The relevance of the complementary spherical electron density model to organometallic intermediates involved in homogeneous catalysis

The implications of the Complementary Spherical Electron Density Model, originally developed by Mingos and Hawes in 1985 and amplified in 2004, to co-ordinatively unsaturated intermediates in homogenous catalytic processes are discussed. The geometric consequences of the model for 16 and 14 electron complexes are particularly important and are supported by numerous recent X-ray crystallographic investigations. The character of the important frontier orbitals have been explored using density functional calculations.     

Ground-state energy of an s-state model of the inhomogeneous electron liquid in relation to an exactly solvable model of He with additional radial correlation

Following Temkin’s proposal of the so-called s-wave model, Amovilli, Howard and March (AHM) displayed an exactly solvable model Hamiltonian in which an additional radial correlation is added. The ground-state wave function for this Hamiltonian, for modelling He-like atomic ions with nuclear charge Ze, is used here to compare and contrast with the Temkin Model. The differences only appear near the critical charges Z_ce at which one electron ionises, Z_c being precisely unity for the AHM model and having the value 0.948768 in Serra’s variational study of the s-wave model. These two models are then compared with He-like ions having the correct e²/r₁₂ interaction.     

High-dimensional model representations generated from low order terms--lp-RS-HDMR

High-dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for improving the efficiency of deducing high dimensional input-output system behavior. RS-HDMR is a particular form of HDMR based on random sampling (RS) of the input variables. The component functions in an HDMR expansion are optimal choices tailored to the n-variate function f(x) being represented over the desired domain of the n-dimensional vector x. The high-order terms (usually larger than second order, or equivalently beyond cooperativity between pairs of variables) in the expansion are often negligible. When it is necessary to go beyond the first and the second order RS-HDMR, this article introduces a modified low-order term product (lp)-RS-HDMR method to approximately represent the high-order RS-HDMR component functions as products of low-order functions. Using this method the high-order truncated RS-HDMR expansions may be constructed without directly computing the original high-order terms. The mathematical foundations of lp-RS-HDMR are presented along with an illustration of its utility in an atmospheric chemical kinetics model.     

The localized electrons detector as an ab initio representation of molecular structures

The local single particle momentum is proposed as a localized‐electrons detector (LED) that provides a direct three‐dimensional representation of bonding interactions in molecules. It is given exclusively in terms of the electron density and its gradient. We show that the graphical representation of bonding interactions given by LED is consistent with the local curvatures of the electron density as given by the eigenvalues of the Hessian matrix, according to a local symmetry classification of the critical points here introduced. LED consistently complements the topological analysis of the electron density given by the quantum theory of atoms in molecules, by providing a graphical representation of the symmetry of the bonding interactions in molecular systems. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2418–2425, 2010     

Infrared radiation from an arc plasma and its application to plasma diagnostics

In this paper, a feasibility stud v has been conducted to determine if infrared radiation from an arc plasma can be used for diagnostic purposes. The properties of IR radiation of an atmospheric-pressure arc plasma are described from the viewpoint of continuous radiation theory, and the effects of electron density and temperature on the spectral radiance of an arc plasma column of finite size have been evaluated using a plasma slab model. As a result, it is shown that the spectral radiance of the atmospheric arc plasma column is very sensitive to the electron density in the near infrared frequency range, and the temperature dependence of the spectral radiance is negligibly small in this frequency range. Finally, it is concluded that IR radiation in the wavelength range of 3-15 m can be used to measure the electron density of the arc plasma, and a simple formula for the measurement is proposed.     

Hybrid density functional theory for pi-stacking interactions: application to benzenes, pyridines, and DNA bases

The suitability of a hybrid density functional to qualitatively reproduce geometric and energetic details of parallel pi-stacked aromatic complexes is presented. The hybrid functional includes an ad hoc mixture of half the exact (HF) exchange with half of the uniform electron gas exchange, plus Lee, Yang, and Parr's expression for correlation energy. This functional, in combination with polarized, diffuse basis sets, gives a binding energy for the parallel-displaced benzene dimer in good agreement with the best available high-level calculations reported in the literature, and qualitatively reproduces the local MP2 potential energy surface of the parallel-displaced benzene dimer. This method was further critically compared to high-level calculations recently reported in the literature for a range of pi-stacked complexes, including monosubstituted benzene-benzene dimers, along with DNA and RNA bases, and generally agrees with MP2 and/or CCSD(T) results to within +/-2 kJ mol(-1). We also show that the resulting BH&H binding energy is closely related to the electron density in the intermolecular region. The net result is that the BH&H functional, presumably due to fortuitous cancellation of errors, provides a pragmatic, computationally efficient quantum mechanical tool for the study of large pi-stacked systems such as DNA.     

