Linear Combination Of Atomic Orbitals Approach Research Articles

Valence-to-core X-ray emission spectroscopy of transition metal tetrahalides: mechanisms governing intensities.

Valence-to-core (VtC) X-ray emission spectroscopy offers the opportunity to probe the valence electronic structure of a system filtered by selection rules. From this, the nature of its ligands can be inferred. While a preceding 1s ionization creates a core hole, in VtC XES this core hole is filled with electrons from mainly ligand based orbitals. In this work, we investigated the trends in the observed VtC intensities for a series of transition metal halides, which spans the first row transition metals from manganese to copper. Further, with the aid of computational studies, we corroborated these trends and identified the mechanisms and factors that dictate the observed intensity trends. Small amounts of metal p contribution to the ligand orbitals are known to give rise to intensity of a VtC transition. By employing an LCAO (linear combination of atomic orbitals) approach, we were able to assess the amount of metal p contribution to the ligand molecular orbitals, as well as the role of the transition dipole moment and correlate these factors to the experimentally observed intensities. Finally, by employing an ano (atomic natural orbital) basis set within the calculations, the nature of the metal p contribution (3p vs. 4p) was qualitatively assessed and their trends discussed within the same transition metal halide series.

Molecular Mechanism of the Piezoelectric Response in the β-Phase PVDF Crystals Interpreted by Periodic Boundary Conditions DFT Calculations.

A theoretical approach based on Periodic Boundary Conditions (PBC) and a Linear Combination of Atomic Orbitals (LCAO) in the framework of the density functional theory (DFT) is used to investigate the molecular mechanism that rules the piezoelectric behavior of poly(vinylidene fluoride) (PVDF) polymer in the crystalline β-phase. We present several computational tests highlighting the peculiar electrostatic potential energy landscape the polymer chains feel when they change their orientation by a rigid rotation in the lattice cell. We demonstrate that a rotation of the permanent dipole through chain rotation has a rather low energy cost and leads to a lattice relaxation. This justifies the macroscopic strain observed when the material is subjected to an electric field. Moreover, we investigate the effect on the molecular geometry of the expansion of the lattice parameters in the (a, b) plane, proving that the rotation of the dipole can take place spontaneously under mechanical deformation. By band deconvolution of the IR and Raman spectra of a PVDF film with a high content of β-phase, we provide the experimental phonon wavenumbers and relative band intensities, which we compare against the predictions from DFT calculations. This analysis shows the reliability of the LCAO approach, as implemented in the CRYSTAL software, for calculating the vibrational spectra. Finally, we investigate how the IR/Raman spectra evolve as a function of inter-chain distance, moving towards the isolated chain limit and to the limit of a single crystal slab. The results show the relevance of the inter-molecular interactions on the vibrational dynamics and on the electro-optical features ruling the intensity pattern of the vibrational spectra.

Raman activity of the longitudinal optical phonons of the LiNbO3 crystal: Experimental determination and quantum mechanical simulation

AbstractIn 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 correlation between experimental polarized Raman spectra and their density functional theory prediction in the LCAO framework: The R3c LiNbO3 crystal as a test case

AbstractIn this study, the polarized Raman spectra of the R3c LiNbO3 crystal are used as a benchmark test for density functional theory (DFT) full periodic boundary conditions linear combination of atomic orbitals (LCAO) calculation of the Raman tensors, according to the implementation in the CRYSTAL software. The theoretical approach used proved to provide excellent results regarding wavenumbers and relative intensities predictions for the transverse optical modes of both A1 and E symmetry, considerably improving over previously reported data based on the plane waves approach. Overall, the present investigation demonstrates that the LCAO approach, as implemented in the CRYSTAL software, gives excellent results regarding the calculation of Raman tensors and polarized Raman spectra. The possibility to put in correspondence the individual Raman tensors components and bands intensities in the different back‐scattering experimental configurations revealed that the computed Raman tensors are very accurate, not only considering their average values (tensors invariant in the combination suitable for the description of Raman scattering of isotropic materials) but also when the tensors individual components are considered. Based on the present results, a reassignment of the E (TO) modes of the R3c LiNbO3 crystal is proposed, in particular for the 2 E and 9 E modes, which have been a matter of discussion in the recent years.

