The role of the exact Hartree-Fock exchange in the investigation of defects in crystalline systems.

The role of the exact Hartree-Fock (HF) exchange in determining the band gap and other properties of defects in crystalline solids is investigated. Two defects in diamond, VHd1 and VHq1 (one first neighbour of the vacancy is saturated with hydrogen, and the three unpaired electrons combine to give a quadruplet, 3 spin up, or a doublet, two spin up and one down), are used as test cases. The results obtained with a gradient corrected functional, PBE, one range separate hybrid, HSE06, two full range hybrids, B3LYP and PBE0, and the Hartree-Fock Hamiltonian are compared.

orbital ordering patterns in KBF (B = Sc, Ti, Fe, Co) perovskites.

The orbital ordering (OO) resulting from the partial occupancy of the subshell of the transition metals in KBF (B = Sc, Ti, Ffe, Co) perovskites, and the many possible patterns arising from the coupling between the B sites, have been investigated at the quantum mechanical level ( Gaussian type basis set, B3LYP hybrid functional) in a 40 atoms supercell. The numerous patterns are distributed into 162 classes of equivalent configurations. For each fluoroperovskite, one representative per class has been calculated.

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.

Jahn-Teller distortion, octahedra rotations and orbital ordering in perovskites: KScF as a model system.

The KScF perovskite has been used as a model for investigating the relative importance of the Jahn-Teller (JT) lift of degeneracy, the ScF octahedra rotation (OR), and the quadrupole-quadrupole interaction linked to different occupancy of the Sc t subshell in various sites of the unit cell (orbital ordering, OO). The group-subgroup sequence , , , and , supplemented by and , has been explored by using an Gaussian type basis set, hybrid functionals, and the CRYSTAL17 code. The JT lift of degeneracy provides a stabilization about 5 times larger than the sum of the OO and OR effects.

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

The LaTiO 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.

The role of the A monovalent cation in the AVF perovskite series. A quantum mechanical investigation.

The relative stability of various phases of five AVF compounds (A = Li, Na, K, Rb and Cs) is investigated starting from the cubic (C) 3̄ (221) prototype structure, with five atoms (one formula unit) in the primitive cell. To the authors' knowledge, only three of these compounds have been investigated experimentally (Na, K and Rb), and they are reported as being cubic. The picture emerging from the present simulation is quite different: CsVF and RbVF are dynamically stable in the cubic structure, KVF is tetragonal, with space group (SG) 4/ (no.

The Electronic Structures and Energies of the Lowest Excited States of the N, N, N and N-H Defects in Diamond.

This paper reports the energies and charge and spin distributions of the mono-substituted N defects, N, N, N and N-H in diamonds from direct Δ-SCF calculations based on Gaussian orbitals within the B3LYP function. These predict that (i) N, N and N all absorb in the region of the strong optical absorption at 270 nm (4.59 eV) reported by Khan et al.

The Orbital Multi Pattern Occupancy in a Partially Filled d Shell: The KFeF Perovskite as a Test Case.

The occupancy of the d shell in KFeF3 is t2g4eg2, with five α and one β electrons. The Jahn-Teller lift of degeneracy in the t2g sub-shell produces a tetragonal relaxation of the unit cell (4.09 vs.

Geometrical Stability and Nonlinear Optical Properties of Crystallogen and Pnictogen Fullerene Analogues.

The linear and nonlinear optical (NLO) properties of fullerene and fullerene-like structures, including crystallogen and pnictogen elements, are computed quantum mechanically. The tensors of optical polarizability, α, and second hyperpolarizability, γ, for a series of buckyball fullerene analogues, namely, Si, Ge, Sn, Pb, P, As, Sb, and Bi, are reported and analyzed. The eight considered nanocages are here classified into four categories: nanocages stabilized in the X form, including C, As, Sb, and Bi; nanocages that are not stabilized in the X form but are found to be stable in a distorted buckled b-X form, with X = Si and Ge; nanocages stabilized in an exohedral decorated X-Y form, X = Sn, Y = H or F; and finally nanocages that are not stable in either distorted or decorated form; however, their corresponding tabular nanotubes are found to be stable; such group includes P and Pb elements.

The effect of composition on phonon softening in ABO-type perovskites: DFT modelling.

