14 0.31 0.52
the value grows from 0.39 eto 0.52 e, corresponding to an
increase of about 30% in both cases. The enhanced CT is
straightforwardly rationalized with electrostatic consid-
erations. As mentioned before, the complex has a dipole
moment in the stacking direction due to intermolecular
CT. The reaction field due to the solvent polarization is
oriented such that it increases the dipole moment of the
system by additionally polarizing it, thereby enhancing
the CT. As such, the solvent polarization charges cause
an additional driving force for CT. As the strength of the
reaction field is roughly proportional to the Onsager fac-
tor 2(−1)/(2+1) [116], we find an approximately linear
increase in CT as a function of 2(−1)/(2+ 1), see Fig-
ure 4. Since the factor 2(−1)/(2+1) rapidly approaches
unity as a function of , the enhancement effect saturates
quickly. Hence, two different polar ( > 10) solvents in-
fluence the solute in a very similar way, irrespective of the
exact value of , if no specific solute-solvent interactions
(e.g., hydrogen bonding) come into play.
Performing ground-state calculations in vacuo with the
geometries optimized in solution reveals that the increase
of CT is mainly caused directly by the reaction field (Fig-
ure 4). Changes in the geometry increase the CT only by
a small amount, although this increase becomes slightly
larger when alkyl groups are attached.
By resolving the partial charges on the CH3-
substituted 6T in the complex in different solvents [Table
IIb)], we find the extra charge to be increasingly localized
on the two inner T rings, T3and T4. Larger solvent po-
larity only enhances the charge donation from these two
monomers, further differentiating the inner rings (T3and
T4) from the intermediate ones (T2and T5).
FIG. 4. Ground-state charge transfer in the complex as a
function of the Onsager factor 2(−1)/(2+1), where is the
dielectric constant of the solvent. Circles and solid lines corre-
spond to calculations in an implicit solvent, whereas squares
and dashed curves are the results of calculations in vacuo,
using the solvent-optimized geometry. Red symbols indicate
systems with CH3groups attached to the 6T, blue without
alkyl chains, black and cyan the values for C2H5and C3H7-
functionalizations in vacuo, respectively.
B. Optical properties
The variation of the electronic structure in the consid-
ered systems is reflected in their optical properties. We
first focus on the isolated 6T in its various conformations
before analyzing the (alkyl-functionalized) 6T/F4-TCNQ
complex.
1. 6T in vacuo and in solution
The absorption spectrum of 6T is dominated by a
strong peak around 3.0 eV, stemming from the HOMO-
LUMO transition [96, 117] (details about the orbital
transitions of the first five excited states are listed in
Section S3 of the Supplementary Material). As seen in
Figure 5a), the excitation energy as a function of the
backbone conformation and of the alkyl chain length fol-
lows the same trend as the electronic gap [Figure 3c)].
The oscillator strength (OS) is maximized in the most
planar configurations, i.e. when no alkyl chains are at-
tached [Figure 5b)], and decreases with increasing chain
length. We attribute this behavior to an overall reduc-
tion of the overlap between the HOMO and the LUMO
upon increasing torsion angle.
The photoabsorption characteristics can be influenced
by solvation effects in two ways. The ground-state ge-
ometries and electronic structures are influenced by the
solvent, which, in turn, affects the optical spectrum via
its dielectric constant. Additional changes are directly

9
FIG. 5. a) Optical gap (∆Eopt) and b) oscillator strengths (OS) of 6T in the inspected configurations (see Figure 1) in vacuo and
with alkyl chains of increasing length. c) Excitation energies, computed within linear-response TDDFT (red) and state-specific
TDDFT (blue), and d) OS of CH3-functionalized 6T in solution with solvents of increasing polarity.
