Spin Currents via the Gauge Principle for Meta-Generalized Gradient Exchange-Correlation Functionals.

The prominence of density functional theory in the field of electronic structure computation stems from its ability to usefully balance accuracy and computational effort. At the base of this ability is a functional of the electron density: the exchange-correlation energy. This functional satisfies known exact conditions that guide the derivation of approximations. The strongly constrained and appropriately normed (SCAN) approximation stands out as a successful, modern, example. In this Letter, we demonstrate how the SU(2) gauge invariance of the exchange-correlation functional in spin current density functional theory allows us to add an explicit dependence on spin currents in the SCAN functional (here called JSCAN)-and similar meta-generalized-gradient functional approximations-solely invoking first principles. In passing, a spin-current dependent generalization of the electron localization function (here called JELF) is also derived. The extended forms are implemented in a developer's version of the crystal23 program. Applications on molecules and materials confirm the practical relevance of the extensions.

Unveiling the Role of Spin Currents on the Giant Rashba Splitting in Single-Layer WSe2.

The Rashba spin splitting in uniaxial, inversion-asymmetric materials has attracted considerable interest for spintronic applications. The most widely used theoretical framework to model such states is Kohn-Sham density functional theory (DFT) in combination with standard (semi)local exchange-correlation density functional approximations (DFAs). However, in the presence of spin-orbit coupling, DFT misses contributions due to modification of the many-body interaction by spin currents J⃗. Inclusion of the latter effects requires a spin current DFT (SCDFT) formulation, which is seldom considered. We investigate the giant Rashba splitting in single-layer WSe2, and we quantify the effect of including spin currents in DFAs of the SCDFT. Crucially, we show that SCDFT allows fully capturing the giant Rashba band splitting in single-layer WSe2, otherwise previously systematically underestimated by standard (semi)local DFAs within the DFT framework. We find the inclusion of J⃗ on the DFA increases the Rashba splitting by about 20%.

First-Principles Anharmonic Infrared and Raman Vibrational Spectra of Materials: Fermi Resonance in Dry Ice.

We introduce a computational tool for the quantum-mechanical simulation of anharmonic infrared and Raman vibrational spectra of materials. The approach, implemented in the CRYSTAL software, stems from Taylor's expansion of the potential energy surface (PES) on the basis of normal modes up to cubic and quartic terms. The PES can be sampled with four different numerical schemes at the level of density functional theory (DFT), with local, generalized-gradient, and hybrid density functional approximations. Anharmonic states are obtained by solving Shrödinger's nuclear equation with either the vibrational self-consistent field (VSCF) or vibrational configuration interaction (VCI) methods. Nuclear quantum effects (NQEs) are thus fully accounted for. Infrared intensities are computed numerically through a Berry phase approach or analytically through a coupled-perturbed (CP) approach. Raman intensities are computed analytically via the CP approach. A variety of anharmonic features of vibrational spectra of materials can be simulated, including band shifts, combination bands, overtones, resonances (first-order Fermi, second-order Darling-Dennison), and hot bands. We showcase the effectiveness of the approach on the description of a first-order Fermi resonance (FR) in CO2 dry ice: a challenging test-case given that the FR occurs in the Raman spectrum, requires NQEs, and involves two- and three-mode couplings. Fundamental mechanistic differences with respect to the well-known FR in molecular CO2 are addressed. This application represents the first quantum-mechanical, periodic description of FR in dry ice.

Photoelasticity of CNGS crystals.

All piezo-optic coefficients (POCs) and elasto-optic coefficients (ELOCs) of C a 3 N b G a 3 S i 2 O 14 (CNGS) and C a 3 T a G a 3 S i 2 O 14 (CTGS) trigonal crystals of the langasite group are determined from quantum mechanical calculations based on the hybrid density functional theory, as implemented in the CRYSTAL program. The calculation results for CTGS crystals are compared with experimental data. Indicative surfaces of piezo- and elasto-optic effects are constructed based on the POC and ELOC matrices of CNGS crystals and the largest values of these effects are determined. The maximum values of the coefficient of the acousto-optic figure of merit M 2 of the CNGS crystal are determined for the geometries of elasto-optic interaction, which correspond to the maxima of the elasto-optic effect. These results are compared to the corresponding results for CTGS and langasite crystals. The spectral dependence of the POCs and ELOCs of CNGS and CTGS crystals on the light wavelength is investigated in the 600-1500 nm range.

Anharmonic Coupling of Stretching Vibrations in Ice: A Periodic VSCF and VCI Description.

