Phase Space View of Ensembles of Excited States

The density functional theory and its extension to ensembles of excited states can be formalized as thermodynamics. However, these theories are not unique because one of their key quantities, the kinetic energy density,can be defined in several ways. Usually, the everywhere positive gradient form is applied; however, other forms are also acceptable, provided they integrate to the true kinetic energy. Recently, a kinetic energy density of the ground-state theory maximizing the information entropy has been proposed. Here, ensemble kinetic energy density, leading to extremum information entropy, is derived via constrained search. The corresponding ensemble temperature is found to be constant.     

A statistical theory of the kinetics of bimolecular reactions in condensed media

A statistical theory for a system of reactive species A and B distributed in an inert condensed medium is developed. The decay of species due to a bimolecular reaction A + B → P (products) is assumed to occur simultaneously with their creation under the action of radiation. The theory is based on the concept of localization of reactive species in the matrix and takes into account correlations of their spatial distributions. Many-species distribution functions describing creation and decay of species are introduced by means of specially defined statistical ensembles. Kinetic equations for such functions are obtained. Earlier kinetic theories of bimolecular reactions and accumulation of reactive species in condensed media are statistically validated.     

Quantum Chemical Study of Spatial Structure and Stereoelectronic Properties of Iminodihydrofuran Ensembles

A quantum chemical study of structural peculiarities of iminodihydrofuran ensembles (from dimers to tetramers with individual calculations for penta- and hexamers) associated with their rotation isomerism was carried out. Three basic spatial packings of the iminodihydrofuran chains were distinguished with increasing the number of ensemble elements. The spiral and linear packings are equally probable from the standpoint of their thermodynamic stability. The third packing, exhibiting the curvature radius, is inferior to the former two, as judged from the relative stability. It was shown that ensembles in the alternating linear-spiral form are fundamentally possible to exist. Data was obtained testifying to a possibility for the intramolecular hydrogen bond forming between the imine and amine moieties in the tetramer spiral structures; activation barriers of intramolecular prototropic rearrangement were determined.     

Application of the group function theory to infinite systems

We consider application of the group function theory to an arbitrary infinite system consisting of weakly overlapping structural elements which may be atoms, ions, molecules, bonds, etc. We demonstrate that the arrow diagram (AD) expansion developed previously is ill‐defined for such a system resulting in divergences in any physical quantity associated with the entire system such as, for example, the energy and charge density. A “linked‐AD” theorem is then formulated and proven, which results in a diagrammatic expansion that scales correctly with the system size. Coulomb systems with long‐range interactions between structure elements are also considered and the diagrammatic expansion is rearranged in such a way as to also give the correct (linear) scaling. We give an explicit expression for the total energy up to the third order with respect to overlap. Finally, we discuss the problem of choosing structure elements (SE) in a general insulating system and propose a variational method based on a configuration interaction (CI) type expansion within the Fock subspace associated with every SE. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 511–534, 2000     

Effect of Temperature on Henry's Constant in Simple Mixtures

Abstract

The molecular theory of dense fluids is progressing rapidly and its extension to mixtures is well underway. The purpose of this note is to call attention to a possibly serious difficulty in comparing experimental Henry's constants with those calculated from theory. The difficulty arises because whereas theorists choose temperature and density as independent variables, experimental equilibrium measurements on mixtures are often made along the saturation line where (at fixed composition) temperature and density are not both independent variables. Unless Henry's constants are defined with care, the effect of temperature on Henry's constants calculated from molecular theory may be qualitatively different from that observed.     

Structurally Organized Nanocomposites in the Catalysis of Chlorohydrocarbon Reactions

Catalysis by closely packed metal films containing monodispersed nanocluster ensembles was considered using the reactions of chlorinated hydrocarbons as an example; these reactions include a step of electron transfer from a catalyst to a reactant. A new laser electrodispersion technique was used for preparing films that consisted of spherical copper grains 5 nm in size coated with thin (0.7 nm) layers of copper(I) oxide with different particle packing densities on the surface of thermally oxidized silicon. A comparison of the catalytic activity of films with varied packing density in media with different permittivities allowed us to assume that the observed maximum activity of closely packed films was associated with the appearance of charged grains in the ensembles of interacting nanoparticles due to the thermal fluctuations of electrons between closely spaced grains.     

Improved fitting of solution X-ray scattering data to macromolecular structures and structural ensembles by explicit water modeling

A new procedure, AXES, is introduced for fitting small-angle X-ray scattering (SAXS) data to macromolecular structures and ensembles of structures. By using explicit water models to account for the effect of solvent, and by restricting the adjustable fitting parameters to those that dominate experimental uncertainties, including sample/buffer rescaling, detector dark current, and, within a narrow range, hydration layer density, superior fits between experimental high resolution structures and SAXS data are obtained. AXES results are found to be more discriminating than standard Crysol fitting of SAXS data when evaluating poorly or incorrectly modeled protein structures. AXES results for ensembles of structures previously generated for ubiquitin show improved fits over fitting of the individual members of these ensembles, indicating these ensembles capture the dynamic behavior of proteins in solution.     

