Orbital Approximation Research Articles

The density response kernel, the Fukui function, and other response functions from the Kohn–Sham orbitals

A novel approach to the response theory for the Kohn–Sham formalism is presented, and it shows that the linear responses of the electron density to changes in the number of electrons and in the external potential connected and they can be computed simultaneously. This procedure also applies to other quantities related to the density response kernel, such as the Hessian matrix, the dipole polarizability, and the perturbed density. Expressions for the directional Fukui functions go beyond the frontier orbital approximation, showing differential relaxation effects for electron-releasing and electron-withdrawing processes. Even for the simplest approximation, when only the frontier orbitals are included in the sum-over-states, the relaxation effects are different in each direction.

Single-Capture Cross Sections from Biological Molecules and Noble Gases by Bare Ion Impact

In this work, we report theoretical electron capture cross sections for single-electron removal from molecules of biological interest and noble gases by bare ion (H+ and He2+) impact at energies ranging from 25 to 10,000 keV/amu. We use a distorted wave (DW) method where the intermediate continuum state of the active electron with the target ion has been taken into account. This method is developed within the framework of the independent electron model taking particular care of the representation of the bound continuum target states. Two different approximations have been considered for molecular targets: molecular representation of the bound-state target wavefunction and Bragg’s additivity rule. The molecular orbital for targets are described within the framework of the complete neglect of differential overlap (CNDO) method based on the linear combination of atomic orbital (LCAO) approximation. Using the DW method, we have also calculated the K-, L- and M- shell electron capture in collisions of bare ions with three noble gases He, Ne, and Ar respectively. Contributions from different molecular orbitals and different shells to the total cross sections (TCS) are studied. The preference of electron capture occurs in accordance as the binding energy of the active electron in molecular orbital and atomic shell. The maximum contributions to TCS for SC comes from the less bound electrons in repetitive orbitals, whereas the tightly bound electrons dominate the TCS at higher projectile energy regime. Variation of TCS with impact energy are compared with the available experimental observation and other theoretical findings. We find that the present theoretical method is satisfactory in both intermediate and high-energy region for molecules as well as noble gas targets to give reliable outcomes compared to other theoretical methods.

Ab initio simulation of (Ba,Sr)TiO3 and (Ba,Ca)TiO3 perovskite solid solutions

The results of ab initio (first-principles) computations of structural, elastic and piezoelectric properties of Ba(1−x)SrxTiO3 (BSTO) and Ba(1−x)CaxTiO3 (BCTO) perovskite solid solutions are presented, discussed and compared. Calculations are performed with the CRYSTAL14 computer code within the linear combination of atomic orbitals (LCAO) approximation, using advanced hybrid functionals of the density-functional-theory (DFT). Supercell model allows us to simulate solid solutions with different chemical compositions (x = 0, 0.125 and 0.25) within ferroelectric tetragonal phases (x < 0.3) of both solid solutions. It is shown that configurational disorder has to be taken into account in simulations of BCTO solid solutions, while for BSTO this effect is rather small. Both BSTO and BCTO show significantly enhanced piezoelectric properties, in a comparison with pure BaTiO3. However, these solid solutions demonstrate opposite behaviour of a tetragonal ratio c/a and elastic constants as the functions of chemical composition. It is predicted that due to decrease of the elastic constants in BCTO, it has much higher converse piezoelectric constants than BSTO.

The importance of diffuse functions in basis sets to produce reliable 3D pictures of dual descriptor

Abstract The finite difference approximation (FDA) allows us to compute dual descriptor correctly because it takes into account the relaxation effects that inner molecular orbitals experience. When these effects are irrelevant, we can use the frontier molecular orbital approximation (FMOA). Although FMOA omits relaxation effects and not FDA, both procedures should not yield too much different 3D representations of the dual descriptor. If so, the cause of such result lies in the fact that the respective basis set lacks diffuse functions, so artificially exacerbating the absence of relaxation effects aforementioned and yielding a remarkable inconsistency between FDA and FMOA.

