Long-range corrected DFT calculations of charge-transfer integrals in model metal-free phthalocyanine complexes
An assessment of several widely used exchange--correlation potentials in computing charge-transfer integrals is performed. In particular, we employ the recently proposed Coulomb-attenuated model which was proven by other authors to improve upon conventional functionals in the case of charge-transfer excitations. For further validation, two distinct approaches to compute the property in question are compared for a phthalocyanine dimer.
KeywordsCharge-transfer integral Density functional theory Long-range corrected functionals Organic electronics Phthalocyanine
The absolute values of effective charge transfer integrals (|Jeff|, given in eV) computed with the aid of Eqs. (3)–(6) and the charge transfer integrals calculated using energy splitting in dimer approach (|∆/2|). The cc-pVDZ basis set was employed in all calculations. R is the intermolecular distance
As a model system to evaluate the performance of conventional exchange–correlation potentials in computing charge–transfer integrals we have chosen metal–free phthalocyanine dimer. Phthalocyanines are often considered as conductive materials with potential applications in organic electronics [33, 34, 35, 36]. In crystalline phase phthalocyanine molecules usually form regular columns and liquid crystals composed of phthalocyanines are promising materials for organic electronics . The liquid crystals in question are usually built from flat aromatic phthalocyanine center and aliphatic side groups. Likewise, aromatic core of molecules in liquid crystal state form regular columns with molecules in stacked conformations and the fastest charge transport is observed inside a column with much smaller probability of charge transport between columns. The charge–transfer integral between monomers in dimer can be used to describe charge transport inside of column composed of phthalocyanine molecules and as a first approximation of charge–transfer in phthalocyanine based liquid crystals. In this work only charge–transfer integrals between highest occupied molecular orbitals (HOMOs) of adjacent monomers are considered. This represents the charge–transfer integral related to the transport of positive charge carrier (hole transport).
Calculations were performed with the aid of several exchange–correlation potentials using different basis sets, including Dunning’s correlation consistent cc-pVDZ basis set  as well as recently proposed Jensen’s basis set . The results of calculations presented in this work were carried out using the GAUSSIAN 09 program .
Results and discussion
The values of the spatial overlap for different geometrical parameters calculated with the aid of different exchange–correlation potentials as well as using the Hartree–Fock method are presented in Fig. 2b. As seen in the figure, the values of the spatial overlap calculated with use of different DFT functionals are comparable for all considered geometrical parameters. The values of spatial overlap integral calculated using the HF wavefunction seem to be overestimated and differ substantially from the values determined within the DFT framework.
A comparison of the effective charge-transfer integrals calculated using Eq. (3) and the charge-transfer integrals determined from the energy splitting (Eq. (9)) is shown in Table 1. The data show that the differences in the values of charge–transfer integrals calculated based on the two approaches are insignificant and do not exceed a few thousandths of eV. At first glance, it appears that it is sufficient to employ less accurate method, based on the energy splitting in dimer with assumption of zero spatial overlap, to compute J between molecules in π interacting system. However, as it has already been mentioned, it is important to include spatial overlap in calculations of charge–transfer integrals from the definition. Otherwise, the values of J might strongly depend on the size of the basis set used in calculations. The other drawback of the method based on energy splitting in dimer is the lack of information about the sign of charge–transfer integral. However, if the knowledge of the sign is important, it can be subsequently determined from the bonding–antibonding character of the interaction between the corresponding orbitals .
The primary aim of the present study was to evaluate the performance of commonly employed conventional exchange–correlation potentials that are used to compute charge–transfer integrals. In doing so, we apply the recently proposed Coulomb–attenuated model as a reference as this approach is proven to be very successful in predicting excitation energies to charge–transfer states. It is shown that for certain areas of conformational space in phthalocyanine dimer the differences in values of charge-transfer integrals between the conventional schemes and the CAM-B3LYP functional in values of charge–transfer integrals might be quite significant. The same is revealed for triphenylene dimer . As a result, the values of charge carrier mobilities estimated using Marcus formula might differ by 20% and more. Likewise, theoretical predictions of peaks intensity in electro-absorption spectrum of molecular crystals and molecular aggregates [53, 54] might be determined to a large extent by the accuracy of charge-transfer integrals (Kulig W, Petelenz P, (2010). Private communication). We have also confirmed the findings reported by other authors  that the size of the basis set used in calculations of charge–transfer integrals plays only a minor role provided the spatial overlap is included in the theoretical model.
This work was supported by computational grants from Wroclaw Center for Networking and Supercom- puting (WCSS) and ACK Cyfronet. Work in the USA was supported by the HRD-0833178 grant. One of the authors (RZ) would like to acknowledge support from a grant from Iceland, Liechtenstein and Norway through the EEA Financial Mechanism - Scholarship and Training Fund. Financial support from Wroclaw University of Technology and the Czech Science Foundation (Project No. P205/10/2280) and the European Commission through the Human Potential Programme (Marie-Curie RTN BIMORE, Project No. MRTN-CT-2006-035859) is also acknowledged.
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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