Local Orbital Basis Research Articles

Exploration of the structure, electronic and optical properties of AB 2(PO3)5 polyphosphates: a first-principle approach

The density functional theory method was applied using the gradient PBE, incorporating the hybrid PBE0 functional along with dispersion corrections D3(BJ). These objectives were accomplished through the utilization of the CRYSTAL package, employing a localized atomic orbital basis. Calculations encompassing crystal properties, including electronic, structural, and linear/nonlinear opto-electronic characteristics, were conducted for monoclinic AB 2(PO3)5. Specifically, the polyphosphates investigated in this study are RbPb2(PO3)5, CsPb2(PO3)5, KBa2(PO3)5, and RbBa2(PO3)5. It was demonstrated that in monoclinic phosphates, phosphorus and oxygen atoms form infinite chains [PO4]∞ based on the· ⋯ O1-P-O1 ⋯ ·structure. Alkali metal and lead (barium) atoms are surrounded by oxygen atoms O2, forming polyhedra. Infrared absorption spectra calculations confirmed the presence of chain backbone structural units. Additionally, band structure and partial density of electronic states were determined. The nature of valence and unoccupied states was also investigated. In lead-doped compounds, lead atoms contribute to the formation of upper-valence and lower-unoccupied states. Conversely, in barium-doped compounds, the upper valence states are primarily formed by O2 p-states, while the lower unoccupied states are formed by phosphorus. Also, the coefficients of second harmonic generation and birefringence were calculated, assessing the potential use of phosphates as nonlinear optical materials.

Improving Predictions of Spin-Crossover Complex Properties through DFT Calculations with a Local Hybrid Functional.

We conducted a study on the performance of the local hybrid exchange-correlation functional PBE0r for a set of 95 experimentally characterized iron spin-crossover (SCO) complexes [Vennelakanti, V.; J. Chem. Phys. 2023, 159, 024120]. The PBE0r functional is a variant of PBE0 where the exchange correction is restricted to on-site terms formulated on the basis of local orbitals. We determine the free parameters of the PBE0r functional against the experimental data and other hybrid functionals. With a Hartree-Fock (HF) exchange factor of 4%, the PBE0r functional accurately reproduces the electronic and free-energy trends predicted in prior DFT studies for these 95 complexes by using the B3LYP functional. Larger values of HF exchange stabilize high-spin states. The PBE0r-predicted bond lengths tend to exceed the experimental bond lengths, although bond lengths are less sensitive to HF exchange than in global hybrids. The predicted SCO transition temperatures T1/2 from PBE0r correlate moderately with the experimental transition temperatures, showing a slight improvement compared to the previous modB3LYP-predicted T1/2. This study suggests that the PBE0r functional is computationally cost-effective and offers the possibility of simulating larger complexes with accuracy comparable to global hybrid functionals, provided the HF-exchange parameter is carefully optimized.

Nonlinear optical, dielectric, and piezoelectric properties of hexagonal fluorocarbonates ABCO3F (A: K, Rb, Cs; B: Mg, Ca, Sr, Zn, Cd, Pb) from first principles

Within the density functional theory, the Hartree–Fock/Kohn–Sham-coupled perturbation method using the basis of localized orbitals, the gradient PBE functional with dispersion correction D3(BJ) and hybrid PBE0 and B3LYP functionals, the structural, dielectric, and piezoelectric properties of hexagonal alkali fluorocarbonates ABCO3F (A: K, Rb, Cs; B: alkaline earth (Mg, Ca, Sr) and [Formula: see text] (Zn, Cd, Pb)) were evaluated. In the series of crystals, fluorocarbonates with lead have the highest values of the calculated components of the dielectric constant tensor, piezoelectric constants, and nonlinear optical (NLO) coefficients.

