An expansion method for calculating molecular properties IV.

The energies of the 2pσ and 2sσ states of H₂ ⁺ and HeH²⁺ and those of the a ³, A ¹, b ³, B ¹Σ⁺ states of HeH⁺ are calculated up to second order in the heavy nuclear charge. For the one-electron systems the first-order equation is solved analytically employing a special separation technique for degeneracies. The consideration of screening enables a recently proposed interchange result for the degenerate case to be tested. The results for the 2sσ states are good while those for the 2pσ states are only good at small internuclear distances.

For the two-electron systems the method employed is a single perturbation approach for two perturbations in the presence of degeneracy. The results for HeH⁺ appear to be good only at small internuclear distances. The corresponding results for the excited states of H₂ are omitted since an interesting problem arises at first order.     

On the cohesive energy and charge density of uranium dioxide

Self-consistent band structure calculations have been used to calculate the cohesive energy of UO₂. The computed cohesive energy was 1.641 Ry/formula unit compared with an experimental value of 1.614 Ry/formula unit. The self consistent charge density has been compared with free atom charge densities to illustrate the formation of bonding charge between the atoms.     

An alternative approach on the calculation of cohesive energy density and isothermal compressibility of alkali metal halides

In the present paper, new and useful theoretical methods for the estimation of cohesive energy density (Ced) and isothermal compressibility (k_T) of alkali metal halides are described. The mentioned theoretical methods include the use of Kaya molecular hardness equation published by us in recent years. Cohesive energy density and isothermal compressibility of alkali metal halides were calculated in the framework of mentioned theoretical methods and the results obtained were compared with both experimental data and the results of previous theoretical methods proposed to calculate the aforementioned quantities, namely cohesive energy density and isothermal compressibility. It is important to note that the results obtained in the study are in good agreement with the available experimental data and with the results of previous theoretical methods. Additionally, we also investigated the correlation with lattice energy of cohesive energy density and isothermal compressibility for alkali halides.     

A double expansion method for calculating molecular properties

Using a form of double perturbation theory we present results of calculations on the ground state energies for the diatomic systems H₂ ⁺, HHe²⁺, H₂ and HHe⁺. For the homonuclear systems the energy values are unexpectedly good. For the heteronuclear cases the results are very encouraging and lead to optimism about the application of the method to larger systems which contain one heavy atom.     

Combined interpolation scheme for calculating the electron energy spectra of alloys of 3d transition metals

A model Hamiltonian is used as the basis of a combined interpolation scheme for calculating the spectra of ordered alloys of 3d transition elements with the CsCl and Cu₃Au structures. The parameters of the model Hamiltonian are found for the alloys FeCo and Co₃Ti and the histograms of the density of states are calculated at 165 points in 1/48-th part of the Brillouin zone. The results are evidence of the effectiveness of the use of such a combined interpolation scheme in calculating the integrated characteristics of the electron structure of alloys with large numbers of atoms in a unit cell.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 65–70, June, 1980.     

A method for calculating the ground-state properties of light closed-shell nuclei

The He⁴ nucleus ground state is studied by means of the Goldstone perturbation theory. Explicit expressions for the binding energy up to the second order in the t-interaction and for expectation values of single-particle operators (mean square radius, mass and charge distribution) up to the first order are derived. The effects of the centre-of-mass motion of the whole nucleus are considered in detail, especially with respect to mass and charge distribution. The numerical results for the charge form factor and distribution confirm the deviation from the Gaussian model measured recently.The author thanks Professor I. Úlehla for interesting discussions and M. Plchová for technical assistance.     

