Three-atom Exchange Research Articles

On the crystal structure problem for heavy rare-gas solids: A three-atom exchange perturbation analysis

The observed higher stability of a face-centered cubic (fcc) arrangement of atoms in heavy rare-gas solids, relative to that of a hexagonal close-packed (hcp) structure, is ascribed to the effect of three-atom short-range (exchange) interactions on the static lattice energy, evaluated in first- and second-order exchange perturbation theory. The summations are limited to 66 isosceles triangles with two atoms nearest neighbors of a central atom in the solid. Highly accurate results are reported, in part supplementing those of early work. An approach is taken in which the electrons of each atom are replaced by one electron on a Gaussian orbital with characteristic parameter β chosen such as to reproduce the attractive part of a Lennard-Jones (6, 12) pair potential, thus implicitly including intra- and inter-atomic electronic correlations. The results, for a wide range of values for the dimensionless parameter βR ( R is the nearest-neighbour distance in the solid at ambient pressure), invariably favor the fcc lattice, with a difference between fcc and hcp amounting to 0.4% of the total pair cohesive energy for solid argon, krypton and xenon (solid neon is a border case in thisanalysis). Recent papers on the crystal stability of rare-gas solids are critically examined.

Spin-one Heisenberg ferromagnet with three-atom exchange

We study the statistical mechanics of a spin-one ferromagnet with the nearest-neighbour bilinear Heisenberg exchange constant J and the three-atom coupling constant L using the equation-of-motion method for the two-time temperature-dependent Green function. It is seen that, as the three-atom coupling parameter alpha =L/J is increased positively, the Curie temperature TC first increases steeply and then increases very slowly and ultimately approaches the limiting value kBTC/Jz=4/3 as alpha tends to infinity. The situation is much more complicated for negative alpha but, as alpha to infinity , TC approaches the limiting value 4/3. The temperature variation in spontaneous magnetization m and the quadrupolar ordering parameter lambda for various values of alpha are studied. It is seen that there exists a critical value of alpha (which we shall call alpha c) beyond which the phase transition is first order for SC, BCC and FCC lattices. alpha c decreases as the number z of nearest neighbour increases. The discontinuity in m has been found to be extremely sensitive near alpha c. The results are discussed with reference to those obtained by earlier workers.

Time-dependent calculation of the energy resolved state-to-state transition probabilities for three-atom exchange reactions

A procedure for extracting reactive and inelastic scattering probabilities from a time-dependent wave function is presented. The power of this procedure is due to the combination of two features: the ability to obtain the probabilities for a large range of energy within a single wave packet propagation and the usefulness for long time scale processes. It is applied to the colinear reaction H + H 2 at energies between 0.4 and 1.8 eV. A comparison with previous time-independent calculations shows that resonances are accurately reproduced with this time-dependent procedure.

Theoretical study of the reaction C( 3P)+SH(X 2Π). III. Two analytic models of the lowest potential energy surface

We present two analytical models of potential energy surface (PES) describing three-atom exothermic reactions involving one or two intermediate wells. Each of these wells corresponds to a stable species of bent equilibrium geometry. The purpose of this construction is twofold: (i) the study of the dynamics of the specific three-atom exchange reaction C( 3P)+SH(X 2Π)→ CS(X 1Σ +)+H( 2S) and (ii) a more general approach concerning the role of different topological factors on the nascent distribution of energy of the motion of product nuclei. The latter goal can be achieved by means of the flexibility of the model which allows some change of topological factors almost independently. This property of flexibility inherent in the models is due to the way this kind of model is developed. The models are made up in parts, each describing a portion of the surface. Each part is coupled with the others by means of a 2×2 determinantal equation, the coupling taking place in a limited domain of spatial conformation.

Quantum time-dependent methods usable in reaction dynamics: Application to the reaction C + NO

Several techniques to solve the time-dependent SchrOdinger equation are briefly presented. The central problem in grid methods is the representation of the operators in a discrete Hilbert space. We present two approximations to compute the Hamiltonian : the Finite Difference method and the Fourier method. The properties of lour time-propagator approximations are summarized. Their respective accuracy and efficiency are compared in the case of the harmonic oscillator. Finally the Crank-Nicholson method is applied on a molecular dynamic problem which is the three-atom exchange reaction C + NO → CN + 0. This reaction has already been studied by means of a classical trajectory approach.

Molecular-dynamics simulations in systems of rare gases using Axilrod-Teller and exchange three-atom interactions.

Molecular-dynamics simulations on cluster formation in compressed argon and xenon gases were performed, with use of a Lennard-Jones (6,12) potential together with Axilrod-Teller three-atom interactions and those of exchange type, applying results of a recent analysis of these three-body potentials [Phys. Rev. A 30, 1593 (1984)]. Selective stabilization of clusters ${\mathrm{Ar}}_{19}$, ${\mathrm{Xe}}_{13}$, and ${\mathrm{Xe}}_{19}$ (possibly also ${\mathrm{Xe}}_{25}$) was established, predominantly as a result of the three-atom exchange potential. It is conjectured that these exchange contributions, in combination with selective stability due to cluster ionization, explain the phenomena observed in time-of-flight mass spectroscopy experiments on rare-gas-atom clusters.

New fit of the 3He solid exchange parameters.

Using mean field theory and the high-temperature expansion we have calculated most measured quantities of magnetic solid $^{3}\mathrm{He}$ including the phase diagram. We have obtained a new fit using three kinds of exchange: direct nearest-neighbor exchange ${J}_{\mathrm{nn}}$, three-atom exchange ${J}_{t}$, and planar four-atom exchange ${K}_{p}$. We show that it is possible to fit almost all measured quantities using these three parameters with good accuracy, including the zero-temperature first-order phase-transition field, ${H}_{1}$.

Analysis of three-body potentials in systems of rare-gas atoms: Axilrod-Teller versus three-atom exchange interactions

The triple-dipole (Axilrod-Teller) and the exchange three-atom potentials are compared for a number of specific arrangements of three argon and xenon atoms. For these configurations, total potentials are constructed, taking a Lennard-Jones (6-12) potential for each pair. It is found that for all arrangements the exchange three-atom potential is by far the more important correction to the two-body interaction. Qualitatively, the changes with respect to the two-body potential are more pronounced for xenon than for argon.

Elementary excitations in spin systems with the three-atom exchange

A system of spins localised on lattice sites is investigated at low temperatures. The Hamiltonian contains the bilinear (Heisenberg) and biquadratic pair interactions as well as the three-atom exchange of the form (SfSg)(SgSf'). The spectra of non-interacting spin waves and quadrons are calculated by means of the diagrammatic technique applied to green functions. All calculations are carried out in the zeroth-order approximation in 1/z, where z is the number of spins interacting with any given spin. In the ferromagnetic phase at T=0 the spectra are calculated for arbitrary spin s. The spin-wave spectrum in this case is then rederived by a more elementary method of solving the energy eigenproblem in the one-particle subspace of the system. For s=1 the spectra are determined for T not=0, the magnon spectrum in arbitrary one-sublattice phase and the quadron spectrum in the ferromagnetic phase. The particular case of magnons in the ferromagnetic and quadrupolar phases at T=0 in the nearest-neighbours approximation is illustrated graphically.

Exchange interactions between atoms or molecules in different perturbation formalisms. Application to three-atom exchange forces

An explicit comparison is made between first- and second-order perturbation expressions for exchange interactions given by the Eisenschitz-London-Van der Avoird formalism and by a Schroedinger-type procedure. Relative three-atom exchange interactions are found to be very similar in the two formalisms.