The anharmonicity of O-H stretching vibrations of water ice is characterized by use of a periodic implementation of the vibrational self-consistent field (VSCF) and vibrational configuration interaction (VCI) methods, which take phonon-phonon couplings explicitly into account through numerical evaluation of high-order terms of the nuclear potential. The low-temperature, proton-ordered phase of water ice (namely, ice XI) is investigated. The net effect of a coupled anharmonic treatment of stretching modes is not just a rigid blue-shift of the respective harmonic spectral frequencies but rather a complex change of their relative spectral positions, which cannot be captured by simple scaling strategies based on harmonic calculations. The adopted techniques allow for a hierarchical treatment of anharmonic terms of the nuclear potential, which is key to an effective identification of leading factors. We show that the anharmonic independent-mode approximation─only describing the "intrinsic anharmonicity" of the O-H stretches─is unable to capture the correct physics, and that couplings among O-H stretches must be described. Inspection of harmonic normal coordinates allows identification of specific features of the O-H stretching motions which most likely enable strong mode-mode couplings. Finally, by coupling O-H stretches to all other possible modes of ice XI (THz collective vibrations, molecular librations, bendings), we identify specific types of motion which significantly affect O-H stretching states: in particular, molecular librations are found to affect the stretching states more than molecular bendings.

Thermoelasticity of Flexible Organic Crystals from Quasi-harmonic Lattice Dynamics: The Case of Copper(II) Acetylacetonate.

A computationally affordable approach, based on quasi-harmonic lattice dynamics, is presented for the quantum-mechanical calculation of thermoelastic moduli of flexible, stimuli-responsive, organic crystals. The methodology relies on the simultaneous description of structural changes induced by thermal expansion and strain. The complete thermoelastic response of the mechanically flexible metal-organic copper(II) acetylacetonate crystal is determined and discussed in the temperature range 0-300 K. The elastic moduli do not just shrink with temperature but they do so anisotropically. The present results clearly indicate the need for an explicit account of thermal effects in the simulation of mechanical properties of elastically flexible organic materials. Indeed, predictions from standard static calculations on this flexible metal-organic crystal are off by up to 100%.

Probing the Site-Selective Doping in SrSnO3:Eu Oxides and Its Impact on the Crystal and Electronic Structures Using Synchrotron Radiation and DFT Simulations.

The impact of Eu3+ doping at the Sr2+ and Sn4+ sites in SrSnO3 on its structural and electronic properties was studied and correlated with the photocatalytic efficiency. The compounds were synthesized using a modified Pechini method. Refinement of the synchrotron X-ray diffraction (S-XRD) data showed that the samples had an orthorhombic Pbnm symmetry. The incorporation of Eu into the lattice led to increased short- and long-range disorder, inducing additional distortion in the SnO6. XANES measurements revealed that mixed Eu valences (Eu3+ and Eu2+) were present in Eu-doped samples, and DFT calculations confirmed the presence of these ions at Sr2+/Sr4+ sites in the SrSnO3, resulting in changes in the electronic behavior. The catalytic performance toward Remazol yellow dye photodegradation and the catalysts' surface properties were also evaluated. The catalytic efficiency followed the order of Sr(Sn0.99Eu0.01)SnO3 > (Sr0.99Eu0.01)SnO3 > SrSnO3. The order was clearly related to selected-site doping that changed the degree of the inter- and intraoctahedral distortion and the introduction of different Eu midgap states, which apparently favor charge separation upon photoexcitation during photocatalysis. The results shown here are of great importance to the functionalization of SrSnO3 and other perovskite materials by lanthanoid ions, especially Eu3+, for effective applications as photocatalysts.

Elucidating the structure and dynamics of CO ad-layers on MgO surfaces.

The combination of quantum-mechanical simulations and infrared absorption spectroscopy measurements provides a clear picture for a long standing puzzle in surface science: the actual structure and vibrational dynamics of the low-temperature ordered CO monolayer adsorbed on (001) MgO surfaces. The equilibrium structure of the commensurate (4 × 2) adsorbed phase consists of three CO molecules per primitive cell (surface coverage of 75%) located at two inequivalent sites: one molecule seats upright on top of a Mg site while two molecules, tilted off the normal to the surface, are symmetrically positioned relative to the upright one with anti-parallel projections on the surface. This configuration, long believed to be incompatible with measured polarization infrared spectra, is shown to reproduce all observed spectral features, including a new, unexpected one: the vanishing anharmonicity of CO stretching modes in the monolayer.

Anharmonic Vibrational States of Solids from DFT Calculations. Part I: Description of the Potential Energy Surface.