Squeezing a helium nanodroplet with a Rydberg electron

We have investigated, by means of density functional theory, the structure of a "scolium", that is, an electron circulating around a positively charged 4He nanodroplet, temporarily prevented from neutralization by the helium-electron repulsion. The positive ion core resides in the center of the nanodroplet where, as a consequence of electrostriction, a strong increase in the helium density with respect to its bulk value occurs. The electron enveloping the 4He cluster exerts an additional electrostatic pressure which further increases the local 4He density around the ion core. We argue that under such pressure, sufficiently small 4He nanodroplets may turn solid. The stability of a scolium with respect to electron-ion recombination is investigated.     

元素电负性和硬度的密度泛函理论研究

应用密度泛函理论的DFT LDA、DFT LDA/NL和改进的Slater过渡态方法,把元素的电离能和电子亲合能的计算扩展到周期表的103种元素.并用有限差分方法计算了这103种元素的电负性和硬度.计算中考虑了相对论效应.计算结果比以前Robles等用密度泛函理论的XGL和Xα近似的交换相关泛函的计算结果有所改进,更接近实验值.     

Modeling of Adsorption in Finite Cylindrical Pores by Means of Density Functional Theory

Adsorption of argon at its boiling point in finite cylindrical pores is considered by means of the non-local density functional theory (NLDFT) with a reference to MCM-41 silica. The NLDFT was adjusted to amorphous solids, which allowed us to quantitatively describe argon adsorption isotherm on nonporous reference silica in the entire bulk pressure range. In contrast to the conventional NLDFT technique, application of the model to cylindrical pores does not show any layering before the phase transition in conformity with experimental data. The finite pore is modeled as a cylindrical cavity bounded from its mouth by an infinite flat surface perpendicular to the pore axis. The adsorption of argon in pores of 4 and 5 nm diameters is analyzed in canonical and grand canonical ensembles using a two-dimensional version of NLDFT, which accounts for the radial and longitudinal fluid density distributions. The simulation results did not show any unusual features associated with accounting for the outer surface and support the conclusions obtained from the classical analysis of capillary condensation and evaporation. That is, the spontaneous condensation occurs at the vapor-like spinodal point, which is the upper limit of mechanical stability of the liquid-like film wetting the pore wall, while the evaporation occurs via a mechanism of receding of the semispherical meniscus from the pore mouth and the complete evaporation of the core occurs at the equilibrium transition pressure. Visualization of the pore filling and empting in the form of contour lines is presented.     

Information theory and electron density

The intriguing concept of inherent uncertainty of probability schemes in information theory and statistical inference is applied to the molecular electron density. The electron density function is treated as a multimodal, three-dimensional probability density function describing the distribution of the electrons of a molecule in real space. A simple theory is proposed to introduce the amount of information associated with perturbations of the nuclear geometry such as molecular vibrations and reaction paths, in particular. It is shown by computations that the amount of information associated with the normal modes of vibration is related to the reduced mass. The proposed theory also suggests a novel Riemannian nuclear configuration space which is completely defined by the observable electron density of a molecular system.     

Computer simulations of thin polymer layers

Molecular dynamics calculations are used to explore the structure of dense monolayers of long-chain molecules supported on a planar surface. As a model we consider ensembles of flexible chains consisting of N segments (N=32, 64 and 128) in a box with lateral (x, y) periodicity conditions. The effect of surface coverage on the conformational properties of chains is studied. At high coverages, the results of the simulations show that each chain is strongly stretched along the normal to the surface and the mean layer thickness is linear in N. The segment density distribution along the normal is found to be an universal function A^2/3 f (zA^1/3 N), where A is the surface area per chain. The high-coverage distribution has a well defined broad plateau, in agreement with the so-called blob model. In contrast to the predictions of this model, however, we observe that the chains are strongly stretched at all space scales. Differences between the results of simulations and those predicted by the mean-field theory are also discussed.     

