Charge-overlap effects in the non-additive triple-dipole interaction

A formal partial wave analysis of the third-order energy for the interaction of three non-degenerate S-state atoms is used to identify those non-additive terms which, in the limit of negligible charge overlap between the interacting atoms, reduce to the usual long-range expanded form of the triple-dipole energy. Pseudo-state techniques are used to evaluate these terms, both with and without the inclusion of charge-overlap effects, over a range of interatomic separations and angles for the interaction of three ground-state hydrogen atoms. These results are used as a model to discuss the way in which charge-overlap effects modify the usual long-range result for the triple-dipole energy. In addition to the familiar modification of the radial dependence of the interaction energy, charge-overlap effects are found to give rise to a modification of the angular dependence; the latter effect has no analogue in two-atom interactions. The significance of these results is discussed briefly.     

On the evaluation of high-order interaction energies using pseudo state methods

General expressions for the coefficients of the R ^-1 multipole expansion of the third and fourth-order interaction energies are derived in (pseudo) spectral form for the interaction of two S-state atoms. Explicit accurate results, for the H(ls)-H(ls) interaction, are obtained for the lead O(R ^-11) third-order energy and the lead O(R ^-12) fourth-order energy by using one centre pseudo state methods. These calculations, together with the appropriate second-order results, furnish an accurate expression for the total long-range interaction energy through O(R ^-12) and illustrate the applicability of the pseudo state approach for the evaluation of high-order interaction energies.     

Charge overlap effects dependence on the nature of the interaction

The He-He, He-H(1s), H(1s)-H(1s) and H(1s)-H(2s) interactions are considered as model systems for studying how charge overlap effects in second-order dispersion energies vary as a function of the nature of the interacting species. The non-expanded second-order energy and the corresponding multipole R ^-1 expansions, through all powers of R ^-1, are obtained for each interaction using Unsöld's average energy approximation. The results are used to discuss the limitations of the usefulness of the R ^-1 expansions.     

Padé approximation methods applied to the intermolecular force series

The H(1s)-H⁺, He-He, H(1s)-H(1s) and H(1s)-H(2s) interactions are considered as model systems for investigating the use of the Padé approximation method in summing the R ^-1 intermolecular force series. Various Padé approximants and partial sums of the R ^-1 expansions of the second-order Coulomb interaction energies are compared with the corresponding non-expanded results for each interaction. The computations are based on Unsöld's average energy approximation and on exact results for the H(1s)-H interaction. The results indicate that the Padé approximation method is a simple, useful way to remove some of the difficulties associated with the slow rate of convergence of the R ^-1 force series but that it does not alleviate the problems associated with the asymptotic divergent nature of the series. The results for the H(1s)-H⁺ interaction illustrate a possible difficulty in using Unsöld's method in the calculation of interaction energies.     

A reliable single parameter interatomic potential for argon

A simple semiempirical approximation previously proposed for the isotropic intermolecular forces between two closed shell systems is tested in detail for the argon-argon interaction. The potential is based on the knowledge of the first-order coulomb interaction energy, a suitably damped three term long range asymptotic expansion of the second order coulomb energy, and a semiempirical representation of the exchange interaction energy which contains one adjustable parameter. The single adjustable parameter can be reliably determined by fitting the second virial coefficient for argon in the 130–773 K temperature range with the long range interaction coefficients being constrained within the theoretical bounds specified by Tang, Norbeck and Certain. The reliability of the potential is compared with that of several literature potentials by comparing the theoretical predictions obtained from the potentials with experimental results for the second virial coefficient, viscosity, thermal conductivity and thermal diffusion ratios for dilute argon gas, and with spectroscopic data for the dimer, and with SCF calculations of the Ar-Ar potential at small interatomic separations. Our best potential predicts these properties with a precision as good as or better than other recent potentials which generally contain more adjustable parameters and/or involve more input data. The results confirm earlier work that suggested that the scheme tested is capable of yielding reliable isotropic potentials for the interaction of closed shell systems for 0·3 ? R/R_m ? ∞ where R_m is the intermolecular distance at the van der Waals minimum. The scheme appears to offer a method for obtaining reliable potentials while avoiding problems associated with optimizing many parameters with respect to fitting experimental constraints.     