A computational approach is presented to compute anharmonic vibrational states of solids from quantum-mechanical DFT calculations by taking into explicit account phonon-phonon couplings via the vibrational configuration interaction (VCI) method. The Born-Oppenheimer potential energy surface (PES) is expanded in a Taylor's series in terms of harmonic normal coordinates, centered at the equilibrium nuclear configuration, is truncated to quartic order, and contains one-mode, two-mode, and three-mode interatomic force constants. The description of the anharmonic terms of the PES involves the numerical evaluation of high-order energy derivatives (cubic and quartic in our case) with respect to nuclear displacements and constitutes the most computationally demanding step in the characterization of anharmonic vibrational states of materials. Part I is devoted to the description of the PES. Four different numerical approaches are presented for the description of the potential, all based on a grid representation of the PES in the basis of the normal coordinates, that require different ingredients (energy and/or forces) to be evaluated at each point (i.e., nuclear configuration) of the grid. The numerical stability and relative computational efficiency of the various schemes for the description of the PES are discussed on two molecular systems (water and methane) and two extended solids (Ice-XI and MgH2). All the presented algorithms are implemented into a developmental version of the Crystal program.

Anharmonic Vibrational States of Solids from DFT Calculations. Part II: Implementation of the VSCF and VCI Methods.

Two methods are implemented in the Crystal program for the calculation of anharmonic vibrational states of solids: the vibrational self-consistent field (VSCF) and the vibrational configuration-interaction (VCI). While the former is a mean-field approach, where each vibrational mode interacts with the average potential of the others, the latter allows for an explicit and complete account of mode-mode correlation. Both schemes are based on the representation of the adiabatic potential energy surface (PES) discussed in Part I, where the PES is expanded in a Taylor's series so as to include up to cubic and quartic terms. The VSCF and VCI methods are formally presented and their numerical parameters discussed. In particular, the convergence of computed anharmonic vibrational states, within the VCI method, is investigated as a function of the truncation of the expansion of the nuclear wave function. The correctness and effectiveness of the implementation is discussed by comparing with available theoretical and experimental data on both molecular and periodic systems. The effect of the adopted basis set and exchange-correlation functional in the description of the PES on computed anharmonic vibrational states is also addressed.

A quantum-mechanical investigation of oxygen vacancies and copper doping in the orthorhombic CaSnO3 perovskite.

In this study we explore the implications of oxygen vacancy formation and of copper doping in the orthorhombic CaSnO3 perovskite, by means of density functional theory, focusing on energetic and electronic properties. In particular, the electronic charge distribution is analyzed by Mulliken, Hirshfeld-I, Bader and Wannier approaches. Calculations are performed at the PBE and the PBE0 level (for doping with Cu, only PBE0), with both spin-restricted and spin-unrestricted formulations; unrestricted calculations are used for spin-polarized cases and for the naturally open-shell cases (Cu doping). An oxygen vacancy is found to have the tendency to reduce Sn neighbors by giving rise to an energy band within the energy band-gap of the pristine system, close to the valence band. At variance with what happens in the CaTiO3 perovskite (also investigated here), an oxygen vacancy in the CaSnO3 perovskite is found to lose two valence electrons and thus to be positively charged so that no F-center is formed. Regarding Cu doping, when one Sn atom is substituted by a Cu one, the most stable configuration corresponds to having the Cu atom as a first neighbor to the vacancy. These findings shed some light on the catalytic and phosphorous host properties of this perovskite.

Thermal properties of molecular crystals through dispersion-corrected quasi-harmonic ab initio calculations: the case of urea.

An ab initio quantum-mechanical theoretical framework is presented to compute the thermal properties of molecular crystals. The present strategy combines dispersion-corrected density-functional-theory (DFT-D), harmonic phonon dispersion, quasi-harmonic approximation to the lattice dynamics for thermal expansion and thermodynamic functions, and quasi-static approximation for anisotropic thermo-elasticity. The proposed scheme is shown to reliably describe thermal properties of the urea molecular crystal by a thorough comparison with experimental data.

Assessing thermochemical properties of materials through ab initio quantum-mechanical methods: the case of α-Al2O3.

The thermochemical behavior of α-Al2O3 corundum in the whole temperature range 0-2317 K (melting point) and under pressures up to 12 GPa is predicted by applying ab initio methods based on the density functional theory (DFT), the use of a local basis set and periodic-boundary conditions. Thermodynamic properties are treated both within and beyond the harmonic approximation to the lattice potential. In particular, a recent implementation of the quasi-harmonic approximation, in the Crystal program, is here shown to provide a reliable description of the thermal expansion coefficient, entropy, constant-volume and constant-pressure specific heats, and temperature dependence of the bulk modulus, nearly up to the corundum melting temperature. This is a remarkable outcome suggesting α-Al2O3 to be an almost perfect quasi-harmonic crystal. The effect of using different computational parameters and DFT functionals belonging to different levels of approximations on the accuracy of the thermal properties is tested, providing a reference for further studies involving alumina polymorphs and, more generally, quasi-ionic minerals.