TABLE III. Magnitude of the bathochromic shifts (in meV)
for the HOMO-LUMO transition of the three indicated con-
formations of CH3-functionalized 6T, and the excitations P1
and P2in the 6T/F4-TCNQ CT complex, for the three con-
sidered solvents, calculated from a) linear-response TDDFT
and b) state-specific TDDFT
a)
excitation C6H6CHCl3CH3NO2
H→L (arc) 120 160 190
H→L (helix) 180 220 230
H→L (planar) 150 150 150
P150 40 30
P270 70 70
b)
excitation C6H6CHCl3CH3NO2
H→L (arc) 40 80 120
H→L (helix) 100 140 250
H→L (planar) 40 50 60
P130 10 0
P2170 160 150
related to the interaction between the dynamical elec-
tron density of the excited solute and the solvent, and
are determined by the refractive index of the solvent.
In the event of an optical excitation, the induced den-
sity of the molecule, i.e. the difference between the ex-
cited, time-dependent electron density and the ground-
state density, is given by the superposition of the transi-
tion density of the excitation and the stationary density
difference of the two states involved [118]. Both these
charge densities interact with the fast degrees of free-
dom of the solvent, each contributing to a total solva-
tochromic shift. The transition density oscillates at the
transition frequency, giving rise to a corresponding in-
phase solvent polarization. This represents a stabilizing
induced dipole· · · induced dipole interaction, generated
by dispersion forces[119]. The density difference, on the
other hand, is static. It also polarizes the solvent and
interacts with the corresponding reaction field. These
interactions are of electrostatic origin. It is important
to make this distinction, as linear-response TDDFT cap-
tures the dispersion contribution, but only part of the
electrostatic one [120, 121]. Specifically, it misses the
adaptation of the solvent to the density difference and
only considers the interaction between the density dif-
ference and the ground-state polarization charges. The
state-specific method, on the other hand, captures the
electrostatic interactions in full, including solvent relax-
ation, but lacks the dispersion part[120, 121]. Thus, the
two methods are complementary in the prediction of sol-
vatochromic shifts; in case the dispersion part is domi-
nant, linear-response TDDFT turns out to be more accu-
rate, whereas state-specific TDDFT is more appropriate
when the electrostatic contribution is the major one. As a
rule of thumb, dispersion forces are stronger for local ex-

10
citations with high OS, whereas the electrostatic contri-
bution is larger for charge-transfer excitations, which are
characterized by a large density redistribution and low
OS. In terms of computational costs, the linear-response
method is much cheaper. It yields multiple excited states
at once, alongside transition properties such as the OS.
The state-specific method, on the other hand, requires
two calculations for a single excited state, and yields only
the corresponding excitation energy. Thus, it is usually
put to use more selectively for states of particular inter-
est [122].
An indicator for the relative weight of the aforemen-
tioned contributions (dispersion forces vs. electrostatic
interactions) are the two dipole moments characteriz-
ing an excitation: the transition dipole moment µg→e,
related to the peak height, as the OS is proportional
to its square modulus, and the static dipole difference,
expressed by µe−µg[120, 121]. In the case of the
HOMO-LUMO transition in 6T, |µg→e| ≈ 10 D and
|µe−µg|<1 D, which clarifies that the bathochromic
shifts are mainly due to dispersion interactions. Thus,
the linear-response formalism features significantly larger
shifts compared to the state-specific one [see Figure 5c)
and Table III]. The state-specific shift is still sizeable, as
a large portion of it is related to solvation-induced struc-
tural distortions rather than direct interactions. Con-
sequently, the overall shifts are most pronounced in the
helix configuration, as its geometry is particularly sensi-
tive to external perturbations, as evidenced by the large
differences in the torsion angles in the different solvents
[Table Ib)].
Regardless of the adopted flavor of PCM/TDDFT, the
redshift of the HOMO-LUMO peak of 6T becomes larger
for increasing solvent polarity [Figure 5c)]. This increase
cannot be explained in terms of dynamical interactions
between solute and solvent, as the refractive index nis al-
most equal in all considered solvents (1.38-1.50). Hence,
the solvent-induced changes to the ground-state proper-
ties and to the electronic structure, which are instead
related to the dielectric constant , are the underlying
cause of the redshift increase. Indeed, as noted in Sec-
tion III A 2, the solvent decreases the torsion angles in
the 6T according to its polarity [see Table Ib)], which
correspondingly narrows electronic and optical gaps. In
general, the OS increases when the molecule is immersed
in a solvent [Figure 5d)], as a consequence of reduced tor-
sion and direct interactions with the solvent. The rather
small changes upon increasing the polarity suggest the
direct interactions to be the key factor in this context.