Investigation of the Optical Spectra of Barium-Zinc (Aluminum) Fluoroborates and Barium-Zinc Fluorocarbonate from First Principles

The Raman scattering, infrared absorption, and reflection spectra of hexagonal non-centrosymmetric BaZnBO3F and BaAlBO3F2 and centrosymmetric BaZn3BO3F2 and BaZnCO3F2 are calculated using the standard procedures of the CRYSTAL package with the basis of localized orbitals and the B3LYP hybrid functional within the framework of the Hartree-Fock conjugate perturbation method. It is shown that the layered structure of crystals manifests itself in the spectra of vibrational modes polarized along and perpendicular to the c axis with wavenumbers for the lattice region formed by displacements of atoms in [BaF]∞ and [MAO3]∞ (M: Zn, Al; A: B, C) layers, for molecular deformation outside and in the plane of anions BO3 and CO3. The quantitative and qualitative composition of the spectra is determined by the symmetry of the crystal lattice.

A comprehensive study of the velocity, momentum and position matrix elements for Bloch states: Application to a local orbital basis

We present a comprehensive study of the velocity operator, \hat{\boldsymbol{v}}=\frac{i}{\hbar} [\hat{H},\hat{\boldsymbol{r}}]\,𝐯̂=iℏ[Ĥ,𝐫̂], when used in crystalline solids calculations. The velocity operator is key to the evaluation of a number of physical properties and its computation, both from a practical and fundamental perspective, has been a long-standing debate for decades. Our work summarizes the different approaches found in the literature, but never connected before in a comprehensive manner. In particular we show how one can compute the velocity matrix elements following two different routes. One where the commutator is explicitly used and another one where the commutator is avoided by relying on the Berry connection. We work out an expression in the latter scheme to compute velocity matrix elements, generalizing previous results. In addition, we show how this procedure avoids ambiguous mathematical steps and how to properly deal with the two popular gauge choices that coexist in the literature. As an illustration of all this, we present several examples using tight-binding models and local density functional theory calculations, in particular using Gaussian-type localized orbitals as basis sets. We show how the the velocity operator cannot be approximated, in general, by the k-gradient of the Bloch Hamiltonian matrix when a non-orthonormal basis set is used. Finally, we also compare with its real-space evaluation through the identification with the canonical momentum operator when possible. This comparison offers us, in addition, a glimpse of the importance of non-local corrections, which may invalidate the naive momentum-velocity correspondence.

A full-potential and multiscale computational scheme for interactions between ultrafast intense laser pulses and condensed medium

We have presented a multiscale computational scheme for the simulation of interactions between ultrafast intense laser pulses and condensed medium. This approach solves the coupled time-dependent Kohn-Sham (TDKS) and Maxwell equations in real time and provides a unified description of microscopic electron dynamics and macroscopic light propagation from first principles and applicable to wide ultrafast phenomena. Especially, as the TDKS equation was solved within the framework of all-electron full-potential and the augmented plane wave with local orbitals basis sets were adopted, this approach overcomes the drawbacks of real space grids and pseudopotential approximations and works well for some extreme conditions that the information near the nucleus is important. We demonstrated the approach by calculating the microscopic electron dynamics of crystalline silicon (Si) excited with an intense laser pulse and the macroscopic propagation of a laser pulse in a ∼3.5 μm free standing Si film with the feedback of microscopic electron dynamics coupled together. We also verified the availability of this approach under extreme condition with hundreds TPa (1 TPa = 1012 Pa) pressure in a metallic solid neon, and reasonable results were obtained. Our approach provides a new paradigm for multiscale simulations of ultrafast phenomena that induced by intense laser pulses in condensed medium.

Chemical Bonding Effects and Physical Properties of Noncentrosymmetric Hexagonal Fluorocarbonates ABCO3F (A: K, Rb, Cs; B: Mg, Ca, Sr, Zn, Cd).