The evolution of ferroelectric instability in ABO perovskites is systematically investigated for tantalates, niobates and titanates at the hybrid density-functional theory level. The influence of the A cation is analysed in terms of the frequency of the lowest F IR-active phonon mode at different volumes for (Cs, Rb, K, Na)TaO, (Ba, Pb, Sn, Ge)TiO and (Rb, K, Na, Li)NbO and correlated with the ionic radius as well as the degree of hybridization in the bonds. The atomic displacement corresponding to each mode is described as a function of volume, and the static permittivity is calculated for the stable 3̄ phases.

How deeply are core electrons perturbed when valence electrons are spin polarized? The case study of transition metal compounds.

The ferromagnetic and antiferromagnetic wave functions of the KMnF perovskite have been evaluated quantum-mechanically by using an all electron approach and, for comparison, pseudopotentials on the transition metal and the fluorine ions. It is shown that the different number of α and β electrons in the d shell of Mn perturbs the inner shells, with shifts between the α and β eigenvalues that can be as large as 6 eV for the 3s level, and is far from negligible also for the 2s and 2p states. The valence electrons of F are polarized by the majority spin electrons of Mn, and in turn, spin polarize their 1s electrons.

Self-trapped excitons in diamond: A Δ-SCF approach.

This paper reports the first variationally based predictions of the lowest excited state in diamond (Γ → Γ) 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.

The role of spin density for understanding the superexchange mechanism in transition metal ionic compounds. The case of KMF (M = Mn, Fe, Co, Ni, Cu) perovskites.

In many recent papers devoted to first row transition metal fluorides and oxides, not much attention is devoted to the spin density, a crucial quantity for the determination of the superexchange mechanism, and then for the ferro-antiferromagnetic energy difference. Usually, only the eigenvalues of the system are represented, in the form of band structures or, more frequently, of density of states (DOS). When discussing the orbital ordering and the Jahn-Teller effect, simple schemes with cubes and lobes are used to illustrate the shape of the d occupancy.

Quantum mechanical simulation of various phases of KVFperovskite.

The relative stability Δof the cubic3¯(C), of the two tetragonal4m(T1) and4m(T2), and of the orthorhombic(O) phases of KVFhas 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 (152Ha for B3LYP, 180Ha for HF, per 2 formula units) is due to the rotation of the VFoctahedra with respect to theaxis, by 4.1-4.

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

This paper reports the energies and charge and spin distributions of both the vertically excited and fully relaxed GR1 states of the neutral singlet vacancy in diamond obtained from direct Δ-SCF calculations used previously to describe the low-lying excited states in AF NiO and α-AlO. The calculations are based on the B3LYP functional in its standard form, with a C basis set that is identical to that which was used previously in numerous calculations of the ground state properties of defective diamond. Both the vertically excited and thermally relaxed GR1 states are predicted to be excitonic and insulating, with extensive re-distribution of charge and spin density and back-donation to the donor site.

The ferromagnetic and anti-ferromagnetic phases (cubic, tetragonal, orthorhombic) of KMnF. A quantum mechanical investigation.

Many space groups are proposed in the literature for the KMnF perovskite (see, for example, Knight , , 2020, , 155935), ranging from cubic (C) (3̄) to tetragonal (T) ( or 4/) down to orthorhombic (O) (). The relative stability Δ of these phases, both ferromagnetic (FM) and antiferromagnetic (AFM), has been investigated quantum mechanically by using both the B3LYP hybrid functional and the Hartree-Fock Hamiltonian, an all-electron Gaussian type basis set and the CRYSTAL code. The O phase is slightly more stable than the T phase which in turn is more stable than the C phase, in agreement with experimental evidence.

Strategies for the optimization of the structure of crystalline compounds.

When different proposals exist (or can reasonably be formulated) for the size of the unit cell (in terms of number of atoms) and space group of crystalline compounds, a strategy for exploring with simulation methods the various cases and for investigating their relative stability must be defined. The optimization schemes of periodic quantum mechanical codes work in fact at fixed space group and number of atoms per unit cell, so that only the fractional coordinates of the atoms and the lattice parameters are optimized. A strategy is here presented, based on four standard tools, used synergistically and in sequence: (1) the optimization of inner coordinates and unit cell parameters; (2) the calculation of the vibrational frequencies not only at , but also at a set of points (in the example presented here they are eight, generated by a shrinking factor 2), looking for possible negative wavenumbers.

The superexchange mechanism in crystalline compounds. The case of KMF(M = Mn, Fe, Co, Ni) perovskites.