Finally, we inspect the optical properties of the isolated
locally planar 6T extracted from the geometry of the CT
complex formed with F4-TCNQ. Functionalizations with
alkyl chains of increasing length are considered. Similarly
to what is observed for the arc and helix configurations,
the computed optical gaps follows the trend obtained for
the electronic gaps, exhibiting only a rigid shift with re-
spect to them [Figure 3c) and 5a)]. We recall that these
energies are generally lower than in the other configura-
tions, as a result of the increased planarity of the four
T rings interacting with the F4-TCNQ, which in turn
implies increased coupling between the monomers. This
effect is partly counteracted by the increased torsion of
T1and T6, which is also responsible for the anti-trend
gap opening observed in the C3H7-functionalized 6T. The
corresponding sharp drop in the OS [see Figure 5b)] is a
consequence of the enhanced localization of the HOMO
and the LUMO on the center of the molecular backbone,
overall diminishing the orbital density localized on T1,
which is weakly coupled to the other rings. This phe-
nomenon leads to a decrease of the magnitude of the
transition dipole moment, which can be approximately
expressed as
µH→L≈Zd3r ψ∗
LUMO(r) (−r)ψHOMO (r).(6)
due to the dominant HOMO →LUMO character of the
excitation (∼90%, see Section S3 in the Supplementary
Material). It is evident from Eq. (6) that µH→Ldepends
on the overlap as well as on the spatial extent of the
orbitals, due to the presence of the dipole operator, −r.
The OS is proportional to |µH→L|2.
Moving on to the solvation effects, we find that
the CH3-functionalized, locally planar 6T experiences a
bathochromic shift in solution [Figure 5c)]. Contrary to
the arc and helix structures, this shift is independent
of the solvent polarity. For the undoped structures, we
rationalized the dependence of the excitation energy on
the solvent polarity in terms of changes of the underlying
geometry. The geometry of the CT complex, however,
is much less affected by the solvent, since the coupling
between the 6T and the F4-TCNQ is stronger than the
electrostatic interactions with the solvent molecules, and,
as such, defines the local structure of the complex.
2. 6T/F4-TCNQ charge-transfer complex in vacuo and in
solution
The previous discussion leads us to the analysis of ex-
cited states of the 6T/F4-TCNQ complex. We start by
considering the system with the H-terminated 6T as a
donor. In this case, the linear absorption spectrum [Fig-
ure 6a)] shows two features at low energy, P1and P2, at
1.5 eV and 2.0 eV, respectively, which cannot be assigned
to either molecular component individually. Indeed, they
correspond to excitations involving the hybridised fron-
tier states (hereafter called hybrid excitations). P1is
formed by a transition from the HOMO to the LUMO,
and P2by a transition from the HOMO-1 to the LUMO
of the complex [13, 18, 19], respectively (details about
the first ten excited states and their constituting orbital
transitions are listed in Section S4 of the Supplemen-
tary Material). They are both experimentally detectable
signatures of CT complex formation [33]. At higher en-
ergies, the maximum P3corresponds likewise to a hy-
brid excitation, whereas the strongest peak at 3.0 eV, P4

11
[see Figure 6a)], is related to the intramolecular HOMO-
LUMO transitions of the individual constituents.
The accuracy of excited-state calculations is known
to be improved by adding diffuse functions to the ba-
sis set. [123] We investigate their effect by comparing
results obtained with the 6-31G(d,p), 6-31+G(d,p), and
6-31++G(d,p) basis sets, which feature no diffuse func-
tions, diffuse functions on heavy atoms, and diffuse func-
tions on heavy atoms and hydrogens, respectively (all
results in Section S4.5 in the Supplementary Material).
