Function Of Interatomic Distance Research Articles

Degree of Atomicity in the Chemical Bonding: Why Return to the H2 Molecule?

We analyze two-particle binding factors for the case of \ch{H2} molecule with the help of our original Exact Diagonalization \textit{Ab Intio} (EDABI) approach. Explicitly, we redefine the many-particle covalency and ionicity factors as a function of interatomic distance. Insufficiency of those basic characteristics is stressed and the concept of \textit{atomicity} is introduced and corresponds to the Mott and Hubbard criteria concerning the localization in many-particle systems. This additional characteristic introduces atomic ingredient into the essentially molecular states and thus eliminates a spurious behavior of the standard covalency factor with the increasing interatomic distance, as well as provides a physical reinterpretation of the chemical bond's nature.

Study of High-Temperature Behaviour of ZnO by Ab Initio Molecular Dynamics Simulations and X-ray Absorption Spectroscopy.

Wurtzite-type zinc oxide (w-ZnO) is a widely used material with a pronounced structural anisotropy along the c axis, which affects its lattice dynamics and represents a difficulty for its accurate description using classical models of interatomic interactions. In this study, ab initio molecular dynamics (AIMD) was employed to simulate a bulk w-ZnO phase in the NpT ensemble in the high-temperature range from 300 K to 1200 K. The results of the simulations were validated by comparison with the experimental Zn K-edge extended X-ray absorption fine structure (EXAFS) spectra and known diffraction data. AIMD NpT simulations reproduced well the thermal expansion of the lattice, and the pronounced anharmonicity of Zn–O bonding was observed above 600 K. The values of mean-square relative displacements and mean-square displacements for Zn–O and Zn–Zn atom pairs were obtained as a function of interatomic distance and temperature. They were used to calculate the characteristic Einstein temperatures. The temperature dependences of the O–Zn–O and Zn–O–Zn bond angle distributions were also determined.

Multiple-scattering approach for multi-spin chiral magnetic interactions: application to the one- and two-dimensional Rashba electron gas

Various multi-spin magnetic exchange interactions (MEI) of chiral nature have been recently unveiled. Owing to their potential impact on the realisation of twisted spin-textures, their future implication in spintronics or quantum computing is very promising. Here, I address the long-range behavior of multi-spin MEI on the basis of a multiple-scattering formalism implementable in Green functions based methods such as the Korringa–Kohn–Rostoker (KKR) Green function framework. I consider the impact of spin–orbit coupling (SOC) as described in the one- (1D) and two-dimensional (2D) Rashba model, from which the analytical forms of the four- and six-spin interactions are extracted and compared to the well known bilinear isotropic, anisotropic and Dzyaloshinskii–Moriya interactions (DMI). Similarly to the DMI between two sites i and j, there is a four-spin chiral vector perpendicular to the bond connecting the two sites. The oscillatory behavior of the MEI and their decay as function of interatomic distances are analysed and quantified for the Rashba surfaces states characterizing Au surfaces. The interplay of beating effects and strength of SOC gives rise to a wide parameter space where chiral MEI are more prominent than the isotropic ones. The multi-spin interactions for a plaquette of N magnetic moments decay like simplifying to for equidistant atoms, where d is the dimension of the mediating electrons, qF the Fermi wave vector, L the perimeter of the plaquette while P is the product of interatomic distances. This recovers the behavior of the bilinear MEI, , and shows that increasing the perimeter of the plaquette weakens the MEI. More important, the power-law pertaining to the distance-dependent 1D MEI is insensitive to the number of atoms in the plaquette in contrast to the linear dependence associated with the 2D MEI. Furthermore, the N-dependence of qF offers the possibility of tuning the interactions amplitude by engineering the electronic occupation.