Efficiently evaluating the Krieger-Li-Iafrate and common-energy-denominator approximations in the frequency-dependent Sternheimer scheme

We show that within the Krieger-Li-Iafrate and common-energy-denominator approximations, the linearized time-dependent Kohn-Sham equations for orbital functionals can be solved very efficiently using the frequency-dependent Sternheimer scheme. The Kohn-Sham response can be obtained without the need to explicitly evaluate the exchange-correlation kernel as a functional derivative with respect to the density. Instead, it suffices to compute functional derivatives with respect to the orbitals. The scheme allows for the computationally efficient use of orbital functional potential approximations in Kohn-Sham response theory.

Theoretical and Experimental Study of (Ba,Sr)TiO3 Perovskite Solid Solutions and BaTiO3/SrTiO3 Heterostructures

The results of experimental and theoretical ab initio study of structural and piezoelectric properties of (Ba,Sr)TiO3 perovskite solid solutions are discussed and compared. Experimentally, plate-like (Ba,Sr)TiO3 particles were synthesized by the topochemical conversion in the molten salt from Bi4Ti3O12 template plates. All dimensions (side length ≈1 μm, thickness ≈200–400 nm) were well above the critical size necessary for observation of piezo- and ferroelectricity. The first-principles computations of the structural and electromechanical properties of solid solutions were performed with the CRYSTAL14 computer code within the linear combination of atomic orbitals approximation, using three advanced hybrid functionals of density functional theory. Different chemical compositions are considered for the ferroelectric and paraelectric phases. The calculated structural properties of solid solutions in tetragonal and cubic phases are in very good agreement with experimental data. Experimentally obtained and cal...

Systematic analysis of the fine structure of energy levels and spin-Hamiltonian parameters of V3+ ion in corundum with dynamic Jahn-Teller effect

Systematic analysis of fine structure of the whole energy levels and spin-Hamiltonian parameters (zero-field splitting (ZFS) parameter D and g-factors g// and g⊥) for the ground state 3A2 (3T1) of V3+ ion in corundum are presented in detail with complete diagonalization method (CDM) of 45 × 45 energy matrix, in which the full configuration interactions are taken into account. The reduction of the splittings of excited electronic 3T2 (t2 ge) term with orbital triplet degenerate caused by spin-orbit (SO) and lower trigonal crystal field (CF) is studied by T2⊗e model dynamic Jahn-Teller theory, and Ham deduction factor, the Jahn-Teller energy EJT and Huang-Rhys factor S are estimated. The studies are performed within the strong-field scheme with molecular orbit (MO) approximation, in which the two SO coupling parameter model is used and the SO contributions from both the central 3d ion and ligands are taken in account. The calculated results are in good agreement with the experimental data, and the local structure of [VO6]9- cluster with C3 point group symmetry are determined quantitatively.

Range-Separated Hybrid Functionals with Variational Fitted Exact Exchange

This work presents a variationally fitted long-range exact exchange algorithm that can be used for the computation of range-separated hybrid density functionals in the linear combination of Gaussian type orbital (LCGTO) approximation. The obtained LCGTO energy and gradient expressions are free of four-center integrals and employ modified three-center integral recurrence relations to obtain optimal computational performance. The accuracy and performance of selected range-separated hybrid functionals with variational fitted long-range exact exchange are analyzed and discussed. A parallel implementation is presented and benchmarked.