Simulation studies of the fidelity of biomolecular structure ensemble recreation

We examine the ability of Bayesian methods to recreate structural ensembles for partially folded molecules from averaged data. Specifically we test the ability of various algorithms to recreate different transition state ensembles for folding proteins using a multiple replica simulation algorithm using input from "gold standard" reference ensembles that were first generated with a Go-like Hamiltonian having nonpairwise additive terms. A set of low resolution data, which function as the "experimental" phi values, were first constructed from this reference ensemble. The resulting phi values were then treated as one would treat laboratory experimental data and were used as input in the replica reconstruction algorithm. The resulting ensembles of structures obtained by the replica algorithm were compared to the gold standard reference ensemble, from which those "data" were, in fact, obtained. It is found that for a unimodal transition state ensemble with a low barrier, the multiple replica algorithm does recreate the reference ensemble fairly successfully when no experimental error is assumed. The Kolmogorov-Smirnov test as well as principal component analysis show that the overlap of the recovered and reference ensembles is significantly enhanced when multiple replicas are used. Reduction of the multiple replica ensembles by clustering successfully yields subensembles with close similarity to the reference ensembles. On the other hand, for a high barrier transition state with two distinct transition state ensembles, the single replica algorithm only samples a few structures of one of the reference ensemble basins. This is due to the fact that the phi values are intrinsically ensemble averaged quantities. The replica algorithm with multiple copies does sample both reference ensemble basins. In contrast to the single replica case, the multiple replicas are constrained to reproduce the average phi values, but allow fluctuations in phi for each individual copy. These fluctuations facilitate a more faithful sampling of the reference ensemble basins. Finally, we test how robustly the reconstruction algorithm can function by introducing errors in phi comparable in magnitude to those suggested by some authors. In this circumstance we observe that the chances of ensemble recovery with the replica algorithm are poor using a single replica, but are improved when multiple copies are used. A multimodal transition state ensemble, however, turns out to be more sensitive to large errors in phi (if appropriately gauged) and attempts at successful recreation of the reference ensemble with simple replica algorithms can fall short.     

Quantum theory of dielectric relaxation in polar solids

A novel approach to the impurity dipole relaxation in polar solids is described in which the dipole reorientational sites are formed by an appropriate electron—phonon coupling interaction. The electronic states used for a two-site formulation are defined as ones pertaining to the impurity and/or the associated intrinsic point defect. The theory takes into account the adiabaticity of the electron transfer in addition to the barrier-controlled ionic tunneling. It compares favorably with available experimental relaxation-time data on alkali halides.     

Generalized density functional theory for degenerate states

An extension of density functional theory is proposed for degenerate states. There are suitably selected basic variables beyond the subspace density. Generalized Kohn-Sham equations are derived. A direct method is proposed to ensure the fixed value of ensemble quantities. Then the Kohn-Sham equations are similar to the conventional Kohn-Sham equations. But the Kohn-Sham potential is different for different ensembles. A simple local expression is proposed for the correlation energy.     

Point scattering: a new geometric invariant with applications from (nano)clusters to biomolecules

A new geometric invariant is defined from "first principles" for a point ensemble, which can represent clusters, molecules, crystals, and biomolecules. The scattering of a point ensemble is defined in terms of the Euclidean distance matrix and a vector measuring the weighted departure of the points from the cluster centre. Using the Rayleigh-Ritz theorem this function is maximized obtaining the point scattering of the ensemble. The point scattering shows several properties which are useful for studying clusters, molecules, crystals, and biomolecules. We examined different natural clusters of hard spheres such as colloidal particles and fullerenes, as well as protein-peptide complexes and the effect of temperature on protein structure. In all cases point scattering differentiates point ensembles with different structures, which are not distinguished by other geometric invariants, such as the second moment of mass distribution, surface areas, and volumes. Point scattering also shows better correlation with thermodynamic parameters of binding and describes the interior cavities of hollowed ensembles better than the other geometric measures.     

Classical theory of collisional entropy production

A classical dynamical theory of elementary collision processes is formulated in analogy to the quantum theory of the dynamical scattering matrix, which can be defined for a pure quantum stationary scattering state. The elements of this matrix are probability amplitudes for transitions between internal states defined for given values of a reaction coordinate. The squared magnitudes of these amplitudes, modeled in the proposed classical theory, define normalized internal state population distributions suitable for information theoretical analysis. Statistical entropy and surprisal are defined as dynamical functions of a reaction coordinate. This formalism differs fundamentally from concepts based on the classical Liouville equation.     

Atomic and Ionic Radii of Elements 1–96

Atomic and cationic radii have been calculated for the first 96 elements, together with selected anionic radii. The metric adopted is the average distance from the nucleus where the electron density falls to 0.001 electrons per bohr³, following earlier work by Boyd. Our radii are derived using relativistic all‐electron density functional theory calculations, close to the basis set limit. They offer a systematic quantitative measure of the sizes of non‐interacting atoms, commonly invoked in the rationalization of chemical bonding, structure, and different properties. Remarkably, the atomic radii as defined in this way correlate well with van der Waals radii derived from crystal structures. A rationalization for trends and exceptions in those correlations is provided.