Theoretical Models of Chemical Bond in Molten Binary Cadmium and Zinc Antimonides in AIIBV Semiconductors

A complex approach to the short-range ordering in molten binary cadmium and zinc antimonides has been proposed which considers specific features of the fine structure of chemical bond and interatomic interaction in АIIВV semiconductors. A procedure has been developed and the dissociation energies of nonequivalent chemical bonds in cadmium and zinc antimonides have been calculated as a function of interatomic distances and atomic characteristics of the starting components.

Verifying Self-Consistency of Protein Structure and Dynamics through MD Simulation and WAXS

Molecular Dynamics (MD) simulations based on a crystal structure and selected force field represent a powerful approach to generate models for the internal motions of a protein in order to interpret the results of biological experiments and model the interactions between proteins and ligands. However, there are relatively few experimental probes that can be used to verify the results of MD, particularly with regard to slow, correlated motions of loops, folds or domains. Wide-angle X-ray solution scattering (WAXS) is sensitive to protein structure and dynamics including secondary, tertiary and quaternary structure and slow, correlated motions. Here, we present a method to utilize the crystal structure of a protein and its corresponding MD simulation to predict WAXS data from a protein. First, the WAXS pattern of a rigid protein is calculated using an explicit atom model of the hydration layer with the software package, XS. Second, MD trajectories are utilized to calculate a sigma-r plot (the standard deviation of interatomic distances averaged as a function of interatomic distance) which is subsequently combined with the results of the XS calculation to predict the scattering pattern of the dynamic protein. The difference between observed and calculated intensities is minimized by scaling the sigma-r plot with a single variable factor which provides a measure of the discrepancy between experimental and computational characterization of global dynamics. In examples presented here, we show that the correspondence between observed and calculated intensities are often excellent, providing direct experimental validation of the MD results. In other examples, we demonstrate how the approach can identify over or under-estimates of large scale motions in MD simulations that may arise from under-sampling of the structural ensemble or inappropriate choice of simulation parameters.

Bond-length distributions for ions bonded to oxygen: alkali and alkaline-earth metals.

Bond-length distributions have been examined for 55 configurations of alkali-metal ions and 29 configurations of alkaline-earth-metal ions bonded to oxygen, for 4859 coordination polyhedra and 38 594 bond distances (alkali metals), and for 3038 coordination polyhedra and 24 487 bond distances (alkaline-earth metals). Bond lengths generally show a positively skewed Gaussian distribution that originates from the variation in Born repulsion and Coulomb attraction as a function of interatomic distance. The skewness and kurtosis of these distributions generally decrease with increasing coordination number of the central cation, a result of decreasing Born repulsion with increasing coordination number. We confirm the following minimum coordination numbers: ([3])Li(+), ([3])Na(+), ([4])K(+), ([4])Rb(+), ([6])Cs(+), ([3])Be(2+), ([4])Mg(2+), ([6])Ca(2+), ([6])Sr(2+) and ([6])Ba(2+), but note that some reported examples are the result of extensive dynamic and/or positional short-range disorder and are not ordered arrangements. Some distributions of bond lengths are distinctly multi-modal. This is commonly due to the occurrence of large numbers of structure refinements of a particular structure type in which a particular cation is always present, leading to an over-representation of a specific range of bond lengths. Outliers in the distributions of mean bond lengths are often associated with anomalous values of atomic displacement of the constituent cations and/or anions. For a sample of ([6])Na(+), the ratio Ueq(Na)/Ueq(bonded anions) is partially correlated with 〈([6])Na(+)-O(2-)〉 (R(2) = 0.57), suggesting that the mean bond length is correlated with vibrational/displacement characteristics of the constituent ions for a fixed coordination number. Mean bond lengths also show a weak correlation with bond-length distortion from the mean value in general, although some coordination numbers show the widest variation in mean bond length for zero distortion, e.g. Li(+) in [4]- and [6]-coordination, Na(+) in [4]- and [6]-coordination. For alkali-metal and alkaline-earth-metal ions, there is a positive correlation between cation coordination number and the grand mean incident bond-valence sum at the central cation, the values varying from 0.84 v.u. for ([5])K(+) to 1.06 v.u. for ([8])Li(+), and from 1.76 v.u. for ([7])Ba(2+) to 2.10 v.u. for ([12])Sr(2+). Bond-valence arguments suggest coordination numbers higher than [12] for K(+), Rb(+), Cs(+) and Ba(2+).

