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.
- 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]
- Results and Discussion