Electronic and optical response of zirconium sulphoselenides: Compton spectroscopy and first-principles calculations

We present the first-ever experimental Compton profiles (CPs) of ZrSSe2 and ZrS1.5Se1.5 using 100 mCi 241Am Compton spectrometer. To analyze the experimental momentum densities, we have computed for the first-time the CPs, energy bands and density of states using linear combination of atomic orbitals (LCAO) method. To model the exchange and correlation effects within LCAO approach, we have considered Hartree–Fock (HF), density functional theory (DFT) with revised functional of Perdew–Becke–Ernzerhof (PBEsol) and hybridization of HF and DFT. Going beyond computation of electronic properties using LCAO method, we have also derived electronic and optical properties using the modified Becke–Johnson (mBJ) potential within full potential linearized augmented plane wave (FP-LAPW) method. There is notable decrease in the energy band gap on replacing S by Se atoms in ZrSSe2 to obtain ZrS1.5Se1.5 composition, which is mainly attributed to readjustment of Zr–4d, S–3p and Se–4p states. It is seen that the CPs based on hybridization of HF and DFT show a better agreement with the experimental profiles than those based on individual HF and DFT-GGA-PBEsol schemes. The optical properties computed using FP-LAPW-mBJ method unambiguously depict feasibility of using both the sulphoselenides in photovoltaics and also utility of ZrS1.5Se1.5 in the field of non-linear optics.

Electronic properties and Compton scattering studies of monoclinic tungsten dioxide

We present the first ever Compton profile measurement of WO2 using a 20 Ci 137Cs γ-ray source. The experimental data have been used to test different approximations of density functional theory in linear combination of atomic orbitals (LCAO) scheme. It is found that theoretical Compton profile deduced using generalized gradient approximation (GGA) gives a better agreement than local density approximation and second order GGA. The computed energy bands, density of states and Mulliken׳s populations (MP) data confirm a metal-like behavior of WO2. The electronic properties calculated using LCAO approach are also compared with those obtained using full potential linearized augmented plane wave method. The nature of bonding in WO2 is also compared with isoelectronic WX2 (X=S, Se) compounds in terms of equal-valence-electron-density profiles and MP data, which suggest an increase in ionic character in the order WSe2→WS2→WO2.

Minimax LCAO approach to the relativistic two-centre Coulomb problem and its finite element (FEM) spectrum

The one-electron relativistic diatomic systems H+2 and Th179+2 are solved in a two-spinor linear combination of atomic orbitals (LCAO) approach using a minimax principle equivalent to a constraint minimization. The values are in agreement with those of the finite element method (FEM) and of other approaches as far as results are available in the literature. No spurious or contaminated states are found. The complete spectrum for Th179+2 up to n = 6 correlating s1/2 to h11/2 states is given.

Ab initioperiodic approach to electronic structure and magnetic exchange inA2CuO2X2(A=Ca,Sr andX=F,Cl)high-Tcsuperconductor parent compounds

The electronic structure of ${A}_{2}{\mathrm{CuO}}_{2}{X}_{2}$ $(A=\mathrm{C}\mathrm{a},\mathrm{}\mathrm{Sr}$ and $X=\mathrm{F}\mathrm{},\mathrm{C}\mathrm{l})$ compounds is investigated by means of the periodic unrestricted Hartree-Fock (UHF) method using the linear combination of atomic orbitals approach (LCAO). The relative stability of different alternative structures is discussed. All the systems are described as insulators with strong ionic character and well localized spin moments on the Cu atoms. The O $2p$ nature of the highest occupied bands is clear, supporting the charge transfer nature of this kind of narrow band systems; optical gaps are however, overestimated. The magnetic ordering of these materials is two dimensional in nature with almost independent antiferromagnetic ${\mathrm{CuO}}_{2}$ planes with ${J}_{c}{/J}_{1}\ensuremath{\sim}{10}^{\ensuremath{-}3}.$ The in--plane nearest ${(J}_{1})$ and next-nearest ${(J}_{2})$ magnetic coupling constants are antiferromagnetic and much larger than the interplane interactions ${(J}_{c}),$ with ${J}_{2}{/J}_{1}\ensuremath{\sim}0.02.$ The relative values of the magnetic constants are in qualitative agreement with available experimental results. None of the analyzed properties provide differences between the various compounds so relevant to limit the possible development of a superconducting phase. On the contrary, the close similarity between them suggest that kinetic limitations in the doping process can be responsible of the fact that no superconducting transition has been observed in ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{2}{\mathrm{Cl}}_{2}$ and in the ${T}^{\ensuremath{'}}$ phase of ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{2}{\mathrm{F}}_{2}$ and ${\mathrm{Ca}}_{2}{\mathrm{CuO}}_{2}{\mathrm{F}}_{2}.$

First-principles study of structural, electronic and optical properties of BaF2in its cubic, orthorhombic and hexagonal phases

We present the results of a first-principles study on BaF2in its stable (cubic) and high-pressure phases. A linear combination of atomic orbitalsapproach in the framework of density functional theory is employed for totalenergy calculations in cubic, orthorhombic and hexagonal phases of BaF2.A fitting of the energy surface to the equation of state yields the lattice constant andthe bulk modulus of these phases at zero pressure which are in good agreement withthe corresponding experimental values. Analysis of band structure determines thehigh-pressure phases to be direct-gap materials and no metallization of BaF2is predicted to occur for pressures up to 50 GPa. Furthermore,several peaks observed in the spectroscopic experiments havebeen identified with interband transitions in the cubic BaF2.The calculated mean value of the refractive index is found to increase ingoing from the cubic to orthorhombic to hexagonal phases of BaF2.

