Asymptotic approach to the description of nonclassical transport processes. Fermat’s principle

A method has been proposed to calculate the concentration distribution at asymptotically long distances from a source of impurity in a medium including long-scale heterogeneities. It has been found that the exponent Γ ? 1 in an expression for the concentration satisfies a nonlinear equation with first-order partial derivatives. This has allowed using the variational principle to calculate the function Γ. The pre-exponential factor in the expression for the concentration has been determined in the leading approximation in the small parameter Γ^?1. An analogy with geometrical optics and semiclassical approximation in quantum mechanics has been demonstrated.     

Real-space finite-difference approach for multi-body systems: path-integral renormalization group method and direct energy minimization method

The path-integral renormalization group and direct energy minimization method of practical first-principles electronic structure calculations for multi-body systems within the framework of the real-space finite-difference scheme are introduced. These two methods can handle higher dimensional systems with consideration of the correlation effect. Furthermore, they can be easily extended to the multicomponent quantum systems which contain more than two kinds of quantum particles. The key to the present methods is employing linear combinations of nonorthogonal Slater determinants (SDs) as multi-body wavefunctions. As one of the noticeable results, the same accuracy as the variational Monte Carlo method is achieved with a few SDs. This enables us to study the entire ground state consisting of electrons and nuclei without the need to use the Born-Oppenheimer approximation. Recent activities on methodological developments aiming towards practical calculations such as the implementation of auxiliary field for Coulombic interaction, the treatment of the kinetic operator in imaginary-time evolutions, the time-saving double-grid technique for bare-Coulomb atomic potentials and the optimization scheme for minimizing the total-energy functional are also introduced. As test examples, the total energy of the hydrogen molecule, the atomic configuration of the methylene and the electronic structures of two-dimensional quantum dots are calculated, and the accuracy, availability and possibility of the present methods are demonstrated.     

Molecular Ordering of a Nematogen at Phase Transition Temperature - A Theoretical Study

Molecular ordering in 4-cyano-4'- n -propylbiphenyl ( CB3 ), a nematic liquid crystal, has been studied with the help of intermolecular interaction energy calculations. The CNDO / 2 method has been employed to compute the net atomic charge and atomic dipole moment at each atomic centre. Modified Rayleigh-Schrodinger perturbation theory along with multicentered-multipole expansion method has been employed to evaluate long-range intermolecular interactions, while a ' 6-exp ' potential function has been assumed for short-range interactions. The interaction energy values obtained through these computations were used to calculate the probability of each configuration at the phase transition temperature using Maxwell-Boltzmann formula. All possible geometrical arrangements between molecular pair have been considered during stacking, in-plane and terminal interactions. An attempt has been made to identify the most probable configuration at the phase transition temperature during stacking, in-plane and terminal interactions. Results obtained have been discussed in the light of experimental as well as other theoretical observations.     

Interaction of a dielectric macroparticle with a point charge in plasma

The electrostatic interaction of a charged spherical dielectric macroparticle with a point charge in a plasma in the presence of an external uniform electric field is considered. The electrostatic force and the torque acting on the macroparticle have been determined, and the form of the interaction potential has been established for a nonuniform distribution of free charge on the macroparticle surface. A simple (for calculations) expression for the interaction potential that describes well the exact potential at all interparticle distances is proposed. The angular velocity of the spinning of dust particles caused by a nonuniform distribution of free charge over their surface has been estimated.     

Electronic structure and chemical bonding in actinide oxides: Monoxides and dioxides of Np,Pu, Am,Cm and Bk

First-principles molecular cluster calculations of the electronic structure of actinide monoxides and dioxides have been carried out in the local density formalism. AcO₆^10? clusters representative of monoxides and AcO₈^12? clusters for dioxides (Ac = Np, Pu, Am, Cm and Bk) have been studied in spin-restricted and spinpolarized models, using the discrete variational method with numerical atomic basis functions. One-electron energy level diagrams, atomic configurations, charge and spin densities were obtained. It is found that significant covalent mixing of O 2ρ and Ac 5f atomic orbitais occurs for heavy actinide compounds, contrary to the assumption of free-ion models. X-ray photoelectron line shape calculations agree rather well with experimental data on the dioxides. Analogies between systematics of the energy levels of actinide and rare-earth compounds are discussed.     

Molecular ordering in a bipolar nematogenic cyanobiphenyl – a computer simulation approach

The molecular ordering of 4-(6-hydroxypropyloxy)-4′-cyanobiphenyl (H3CBP), a bipolar nematogen, has been carried out at room temperature (300 K) with respect to translatory and orientational motions. The complete neglect differential overlap (CNDO/2) method has been employed to compute the net atomic charge and atomic dipole moment at each atomic center. The modified Rayleigh–Schrodinger perturbation theory with multicentered-multipole expansion method has been employed to evaluate long-range intermolecular interactions, while a 6-exp potential function has been assumed for short-range interactions. The interaction energy values obtained through these computations were used to calculate the probability of each configuration at room temperature using the Maxwell–Boltzmann formula. On the basis of stacking, in-plane, and terminal interactions energy calculations, all possible geometrical arrangements of the molecular pair have been considered. Further, an attempt has been made to develop a model for liquid crystallinity based on probability of dimer complexes.     

