Mechanism of Electric Polarization of Water Contact Layer at Its Interface with the Ion Crystal Surface

Russian Journal of Electrochemistry - Molecular mechanisms of the electric polarization of supercooled water at its interface with the basal face of β-AgI crystal are studied by computer...     

Exchange and spin states in quantum dots under strong spatial correlations. Computer simulation by the Feynman path integral method

The fundamental laws in the behavior of electrons in model quantum dots that are caused by exchange and strong Coulomb correlations are studied. The ab initio path integral method is used to numerically simulate systems of two, three, four, and six interacting identical electrons confined in a three-dimensional spherical potential well with a parabolic confining potential against the background of thermal fluctuations. The temperature dependences of spin and collective spin magnetic susceptibility are calculated for model quantum dots of various spatial sizes. A basically exact procedure is proposed for taking into account the permutation symmetry and the spin state of electrons, which makes it possible to perform numerical calculations using modern computer facilities. The conditions of applicability of a virial energy estimator and its optimum form in exchange systems are determined. A correlation estimator of kinetic energy, which is an alternative to a basic estimator, is suggested. A fundamental relation between the kinetic energy of a quantum particle and the character of its virtual diffusion in imaginary time is demonstrated. The process of natural “pairing” of electron spins during the compression of a quantum dot and cooling of a system is numerically reproduced in terms of path integrals. The temperature dependences of the spin magnetic susceptibility of electron pairs with a characteristic maximum caused by spin pairing are obtained.     

Simulation of thermal ionization in a dense helium plasma by the Feynman path integral method

The region of equilibrium states is studied where the quantum nature of the electron component and a strong nonideality of a plasma play a key role. The problem of negative signs in the calculation of equilibrium averages a system of indistinguishable quantum particles with a spin is solved in the macroscopic limit. It is demonstrated that the calculation can be conducted up to a numerical result. The complete set of symmetrized basis wave functions is constructed based on the Young symmetry operators. The combinatorial weight coefficients of the states corresponding to different graphs of connected Feynman paths in multiparticle systems are calculated by the method of random walk over permutation classes. The kinetic energy is calculated using a viral estimator at a finite pressure in a statistical ensemble with flexible boundaries. Based on the methods developed in the paper, the computer simulation is performed for a dense helium plasma in the temperature range from 30000 to 40000 K. The equation of state, internal energy, ionization degree, and structural characteristic of the plasma are calculated in terms of spatial correlation functions. The parameters of a pseudopotential plasma model are estimated.     

Structure of water in microscopic fractures of a silver iodide crystal

The results of a computer simulation of flat fractures with widths of 0.63, 1.25, and 2.5 nm filled with vapor molecules in a silver iodide crystals at 260 K were presented. The two-dimensional gas of molecules adsorbed on the walls was found to be strongly clustered. Before the pore was filled, its walls had been covered with a monomolecular water film with a characteristic hexagonal structure. The perpendicular growth of the film was hindered by the hydrophobicity of its surface; the adsorbed molecules were bonded with the walls by interactions with the ions of the second crystal layer to form a specific orientational molecular order in the region of contact with the wall. On the wall with silver cations, the molecular energy was lower and the entropy higher than on the wall with iodide anions; on the wall with a lower energy, the adsorption started earlier and was more active. In an extremely narrow pore having room for only one molecular layer, the monomolecular film consists of spots held on opposite walls; in each spot, the orientational molecular order is the one characteristic of the wall with which the spot is in contact.     

Calculation of the equation of state of a dense hydrogen plasma by the Feynman path integral method

A method is developed for calculating the equation of state of a system of quantum particles at a finite temperature, based on the Feynman formulation of quantum statistics. A general analytical expression is found for the virial estimator for the kinetic energy of a system with rigid boundaries at a finite pressure. An effective method is developed for eliminating the unphysical singularity in the electrostatic potential between a discretized Feynman path of an electron and a proton. It is shown that the “refinement” of an expansion of a quantum-mechanical propagator by addition of high powers of time exacerbates, rather than eliminates, the divergence of a Feynman path integral. A brief summary of the current status of the problem is presented. The proposed new approaches are presented in relation to progress made in this field. Path integral Monte Carlo simulations are performed for nonideal hydrogen plasmas in which both indistinguishability and spin of electrons are taken into account under conditions preceding the formation of the electron shells of atoms. The electron permutation symmetry is represented in terms of Young operators. It is shown that, owing to the singularity of the Coulomb potential, quantum effects on the behavior of the electron component cannot be reduced to small corrections even if the system must be treated as a classical system according to the formal de Broglie criterion. Quantum-mechanical delocalization of electrons substantially weakens the repulsion between electrons as compared to protons. In relatively cold plasmas, many-body correlations lead to complex behavior of the potential of the average force between particles and give rise to repulsive forces acting between protons and electrons at distances of about 5 angstroms. Plasma pressure drops with decreasing plasma temperature as the electron shells of atoms begin to form, and the electron kinetic energy reaches a minimum at a temperature of about 31000 K. The minimum point weakly depends on plasma density. Owing to quantum effects, the electron component is “heated” well before electrons are completely bound in the field of protons.     

Mean Force Potential between H3O+ and Cl– Ions in Molecular Water Clusters: 1. Atmospheric Surface Layer Conditions

A method for calculating mean force potential for particles in systems with high potential barriers was developed. It was shown that the hydration of HCl resulted in the formation of molecular water clusters, which remained thermodynamically stable at 313 K. Two minima separated by the barrier were disclosed on the dependence of mean force potential between H₃O⁺ and Cl^– ions on interionic spacing in a cluster. Based on the data obtained, a general kinetic model was proposed that explained experimental observations (in atmosphere) of a large population of stable molecular water clusters containing ion pairs.     

Electron wave packets: Quantum statistics in path integral representation

Fundamental relations between ensemble-averaged kinetic energy, pressure, and virial are obtained for quantum many-particle systems at finite temperatures. A path-integral method is developed for calculating kinetic energy for mixed (quantum-classical) systems. The method eliminates the problem of divergent variance. Path-integral Monte Carlo simulations are performed to validate the method as applied to single-electron and electron-pair wave packets, with exact treatment of exchange symmetry and spin states. Quantitative results are compared with corresponding characteristics calculated for point charges.     

Interaction of water molecules with the electric field of an ionic-crystal surface

A theoretical investigation of the coulombic interaction of water molecules with an ideal surface of an ionic crystal is conducted. The calculation is based on the Fourier transform of the long-range part of an coulombic potential with subsequent summation of its Fourier images and tabulation of the results. The method is numerically tested when solving the problem concerning the interaction with the surface of a silver iodide crystal. A comparison of the electric field near an ideal crystalline surface and its finite fragment is performed. The data obtained point to a strong dependence of electrochemical properties of the surface on the presence of crystalline defects on it.