A Direct Calculation of First-Order Wave Function of Helium

We develop a simple analytic calculation for the first order wave function of helium in a model in which nuclear charge screening is caused by repulsive coulomb interaction. The perturbation term, first-order correlation energy, and first-order wave function are divided into two components, one componentassociated with the repulsive coulomb interaction and the other proportional to magnetic shielding. The resulting first-order wave functions are applied to calculate second-order energies within the model. We find that the second-order energies are independent of the nuclear charge screening constant in the unperturbed Hamiltonian with a central coulomb potential.     

The effect of long-range three-particle forces on the surface energy and physisorption energy of rare gas crystals

The contribution of the triple-dipole interactions to the surface energy of rare gas crystals is considered. The result is obtained by direct summation of triplet bonds broken by a cleavage process. This non-additive effect proves to be 50% more important in the surface energy problem than in the corresponding bulk cohesive energy problem. In addition, the long-range threebody effect is evaluated for the physisorption energy of rare-gas atoms on rare-gas crystals and is shown to modify the pair binding energies by some 10%. In both problems the three-particle forces are found to be repulsive.     

Quantum Teleportation and Resonance Information Transfer from One Atom to Another at Arbitrary Interatomic Distances

The feasibility of resonance transfer of quantum information from one double-level atom to another that is at an arbitrary distance from the former one has been proved. Symmetric and antisymmetric combinations of the wave functions of individual atoms are considered. When taking into account the interatomic dipole–dipole interaction, a certain energy corresponds to each wave function. A solution has been found to a system of equations for the amplitudes of the probability that a resonance photon will be absorbed by one of the system atoms, and it has been shown that the interaction of the system with actual photons has the result that the wave function of the final state of the system can be represented as a linear combination of the functions < 00|, < 0n|, and < n0| corresponding to the ground and excited states of individual atoms. The amplitude of the probability of each of these states depends on the interatomic distance and on the parameters of the action of actual photons on atoms. Three types of solution to the system of equations have been investigated for the resonance and nonresonance absorption of photons and different interatomic distances. It has been shown that when atoms are at an infinite distance from one another, so that there is no dipole–dipole interaction of atoms, quantum information can be transferred from one atom to another with a characteristic time considerably shorter than the time it takes for a photon to cover the interatomic distance. This effect is referred to as the effect of quantum teleportation in a system of resonance atoms.     

Structure and vibrational properties of cobalt clusters (n ≤ 20)

The binding energies and vibration frequencies of free small cobalt clusters containing up to twenty atoms inclusive have been calculated using the interatomic interaction potential obtained in the tight-binding approximation. The minimum frequency of the cluster vibrations has been shown to play the determining role in the evaluation of its dynamic stability. The analysis of the energy parameters and vibrations of clusters has demonstrated that the cobalt clusters in which the number of atoms is n = 4, 6, 13, and 19 are stable.     

Long range interaction energies between ground and first excited state hydrogen atoms using a one centre method

A one centre method is used to evaluate the long range interaction energies, through O(R ^-10), between ground and first excited state hydrogen atoms. General pseudo spectral results for both the direct and resonant parts of the expanded second and third order interaction energies are given through any order in R ^-1. Of particular interest is an O(R ^-9) third order energy which is totally resonant in character. The advantage of the one centre method for interactions involving degenerate energy states is discussed briefly.     

Higher Order Multipole Potentials and Electrostatic Screening Effects on Cohesive Energy and Bulk Modulus of Metallic Nanoparticles

Higher order multipole potentials and electrostatic screening effects are introduced to incorporate the dangling bonds on the surface of a metallic nanopaticle and to modify the coulomb like potential energy terms, respectively. The total interaction energy function for any metallic nanoparticle is represented in terms of two- and three-body potentials. The two-body part is described by dipole-dipole interaction potential, and in the
three-body part, triple-dipole (DDD) and dipole-dipole-quadrupole (DDQ) terms are included. The size-dependent cohesive energy and bulk modulus are observed to decrease with decreasing sizes, a result which is in good agreement with the experimental values of Mo and W nanoparticles.     