Hill stability in the AMD framework

In a two-planet system, a topological boundary that is created by Sundman (1912, Acta Math., 36, 105) inequality can forbid close encounters between the two planets for an infinite time. A system is said to be Hill stable if it verifies this topological condition. Hill stability is widely used in the study of extrasolar planet dynamics. However, the coplanar and circular orbit approximation is often used. In this paper, we explain how the Hill stability can be understood in the framework of angular momentum deficit (AMD). In the secular approximation, AMD allows us to discriminate between a priori stable systems and systems for which a more in-depth dynamical analysis is required. We show that the general Hill stability criterion can be expressed as a function of only semimajor axes, masses, and total AMD of the system. The proposed criterion is only expanded in the planets-to-star mass ratio ε and not in the semimajor axis ratio, eccentricities, nor the mutual inclination. Moreover, the expansion in ε remains excellent up to values of about 10−3 even for two planets with very different mass values. We performed numerical simulations in order to highlight the sharp change of behavior between Hill stable and Hill unstable systems. We show that Hill stable systems tend to be very regular, whereas Hill unstable systems often lead to rapid planet collisions. We also note that Hill stability does not provide protection from the ejection of the outer planet.

High-order harmonic generation in H2+ via multicolor beam superposition: barrier suppression ionization regime

Generation of high-order harmonics (HOHs) and attosecond pulses in the barrier suppression ionization regime for a target of hydrogen molecular ion, $${\text{H}}_{2}^{+}$$ , with large inter nuclear distance is introduced in this work. Some broadband femtosecon laser pulses are designed based on multicolor beam superposition method in order to interact with $${\text{H}}_{2}^{+}$$ . Behavioral study of harmonics cutoff, attosecond pulse widths and intensities, along with the maximum ionization intensity with respect to the spectral width of driving pulses was carried out. Molecular orbitals in this study are estimated via the linear combination of atomic orbital approximation, and temporal variations of these orbitals are studied in the various ionization regimes. It is seen in this work that although the cutoff harmonic is increased by the driving pulse intensity, but it is insensitive to the spectral driving pulsewidth. This study showed that intensities of the generated attosecond pulses gradually decreased by increasing the bandwidth of the driving laser pulse, but the duration of them is shown to be insensitive in this respect.

Dust particles of finite dimensions in complex plasmas: thermodynamics and dust-acoustic wave dispersion

Grounded on the premise that dust particles are charged hard balls, the analysis in Davletov et al. (Contrib. Plasma Phys., vol. 56, 2016, 308) provides an original pseudopotential model of intergrain interaction in complex (dusty) plasmas. This accurate model is engaged herein to consistently treat the finite-size effects from the process of dust particle charging to determination of the thermodynamic quantities and the dust-acoustic wave dispersion in the strongly coupled regime. The orbital motion limited approximation is adopted to evaluate an electric charge of dust grains immersed in a neutralizing background of the buffer plasma. To account for finite dimensions of dust particles, the radial distribution function is calculated within the reference hypernetted-chain (RHNC) approximation to demonstrate a well-pronounced short-range order formation at rather large values of the coupling parameter and the packing fraction. The evaluated excess pressure of the dust component is compared to the available theoretical approaches and the simulation data and is then used to predict the dust-acoustic wave (DAW) dispersion in the strongly coupled regime under the assumption that the dust particles charge varies in the course of propagation. In contrast to many previous investigations, it is demonstrated for the first time ever that for DAWs the charge variation of dust particles should necessarily be taken into account while evaluating the dust isothermal compressibility.

Introducing a new methodology for the calculation of local philicity and multiphilic descriptor: an alternative to the finite difference approximation

ABSTRACTThis work presents a new development based on the condensation scheme proposed by Chamorro and Pérez, in which new terms to correct the frozen molecular orbital approximation have been introduced (improved frontier molecular orbital approximation). The changes performed on the original development allow taking into account the orbital relaxation effects, providing equivalent results to those achieved by the finite difference approximation and leading also to a methodology with great advantages. Local reactivity indices based on this new development have been obtained for a sample set of molecules and they have been compared with those indices based on the frontier molecular orbital and finite difference approximations. A new definition based on the improved frontier molecular orbital methodology for the dual descriptor index is also shown. In addition, taking advantage of the characteristics of the definitions obtained with the new condensation scheme, the descriptor local philicity is analysed by separating the components corresponding to the frontier molecular orbital approximation and orbital relaxation effects, analysing also the local parameter multiphilic descriptor in the same way. Finally, the effect of using the basis set is studied and calculations using DFT, CI and Möller–Plesset methodologies are performed to analyse the consequence of different electronic-correlation levels.

