the electron–phonon coupling. If this coupling is particularly strong, the frontier
orbitals may be delocalized over many monomers. However, when an excess
charge is added, the nuclear polarization localizes the charge, completely modifying the electronic wavefunction with respect to the neutral calculation. There is
some general consensus [128, 129] that the localization of the wavefunction in
P3HT largely originates from disorder and not from electron–phonon coupling
because there is a correlation between increased order of P3HT and increased
mobility [20]. Alternatively, one can be convinced that the conformational disorder
is stronger than the electron–phonon coupling by comparing the polaron size of a
perfectly ordered polymer chain with the localization of the orbitals computed from
calculation of large realistic models of disordered chains. If the polaron size of the
perfectly ordered system is much larger than the orbital in the disordered model, it
is acceptable to determine the charge localization from calculations that neglect the
electron–phonon coupling as a first approximation. Calculations for P3HT support
this approximation [108, 130] but it should be noticed that polaron sizes are
strongly dependent on the DFT methodology [131] and that the same assumption
may not hold for the new families of semiconducting polymers [132], where large
conjugated units are more weakly coupled by smaller conjugated linkers.
5.2 Strategies for Large-Scale Electronic-Structure
Calculations of Polymer Models
Under the conditions that the calculation of a ground state wavefunction of a
polymer model yields information about the charge localization for the carrier
states, it is still not trivial to carry out such calculations. It is not obvious to know
in advance how large a model of bulk polymer should be in order to reproduce the
DOS and localization length without the results being affected by finite-size effects.
The experience of available calculations with P3HT and PPV suggests that a model
containing several chains of 20–40 monomers displays electronic properties that do
not depend appreciably on the chain length [133] (it should not be forgotten that the
morphology depends on the chain length up to much larger molecular weights
[134]). Such models contain tens of thousands of atoms, a number that is still one
order of magnitude larger than that normally achievable by current software
specialized in linear scaling ab initio calculations, like SIESTA [135] or ONETEP
[136]. It is certainly possible that such methods can be employed in the near future
in benchmark calculations, but it is important to remember that what is needed is a
methodology able to evaluate the wavefunction for many replicas of the equilibrated systems in order to provide statistically meaningful results.
However, ideas from linear scaling methodologies can be used to develop ad hoc
methods that are able to compute in a more approximate fashion the wavefunction
for large systems. Essentially, all linear scaling methods are based on the definition
of a very localized basis set that reduces the number of matrix elements to be
Morphology and Charge Transport in P3HT: A Theorist’s Perspective
171
orbitals may be delocalized over many monomers. However, when an excess
charge is added, the nuclear polarization localizes the charge, completely modifying the electronic wavefunction with respect to the neutral calculation. There is
some general consensus [128, 129] that the localization of the wavefunction in
P3HT largely originates from disorder and not from electron–phonon coupling
because there is a correlation between increased order of P3HT and increased
mobility [20]. Alternatively, one can be convinced that the conformational disorder
is stronger than the electron–phonon coupling by comparing the polaron size of a
perfectly ordered polymer chain with the localization of the orbitals computed from
calculation of large realistic models of disordered chains. If the polaron size of the
perfectly ordered system is much larger than the orbital in the disordered model, it
is acceptable to determine the charge localization from calculations that neglect the
electron–phonon coupling as a first approximation. Calculations for P3HT support
this approximation [108, 130] but it should be noticed that polaron sizes are
strongly dependent on the DFT methodology [131] and that the same assumption
may not hold for the new families of semiconducting polymers [132], where large
conjugated units are more weakly coupled by smaller conjugated linkers.
5.2 Strategies for Large-Scale Electronic-Structure
Calculations of Polymer Models
Under the conditions that the calculation of a ground state wavefunction of a
polymer model yields information about the charge localization for the carrier
states, it is still not trivial to carry out such calculations. It is not obvious to know
in advance how large a model of bulk polymer should be in order to reproduce the
DOS and localization length without the results being affected by finite-size effects.
The experience of available calculations with P3HT and PPV suggests that a model
containing several chains of 20–40 monomers displays electronic properties that do
not depend appreciably on the chain length [133] (it should not be forgotten that the
morphology depends on the chain length up to much larger molecular weights
[134]). Such models contain tens of thousands of atoms, a number that is still one
order of magnitude larger than that normally achievable by current software
specialized in linear scaling ab initio calculations, like SIESTA [135] or ONETEP
[136]. It is certainly possible that such methods can be employed in the near future
in benchmark calculations, but it is important to remember that what is needed is a
methodology able to evaluate the wavefunction for many replicas of the equilibrated systems in order to provide statistically meaningful results.
However, ideas from linear scaling methodologies can be used to develop ad hoc
methods that are able to compute in a more approximate fashion the wavefunction
for large systems. Essentially, all linear scaling methods are based on the definition
of a very localized basis set that reduces the number of matrix elements to be
Morphology and Charge Transport in P3HT: A Theorist’s Perspective
171