Employing 6-31+G(d,p) yields excitations that are sys-
tematically redshifted by about 50 meV with respect to
those obtained with 6-31G(d,p), whereas going one step
further to 6-31++G(d,p) does not lead to additional im-
provements. The OS predicted by these three basis sets
differ by 0.03 at maximum. Comparing the double-ζ
cc-pVDZ and triple-ζcc-pVTZ basis sets, we find sim-
ilarly small improvements in the spectra [see inset of
Fig. 6a) and Section S4.4 in the Supplementary Mate-
rial]. In summary, enlarging the basis set leads to only
small and predictable improvements of the spectra, while
at the same time it increases significantly the computa-
tional complexity. We conclude that the double-ζbasis
set without diffuse functions is sufficient for our purposes
and allows us to deal efficiently also with the largest of
the complexes.
By means of natural population analysis of the excited
states calculated via state-specific TDDFT, we find that
in both hybrid excitations, P1and P2, the CT is enhanced
with respect to the ground state. As discussed in Sec-
tion III A 3, the ground-state electron transfer from the
6T to the F4-TCNQ in vacuo amounts to 0.28 e. In the
first excited state, corresponding to P1, it is increased to
0.60 e. This behavior can be understood by analyzing the
character of the HOMO and the LUMO of the complex,
which are involved in this transition. While they corre-
spond to bonding and antibonding superpositions of the
HOMO of the 6T and of the LUMO of the F4-TCNQ, the
HOMO of the complex has predominantly the character
of the HOMO of the 6T, while the LUMO of the complex
is more resemblant of the LUMO of the F4-TCNQ [114].
This is a general feature of CT complexes; hence, the
excited state corresponding to the antibonding superpo-
sition has a more ionic character [115]. In the excited
state P2, the CT is further increased to 0.78 e, thus ap-
proaching an integer value. This is a consequence of the
initial state of this transition, the HOMO-1 of the com-
plex, being mainly localized on the 6T, in spite of being
a hybridized orbital [18]. The excited states P3and P4
lead to CTs of 0.29 eand 0.36 e, respectively.
The addition of alkyl chains to the F4-TCNQ-doped
6T causes an overall red-shift of the absorption spectrum
of the complex [Figure 6a)]. This characteristic can be
traced back to the readjustment of the orbital energies of
6T, due to the dopant-induced structural distortions and
to the reduction of the IP induced by the alkyl groups
(see above). In particular, the shift of P4, which corre-
sponds to the two intramolecular HOMO-LUMO transi-
tions in the individual constituents, is related to struc-
tural changes in the alkylated 6T. Indeed, the shift can
be observed already in the locally planar 6T, and is re-
lated to the increased planarization of the four T rings
underneath the acceptor upon prolongation of the alkyl
chains [see Table Ia)]. The redshifts of the hybrid peaks,
P1and P2, are a consequence of the generally increased
energies of the orbitals of 6T due to alkyl functionaliza-
tion, which also raises the energies of the hybrid orbitals
of the complex. The LUMO of the complex, though,
corresponds mainly to the LUMO of the F4-TCNQ, as
discussed above, and is thus less affected by the level
readjustment in the 6T. As a consequence, its energy
does not shift up as much as that of the HOMO, giving
rise to reduced electronic and optical gaps in the alkyl-
ized complexes. Hence, the spectral shifts displayed in
Figure 6a) have different causes depending on the char-
acter of the excitation: The shift of P4is related to the
planarization-induced bandgap decrease of 6T, whereas
the shift of the hybrid excitations is related to the direct
electronic influence of the alkyl chains. The small anti-
trend blue-shift of P1and P2upon increasing the alkyl
chain length from C2H5to C3H7is caused once again
by the effect of the pronounced torsion of T1, due to at-
tractive interaction between the C3H7chain and the N
atoms in the F4-TCNQ, which decreases the energy of
the highest occupied orbitals of the 6T.