The Competition Effect of Strain and Interatomic Distance on Ferromagnetic Critical Temperature in Ising Ultra-Thin-Film: Monte Carlo Simulation

This work used Monte Carlo simulation to investigate the effect of lattice strain on critical temperature of the ferromagnetic Ising ultra-thin-film. Using Bethe-Slater interpretation, exchange interaction was assumed Lennard-Jones (LJ) potential function, and becomes functions of interatomic distance. The cluster flip algorithm was used to update the spin configuration, where energy and magnetization were measure to extract critical temperature via the fourth order cumulant of the magnetization. Results show that initial interatomic distance and strain have strong effect on magnetic critical point behavior. The critical point can be enhanced or suppressed depending on how exchange interaction is modified by the values of initial interatomic distance and strain. A scaling function in predicting critical temperatures is also given in this work. Results agree well with previous applicable works, which confirms the reliability of the reported results.

Plasmon resonances and electron transport in linear sodium atomic chains

The plasmon resonances and electron transport in linear sodium atomic chains are investigated using time-dependent density functional theory. The dipole response and dynamic conductance are obtained as a function of inter-atomic distance d and the chain length, under an impulse excitation polarized along the chains axis. We found that the current enhancement associated with the plasmon-induced field enhancement is mainly due to plasmon excitation of the hybridized bonding dipolar plasmons (BDP) mode. And the high energy plasmon modes are relatively weaker and are more delocalized in space than the BDP mode. The intensity of the dipole response and the current show an opposite tendency as the d is decreased while a same tendency is found as the number of atom increased. This can be understood from the competition between global quantization and local atomic confinement.

Equation of state from the Potts-percolation model of a solid

We expand the Potts-percolation model of a solid to include stress and strain. Neighboring atoms are connected by bonds. We set the energy of a bond to be given by the Lennard-Jones potential. If the energy is larger than a threshold the bond is more likely to fail, whereas if the energy is lower than the threshold, the bond is more likely to be alive. In two dimensions we compute the equation of state: stress as a function of interatomic distance and temperature by using renormalization-group and Monte Carlo simulations. The phase diagram, the equation of state, and the isothermal modulus are determined. When the Potts heat capacity is divergent the continuous transition is replaced by a weak first-order transition through the van der Waals loop mechanism. When the Potts transition is first order the stress exhibits a large discontinuity as a function of the interatomic distance.

Optimized Wannier Functions for Hubbard Chain

One-dimensional atomic chain with a variable-range hopping is described within the extended Hubbard model. The Gutzwiller-ansatz approximation is used to determine the optimized single-particle (Wannier) wave functions in the correlated state. Hopping integral up to the third neighbors is taken into account and the results are compared with those for the inflnite hopping range. Ground state energy of the system is compared with that making use of the rigorous Lieb{Wu solution with the optimized wave functions. The evolution of the properties as a function of interatomic distance is discussed.

Extended Hubbard model with renormalized Wannier wave functions in the correlated state: beyond the parametrized models