New method for calculating the potential energy of deformed nuclei within the liquid-drop model

The method that we previously developed for going over from double volume integrals to double surface integrals in calculating the Coulomb energy of nuclei that have a sharp surface is generalized to the case of nuclei where the range of nuclear forces is finite and where the nuclear surface is diffuse. New formulas for calculating the Coulomb and the nuclear energy of deformed nuclei are obtained within this approach. For a spherically symmetric nucleus, in which case there is an analytic solution to the problem in question, the results are compared with those that are quoted in the literature, and it is shown that the respective results coincide identically. A differential formulation of the method developed previously by Krappe, Nix, and Sierk for going over from double volume integrals to double surface integrals is proposed here on the basis of the present approach.     

A method for calculating the ground state properties of light closed-shell nuclei

A method for solving the reaction matrix equation in closed-shell nuclei using a spherical harmonic-oscillator representation is presented. The equation is transformed to an infinite algebraic system for the matrix elements, the exclusion operator being treated exactly. The system can be solved with arbitrary accuracy which depends only on the chosen truncation.     

A universal relation for the cohesive energy of nanoparticles

A universal relation between the cohesive energy and the particle size has been predicted based on the liquid-drop model. The universal relation is well supported by other theoretical models and the available experimental data. The universal relations for intermediate size range as well as for particles with very few atoms are discussed. A comparison of onset temperature of evaporation also establishes a universal relation.     

Hybridized kinetic energy functional for orbital-free density functional method

We propose a hybridized kinetic energy functional, aTTF+bTvW, where TTF is the Thomas-Fermi functional and TvW the von Weizsäcker functional while a and b are adjustable parameters. The new functional is implemented in orbital-free plane-wave density functional method, in which a conjugate-gradient line-search scheme of electronic minimization is incorporated. Calculations with the fitted a and b show that this kinetic energy functional can describe the structures of small Si, Al and Si-Al alloy clusters with reasonable accuracy.     

An engineering method for calculating the parameters and characteristics of pulse detonation engines

Theoretical fundamentals for calculating the thermodynamic cycle of engines with fuel detonation (FD cycle), which is realized in the thrust units of pulse detonation engines (PDE), are presented. A system of equations for calculating the parameters of the detonation waves under various conditions of their initiation is derived. These equations were used to examine how various factors influence the parameters of detonation waves and, consequently, the work of the cycle, thermal efficiency, and the specific parameters of the PDE. It was demonstrated that the maximum thermal efficiency of the FD cycle virtually coincides with the minimum losses caused by the irreversibility of heat input into the detonation wave. It was established that the losses are substantially dependent on the temperature of the working substance (compressed air or heated gas) supplied into the thrust units, more specifically, they decrease with increasing temperature.     

Adhesive and cohesive properties by indentation method of plasma-sprayed hydroxyapatite coatings

Adhesive and cohesive properties of the plasma-sprayed hydroxyapatite (HA) coatings, deposited on Ti-6Al-4V substrates by varying the plasma power level and spray distance (SD), were evaluated by an indentation method. The crystallinity and the porosity decreased with increasing both of these two parameters. The microhardness value, Young's modulus (E) and coating fracture toughness (K_C) were found to increase with a combinational increase in spray power and SD. The Knoop and Vickers indentation methods were used to estimate E and K_C, respectively. The critical point at which no crack appears at the interface was determined by the interface indentation test. This was used to define the apparent interfacial toughness (K_Ca) which is representative of the crack initiation resistance of the interface. It was found that K_Ca reaches to a maximum at a medium increase in both spray power and SD, while other mechanical properties of the coatings reaches to the highest value with further increase in these two plasma parameters. The tensile adhesion strength of the coatings, measure by the standard adhesion test, ISO 13779-4, was shown to alter in the same manner with K_Ca results. It was deduced that a combinational increase in spray power and SD which leads to a higher mechanical properties in the coatings, does not necessarily tends to a better mechanical properties at the interface.     

Cluster method density of states for noble metals and comparison with photoemission spectra

The multiple scattering cluster method is used to calculate densities of states for Cu, Ag, and Au. The results compare favorably with experimental photoemission spectra. The method converges rapidly with the cluster size used for the calculation.