Solvents cause an overall redshift of the absorption
[Figure 6b)], ranging from 50 meV (P1) to 150 meV
(P4). In the following, we focus mainly on the hybrid
excitations, P1and P2, which represent a fingerprint of
CT complexes. Since both excitations cause additional
CT from the 6T to the F4-TCNQ (see above), they in-
crease the static dipole moment of the complex in the
z-direction [see coordinate system in Figure 1e)]. Thus,
they offer the opportunity to compare linear-response
and state-specific TDDFT results. In the case of P1,
we find a transition dipole moment of |µg→e| ≈ 5 D and
a static dipole difference of |µe−µg| ≈ 2 D, which is
consistent with the relative shifts from linear-response
and state-specific methods (Table III). In the case of P2,
on the other hand, |µg→e| ≈ 7 D and |µe−µg| ≈ 4 D,
but the state-specific shift is much larger than the linear-
response one (see Table III). Hence, the relative mag-
nitudes of the two dipole moments do not necessarily
predict the relative shifts quantitatively. However, we
can clearly see how a large change of the static dipole
moment entails a significant redshift which is captured
only by state-specific TDDFT. This method is therefore
more appropriate for excitations with CT character such
as P2. Notably, P2is still a moderate representative of
CT excitations; long-range CT excitations with dimin-
ished orbital overlap can have an OS close to zero (and
thus, |µg→e| ≈ 0), but a static dipole difference of order
∼10 D.
The presence of a solvent additionally increases the
OS of all excitations. Particularly P2grows notably in
intensity, similarly to the behavior experienced upon the

12
FIG. 6. Optical absorption spectra of the CT complexes, calculated with linear-response TDDFT: a) in vacuo with alkyl chains
of increasing length, and b) in different solvents, with CH3groups attached to the 6T. The inset in panel a) shows the first two
peaks of the spectrum of the H-terminated complex, as calculated with the cc-pVDZ (2ζ) and cc-pVTZ (3ζ) basis sets.
TABLE IV. Charge transfer (in e) from methylized 6T to F4-
TCNQ in the ground state and in the excited states P1and
P2
solvent GS P1P2
none 0.39 0.60 0.78
C6H60.45 0.68 0.88
CHCl30.48 0.73 0.95
CH3NO20.52 0.80 1.04
addition of alkyl chains [Figure 6a)]. Since the 6T of the
analyzed solvated complex is methylized, we find that the
effects of alkylization and solvation add up. It was pre-
viously found that the OS of P2is furthermore increased
by prolonging the length of the oligothiophene backbone,
which concomitantly causes a redshift of the peak en-
ergy [18]. Combined with the fact that the redshift seen
in Figure 6b) is already underestimated by the linear-
response formalism, this result suggests that in the poly-
mer limit, P2might come energetically close to P1or even
surpass it, while having much higher absorption strength.
Differences between the spectra in different solvents are
barely noticeable, which is a consequence of the increased
stiffness of the overall structure. While the twist angles
in the 6T alone represent loose degrees of freedom with
shallow potential energy curves[75], the torsion is locked
in the vicinity of F4-TCNQ. Thus, the properties of the
former are more strongly correlated with the parameters
of the environment.
We evaluate the excited-state CT from the alkylated
6T to the F4-TCNQ in solution by conducting a nat-
ural population analysis on the density obtained with
non-equilibrium state-specific TDDFT. Similarly to the
ground-state case, we obtain that the CT in the excited
states P1and P2is enhanced by the solvent polariza-
tion (Table IV). Notably, a higher solvent polarity leads
to a larger increase in CT, despite the refractive indices
of the different solvents being similar. The polarity-
dependent enhancement is thus related to the part of
the ground-state reaction field that stays frozen in the
non-equilibrium calculation. In the excited state P2, the
CT is higher than 1.
We recall that the scenario described above corre-
sponds to vertical excited states and, as such, differs
from the one of adiabatic excited states. The latter
lie at the minimum of the excited-state potential en-
ergy surface and are reached after internal nuclear re-
laxation and the reorientation of solvent molecules upon
photo-absorption. This scenario can be explored after an
excited-state geometry optimization with linear-response
TDDFT and equilibrium PCM, also giving access to flu-
orescence wavelengths [124, 125]. Such an analysis, how-
ever, goes beyond the scope of this work.