The ferromagnetic and antiferromagnetic wavefunctions of four KMF(M = Mn, Fe, Co and Ni) perovskites have been obtained quantum-mechanically with the CRYSTAL code, by using the Hartree-Fock (HF) Hamiltonian and three flavours of DFT (PBE, B3LYP and PBE0) and anGaussian type basis set. In the Fe and Co cases, with dand doccupation, the Jahn-Teller distortion of the cubic cell is as large as 0.12 Å.

The NVN charged pair in diamond: a quantum-mechanical investigation.

The NVN charged pair in diamond has been investigated by using a Gaussian-type basis set, the B3LYP functional, the supercell scheme and the CRYSTAL code. It turns out that: (i) when the distance between the two defects is larger than 6-7 Å, the properties of the double defect are the superposition of the properties of the individual defects. (ii) The energy required for the reaction NV + N→ NV + N is roughly -1.

Oxygen and vacancy defects in silicon. A quantum mechanical characterization through the IR and Raman spectra.

The Infrared (IR) and Raman spectra of various defects in silicon, containing both oxygen atoms (in the interstitial position, O) and a vacancy, are computed at the quantum mechanical level by using a periodic supercell approach based on a hybrid functional (B3LYP), an all-electron Gaussian-type basis set, and the Crystal code. The first of these defects is VO: the oxygen atom, twofold coordinated, saturates the unpaired electrons of two of the four carbon atoms on first neighbors of the vacancy. The two remaining unpaired electrons on the first neighbors of the vacancy can combine to give a triplet (S = 1) or a singlet (S = 0) state; both states are investigated for the neutral form of the defect, together with the doublet solution, the ground state of the negatively charged defect.

Interstitial carbon defects in silicon. A quantum mechanical characterization through the infrared and Raman spectra.

The Infrared (IR) and Raman spectra of various interstitial carbon defects in silicon are computed at the quantum mechanical level by using an all electron Gaussian type basis set, the hybrid B3LYP functional and the supercell approach, as implemented in the CRYSTAL code (Dovesi et al. J. Chem.

First principles calculations of the vibrational properties of single and dimer F-type centers in corundum crystals.

The present paper investigates the F-type centers in α-AlO through their electronic and vibrational properties from first principle calculations using a periodic supercell approach, a hybrid functional, and all-electron Gaussian basis sets as implemented in the CRYSTAL17 code. Single F-type and dimer F-type centers related to oxygen vacancies in various charge states were considered. The defect-induced vibrational modes were identified and found to appear mainly in the low (up to 300 cm) and high (above 700 cm) frequency regions, depending on the defect charge.

Predicted strong spin-phonon interactions in Li-doped diamond.

DFT calculations of the Li substitutional defect in diamond based on the B3LYP functional and a 64-atom supercell indicate that (i) the quartet (Sz = 3/2) state is lower in energy than the doublet (Sz = 1/2) state by 0.07 eV (810 K) for fully relaxed static structures and by 0.09 eV (1045 K) with the inclusion of zero-point vibrations, (ii) the effective charges at the Li and four neighbouring C sites are similar in the two spin states, but there are substantial differences in the corresponding spin distributions, and (iii) there are unprecedented differences in the Raman spectra of the two spin states, in terms of both frequency distributions and intensities, that can most reasonably be attributed to strong spin-phonon coupling, in view of the very similar charge distributions in the two states.

Microscopic Characterization of Oxygen Defects in Diamond as Models for N3 and OK1 Defects: A Comparison of Calculated and Experimental Electron Paramagnetic Resonance Data.

The local structure and composition of the diamond paramagnetic defects labelled N3 and OK1 in which two heteroatoms (one of them is nitrogen) occupy vicinal substitutional positions are still a matter of debate. The electron paramagnetic resonance (EPR) is the technique adopted experimentally to characterize these defects, whose ground state is a doublet. In the present study, two models suggested in literature that contain N and O impurities are investigated at the quantum mechanical level by using the supercell model, a local Gaussian-type basis set, and the hybrid B3LYP functional as implemented in the CRYSTAL code.

Interstitial defects in diamond: A quantum mechanical simulation of their EPR constants and vibrational spectra.

The local geometry, electronic structure, and vibrational features of three vicinal double interstitial defects in diamond, II, II, and II, are investigated and compared with those of three "simple" ⟨100⟩ interstitial defects, I, I, and I, previously reported by Salustro et al. [Phys. Chem.