On the exchange repulsion between beryllium atoms

Assuming the wave functions for free atoms in the form of the closed-shell SCF determinants, the first-order interaction energy for a system of three ground-state beryllium atoms has been computed. The decomposition of two and three-body interaction energies into individual, intershell contributions has been proposed. The results show that only the electrostatic energy is well approximated by the interaction of outer shells. For the two and three-body exchange energies this approximation is reliable only in the region of small orbital overlap. It has also been found that the three-body contribution to the interaction energy is considerably greater than in the case of the interaction of helium atoms.     

Long-range interaction of two ls-hydrogen atoms expressed in terms of natural spin-orbitals

The interaction between two hydrogen atoms in their ground state at large separation is treated by means of a variational form of the perturbation theory, which essentially involves the calculation of the reciprocal of the unperturbed matrix by means of successive inversion. A basic set which avoids the continuum is used. The energy of the system of two hydrogen atoms at large separations is found to be

where the separation R is measured in units of c ₀. The coefficient of R ^-6 agrees with the calculations of Pauling and Beach but the coefficient of R ^-8 is quite different from theirs. The wave function is greatly simplified by introducing natural orbitals. If the wave function is approximated by using only one or two sets of natural orbitals, very little error results in the calculated dispersion energy. Also, it is shown that such an approximation leads to very little error in the mean square deviation of the approximate wave function from the exact function. This illustrates the theorem that an approximate wave function composed of n natural orbitals has a smaller mean square deviation from the true function than an approximate wave function made up from n other sorts of orbitals. An application of long-range intermolecular force calculations to collision theory is also given.     

The interaction between first excited state hydrogen atoms and a different non-degenerate atom: an example of second-order resonance forces

The interaction of a first excited state hydrogen atom with a different non-degenerate atom is considered in the R ^-1 multiple approximation. The interaction energies for the Π states arising from this interaction have the form usually associated with second-order dispersion energies while those for the Σ states behave quite differently as a function of R. Because of a second-order ‘resonance within one molecule effect’ the second-order Σ-state energies do not possess single R ^-1 expansions that are formally valid for all values of R consistent with the multipole treatment. The expansions of these Σ-state energies, that are valid for ‘small’ R, contain terms varying as both even and odd powers of R ^-1; the lead R ^-7 ‘odd’ term competes strongly with the usual R ^-6 dispersion energy. The expansions that are valid for ‘large’ R contain terms varying as even powers of R ^-1 only and usually have little physical meaning. The He(¹S)-H(n=2) interaction is considered as a specific example of these results and the interaction energies for this system are evaluated through O(R ^-8) by using one-centre pseudostate methods. The general significance of the results is also discussed briefly.     

Violation of the equipartition theorem for thermally insulated clusters of atoms with different masses

An expression is derived for calculating microcanonical-ensemble averages of the kinetic energies of atoms of different types in clusters isolated from the environment. This expression is a natural generalization of the solution to the problem of hard spheres with different masses to a system with a many-particle interatomic interaction potential. The dynamics of a C₈H₈ cubane is simulated numerically. The data on the numerical simulation confirm the validity of the results obtained.     

One-centre multipole calculation of second-order perturbation energies for H+ 2

A knowledge of the H(1s) pseudospectrum allows one to calculate the one-centre second-order perturbation energies for the H(1s)-H⁺ interaction. The efficiency of such calculations is tested in detail for induction, exchange-induction, first-order overlap and Murrell-Shaw-Musher-Amos second-order energies for the ground and excited state H₊ ² at different internuclear distances. It is found that a large number of STO functions accounting for at least the first sixteen non-expanded multipoles is needed to obtain three figure accuracy in the short to medium range of internuclear separations. Higher accuracy can be obtained only in terms of a sensibly smaller number of two-centre functions which automatically satisfy the electron-nucleus cusp requirement.     