The present work applied the methods of density functional theory and the van der Waals interaction PBE + D3(BJ) on the basis of localized orbitals of the CRYSTAL17 package. It featured the effect of interactions between structural elements of fluorocarbonates ABCO3F (A: K, Rb, Cs; B: Mg, Ca, Sr, Zn, Cd) on their elastic and vibrational properties. The hexagonal structures proved to consist of alternating ···B-CO3··· and ···A-F··· layers in planes ab, interconnected along axis c by infinite chains ···F-B-F···, where cations formed polyhedra AOnF3 and BOmF2. The calculations included the band energy structure, the total and partial density of electron states, the energy and band widths of the upper ns- and np-states of alkali and alkaline-earth metals, as well as nd-zinc and nd-cadmium. For hydrostatic compression, we calculated the parameters of the Birch–Murnaghan equation of state and the linear compressibility moduli along the crystal axes and bond lines. We also defined the elastic constants of single crystals to obtain the Voigt–Reuss–Hill approximations for the elastic moduli of polycrystalline materials. The study also revealed the relationship between the elastic properties and the nature of the chemical bond. Hybrid functional B3LYP made it possible to calculate the modes of normal long-wavelength oscillations, which provided the spectra of infrared absorption and Raman scattering. Intramolecular modes ν1 and ν4 with one or two maxima were found to be intense, and their relative positions depended on the lengths of nonequivalent C–O bonds.

Effective hamiltonian of crystal field method for periodic systems containing transition metals

Effective Hamiltonian of Crystal Field (EHCF) is a hybrid quantum chemical method originally developed for an accurate treatment of highly correlated d-shells in molecular complexes of transition metals. In the present work, we generalise the EHCF method to periodic systems containing transition metal atoms with isolated d-shells, either as a part of their crystal structure or as point defects. A general solution is achieved by expressing the effective resonance interactions of an isolated d-shell with the band structure of the crystal in terms of the Green's functions represented in the basis of local atomic orbitals. Such representation can be obtained for perfect crystals and for periodic systems containing atomic scale defects. Our test results for transition metal oxides (MnO, FeO, CoO, and NiO) and MgO periodic solid containing transition metal impurities demonstrate the ability of the EHCF method to accurately reproduce the spin multiplicity and spatial symmetry of the ground state. For the studied materials, these results are in a good agreement with experimentally observed d-d transitions in optical spectra. The proposed method is discussed in the context of modern solid state quantum chemistry and physics.

Ionic forces and stress tensor in all-electron density functional theory calculations using an enriched finite-element basis

The enriched finite-element basis---wherein the finite-element basis is enriched with atom-centered numerical functions---has recently been shown to be a computationally efficient basis for systematically convergent all-electron density functional theory (DFT) ground-state calculations. In this work, we present the expressions to compute variationally consistent ionic forces and stress tensor for all-electron DFT calculations in the enriched finite-element basis. In particular, we extend the formulation of configurational forces [P. Motamarri and V. Gavini, Phys. Rev. B 97, 165132 (2018)] to the enriched finite-element basis and elucidate the additional contributions arising from the enrichment functions. We demonstrate the accuracy of the formulation by comparing the computed forces and stresses for various benchmark systems with those obtained from finite differencing the ground-state energy. Further, we also benchmark our calculations against the Gaussian basis for molecular systems and against the linearized augmented plane wave with local orbitals basis for periodic systems.

A closed local-orbital unified description of DFT and many-body effects

Density functional theory (DFT) is usually formulated in terms of the electron density as a function of position n(r). Here we discuss an alternative formulation of DFT in terms of the orbital occupation numbers {n α } associated with a local-orbital orthonormal basis set {ϕ α }. First, we discuss how the building blocks of DFT, namely the Hohenberg–Kohn theorems, the Levy–Lieb approach and the Kohn–Sham method, can be adapted for a description in terms of {n α }. In particular, the total energy is now a function of {n α }, E[{n α }], and a Kohn–Sham-like Hamiltonian is derived introducing the effects of the electron–electron interactions via effective potentials, . In a second step we consider the Hartree and exchange energies and discuss how to describe them, in the spirit of a DFT approach, in terms of the orbital occupation numbers. In this contribution special attention is paid to the description of the (intra-atomic) correlation energy and corresponding correlation potentials {V corr,α }. For this purpose, a model system is analyzed in detail, whereby an atomic Hamiltonian interacts with the environment via a simplified model; the use of this model allows us to obtain the correlation energy and potentials (in terms of {n α }) for different cases corresponding to low, intermediate and high electron correlations.

