Figure 1. Top (top) and side (bottom) views of representative ground-state carbazole dimer conformations in this study. Dimer structures were optimized at SOS-MP2/aug-cc-pVDZ level, and H atoms are hidden for the sake of simplicity.
  1. Computational details
Because the electron correlations are considered to play a pivotal role in the intermolecular π-π interactions of Cz dimers, instead of density functional theory (DFT) calculations, post-Hartree-Fock (HF) calculations were conducted. Scaled opposite spin (SOS)-MP2[27] was chosen for Cz monomer and dimers in the ground state, whereas the SOS-CIS(D0)[28]method was employed for those in the singlet and triplet excited states. These methodologies were supposed to be more accurate than conventional MP2 and CIS(D0) methods by semi-empirically scaling the opposite spin electron correlation; in addition, CIS(D0) is free from the singularity issue regarding the perturbative correction between the degenerate states that the CIS(D) method suffers from. Such methodologies were successfully employed in previous studies to investigate dimers of acene molecules, e.g. , benzene, naphthalene, and anthracene, both in the ground and excited states.[15]
In order to examine the relative stabilities of different dimer conformations, PESs of dimer were calculated using 6-311+G(d) level with the monomer structure frozen;[29] PESs were constructed as a function of the intermolecular distance (R π-π) and that of the rotational angle (θ ) around the normal axis to the molecular plane at the center of mass of the Cz molecule. In addition to the Cz monomer structure, for the most representative cofacial dimers, i.e. , syn ,anti , and Stg conformations, dimer structures were further optimized with aug-cc-pVDZ (aDZ) basis sets. To assess the effect of incompleteness of the basis sets in this study, we considered basis set superposition error (BSSE).[30] Then, we also performed additional single-point coupled cluster (CC) calculations, i.e. , CCSD and EOM-CCSD, and compared the results with those at the SOS-MP2 and SOS-CIS(D0) levels, for the ground and excited states, respectively. In this comparison, 6-31+G(d) basis sets were used owing to the high computational cost of CC calculations. In addition, natural transition orbital (NTO) analyses[31] were conducted to clarify the nature of the excited states. To obtain a deeper understanding of the intermolecular interactions for the Cz dimers in the ground state, we also performed the symmetry adapted perturbation theory (SAPT0) calculations.[32-34]All these calculations were carried out using the Q-chem program package (version 4.0).[35]
  1. Results and Discussion