The calculated energies and charge and spin distributions of the excited GR1 state in diamond

Band gap, Jahn-Teller deformation, octahedra rotation in transition metal perovskites LaTiO 3

The LaTiO3 perovskite (where Ti is in a d1 state) is investigated by using an all electron Gaussian basis and many functionals, ranging from pure GGA (PBE), to hybrids (full range, B3LYP and PBE0, and range separated, HSE06) to Hartree Fock. Recently, Varignon et al. (Phys. Rev. Res 1, 033131, 2019), showed that, when GGA+U or HSE06 are used, a metallic solution and fractional occupancy of the t2 g subshell are obtained. Here, it is shown that when a full range hybrid functional is used, an integer occupancy is obtained, as suggested by the Jahn-Teller theorem. When the exact exchange percentage varies from 0 to 100, the system is insulating when it exceeds 20. By reducing progressively the symmetry from cubic down to orthorhombic, the relative importance of the Jahn-Teller deformation and of the rotation of the octahedra is explored.

The energies and charge and spin distributions in the low-lying levels of singlet and triplet N2V defects in diamond from direct variational calculations of the excited states

This paper reports the energies and charge and spin distributions of the low-lying excited states in singlet and triplet N2V defects in diamond from direct Δ-SCF calculations based on Gaussian orbitals within the B3LYP, PBE0, and HSE06 functionals. They assign the observed absorption at 2.463 eV, first reported by Davies et al. [Proc. R. Soc. London 351, 245 (1976)], to the excitation of a N(sp3) lone-pair electron in the singlet and triplet states, respectively, with estimates of ∼1.1 eV for that of the unpaired electrons, C(sp3). In both cases, the excited states are predicted to be highly local and strongly excitonic with 81% of the C(sp3) and 87% of the N(sp3) excited charges localized at the three C atoms nearest neighbor (nn) to the excitation sites. Also reported are the higher excited gap states of both the N lone pair and C unpaired electron. Calculated excitation energies of the bonding sp3 hybrids of the C atoms nn to the four inner atoms are close to that of the bulk, which indicates that the N2V defect is largely a local defect. The present results are in broad agreement with those reported by Udvarhelyi et al. [Phys. Rev. B 96, 155211 (2017)] from plane wave HSE06 calculations, notably for the N lone pair excitation energy, for which both predict an energy of ∼2.7 eV but with a difference of ∼0.5 eV for the excitation of the unpaired electron.

The Electronic Structures and Energies of the Lowest Excited States of the Ns0, Ns+, Ns- and Ns-H Defects in Diamond

This paper reports the energies and charge and spin distributions of the mono-substituted N defects, N⁰_s, N⁺_s, N^-_s and N_s-H in diamonds from direct Δ-SCF calculations based on Gaussian orbitals within the B3LYP function. These predict that (i) N_s⁰, N_s⁺ and N_s^- all absorb in the region of the strong optical absorption at 270 nm (4.59 eV) reported by Khan et al., with the individual contributions dependent on the experimental conditions; (ii) N_s-H, or some other impurity, is responsible for the weak optical peak at 360 nm (3.44 eV); and that N_s⁺ is the source of the 520 nm (2.38 eV) absorption. All excitations below the absorption edge of the diamond host are predicted to be excitonic, with substantial re-distributions of charge and spin. The present calculations support the suggestion by Jones et al. that N_s⁺ contributes to, and in the absence of N_s⁰ is responsible for, the 4.59 eV optical absorption in N-doped diamonds. The semi-conductivity of the N-doped diamond is predicted to rise from a spin-flip thermal excitation of a CN hybrid orbital of the donor band resulting from multiple in-elastic phonon scattering. Calculations of the self-trapped exciton in the vicinity of N_s⁰ indicate that it is essentially a local defect consisting of an N and four nn C atoms, and that beyond these the host lattice is essential a pristine diamond as predicted by Ferrari et al. from the calculated EPR hyperfine constants.

Self-trapped excitons in diamond: a Δ-SCF approach

This paper reports the first variationally-based predictions of the lowest excited state in diamond (Γ25՛ → Γ15) in the optical and thermal configurations, from direct Δ-SCF calculations based on B3LYP, PBE0, HSE06 and GGA functionals. For the B3LYP functional the energy of the optical state, 7.27 eV, is within the observed range of (7.2-7.4) eV and is predicted to be insulating, with indirect band gaps of (5.6-5.8) eV. Mulliken analyses of the excited state wavefunction indicate extensive redistributions of charge and spin resulting in a strongly excitonic state with a central charge of -0.8 ǀeǀ surrounded by charges of +0.12 ǀeǀ at the four nearest neighbour sites. Calculations of the ground and excited state relaxations lead to a Stokes' shift of 0.47 eV and predicted Γ-point luminescence energy of 6.89 eV. Assuming a similar shift at the band edge (X1), an estimate of 5.29 eV is predicted for the luminescence energy, which compares with the observed value of 5.27 eV. Excited state vibrational spectra show marked differences from the ground state, with the introduction of an infra-red peak at 1150 cm-1 and a modest shift of 2 cm -1 in the TO(X) Raman mode at 1340 cm-1. Similar calculations of the lowest energy bi- and tri-excitons predict these to be bound states in both optical and thermal configurations and plausible precursors to exciton condensation. Estimates of bi- and triexciton luminescence energies predict red shifts with respect to the single exciton line which are compared to the recently reported values.