First-principle studies of electronic, elastic and vibrational properties of barytocalcite and paralstonite

The crystal structure, electronic, elastic and vibrational properties of two natural BaCa(CO3)2 polymorphs (barytocalcite and paralstonitis) were studied by the density functional theory methods using the hybrid B3LYP and gradient PBE functionals, taking into account the dispersion correction D3 to the total energy in the basis of localized orbitals of the CRYSTAL package, under the pressure about 3 GPa. It is shown that the cell volume of hexagonal paralstonite obtained by the PBE-D3 method per formula unit is 0.065 Å3 larger, and the total energy is 0.011 eV lower than that of a monoclinic barytocalcite. The parameters of the equation of state in the Birch-Murnaghan form are determined. The elastic constants of single crystals and, in the Voigt-Royce-Hill approximation, the elastic moduli and elastic wave velocities of polycrystals are calculated. In the electron energy spectrum, the width of the upper valence band is 0.85 eV in barytocalcite, and 0.94 eV in paralstonite, while the band gap is 4.85 eV and 4.36 eV, respectively, and it decreases with increasing pressure at rates of − 0.01 and − 0.02 eV/GPa. The frequencies and intensities of normal long-wave oscillations are calculated with the B3LYP functional. It is shown that qualitative differences in the spectra of infrared absorption and Raman scattering of light for two phases should be sought in the range of 1300÷1580 cm−1 in the region of intramolecular vibrations, and for the spectra of infrared absorption in the region of 260÷310 cm−1, and for light scattering in the range of 130÷180 cm−1 in the region of lattice vibrations.

First-Principle Studies of the Structural, Electronic, Mechanical, and Vibrational Properties of Double Carbonates with a Dolomite Structure

Density functional theory with a PBE gradient functional and a dispersion correction D3(BJ) in the basis of localized orbitals of the CRYSTAL17 package are used to calculate crystal structure parameters, electronic and vibrational spectra, elastic constants of rhombohedral double carbonates М1М2 (СО3)2 (М1, М2: Mg, Ca, Mn, Cd, Zn) with a dolomite-type structure. The paper demonstrates the possibility for establishing the linear dependences for lattice constants, interatomic distances, elastic constants and polycrystalline moduli, wave numbers of individual vibrational modes on the radii of cations. The same possibility is shown for the dependences of the parameters of chemical bonds and formation energies on their electronegativities. The lattice parameters increase along with the average cation radius, but the elastic constants and moduli demonstrate their decrease. The highest compressibility of carbonates is predicted in the direction of the c axis, which is consistent with the nature of the chemical bond, where stronger carbon — oxygen bonds are present in the ab plane, and weaker metal — oxygen bonds are in the direction of the c axis. The formation energy of binary carbonates CaMg(CO3)2 produced from solid oxides and gaseous CO2 is equal to -2.82 eV. It is equal to -2.71 eV for CaCd(CO3)2, and -0.054 eV, 0.023 eV for simple carbonates, respectively. The resulting formulas can be used to assess and predict the physical properties of solid solutions of carbonates of variable composition.

Ab initio исследования влияния давления на структуру, электронные и упругие свойства карбонатов щелочных--щелочно-земельных металлов

Density functional theory with a gradient PBE functional and dispersion correction D3(BJ) in the basis of localized orbitals of the CRYSTAL17 package was used to study the effect of pressure on the structural, electronic, and elastic properties of K2Ca(CO3)2, K2Mg(CO3)2, Na2Ca2(CO3)3, Na2Mg(CO3)2. The parameters of the third-order Birch-Murnaghan equation of state are determined, and it is shown that the equilibrium volume and compressibility modulus depend linearly on the average cation radius. Under pressure, the widths of the upper valence bands increase maximally in K2Ca(CO3)2 and minimally in Na2Ca2(CO3)3, while the centers of gravity of the cationic states shift by ~0.2 eV. Elastic constants and polycrystalline moduli are calculated, which increase with decreasing average cation radius. The shear modulus for K2Ca(CO3)2 and K2Mg(CO3)2 decreases with increasing pressure, and this leads to anomalous behavior of the longitudinal and transverse acoustic wave velocities.