Free vibration analysis of microtubules based on an atomistic-continuum model

Analysis of free vibration of microtubules, based on an atomistic-continuum model, is presented. The theory bridges the polyatomic structure of microtubules with a macroscopic continuum approach under mesh-free computing scheme. A higher-order gradient continuum constitutive relationship is developed and incorporated into a higher-order Cauchy–Born rule. Instead of considering the atomic interaction between every atom pair in such polyatomic bio-composite textures, interatomic energy between subcomponents in microtubules is evaluated by a homogenization technique, represented by the fictitious bond. Material properties and stiffness matrix are determined, depending on deformation of fictitious bonds. Since the mesh-free approximation automatically satisfies the higher-order continuity and possesses intrinsic nonlocal property, the established quasicontinuum theory takes into consideration both atomic interaction and the size effect for modeling this microscale structure. Natural vibration frequencies of microtubules of different lengths and boundary restrictions are predicted and compared with existing solutions.     

A quantitative approach to ionic adsorption

Binding properties of multi-atomic systems with ionic bonds are calculated by using a recently developed method based on the density functional formalism. The charge density is obtained from a superposition of the respective atomic densities where the charge transfer between these atoms is chosen such that the total energy attains a minimum. The kinetic energy of the electrons can to a very good approximation be calculated by means of a modified Thomas-Fermi-v. Weizsäcker expression. The molecules NaCl and NaW and a NaW₄ cluster have been treated as model systems for ionic interaction. Moreover, we have computed the binding properties of a Na atom adsorbed on a W(100) surface. This particular problem is the primary subject of the present study. The calculations yield binding energies, binding distances, vibrational frequencies, and induced dipole moments.     

镍基单晶高温合金γ/γ′（001）相界面上原子构型的分子动力学研究

用分子动力学方法研究了镍基单晶高温合金γ/γ′（001）相界面上三种各具特征的原子堆垛结构. 能量学计算发现，存在最优构型，动力学模拟显示不同构型的界面弛豫后，在相界面上都“成对”出现刃型错配位错. 相关计算表明体系能量、界面形成能及弛豫能都依赖于界面原子堆垛特征，而几何特征则具共性，即不同原子构型的界面具有同一的应力释放模式.     

Theoretical study of molecular ordering in liquid crystals with the help of intermolecular interaction energy calculations

A theoretical analysis has been carried out to determine the molecular alignment of some nematic liquid crystals like DPAB (4, 4'-di-n-propoxy-azoxybenzene), EPAB (ethyl para-azoxybenzoate) and PAA (para-azoxyanisole). CNDO/2 method has been employed to evaluate the net atomic charge and atomic dipole components at each atomic centre of the molecules. Configurational energy has been computed using a modified Rayleigh-Schrodinger perturbation method at an interval of 1 Å in translation and 10° in rotation between a pair of DPAB molecules. On the basis of stacking, in-plane and terminal interaction energy calculations, all possible geometrical arrangements between a molecular pair have been considered. A comparative picture of molecular parameters like total energy, binding energy, total dipole moment etc., has been obtained. An attempt has been made to explain the nematogenic behaviour of liquid crystal and thereby develop a molecular model for liquid crystallinity.     

Electronic structure of K-(001) surface by the density matrix method

The electronic structure of the (001) surface of b.c.c. K has been studied by a direct determination of the density matrix in a local orbital basis. The method is based on a variational treatment of the ground state energy applying the Hohenberg-Kohn-Sham functional formalism. Surface charge density, work function and surface energy are in good agreement with other first principle self consistent calculations.     

Molecular alignment of biphenyl derivatives -a computational analysis

Molecular alignment of some biphenyl derivatives likes 4'-Nitro-2-biphenylamine (NBPA), 4-Acetyl-3'-chlorobiphenyl (ACBP) and 4-Acetyl-3'-florobiphenyl (AFBP) has been examined. The CNDO/2 method has been employed to compute the net atomic charge and atomic dipole-moment components at each atomic centre. Configurational energy has been computed using a modified Rayleigh- Schrodinger perturbation method at an interval of 0.1 A° in translation and 1° in rotation, and corresponding probabilities have been calculated using MB-statistics. A comparative study of molecular parameters like the total energy, the binding energy and the total dipole moment etc., has been made. On the basis of the stacking and the in-plane interaction energy calculations, all the possible geometrical arrangements between molecular pairing have been obtained. The investigation suggests that a strong intermolecular interaction energy between a pair of NBPA molecules, and the specific minimum energy configuration, determines the alignment of molecules with respect to one another. An attempt has been made to correlate the liquid crystalline properties exhibited by this class of molecules, and thereby develop a molecular model for the liquid crystallinity.     

