Function Of Interatomic Distance Research Articles

Correlation Induced Optimization of Wave Functions: the Hubbard Chain

We determine the explicit form of the single-particle Wannier functions {wi(r)} appearing in the parameters of quantum models. The method is illustrated on the example of the Hubbard chain, for which we derive the renormalized wave equation starting from a variational principle and by treating the system ground state energy as a functional of {wi(r)} and their derivatives. In this manner, the optimized basis is obtained only after the electronic correlations have been included in the rigorous Lieb-Wu solution. The results for the ground state energy and the size of the renormalized s-type orbitals, both as a function of interatomic distance, are calculated explicitly. PACS numbers: 71.10.Fd, 71.15.Fv, 31.25.Nj

Polariton Effective Mass and Spectral Density in III-V Semiconductors Doped with an Ordered Chain of Identical Two-Level Atoms

We study the polariton effective mass and spectral density of III–V semiconductors doped with an ordered chain of identical two-level atoms. The polariton spectrum in these semiconductors has an energy gap which is caused by photon coupling to optical phonons. We found an impurity band within the energy gap when the resonance frequencies ω0 of the two-level atoms lie in the polariton energy gap. We calculated the effective mass of a polariton in this impurity band as a function of interatomic distance. The polariton spectral function is also calculated as a function of the interatomic distance. Numerical calculations are performed for GaAs, GaSb, and InAs semiconductors. It is found that as the interatomic distance increases, the polariton energy band width decreases. It is also found that the effective mass of the polariton is hole-like and its magnitude decreases as the interatomic distance increases.

Polariton spontaneous emission superradiance and polariton-impurity states in III–V semiconductors

In this paper, we study the polariton energy dispersion of two different types of two-level atoms placed within a III–V semiconductor which has a polariton gap due to photon coupling to optical phonons. We employ the spherical harmonic representation to derive the model Hamiltonian within the framework of the dipole resonance approximation. Two polariton impurity states lying within the polariton gap are found. The spontaneous emission rate of a system with two identical two-level atoms placed within a III–V semiconductor is also studied as a function of interatomic distance when the atomic resonance frequency lies in the polariton continuous spectra. It is found that when the interatomic separation between the atoms is small, the polariton-atom system in the symmetric state can radiate a polariton with a probability that is twice that of the independent or single atom case (i.e. superradiance). On the other hand, when the polariton-atom system in the antisymmetric state, the system is prevented from radiating a polariton (i.e. subradiance). Numerical calculations are performed for polariton-impurity states and polariton spontaneous decay rate of the polariton-atom system for GaAs semiconductor.

Magnetoelastic contribution to the interface anisotropy of Pd/Co metallic multilayers.

First-principles calculations of the magnetic anisotropy energies of Pd/Co metallic multilayers have been performed to investigate the effect of strain on the interface magnetic anisotropy. Also, to clarify the contribution of the interface to anisotropy, the anisotropy energies of an unsupported Co monolayer and bulk Co have been calculated. These two systems have different interfaces compared to the Pd/Co multilayer in the sense that an unsupported Co monolayer and bulk Co can be considered as vacuum/Co and Co/Co multilayers, respectively. A Pd/Co multilayer is predicted to exhibit a perpendicular magnetic anisotropy in accordance with experiment. Bulk Co shows perpendicular anisotropy, but the anisotropy energy is quite small compared to that of Pd/Co. On the contrary, an unsupported Co monolayer shows an in-plane anisotropy. These differences suggest the importance of the existence of the interface for perpendicular magnetic anisotropy, which originates from the modification of the local electronic structure of a Co layer due to the presence of the interface. The strength of the hybridization of electronic states at the interface determines the relative position of the Fermi energy to the position of the local density of states (LDOS) of |m|=2 character of Co d electrons of minority spin. If the LDOS of |m|=2 character is large at the Fermi energy, the system shows a perpendicular anisotropy. As for the effect of strain, the anisotropy energy of Pd/Co increases as a function of interatomic distance in the in-plane direction, while that of a Co monolayer decreases. Compared to these two systems, the magnetoelastic constant of bulk Co is considerably smaller. These results suggest that the effect of strain on the anisotropy energy is strongly correlated with the type of atomic species adjacent to the Co layer and cannot be determined solely from the value of strain introduced in the Co layer. In the case of a heterointerface, the strength of hybridization between the orbitals inside the monolayer and that between the orbitals in adjacent monolayers are quite different and this fact leads to the large strain dependence of the anisotropy. \textcopyright{} 1996 The American Physical Society.