The method used earlier for analysis of correlated nanoscopic systems is extended to infinite (periodic) s-band-like systems described by the Hubbard model. The optimized single-particle Wannier wave functions contained in the parameters of the extended Hubbard model (in the nearest-neghbor hopping (-t), in the magnitude of the intraatomic interaction U, and in other parameters) are determined explicitly in the correlated state for the electronic systems of various symmetries and dimensions: Hubbard chain, square and triangular planar lattices, and the three cubic lattices (SC, BCC, FCC). In effect, the evolution of the electronic properties as a function of interatomic distance R is obtained. The model parameters in most cases do not scale linearly with the lattice spacing and hence, their solution as a function of microscopic parameters reflects only qualitatively the system evolution. Also, the atomic energy changes with R and therefore should be included in the model analysis. The solutions in one dimension (D = 1) can be analyzed both rigorously (by making use of the Lieb–Wu solution) and compared with the approximate Gutzwiller treatments. In higher dimensions (D = 2 and 3) only the latter approach is possible to implement within the scheme. The renormalized single particle wave functions are almost independent of the choice of the scheme selected to diagonalize the Hamiltonian in the Fock space in D = 1 case. For dimensions D > 1 the qualitative behavior is independent of the structure considered. The wave-function size increases above the Mott-Hubbard localization threshold and gradually reaches the atomic limit value. The method can be extended to other approximation schemes, as stressed at the end.

Understanding the elusive magnetic behavior of manganese clusters

Manganese is a multifarious element and presents a large variety of behaviors. With the aim of understanding the complex behavior, we performed a systematic study of the magnetic solutions of the manganese dimer as a function of the interatomic distance. The calculation is performed within the framework of an ab initio calculation. We show that a remarkable interplay between different magnetic couplings leads to a transition between antiferromagnetic and ferromagnetic couplings as a function of interatomic distance. We present the electronic spectra for the two configurations for different interatomic distances and show clearly the role of the $4s$ to $3d$ electron transfer to stabilize the antiferromagnetic solution at short distances. Our results are in good agreement with experiment.

Lieb-Wu Solution, Gutzwiller-Wave-Function, and Gutzwiller-Ansatz Approximations with Adjustable Single-Particle Wave Function for the Hubbard Chain

The optimized single-particle wave functions contained in the parameters of the Hubbard model (t and U) were determined for an infinite atomic chain. In effect, the electronic properties of the chain as a function of interatomic distance R were obtained and compared for the Lieb–Wu exact solution, the Gutzwiller-wave-function approximation, and the Gutzwiller-ansatz case. The ground state energy and other characteristics for the infinite chain were also compared with those obtained earlier for a nanoscopic chain within the exact diagonalization combined with an ab initio adjustment of the single-particle wave functions in the correlated state (exact diagonalization combined with an ab initio method). For the sake of completeness, we briefly characterize also each of the solutions. Our approach completes the Lieb–Wu solution, as it provides the system electronic properties evolution as a function of physically controlable parameter — the interatomic distance.

Monte Carlo analysis of neutron diffuse scattering data

This paper presents a discussion of a technique developed for the analysis of neutron diffuse scattering data. The technique involves processing the data into reciprocal space sections and modelling the diffuse scattering in these sections. A Monte Carlo modelling approach is used in which the crystal energy is a function of interatomic distances between molecules and torsional rotations within molecules. The parameters of the model are the spring constants governing the interactions, as they determine the correlations which evolve when the model crystal structure is relaxed at finite temperature. When the model crystal has reached equilibrium its diffraction pattern is calculated and a χ 2 goodness-of-fit test between observed and calculated data slices is performed. This allows a least-squares refinement of the fit parameters and so automated refinement can proceed. The first application of this methodology to neutron, rather than X-ray, data is outlined. The sample studied was deuterated benzil, d-benzil, C 14 D 10 O 2 , for which data was collected using time-of-flight Laue diffraction on SXD at ISIS.

The application of non-polarised ionic radii system for the description of physicochemical properties of solids, liquids and their interfaces

A method based on the calculation of the effective charges Z of interacting ions and the charge density ρ l on their surface as a function of interatomic distance d has been developed to determine the effect of the atomic interaction directionality on the formation of structure and properties of solids and liquids. We examine the relationship between the calculated parameters ( Z, d, and ρ l ) and the experimental values of different physicochemical properties of solids, liquids and their interfaces.