Charge asymmetry and rovibrational excitations of HD+

Average values of the interparticle distances for rovibrationally excited HD⁺ are calculated using a method where the Born–Oppenheimer (BO) approximation is not assumed. The difference between the proton–electron and deuteron–electron distances is used to describe the charge asymmetry in the system. All-particle one-centre explicitly correlated Gaussian functions are used in the calculations of the HD⁺ rovibrational states. In this work, the non-BO method is extended to calculate the rovibrational states corresponding to the total rotational quantum number of two (N = 2). The algorithms for calculating the Hamiltonian and overlap matrix elements, and the matrix elements of the analytical energy gradient determined with respect to the exponential parameters of the Gaussians, are presented. The gradient is employed in the variational optimisation of the parameters, which is key in obtaining very accurate rovibrational energies in the calculations. The algorithm for calculating the average interparticle distances is also shown. The charge asymmetry of HD⁺ near the dissociation limit occurs, as expected, with the electron preferentially being near to the deuteron. The asymmetry for a particular vibrational level increases with rotational excitations. The rovibrational transition energies are also calculated and compared with available experimental data.     

尾流效应对快速双原子分子离子在固体中电荷态及分子轴取向的影响

研究了快速双原子分子离子在固体中穿行时,尾流效应对各离子电荷态以及库仑爆炸过程的影响.借助于线性介电响应理论和局域介电函数,离子之间的动力学相互作用势可以表示成对称的屏蔽库仑势和非对称的尾势.通过对分子离子上所有束缚电子的总能量进行变分和求解单个离子的运动方程,自洽地确定出分子离子中每个离子的电荷态.数值结果表明,由于尾流效应的影响,在初始穿行阶段,分子离子中导航离子的电荷数随穿行深度的增加而单调递增,而尾随离子的电荷数则随穿行深度的增加而振荡.但当穿行深度很大时,两个离子的电荷数都趋于具有相同速度的孤立离子的电荷数.此外,还发现分子轴的取向朝入射速度方向偏转     

A comparison of approximate methods for solving non-conservative problems of elastic stability

The methods of Ritz, Galerkin, and complementary energy are applied to a nonconservative problem in the theory of elastic stability. The numerical calculations are based upon (i) a variational expression, for which no functional can be determined, and (ii) an adjoint variational principle, for which a functional is established in terms of the variables of the original non-self-adjoint eigenvalue problem and the adjoint problem. The adjoint variational principle yields somewhat more accurate values for the critical load parameter than does the variational expression. In addition, the results obtained by means of the complementary energy method are more precise than the corresponding results obtained from the Ritz and Galerkin methods.     

Influence of the image charge effect on the hydrogen-like impurity-bound polaron in a spherical quantum dot in the presence of an electric field

We have investigated the influence of an external electric field on the binding energies and polaronic shifts of the ground and some first few excited states of a hydrogenic impurity in a spherical quantum dot by taking into account the image charge effect. By using Landau–Pekar variational method the general analytical expression is obtained for the impurity bound-polaron energies. It has been numerically identified the conditions (electric field, nominal radius of quantum dot, etc.) in which the bound-polaron states can be existence in GaAs quantum dot. We have shown that the polaronic shifts in the binding energy of 1s-like state are the same in cases with and without image charge effect while they for 2s-like state are not coincide and have different monotonic behavior versus confinement potential. Electron–phonon interaction lifts the degeneracy of the 2px-, 2py-, and 2pz-like states of a donor impurity and reduces their binding energies.     

Determination of a wave function functional

We propose expanding the space of variations in traditional variational calculations for the energy by considering the wave function psi to be a functional of a set of functions chi:psi=psi[chi], rather than a function. A constrained search in a subspace over all functions chi such that the functional psi[chi] satisfies a sum rule or leads to a physical observable is then performed. An upper bound to the energy is subsequently obtained by variational minimization. The rigorous construction of such a constrained-search-variational wave function functional is demonstrated.     

Variationally optimized numerical orbitals for molecular calculations

The problem of variational optimization of the atomic orbitals used in molecular calculations is investigated. It is shown that the variational principle leads to an equation similar to the radial Schrodinger equation but containing an inhomogeneous term. As an example, the equations are solved for the minimum basis set orbitals for the methane molecule. The results show a substantial improvement over those of a previous calculation optimizing in a minimum basis of Slater orbitals.     

Ionization of iridium ions in the Dresden EBIT studied by X-ray spectroscopy of direct excitation and radiative recombination processes

Ir^q+ ( 41≤q≤64) ions with open-shell configurations have been produced in the electron beam of the room-temperature Dresden Electron Beam Ion Trap (Dresden EBIT) at electron excitation energies from 2 keV to 13 keV. X-ray emission from direct excitation processes and radiative capture in krypton-like to aluminium-like iridium ions is measured with an energy dispersive Si(Li) detector. The detected X-ray lines are analyzed and compared with results from multiconfigurational Dirac-Fock (MCDF) atomic structure calculations. This allows to determine dominant produced ion charge states at different electron energies. The analysis shows that at the realized working gas pressure of 5×10^-9mbar for higher charged ions the maximum ion charge state is not preferently determined by the chosen electron beam energy needed for ionization of certain atomic substates, but by the balance between ionization and charge state reducing processes as charge exchange and radiative recombination. This behaviour is also discussed on the basis of model calculations for the resulting ion charge state distribution. Received 12 July 2001 and Received in final form 10 September 2001