Theoretical study on the strain dependence of the magnetic anisotropy of X/Co(X=Pt, Cu, Ag, and Au) metallic multilayers

A first-principles calculation of the magnetic anisotropy energies of X/Co (X=Pt, Cu, Ag and Au) metallic multilayers has been performed to investigate the effect of strain on the magnetic anisotropy. It is successfully predicted that Pt/Co and Au/Co multilayers exhibit perpendicular magnetic anisotropies in accordance with experiments. The strength of the hybridization of electronic states at the interface determines the relative position of the Fermi energy to the local density of states (LDOS) of ‖m‖=2 character of Co d electrons of minority spin. If the LDOS of ‖m‖=2 character is large at the Fermi energy, a system shows a perpendicular anisotropy. The anisotropy energies of all the systems increase as a function of interatomic distance in the in-plane direction. The magneto-elastic constants are more than twice the value of pure Co. The origin of this large value is explained in terms of the change of relative position of the Fermi level to that of the LDOS of ‖m‖=2 character as the value of strain increases.

Oscillating Interatomic Potentials and Growth of Icosahedral Quasicrystals.

The crucial role of frustration in atomic ordering for quasicrystal formation is demonstrated within a simple pmodel for three-dimensional growth of icosahedral quasicrystals in binary alloys (up to $2\ifmmode\times\else\texttimes\fi{}{10}^{6}$ atoms). Two features of the model are important: (1) The ratio of atomic sizes is the one typical for the CsCl structure and (2) the interatomic potential is an oscillating function of interatomic distances (those oscillations cause frustration in atomic ordering). It is shown that different potentials result in different faceting of the grown clusters. Phasonic jumps and the phasonic relaxation in the clusters are discussed.

Many-body trial wave functions for atomic systems and ground states of small noble gas clusters

Clusters of sizes ranging from two to five are studied by variational quantum Monte Carlo techniques. The clusters consist of Ar, Ne, and hypothetical lighter (‘‘1/2-Ne’’) atoms. A general form of trial function is developed for which the variational bias is considerably smaller than the statistical error of currently available diffusion Monte Carlo estimates. The trial functions are designed by a careful analysis of long- and short-range behavior as a function of inter-atomic distance; at intermediate distances, on the order of the average nearest neighbor distance, the trial functions are constructed to have considerable variational freedom. A systematic study of the relative importance of n-body contributions to the quality of the optimized trial wave function is made with 2≤n≤5. Algebraic invariants are employed to deal efficiently with the many-body interactions.

Deformation of coordination polyhedra and their sheets in phyllosilicates

A statistical evaluation of crystal-structure data for 112 phyllosilicates (85 micas, 14 1:1 phyllosilicates, 13 chlorites) shows that the same principles govern the geometry of polyhedra and their sheets irrespective of the phyllosilicate subgroup. Regression relations for octahedral distortions and tetrahedral rotation as a function of interatomic distances are proposed. Multiple regressions were used to obtain generalized values for bond lengths and ionic radii for elements in different coordination. Using the relations derived here, it is possible to start with a chemical composition plus an anticipated cation ordering pattern and obtain estimates of the individual bond lengths and distortion characteristics of the crystal structure concerned. These can be translated into atomic coordinates and, ultimately, into peak intensities on diffraction patterns. The geometry of the coordination of interlayer cations in the micas shows considerable variation and the effective coordination number is seen to correlate with the tetrahedral rotation angle α. When the coordination drops to six, this angle may vary between 16° and 24°

Vibrational Energy as a Function of Interatomic Distance in Rare‐Gas Solids. A Universal Relationship

AbstractA universal relationship between the reduced vibrational energies and average interatomic distances is derived for rare gas solids within the Lennard‐Jones (6‐12) interatomic potential model. This relationship is employed to obtain the zero‐point energies as well as the zero‐pressure heat capacities of the rare gas solids. The overall agreement with the existing data is very good.