Raman spectrum of oxyorthosilicate Lu2SiO5: Ab initio calculation

AbstractRaman spectra of oxyorthosilicate Lu2SiO5 have been computed in the framework of density functional theory with hybrid functionals using molecular orbitals approximation. Results are compared with existing experimental data. With general agreement with experiment, there are differences in some regions of wavenumbers. Analysis of vibrations has been performed using calculated eigenvectors and isotopic substitution method. Optimized crystal structure parameters are in excellent agreement with the experiment with maximum difference less than 2%. Obtained value of the band gap 6.43 eV is also in a good agreement with the literature data (6 eV).

Orbits in elementary, power-law galaxy bars – 1. Occurrence and role of single loops

Orbits in galaxy bars are generally complex, but simple closed loop orbits play an important role in our conceptual understanding of bars. Such orbits are found in some well-studied potentials, provide a simple model of the bar in themselves, and may generate complex orbit families. The precessing, power ellipse (p-ellipse) orbit approximation provides accurate analytic orbit orbits in symmetric galaxy potentials. It remains useful for finding and fitting simple loop orbits in the frame of a rotating bar with bar-like and symmetric power-law potentials. Second order perturbation theory yields two or fewer simple loop solutions in these potentials. Numerical integrations in the parameter space neighborhood of perturbation solutions reveal zero or one ac- tual loops in a range of such potentials with rising rotation curves. These loops are embedded in a small parameter region of similar, but librating orbits, which have a subharmonic frequency superimposed on the basic loop. These loops and their librat- ing companions support annular bars. Solid bars can be produced in more complex potentials, as shown by an example with power-law indices varying with radius. The power-law potentials can be viewed as the elementary constituents of more complex potentials. Numerical integrations also reveal interesting classes of orbits with multiple loops. In two-dimensional, self-gravitating bars, with power-law potentials, single loop orbits are very rare. This result suggests that gas bars or oval distortions are unlikely to be long-lived, and that complex orbits or three-dimensional structure must support self-gravitating stellar bars.

Electromechanical Properties of Ba(1-x)SrxTiO3 Perovskite Solid Solutions from First-Principles Calculations.

An enhancement of the piezoelectric properties of lead-free materials, which allow conversion of mechanical energy into electricity, is a task of great importance and interest. Results of first-principles calculations of piezoelectric/electromechanical properties of the Ba(1-x)SrxTiO3 (BSTO) ferroelectric solid solution with a perovskite structure are presented and discussed. Calculations are performed within the linear combination of atomic orbitals (LCAO) approximation and periodic-boundary conditions, using the advanced hybrid functionals of density functional theory (DFT). A supercell model allows the investigation of multiple chemical compositions x. In particular, three BSTO solid solutions with x = 0, 0.125, 0.25 are considered within the experimental stability domain of the ferroelectric tetragonal phase of the solid solution (x < 0.3). The configurational disorder with x = 0.25 composition is also investigated explicitly considering the seven possible atomic configurations corresponding to this composition. It is predicted that Sr-doping of BaTiO3 makes it mechanically harder and enhances its electromechanical/piezoelectric properties, which are important for relevant applications.

A simple molecular orbital treatment of current distributions in quantum transport through molecular junctions.

A simple molecular orbital treatment of local current distributions inside single molecular junctions is developed in this paper. Using the first-order perturbation theory and nonequilibrium Green's function techniques in the framework of Hückel theory, we show that the leading contributions to local current distributions are directly proportional to the off-diagonal elements of transition density matrices. Under the orbital approximation, the major contributions to local currents come from a few dominant molecular orbital pairs which are mixed by the interactions between the molecule and electrodes. A few simple molecular junctions consisting of single- and multi-ring conjugated systems are used to demonstrate that local current distributions inside molecular junctions can be decomposed by partial sums of a few leading contributing transition density matrices.

