Charge-Transfer States in Pentacene: Dimer versus Crystal

Abstract

According to recent ab initio calculations, the energy gap between the two oppositely polarized charge-transfer (CT) states of a model pentacene dimer is anomalously large, attaining 0.8 eV. Here we introduce the self-consistent charge field approach to evaluate the electrostatic stabilization energies of the pertinent states in the pentacene crystal represented by a dedicated multiscale model system containing the model dimer as its core. We demonstrate that, contrary to common wisdom, the lower of the two CT states is barely affected by the crystalline environment whereas the upper one undergoes a large red shift. Effectively, embedding of the dimer in the crystal bulk reduces the pertinent splitting by an order of magnitude, because most of the intradimer charge−quadrupole interactions are compensated by similar interactions with surrounding molecules. This resolves the apparent contradiction between the ab initio result obtained for the dimer and the splitting of about 0.04 eV resulting from microelectrostatic calculations for the crystal. ■ INTRODUCTIONThe discovery of spontaneous singlet exciton fission (SF) in solid pentacene prompted widespread interest in the electronic properties of this system, in the recent years triggering a surge of theoretical papers that strive to unravel the underlying physical mechanisms. 1−4 Various methodologies have been invoked for this purpose.No matter how vibronic coupling is treated and how the dynamic aspects of the problem are described, 1−3 the process is ultimately controlled by the energetics of the electronic states involved. Yet, as the small energy gaps between the relevant eigenstates are inevitably sensitive to the details of the wave function, the requisite accuracy is just on the verge of the predictive power of the most sophisticated quantum chemistry tools available to date. By these standards, the pentacene molecule is large. Moreover, in order to describe the fission process, it is necessary to take into account at least the two molecules on which the two emerging triplets are located, which makes a dimer the minimum model system to be considered in this context. At the ab initio level, this creates a numerical problem of formidable complexity, practically ruling out inclusion of any elements of the crystal environment in which the pertinent pair of molecules is in reality embedded.In a number of papers 1−3 focusing on diverse aspects of the fission phenomenon, various versions of the dimer model were adopted. In most cases, parametrization of the model Hamiltonian was in principle based on quantum chemistry calculations but fine-tuned on intuitive grounds to account for simplifications of the model and for potential intrinsic errors of the applied quantum chemistry methods.The paper by Zeng et al. 4 stands out from this collection, representing a consistent ab initio approach at a highly advanced level. However, in view of the accuracy it offers, even minor energy shifts resulting from the simplifications of the underlying model may significantly influen...

Partial atomic multipoles for internally consistent microelectrostatic calculations

“…As noted in the past, the splitting between the ac and ca configuration energies is governed by CQ interactions, whereas polarization energy (mean electrostatic stabilization) sets the position of their gravity center. The MR method yields the average excitation energies of and for the dimer and for the 10‐molecule cluster, respectively, with denoting the ionization potential and standing for the electron affinity of the pentacene molecule.…”

“…Both problems were solved in the past within the computationally demanding SCCF approach, against which the MR method is now to be benchmarked. The photophysical context that had prompted us to calculate the energetics of CT excitons in such clusters (which we presently repeat within the new computational framework) is described in our earlier work . Presently, the point is that the component ions of a CT state polarize each other as well as the surrounding cluster molecules, and this polarization contribution is a crucial ingredient of the excitation energy relevant for spectroscopic interpretations, so this test is of practical relevance.…”

“…Besides, even the 20% error, registered for the ESP at some nearest neighbor positions, in energy terms is really quite small when compared to that obtained for ZINDO charges, which was the state‐of‐the‐art value until recently. Moreover, the sign of the discrepancy is different for different relative positions of the interacting entities, so that for a perfect crystal the net value is reduced upon summation over the neighboring molecules. Specifically, in CT states the residual error is marginal owing to additional cancellation between the contributions from the two (oppositely charged) ions .…”

“…Moreover, the sign of the discrepancy is different for different relative positions of the interacting entities, so that for a perfect crystal the net value is reduced upon summation over the neighboring molecules. Specifically, in CT states the residual error is marginal owing to additional cancellation between the contributions from the two (oppositely charged) ions . When the local symmetry is perturbed only partly (e.g., only one of the neighbors is substituted by a vacancy or impurity), the contributions to the total error come mostly from the affected positions.…”

“…Subsequently, we describe the methodology of self‐consistent microelectrostatic calculations utilizing these matrices, and present some tests of the emergent computational framework on model cases. Finally, we report the calculated polarization energies of CT states in model pentacene clusters and compare them with their counterparts obtained from the self‐consistent charge field (SCCF) method …”