Ab initio studies of the effect of pressure on the structure, electronic and elastic properties of carbonates of alkali-alkaline earth metals

Density functional theory with a gradient PBE functional and dispersion correction D3(BJ) in the basis of localized orbitals of the CRYSTAL17 package was used to study the effect of pressure on the structural, electronic, and elastic properties of K2Ca(CO3)2, K2Mg(CO3)2, Na2Ca2(CO3)3, Na2Mg(CO3)2. The parameters of the third-order Birch--Murnaghan equation of state are determined, and it is shown that the equilibrium volume and compressibility modulus depend linearly on the average cation radius. Under pressure, the widths of the upper valence bands increase maximally in K2Ca(CO3)2 and minimally in Na2Ca2(CO3)3, while the centers of gravity of the cationic states shift by ~0.2 eV. Elastic constants and polycrystalline moduli are calculated, which increase with decreasing average cation radius. The shear modulus for K2Ca(CO3)2 and K2Mg(CO3)2 decreases with increasing pressure, and this leads to anomalous behavior of the longitudinal and transverse acoustic wave velocities. Keywords: ab initio calculations, buchliite, eithelite, shortite, equation of state, elastic moduli, density of states, pressure.

Exploiting the nearsightedness principle within the framework of the anti‐Hermitian contracted Schrödinger equation

AbstractThis work exploits the Kohn nearsightedness principle in the algorithms arising from the anti‐Hermitian contracted Schrödinger equation. The procedure provides the implementation of approximations yielding a considerable saving of computational costs in descriptions of N‐electron molecular systems by means of that technique. We report energies, at correlated level, of linear hydrogen chains designed at different geometries, so that we can analyze the strength of the interactions between first‐, second‐, third‐, fourth‐, and so forth neighbor atoms. Using localized molecular orbital basis sets, we observe rapid decays in the values of the elements of the reduced‐density‐matrix cumulant matrices, beyond a cut‐off radius, which justify the proposed approximations. The results, in terms of energies and reduced density matrices, have been compared with those obtained from the full configuration interaction method, showing the usefulness of the nearsightedness principle in this methodology.

Research of cation dependences of structural and elastic properties of metal carbonates series by density functional theory calculations

Using the density functional theory methods with the PBE gradient functional, and taking into account the van der Waals interaction in the basis of localized atomic orbitals, using the CRYSTAL 17 program code, calculations of the structure and elastic constants for MgCO3, ZnCO3, CdCO3 CaCO3 in the calcite structure, CdMg(CO3)2, CaMg(CO3)2, CaZn(CO3)2 in the dolomite structure, BaMg(CO3)2 – norsethite, and CaCO3, SrCO3, PbCO3, BaCO3 in the aragonite structure are calculated. It is shown that the lattice constants, interatomic distances linearly depend on the cation radius RM, and the band gap, atomic charges, overlap populations of electron shells, and crystal density depend on cation electronegativity χM. Elastic compression constants and linear elastic moduli along the c axis are also described by RM. For polycrystalline bulk modulus BH, shear modulus GH, and Young's modulus EH, linear dependences with a good correlation coefficient were obtained: BH (GPa) = 175.95−84.89·RM, GH (GPa) = 87.57−46.05·RM, EH (GPa) = 224.36−103.59·RM. Similar dependences are established for the longitudinal and transverse speeds of sound, the Debye temperature and the coefficient of minimum thermal lattice conductivity. These results can be used to predict the elastic and mechanical characteristics of carbonates with the chemical formula MCO3 and solid solutions based on them.

First-Principle Studies of the Vibrational Properties of Carbonates under Pressure.

