Roberto Dovesi

The IR and Raman spectra of the KCrF ₃ perovskite are evaluated by imposing the monoclinic I112/m space group, experimentally stable at low temperature, and the tetragonal I4/mcm space group, observed above 150 K. The B3LYP total energy difference Δ E between the two phases is very small: 0.2 mE _h (about 0.06 eV) per formula unit. The differences in the spectra for the two space groups are analyzed, as well as the FM to AFM modifications. In spite of the large deformation of the CrF ₆ octahedron (the three Cr‐F distances are 2.01 and 2.36 Å in the ab plane, and 2.05 Å along c in the monoclinic low‐temperature structure), the spectra obtained with the two space groups are very similar and remind one of the ideal reference cubic spectra, characterized by only three IR‐active peaks and no signal for Raman. Calculations are performed at the quantum mechanical level by using an all‐electron Gaussian‐type basis set and the full‐range hybrid B3LYP functional.

The IR and Raman spectra of the LaCoO 3 perovskite (the formal occupancy on Co is d 6 , low spin, t 2g 6 ) are computed by imposing space groups (SG) of decreasing symmetry, from the cubic (SG Pm-3m, N. 221, and Fm-3m, N. 225), to the tetragonal (SG 140), rhombohedral (SG 167) and orthorhombic (SG 62) ones. The total energy differences between these structures, computed at the quantum mechanical level by using an all electron Gaussian type basis set and the full range hybrid B3LYP functional, is extremely small: 0.2 mE h between SG 167 and SG 62, 1.2 mE h between SG 140 and SG 62, and 4.5 mE h between the most stable structure and the cubic, ideal aristotype. These minor differences indicate that the experimentally proposed SG might be one of the (many) possible alternatives. The IR and Raman spectra are very rarely used for the identification of the symmetry of the perovskites at different temperatures. Here we investigate the evolution of the two spectra (IR and Raman) through the various competing space groups, exploring the possibility that they might be used for the identification of the low temperature structure (SG and position of the atoms) of the investigated compounds, and of perovskites in particular.

The geometrical, electronic and vibrational properties of LaCrO have been investigated by using an all electron Gaussian type basis set, the B3LYP functional and the CRYSTAL code, and compared with KVF: in the two compounds the transition metal is formally in d configuration. The high spin t ground state excludes the Jahn Teller deformation and the orbital ordering. The energy gain due to the rotation of the octahedra (from the cubic space group Pm, N. 221, to space group , N.127, and to , N. 140) in the oxide is about 70 times larger than in the fluoride (5.4 vs. 0.08 mE), due to the larger electrostatic forces (a factor four, as the formal charge doubles in going from F⁻ to O²⁻) and the consequently reduced B‐X distances. In KVF, the p states of fluorine are separated by 6.4 eV from the d states of vanadium, whose band is quite narrow (1 eV). In the oxide, on the contrary, the oxygen p states overlap to a large amount with the d states of chromium, whose band is more than 6 eV large. The FM and AFM energy differences, the spin density maps and profiles, and the Mulliken analysis data are also provided for documenting the differences between the oxide and the fluoride.

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.

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.

The influence of the A cation on the ferroelectric instability in ABO₃ perovskites, and its associated F_1u IR-active phonon mode, is systematically investigated for tantalates, niobates and titanates at the hybrid density-functional theory level.

This paper reports the first variationally based predictions of the lowest excited state in diamond (Γ_25′ → Γ₁₅) in the unrelaxed (optical) and structurally relaxed (thermal) configurations, from direct Δ-self-consistent-field (SCF) calculations based on B3LYP, PBE0, HSE06, and GGA functionals. For the B3LYP functional, which has the best overall performance, 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 bandgaps 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 −0.8ǀeǀ surrounded by charges of +0.12ǀeǀ at the four nearest neighbor sites. The thermally relaxed state is predicted to be similarly excitonic, with comparable bandgaps and atomic charges. 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 infrared 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 triexcitons 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.

In this study, the and the two equivalent / polarized Raman spectra of a LiNbO₃ single crystal have been recorded and used as a benchmark test for the density functional theory (DFT) calculation of the longitudinal modes and of their Raman activity. The theoretical approach, based on periodic boundary conditions and a linear combination of atomic orbitals (LCAO), provides excellent predictions of phonon wavenumbers and relative bands intensities for both A₁ and E Longitudinal Optical (LO) modes and complements a previous paper limited to the study of Transverse Optical (TO) modes. Overall, the present investigation demonstrates that the LCAO approach, as implemented in the CRYSTAL software, gives results of similar accuracy for the TO and the LO phonons features. By means of a band deconvolution scheme applied to the experimental spectra, we present, for the first time, a quantitative comparison between experimental and theoretically predicted polarized Raman band intensities of LiNbO₃ LO modes. This analysis highlights the role of the suitable determination of the static and high‐frequency dielectric matrices that are needed for the prediction of the TO/LO frequency split but also the first nonlinear electric susceptibility tensor for an accurate description of the Raman intensity pattern.

The relative stability ΔE of the cubic Pm 3 ¯ m (C), of the two tetragonal P 4 m bm (T1) and I 4 m cm (T2), and of the orthorhombic Pbnm (O) phases of KVF₃ has 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 (152 μHa for B3LYP, 180 μHa for HF, per 2 formula units) is due to the rotation of the VF₆ octahedra with respect to the c axis, by 4.1–4.6 degrees. The O phase is slightly less stable than the T2 phase (by 6 and 20 μHa 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 0.3–0.5 A ˚ 3 at 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.