13
C. Summary and Conclusions
We performed a comprehensive first-principles analy-
sis of the structural, electronic, and optical properties
of sexithiophene, a representative organic semiconduc-
tor molecule, in order to unravel the non-trivial inter-
play of all the degrees of freedom involved. For this
purpose, we considered 6T in vacuo and in solutions of
increasing polarity, and we also inspected its p-doped
and alkyl-functionalized counterparts. We found that
both solvent and alkyl chains heavily affect the struc-
ture of the molecule, by regulating the torsion angle be-
tween adjacent monomers. In turn, this conformational
variability crucially affects the electronic properties of
the molecule, including energy gap, ionization potential,
and band widths. Furthermore, the delocalization of va-
lence electronic states into the alkyl chains directly in-
creases their energy, with notable consequences for the
level alignment with other molecules. The main effect of
the solvent is to decrease the torsion between the thio-
phene rings, which in turns influences the electronic and
the optical properties. Dynamical interactions between
the photo-excited molecule and the solvent cause a red-
shift of the main absorption peak, together with an in-
crease of its oscillator strength.
Doping 6T with a strong acceptor like F4-TCNQ sig-
nificantly impairs the flexibility of the oligomer. The
formation of a charge-transfer complex planarizes the
6T backbone and locks the torsion between the rings,
thereby enhancing the rigidity of the molecular struc-
ture. Hence, the torsion overall plays a less important
role in this case. On the other hand, the alkylization of
6T increases the CT within the complex. Solvation leads
to a further increment of CT, as the interfacial dipole
moment causes a self-reinforcing electric field by polar-
izing the surrounding solvent molecules. The effects of
alkylization and solvation on the optical properties of
the 6T/F4-TCNQ complex are more diverse than in the
case of the pristine 6T. The energy of the hybrid exci-
tations, which dominate the absorption onset, is affected
by alkyl-functionalization through the variation of the
energy levels of 6T, which alter the level alignment with
the dopant. This, in turn, influences orbital hybridiza-
tion and, consequently, the optical absorption. Peaks in
the higher-energy region of the spectra, corresponding to
intramolecular excitations, exhibit a similar behavior as
in the pristine molecule. Comparing linear-response and
state-specific TDDFT methods, we find solvatochromic
shifts that are related to both dynamical and electrostatic
complex-solvent interactions, with the latter being dom-
inant in hybrid excitations with marked charge-transfer
character. This type of excitations is overall most af-
fected by alkylization and solvation, both in terms of
energy and oscillator strength.
Our results provide understanding into the correlation
between solvation, alkylization, and doping, that often
coexist in experimental samples of organic semiconduc-
tors. Furthermore, our findings offer indications to sim-
ulate similar systems from first principles accounting for
all their degrees of freedom in a accurate and yet effi-
cient manner. For example, we find that the addition
of methyl groups is sufficient for modelling alkylated 6T
but does not capture all the desired effects in charge-
transfer complexes, where outer segments of longer alkyl
chains directly couple to the acceptor. As most of our
results depend on rather general properties of organic
semiconductors, such as their structural flexibility and
the tunability of their electronic and optical properties
upon functionalization and doping, we anticipate that
this work will provide useful indications to analyze and
understand computational results on this class of mate-
rials.
IV. ACKNOWLEDGEMENTS
We are thankful to Ahmed E. Mansour for useful
discussions. This work was funded by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foun-
dation) - project number 182087777 - SFB 951 and
286798544 – HE 5866/2-1 (FoMEDOS), by the German
Federal Ministry of Education and Research (Professorin-
nenprogramm III) as well as by the State of Lower Sax-
ony (Professorinnen f¨ur Niedersachsen). Computational
resources are provided by the North-German Supercom-
puting Alliance (HLRN), project bep00076.
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