Molecular-orbital theory for chemisorption: The case of H on normal metals.

An ab initio linear combination of atomic orbitals (LCAO) method is presented to calculate the electronic properties of solids. This method is based on the following points: (i) The total solution of the electronic system is obtained using an expansion of various physical parameters up to second order in the overlap between the different atomic orbitals; extensions to large-overlap cases are also discussed. (ii) The total many-body Hamiltonian is reduced to a superposition of Hamiltonian bonds, defined for each pair of atomic orbitals. (iii) The parameters for hopping between two orbitals are related to the Bardeen tunneling currents between the same wave functions; these tunneling currents play, in our approach, the same role as pseudopotentials in the free-electron theory of solids. (iv) Many-body effects are treated using a Slater-like approximation for the exchange and correlation interaction. We show that a many-body Slater-like potential can be introduced within our LCAO approach. Our method has been demonstrated by considering the simple molecules ${\mathrm{H}}_{2}$ and LiH. A further application has been made for the chemisorption problem of a hydrogen monolayer adsorbed on the Li(100) and Al(100) surfaces. Results are presented for the chemisorption energies, equilibrium distance of the adsorbed layer, and the density of states. Good agreement is found with our theoretical results and experiment. Our results indicate that the main mechanism for the hydrogen adsorption on simple metals is associated with the lowering of the hydrogen affinity level due to the electrostatic interaction with the metal atoms.

One-electron diatomics in momentum space. V. Nonvariational LCAO approach

The Fock transformation reduces the momentum-space Schrödinger equation for one-electron diatomics to a homogeneous Fredholm-type integral equation with a degenerate kernel. Two nonvariational linear combination of atomic orbitals (LCAO) solutions to this integral equation are rederived in a systematic manner and their mutual relation is clarified. The upper boundness of these nonvariational solutions is proved explicitly. Relative superiority of the two solutions is discussed theoretically based on their convergence rates. The momentum-space LCAO method is shown to reproduce the exact electronic energy for the hydrogen molecular ion at various internuclear distances.

Effect of the 110°K Phase Transition on the SrTiO3Conduction Bands

The linear-combination-of-atomic-orbitals (LCAO) model of the preceding paper for the cubic-SrTi${\mathrm{O}}_{3}$ band structure is applied to predict the effect of the 110 \ifmmode^\circ\else\textdegree\fi{}K phase transition on the SrTi${\mathrm{O}}_{3}$ conduction bands. In this cubic-to-tetragonal structural transformation, neighboring octahedral Ti${\mathrm{O}}_{6}$ complexes are rotated rigidly in opposite directions about the $c$ axis through small angles $\ifmmode\pm\else\textpm\fi{}\ensuremath{\phi}$. This LCAO approach is expected to be accurate since nearest-neighbor distances and bond angles are unchanged in this transition. This enables one to apply the LCAO parameters for cubic SrTi${\mathrm{O}}_{3}$ to predict the band structure in the tetragonal state. The effects of the tetragonal distortion are introduced into the LCAO secular equation as small changes in the cubic structure factors, ${e}^{i\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{R}}}_{j}}$. Neglecting spin-orbit coupling, this model predicts a splitting of the ${\ensuremath{\Gamma}}_{{25}^{\ensuremath{'}}}$ conduction-band minimum by an energy proportional to ${\ensuremath{\phi}}^{2}$. At 4.2 \ifmmode^\circ\else\textdegree\fi{}K, where $\frac{c}{a}=1.0006$ and $\ensuremath{\phi}=2.1\ifmmode^\circ\else\textdegree\fi{}$, ${\ensuremath{\Gamma}}_{{25}^{\ensuremath{'}}}$ is split by about 90 meV into a lower doubly degenerate ${\ensuremath{\Gamma}}_{5}$ + state and an upper nondegenerate ${\ensuremath{\Gamma}}_{4}$+state. Spin-orbit coupling further splits the ${\ensuremath{\Gamma}}_{5}$+state by an energy comparable with the titanium $3d$ spin-orbit parameter, ${\ensuremath{\xi}}_{3d}\ensuremath{\approx}25$ meV. This produces a warped single-valley model for the SrTi${\mathrm{O}}_{3}$ conduction bands at low carrier densities $n$ and a two-band model containing "heavy" and "light" electrons for $n>{10}^{19}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. It is shown that the splitting of the conduction-band minimum in SrTi${\mathrm{O}}_{3}$ is similar in magnitude but opposite in sign to that caused by the ferroelectric transition in BaTi${\mathrm{O}}_{3}$.