Effective interatomic potentials in strong-scattering open shell metals: application to bonding force in d-band metals

A method for the calculation of an open shell, strong-scattering metal cohesive energy Ecoh in terms of the effective interaction is presented. It involves a so called reference medium defined as an ensemble of weighted atomic configurations which are significant for the problem under consideration. Ecoh is written as a sum of n-body interactions up to n=M plus a residual error epsilon M. The effective forces are determined in a unique way by making epsilon M statistically small for the reference medium configurations. The M=2 (up to pair-force) description is studied in detail for the bulk, weak defect case. A metal, liquid-like reference medium is then appropriate and the recently developed liquid metal theory is used to derive closed equations for the effective pair interaction within the Kohn-Sham local density approximation. The theory is applied to the study of d-bonding pair interaction in transition metals as a function of interatomic distance R and of d-band charge Zd, within Andersen's tight-binding atomic sphere approximation. The pair interaction is found to be mainly attractive and to behave as Zd(10-Zd)/R10 when R is near the physical hard-core diameter. The behaviour is more complicated when R is much larger and is explained with the help of an approximate solution of the full equations. Finally the Dick-Overhauser overlap pair interaction, which is valid for closed shell atoms, is extended to the open-shell case.

Electronic structure, pairwise interactions and ordering energies in binary f.c.c. transition metal alloys

Effective pair interactions for binary f.c.c. transition metal alloys have been computed using a generalized perturbation method starting from the completely disordered state. Their properties, as a function of interatomic distance, band filling, disorder and concentration are discussed. The ordering energy computed from the pair interactions is succesfully compared, for the Cu 3Autype structure, to the energy derived from the band structure determined by the recursion method.

Ab initio studies on polymers. IV. Polydiacetylenes

For pt.III see Solid State Commun., vol.29, p.251 (1979). The electronic ground state of infinite polydiacetylene chains has been investigated with the aid of the crystal orbital method. For both the acetylenic and the butatrienic arrangement the total energy was optimised as a function of interatomic distances and bond angles. The acetylenic structure turned out to be stabilised over the butatrienic one by approximately=12 kcal mol-1 per C4H2 unit. The respective equilibrium geometries and a selected number of force constants are reported as well. The electronic band structure of both isomeric structures is analysed and differences in the occupation schemes are discussed.

Origin of 19F hyperfine interaction in Mn 2+ ion and ion pair

The theory of transferred hyperfine interaction at the F - site in the mixed σ - and π - bonding Mn 2+F - and Mn 2+F -Mn 2+ systems is developed from first principles. The transfer of electrons from the occupied p and s orbitals of F - ion to the empty d orbits on the Mn 2+ ion is considered and all the integrals of the kinetic energy and the Coulomb interactions are evaluated using the Hartree-Fock wave functions. The spin density for 1s, 2s, 2p σ and 2p π orbits at the F - ion is calculated as a function of interatomic distance and from the hyperfine field is calculated. It is found that there are large cross terms between 1s and 2s functions. The order of magnitude of the hyperfine field at the F - site can be predicted only if the covalency is taken into account. There occurs considerable change in the spin density in going from the single magnetic ion to the magnetic ion pair as a result of a change redistribution effect associated with the electron transfer in the pair.

Coexistence curves for fourth-neighbor Ising models on the face-centered-cubic lattice

In this paper we investigate the influence of the range of the potential on the phase diagram for higher-neighbor Ising systems on the face-centered-cubic lattice. The density weight factors and lattice constants needed to evaluate the diagrams that contribute to the first six terms in the high-temperature expansion at arbitrary density are obtained. The resulting expression for the free energy is in the form of a series in the density and the four coupling constants ${J}_{1}$, ${J}_{2}$, ${J}_{3}$, and ${J}_{4}$ describing the potential energy as a function of interatomic distance. Differentiation of this expression with respect to density yields a series for the chemical potential. The phase diagram is obtained by straightforward analysis of this series. The results show that the coexistence curve depends on the effective number of nearest neighbors but is insensitive to the shape of the potential.