Triple differential cross sections for the ionization of formic acid by electron impact

Theoretical triple differential cross sections for the simple ionization of the two outermost valence orbitals of formic acid monomer are given in this work. The first Born approximation is used to describe the collision dynamics with one Coulomb wave function for the ejected electron. Single-center molecular wave functions are generated using the Gaussian 09 program. The cross sections are calculated for an average molecular orientation with the proper average method. The results show that the proposed framework provides better agreement with experimental data than the previously used orientation averaged molecular orbital approximation. Consequently, this work shows the importance of performing the orientation averaging on the cross sections and not on the molecular wave functions. It also provides a methodology that reduces the complexity of calculations while maintaining a good quality of the results.

Particle-in-cell simulations of the plasma interaction with poloidal gaps in the ITER divertor outer vertical target

Predictive modelling of the heat flux distribution on ITER tungsten divertor monoblocks is a critical input to the design choice for component front surface shaping and for the understanding of power loading in the case of small-scale exposed edges. This paper presents results of particle-in-cell (PIC) simulations of plasma interaction in the vicinity of poloidal gaps between monoblocks in the high heat flux areas of the ITER outer vertical target. The main objective of the simulations is to assess the role of local electric fields which are accounted for in a related study using the ion orbit approach including only the Lorentz force (Gunn et al 2017 Nucl. Fusion 57 046025). Results of the PIC simulations demonstrate that even if in some cases the electric field plays a distinct role in determining the precise heat flux distribution, when heat diffusion into the bulk material is taken into account, the thermal responses calculated using the PIC or ion orbit approaches are very similar. This is a consequence of the small spatial scales over which the ion orbits distribute the power. The key result of this study is that the computationally much less intensive ion orbit approximation can be used with confidence in monoblock shaping design studies, thus validating the approach used in Gunn et al (2017 Nucl. Fusion 57 046025).

On the performance of natural orbital functional approximations in the Hubbard model

Strongly correlated materials are now under intense development, and natural orbital functional (NOF) methods seem to be able to capture the physics of these systems. We present a benchmark based on the Hubbard model for a class of commonly used NOF approximations (also known as reduced density matrix functional approximations). Our findings highlight the importance of imposing ensemble N-representability conditions in order to obtain consistent results in systems with either weak or strong electronic correlation, such as the Hubbard system with a varying two-particle interaction parameter. Based on the accuracy of the results obtained using PNOF7, which retrieves a large amount of the total strong nondynamic correlation, the Hubbard model points out that N-representability gives solid foundations for NOF development.

First-principles investigation on the mechanical and electronic properties of novel Pb1−xCexY alloys (Y = S, Se, and Te): an ab initio study

The first-principles full-potential linearized augmented plane-waves with local orbitals approximation within the density functional theory is used to treat in detail the structural, elastic, and electronic properties of new Pb1−xCexY (Y = S, Se, and Te) alloys at different concentrations (x = 0.25, 0.50, and 0.75). The generalized gradient approximation of calculations show that the ground stable state of Pb1−xCexY alloys is in rock-salt structure, where the equilibrium structural parameters such as, lattice constant, bulk modulus, and its first pressure derivative are performed and compared to the previous theoretical and experimental data. The elastic study is considered to determine the elastic moduli C11, C12, and C44 of the cubic crystal. Through the obtained results of the elastic moduli, the derivative mechanical moduli including Young’s modulus, shear modulus, Poisson’s ratio, Kleinman parameter, and anisotropy factor are calculated in the fact to demonstrate the mechanical stability of these alloys. The nature of the electronic structure of these studied alloys is characterized with the help of the band structure and the density of states plots.