An all-electron study of the low-lying excited states and optical constants of Al2O3 in the range 5-80 eV

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.

Quantum mechanical simulation of various phases of KVF3perovskite

The relative stability ΔEof the cubicPm3¯m(C), of the two tetragonalP4mbm(T1) andI4mcm(T2), and of the orthorhombicPbnm(O) phases of KVF₃has been computed both for the ferromagnetic (FM) and antiferromagnetic (AFM) solutions, by using the B3LYP full range hybrid functional and the Hartree-Fock (HF) Hamiltonian, an all-electron Gaussian type basis set and the CRYSTAL code. The stabilization of the T2 phase with respect to the C one (152μHa for B3LYP, 180μHa for HF, per 2 formula units) is due to the rotation of the VF₆octahedra with respect to thecaxis, by 4.1-4.6 degrees. The O phase is slightly less stable than the T2 phase (by 6 and 20μHa for B3LYP and HF); it is, however, a stable structure as the dynamical analysis confirms. The mechanism of the stabilization of the AFM solution with respect to the FM one is discussed through the spin density maps, and is related to the key role of the exact exchange term (20% in B3LYP, 100% in HF). The G-AFM phase (the first six neighbors of the reference V ion with spin reversed) is more stable than the FM one by about 500 (HF) and 1800 (B3LYP)μHa per two formula units. A volume reduction is observed in the C to T passage, and in the FM to AFM one, both being of the order of 0.3-0.5A˚3at the B3LYP level. Atomic charges, magnetic moments and bond populations, evaluated according to a Mulliken partition of the charge a spin density functions, complete the analysis. The IR and Raman spectra of the FM and AFM C, T2 and O cells are discussed; the only noticeable difference between the various space groups appears in the modes with wavenumbers lower than 100 cm^-1.

Vibrational Analysis of Paraelectric–Ferroelectric Transition of LiNbO3: An Ab-Initio Quantum Mechanical Treatment

The phase transitions between paraelectric (PE) and ferroelectric (FE) isomorph phases of LiNbO3 have been investigated quantum mechanically by using a Gaussian-type basis set, the B3LYP hybrid functional and the CRYSTAL17 code. The structural, electronic and vibrational properties of the two phases are analyzed. The vibrational frequencies evaluated at the Γ point indicate that the paraelectric phase is unstable, with a complex saddle point with four negative eigenvalues. The energy scan of the A2u mode at −215 cm−1 (i215) shows a dumbbell potential with two symmetric minima. The isotopic substitution, performed on the Li and Nb atoms, allows interpretation of the nontrivial mechanism of the phase transition. The ferroelectric phase is more stable than the paraelectric one by 0.32 eV.