Using the density functional theory with the hybrid functional B3LYP and the basis of localized orbitals of the CRYSTAL17 program code, the dependences of the wavenumbers of normal long-wave ν vibrations on the P(GPa) pressure ν(cm−1) = ν0 + (dv/dP)·P + (d2v/dP2)·P and structural parameters R(Å) (R: a, b, c, RM-O, RC-O): ν(cm−1) = ν0 + (dv/dR) − (R − R0) were calculated. Calculations were made for crystals with the structure of calcite (MgCO3, ZnCO3, CdCO3), dolomite (CaMg(CO3)2, CdMg(CO3)2, CaZn(CO3)2) and aragonite (SrCO3, BaCO3, PbCO3). A comparison with the experimental data showed that the derivatives can be used to determine the P pressures, a, b, c lattice constants and the RM-O metal-oxygen, and the RC-O carbon-oxygen interatomic distances from the known Δν shifts. It was found that, with the increasing pressure, the lattice constants and distances R decrease, and the wavenumbers increase with velocities the more, the higher the ν0 is. The exceptions were individual low-frequency lattice modes and out-of-plane vibrations of the v2-type carbonate ion, for which the dependences are either nonlinear or have negative dv/dP (positive dv/dR) derivatives. The reason for this lies in the properties of chemical bonding and the nature of atomic displacements during these vibrations, which cause a decrease in RM-O and an increase in RC-O.

Population analysis with Wannier orbitals.

We formulate Wannier orbital overlap population and Wannier orbital Hamilton population to describe the contribution of different orbitals to electron distribution and their interactions. These methods, which are analogous to the well-known crystal orbital overlap population and crystal orbital Hamilton population, provide insight into the distribution of electrons at various atom centers and their contributions to bonding. We apply this formalism in the context of a plane-wave density functional theory calculation. This method provides a means to connect the non-local plane-wave basis to a localized basis by projecting the wave functions from a plane-wave density functional theory calculation to a localized Wannier orbital basis. The main advantage of this formulation is that the spilling factor is strictly zero for insulators and can systematically be made small for metals. We use our proposed method to study and obtain bonding and electron localization insights in five different materials.

Low-Scaling Tensor Hypercontraction in the Cholesky Molecular Orbital Basis Applied to Second-Order Møller-Plesset Perturbation Theory.

We employ various reduced scaling techniques to accelerate the recently developed least-squares tensor hypercontraction (LS-THC) approximation [Parrish, R. M., Hohenstein, E. G., Martínez, T. J., Sherrill, C. D. J. Chem. Phys. 137, 224106 (2012)] for electron repulsion integrals (ERIs) and apply it to second-order Møller-Plesset perturbation theory (MP2). The grid-projected ERI tensors are efficiently constructed using a localized Cholesky molecular orbital basis from density-fitted integrals with an attenuated Coulomb metric. Additionally, rigorous integral screening and the natural blocking matrix format are applied to reduce the complexity of this step. By recasting the equations to form the quantized representation of the 1/r operator Z into the form of a system of linear equations, the bottleneck of inverting the grid metric via pseudoinversion is removed. This leads to a reduced scaling THC algorithm and application to MP2 yields the (sub-)quadratically scaling THC-ω-RI-CDD-SOS-MP2 method. The efficiency of this method is assessed for various systems including DNA fragments with over 8000 basis functions and the subquadratic scaling is illustrated.

Smart local orbitals for efficient calculations within density functional theory and beyond.

Localized basis sets in the projector augmented wave formalism allow for computationally efficient calculations within density functional theory (DFT). However, achieving high numerical accuracy requires an extensive basis set, which also poses a fundamental problem for the interpretation of the results. We present a way to obtain a reduced basis set of atomic orbitals through the subdiagonalization of each atomic block of the Hamiltonian. The resulting local orbitals (LOs) inherit the information of the local crystal field. In the LO basis, it becomes apparent that the Hamiltonian is nearly block-diagonal, and we demonstrate that it is possible to keep only a subset of relevant LOs that provide an accurate description of the physics around the Fermi level. This reduces to some extent the redundancy of the original basis set, and at the same time, it allows one to perform post-processing of DFT calculations, ranging from the interpretation of electron transport to extracting effective tight-binding Hamiltonians, very efficiently and without sacrificing the accuracy of the results.