Experimental determination of the Cs(7S)-rare-gas potential energy curves and of the 6S-7S collision-induced oscillator strengths

The bands associated with the Cs(6S to 7S) forbidden transition induced by collisions with various rare-gas atoms are studied (Xe to He). The ground-state potential curves being available, the quasi-static interpretation of the temperature dependence of the band profile gives the upper-state potential curves. Additional information about these curves is drawn from the analysis of the vibrational structure of the band. Finally, the values of the induced oscillator strength of the transition are obtained as a function of interatomic distance. A comparison with available theoretical results is presented.

Trends of force constants in diamond and sphalerite-structure crystals

The dependence of force constants (ν 2μ) on equilibrium interatomic distances are analysed for the following three diamond-like crystal groups: IV–IV, III–V and II–VI. We have considered the models due to Varshni and Anderson and arrived at a simpler relation. It is found that the force constants are presented as a function of interatomic distances within an accuracy of ≈ 3%. The model constants are evaluated by least-squares fitting of available experimental data, and the parameters, along with the relative merits of the models, are presented.

Calculation of reduced intensity functions for model amorphous structures, including coupling of thermal vibrations

Coupling of thermal vibrations was introduced into the calculation of the reduced intensity function for two model amorphous structures by using coupling coefficients which are a function of interatomic distance. A microcrystallite model of amorphous silicon and an ion cluster model of amorphous calcium phosphate were examined. Since coupling factors appropriate to these materials were not available, data from several different materials was used to estimate the importance of such coupling. Splitting of certain peaks in the diffraction pattern at high angles was found to be reduced, giving better agreement between calculated patterns and measurements on actual materials. These results suggest that coupled thermal vibrations and other random perturbations which affect large interatomic distances more than smaller ones may have a significant affect on the diffraction pattern.

Atomic volumes of transition metals

We discuss the various repulsive terms which can give rise to a minimum in the energy as a function of interatomic distances and permits the calculation of atomic volumes of transitional metal. We show that the direct overlap between atomic functions provides in a very simple way the repulsive contribution to the energy and must be included in a tight binding calculation in order to calculate interatomic distances.

Mössbauer isomer shifts inZn++67andNi++61nuclei

M\"ossbauer charge density for $^{61}\mathrm{Ni}^{++} (3{d}^{8})$ is calculated using Hartree-Fock wave functions. All the core $s$ functions ${\ensuremath{\varphi}}_{\mathrm{ns}} (n=1,2, \mathrm{and} 3)$ of ${\mathrm{Ni}}^{++}$ and their overlaps with six ${\mathrm{O}}^{\ensuremath{-}\ensuremath{-}}$ arranged in an octahedron corresponding to NiO are calculated as a function of interatomic distance $R$. Similar calculations for $^{67}\mathrm{Zn}^{++}$ in a tetrahedral environment of ${\mathrm{O}}^{\ensuremath{-}\ensuremath{-}}$ ions, appropriate to ZnO, are also performed. It is found that the isomer shift is given approximately by a "power law" $\ensuremath{\sim}{R}^{\ensuremath{-}7}$.

Variation of superexchange with interatomic distance. I. TheT2gsystemV++-F−-V++

The configuration-interaction method is applied to calculate the superexchange in ${\mathrm{V}}^{++}$-${\mathrm{F}}^{\ensuremath{-}}$-${\mathrm{V}}^{++}$ system as a function of interatomic distance. It is found that $\frac{\ensuremath{\partial}\mathrm{ln}J}{\ensuremath{\partial}\mathrm{ln}R}\ensuremath{\simeq}12$ for small variations of the interatomic spacing about an equilibrium ${\mathrm{V}}^{++}$-${\mathrm{F}}^{\ensuremath{-}}$ separation of 2 \AA{}. This may be characteristic of those systems with ground states which transform as the ${T}_{2g}$ irreducible representation of the octahedral group and admit, therefore, of only $d({t}_{2g})\ensuremath{-}{p}_{\ensuremath{\pi}}$ cation-anion bonding.