We introduced two methods to correct the singularity in the calculation of long-range Hartree–Fock (HF) exchange for long-range-corrected density functional theory (LC-DFT) calculations in plane-wave basis sets. The first method introduces an auxiliary function to cancel out the singularity. The second method introduces a truncated long-range Coulomb potential, which has no singularity. We assessed the introduced methods using the LC-BLYP functional by applying it to isolated systems of naphthalene and pyridine. We first compared the total energies and the HOMO energies of the singularity-corrected and uncorrected calculations and confirmed that singularity correction is essential for LC-DFT calculations using plane-wave basis sets. The LC-DFT calculation results converged rapidly with respect to the cell size as the other functionals, and their results were in good agreement with the calculated results obtained using Gaussian basis sets. LC-DFT succeeded in obtaining accurate orbital energies and excitation energies. We next applied LC-DFT with singularity correction methods to the electronic structure calculations of the extended systems, Si and SiC. We confirmed that singularity correction is important for calculations of extended systems as well. The calculation results of the valence and conduction bands by LC-BLYP showed good convergence with respect to the number of k points sampled. The introduced methods succeeded in overcoming the singularity problem in HF exchange calculation. We investigated the effect of the singularity correction on the excitation state calculation and found that careful treatment of the singularities is required compared to ground-state calculations. We finally examined the excitonic effect on the band gap of the extended systems. We calculated the excitation energies to the first excited state of the extended systems using a supercell model at the Γ point and found that the excitonic binding energy, supposed to be small for inorganic semiconductors, was quite large. Our findings suggest that more investigation on the effect of the excitonic binding energy on band gaps is necessary.

Structural properties, electronic structure and UV absorption spectra of mercury(II) mediated metal–DNA complex, thymine–mercury(II)–thymine base pair (T–HgII–T), were theoretically and computationally investigated along with experimental data [Ono et al., J. Am. Chem. Soc., 2006, 128(7), 2172–2173]. The results were obtained by density functional theory (DFT) calculations for ground state and time-dependent DFT (TD-DFT) calculations for excited states associated with the polarized continuum model (PCM) in order to account for the bulk solvent effect. The LUMO of T–HgII–T was stabilized due to the presence of HgII since an unoccupied 6p orbital interacted with the 2p orbitals of thymine N3 atoms in the same way as in a π-conjugated system. Thus, excitations in T–HgII–T involve transitions qualitatively different from those of the thymine–thymine mismatch base pair (T–T). Since conventional DFT functionals lack correct description of dispersion forces, a method previously developed in our research group which combines DFT and a van der Waals correction functional was introduced to study multiple stacking nucleobase pairs. Based on the evaluated distance and the interaction energy between two stacking nucleobase pairs, the selective capturing of HgII ion by T–T compared to other metal ions is explained. The calculated UV absorption spectra of multiple stacking nucleobase pairs reproduced the decrease of absorption around 260 nm and the red-shift of the main peak experimentally observed in the presence of HgII ion. Detailed analysis of the electronic structure revealed that the metal–metal interaction between two HgII in multiple stacking T–HgII–T is the origin of the significant changes in UV absorption spectra.

Structural properties, electronic structure and UV absorption spectra of mercury(II) mediated metal–DNA complex, thymine–mercury(II)–thymine base pair (T–HgII–T), were theoretically and computationally investigated along with experimental data [Ono et al., J. Am. Chem. Soc., 2006, 128(7), 2172–2173]. The results were obtained by density functional theory (DFT) calculations for ground state and time-dependent DFT (TD-DFT) calculations for excited states associated with the polarized continuum model (PCM) in order to account for the bulk solvent effect. The LUMO of T–HgII–T was stabilized due to the presence of HgII since an unoccupied 6p orbital interacted with the 2p orbitals of thymine N3 atoms in the same way as in a π-conjugated system. Thus, excitations in T–HgII–T involve transitions qualitatively different from those of the thymine–thymine mismatch base pair (T–T). Since conventional DFT functionals lack correct description of dispersion forces, a method previously developed in our research group which combines DFT and a van der Waals correction functional was introduced to study multiple stacking nucleobase pairs. Based on the evaluated distance and the interaction energy between two stacking nucleobase pairs, the selective capturing of HgII ion by T–T compared to other metal ions is explained. The calculated UV absorption spectra of multiple stacking nucleobase pairs reproduced the decrease of absorption around 260 nm and the red-shift of the main peak experimentally observed in the presence of HgII ion. Detailed analysis of the electronic structure revealed that the metal–metal interaction between two HgII in multiple stacking T–HgII–T is the origin of the significant changes in UV absorption spectra.