Size dependence of ground-state energy of the excitons in spherical Y2O3

The exciton energies of rare earth oxides (Ln₂O₃) have rarely been calculated by the theory. Experimentally, the blue-shift of exciton energy in nanocrystals deviates from the traditional size confinement effect. Herein, the dependence of the ground-state energy of an exciton in Y₂O₃ spheres on particle radius was calculated by using a variational method. In the model, an exciton confined in a sphere surrounded by a dielectric continuum shell was considered. The ground-state energy of exciton comprises kinetic energy, coulomb energy, polarization energy and exciton–phonon interaction energy. The kinetic and coulomb energy were considered by the effective mass and the dielectric continuum and the exciton–phonon interaction energy was given by the intermediate coupling method. The numerical results demonstrate that the present model is roughly consistent with the experimental results. The confinement effect of the kinetic energy is dominant of the blue-shift of the exciton energy in the region of R < 5 nm, while confinement effect of the coulomb energy is dominant of the blue-shift of the exciton energy in the region of R > 5 nm. The polarization energy contributes largely to the exciton energy as the particle size is smaller than ~ 10 nm, while the exciton–phonon interaction energy takes only a little contribution in all the range.     

Discussion of the He-He interaction energy in the average energy approximation

Using the Unsöld average energy method a double perturbation theory expression for the interaction energy through second order is obtained which includes intra-atomic correction terms arising from the use of trial wavefunctions to represent the non-interacting molecules. These formal expressions are applied to the ground state He-He interaction and results for the interaction energy are obtained that compare favourably with recent semiempirical and ab initio calculations. The Unsöld calculations are used to investigate approximations that have been introduced into the average energy calculation by other workers, and as a model for discussing the relative importance of second-order charge overlap and exchange effects and the convergence of the multipole treatment of the interaction energy for this typical non-bonded interaction. The results illustrate the importance of knowing as many terms as possible in the R ^-1 expansion of the energy. Finally a portion of this work required the recalculation of the He-He repulsive energy obtained by using the Eckart wavefunction to represent the helium atom. The resultant energy is approximately 25 per cent lower than that previously obtained using this wavefunction for most values of R.     

Ab initio calculations of energy transfer and non-additivity in the He-Ne laser system

Ab initio calculations were performed for several suggested mechanisms of energy transfer between helium metastable particles and neon. Optimized geometries and excited-state energies were calculated for neon excited-state complexes and the convergence properties of the non-additive contributions to the interaction energies were examined. The most probable excitation-transfer mechanism was found to be based on an energy difference of 0.0674 eV between the triplet excited state of and the singlet excited state of . No theoretical evidence was found for the production of neon singlet excited-state complexes other than 20.0858 to 20.4875 eV by the considered two-, three- and four-body models of energy transfer processes. The energy curves of the reactions involving the excited-state complexes and are provided and compared with the previously reported experimental results on the reaction . The relation between the probability of energy transfer and laser activity is discussed. The non-additive contribution to the total interaction energy of the nominated intermediate complex was found to be negligible, pointing to the possibility of constructing model potentials and simulation of larger systems. Received: 15 December 1998 / Received in final form: 20 March 1999     

Construction of embedded-atom-method interatomic potentials for alkaline metals （Li,Na,and K） by lattice inversion

The lattice-inversion embedded-atom-method interatomic potential developed previously by us is extended to alkaline metals including Li,Na,and K.It is found that considering interatomic interactions between neighboring atoms of an appropriate distance is a matter of great significance in constructing accurate embedded-atom-method interatomic potentials,especially for the prediction of surface energy.The lattice-inversion embedded-atom-method interatomic potentials for Li,Na,and K are successfully constructed by taking the fourth-neighbor atoms into consideration.These angular-independent potentials markedly promote the accuracy of predicted surface energies,which agree well with experimental results.In addition,the predicted structural stability,elastic constants,formation and migration energies of vacancy,and activation energy of vacancy diffusion are in good agreement with available experimental data and first-principles calculations,and the equilibrium condition is satisfied.