Electronic properties of correlated nanoscopic systems from the exact diagonalization combined with an ab initio approach

AbstractWe provide a brief overview of the results for correlated nanoscopic systems obtained from the Exact‐Diagonalization Ab Initio (EDABI) method. Explicitly, after a brief summary of the method and its testing for the atomic and crystal‐field states, we summarize the fundamental properties of nanochains modeling a simple‐metal quantum nanowire. All the results are analyzed as a function of interatomic distance and characterize an evolution of electronic states from the Fermi‐liquid‐like state to a localized state via an intermediate Luttinger‐liquid‐like regime. The renormalized electronic (band) structure and the concept of statistical distribution function are shown to be applicable for N = 8 ÷ 16 atoms arranged in chain or ring configurations. The role of boundary conditions involving a ficticious flux representing the Berry phase is also briefly discussed. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Computer Simulation of High-Pressure Polymeric Solid Nitrogen

We predict the thermodynamic behavior of solid nitrogen in the polymeric “cubic gauche” phase at high pressures and non-zero temperatures on the basis of a new potential model representing the total energy of polymeric nitrogen crystal as a function of interatomic distances and angles between single chemical bonds attached to each atom.

Cooper minima in the photoemission spectra of solids.

Variations of the photoionization cross section of valence states as a function of interatomic distance are studied by means of atomic and solid-state density functional approaches and compared with photoemission data. In contrast to the free atom case, a series of Cooper minima is found for 4d, 5d, and 5f states in Pd, Ag, Au, and U metals. The discovered fundamental phenomenon is of high importance for the correct interpretation of photoemission data.

NMR 1 J(HD) coupling in HD as a function of interatomic distance in the presence of an external magnetic field

A theoretical study has been made of the dependence of the 1 J(HD) coupling in HD on the interatomic distance R in the presence of a static uniform magnetic field B 0. The behaviour of all coupling terms arising from Ramsey's magnetic electron-nucleus interactions, Fermicontact (FC), spin-dipolar (SD) and paramagnetic (PSO) and diamagnetic (DSO) spin-orbital interactions is analysed qualitatively for large R. It is concluded that the PSO, DSO and SD terms become negligibly small as R increases. Detailed calculations were carried out for the FC term following two different approaches: detailed full CI calculations within a non-perturbative approach; and explicit diagonalization of the Hamiltonian operator restricted to the subspace spanned by the 1Σ+;g and the 3Σ+;u states. Within the approximations considered, the FC term of 1 J(HD) is found to be independent of B 0 and to increase by several orders of magnitude, in agreement with previous results by Bacskay, G. B., 1995, Chem. Phys. Lett., 242, 507, until a critical distance R(B 0) is reached, beyond which it almost vanishes. The quenching of the coupling at R(B 0) is due to the splitting of the 3Σ+;u state in the presence of the field B 0. The stronger the field the shorter is R(B 0).

Optimization of single-particle basis for exactly soluble models of correlated electrons

We determine the explicit form of the single-particle wave functions ${{w}_{i}(\mathbf{r})}$ appearing in the microscopic parameters of models in the second-quantization representation. Namely, the general form of the renormalized wave equation is derived from the Lagrange-Euler principle by treating the system ground-state energy of an exact correlated state as a functional of ${{w}_{i}(\mathbf{r})}$ and their derivatives. The method is applied to three model situations with one orbital per atom. For the first example\char22{}the Hubbard chain\char22{}the optimized basis is obtained only after the electronic correlation has been included in the rigorous Lieb-Wu solution for the ground-state energy. The renormalized Wannier wave functions are obtained variationally starting from the atomic basis for the s-type wave functions. The principal characteristics such as the ground-state energy and the model parameters are calculated as a function of interatomic distance. Second, the atomic systems such as the ${\mathrm{H}}_{2}$ molecule or He atom can be treated in the same manner and the optimized orbitals are obtained to illustrate the method further. Finally, we illustrate the method by solving exactly correlated quantum dots of $Nl~8$ atoms with the subsequent optimization of the orbitals. Our method may be regarded as the next step in analyzing exactly soluble many-body models that provides properties as a function of the lattice parameter and defines at the same time the renormalized wave function for a single particle.