极化中子衍射及在电子自旋密度研究中的应用

极化中子衍射方法常用于研究含未配对电子化合物中电子自旋密度的分布．分子中电子自旋密度分布从一个独特的角度反映化合物的磁性质．本文介绍极化中子衍射方法的背景知识和基本原理．包括中子源、中子和X射线衍射、极化中子衍射,以及一些常用的实验数据处理方法．选用几个实例总结了用极化中子衍射方法得到的电子自旋密度分布在无机和有机化学中的应用．通过单分子磁体[Fe8O2（OH）12（tacn）6]^8＋和氰基桥联化合物K2[Mn（H2O）2]3[Mo（CN）7]2·6H2O,说明如何用该方法研究金属原子间的磁相互作用;并通过Ru（acac）3这个只含一个未配对电子的化合物来说明如何获得化合物中金属和配体上小的自旋密度;最后介绍了该方法在nitronylnitroxide自由基研究中的应用．     

A nonlocal correlation energy density functional from a Coulomb hole model

A nonlocal correlation energy density functional based on the approximation of a model Coulomb hole is presented. The functional is constructed to describe both the homogeneous electron gas and nonuniform systems. In the nonuniform case, the functional satisfies all uniform, as well as most nonuniform, coordinate-scaling constraints. The numerical results for the homogeneous electron gas and for atoms He through Ar compare favorably with those of other correlation functionals. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 603–616, 1997     

Electron density in metallic crystal as an extremal with moving boundaries

The reliability of a variational modeling of electron density in metallic crystal is investigated. The crystal is described within muffin-tin approximation referring to some from the ideas of the divide-and-conquer techniques. The calculations are performed with application of density functional and calculus of variation methods. The problem is formulated as finding a transversal with moving boundaries. Solution of the variational equation formulated for ρ indicates that a first derivative of the electron density must be zero on the border of the muffin tin. An illustrative example of lithium crystal is presented. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 543–549, 1997     

Regularized random-sampling high dimensional model representation (RS-HDMR)

High Dimensional Model Representation (HDMR) is under active development as a set of quantitative model assessment and analysis tools for capturing high-dimensional input–output system behavior. HDMR is based on a hierarchy of component functions of increasing dimensions. The Random-Sampling High Dimensional Model Representation (RS-HDMR) is a practical approach to HDMR utilizing random sampling of the input variables. To reduce the sampling effort, the RS-HDMR component functions are approximated in terms of a suitable set of basis functions, for instance, orthonormal polynomials. Oscillation of the outcome from the resultant orthonormal polynomial expansion can occur producing interpolation error, especially on the input domain boundary, when the sample size is not large. To reduce this error, a regularization method is introduced. After regularization, the resultant RS-HDMR component functions are smoother and have better prediction accuracy, especially for small sample sizes (e.g., often few hundred). The ignition time of a homogeneous H₂/air combustion system within the range of initial temperature, 1000 < T ₀ < 1500 K, pressure, 0.1 < P < 100 atm and equivalence ratio of H₂/O₂, 0.2 < R < 10 is used for testing the regularized RS-HDMR.      

Semilocalized approach to investigation of chemical reactivity

Application of the power series for the one‐electron density matrix 36 to the case of two interacting molecules is shown to yield a semilocalized approach to investigate chemical reactivity, which is characterized by the following distinctive features: (1) Electron density (ED) redistributions embracing orbitals of the reaction centers of both molecules and of their neighboring fragments are studied instead of the total intermolecular interaction energy; (2) the ED redistributions are expressed directly in the basis of fragmental orbitals (FOs) without passing to the basis of delocalized molecular orbitals (MOs) of initial molecules; (3) terms describing the ED redistributions due to an intermolecular contact arise as additive corrections to the purely monomolecular terms and thereby may be analyzed independently; (4) local ED redistributions only between orbitals of the reaction centers of both molecules are described by lower‐order terms of the power series, whereas those embracing both the reaction centers and their neighborhoods are represented by higher‐order terms. As opposed to the standard perturbative methods based on invoking the delocalized (canonical) MOs of isolated molecules, the results of the approach suggested are in‐line with the well‐known intuition‐based concepts of the classic chemistry concerning reactivity, namely, with the assumption about different roles of the reaction center and of its neighborhood in a chemical process, with the expectation about extinction of the indirect influence of a certain fragment (substituent) when its distance from the reaction center grows, etc. Such a parallelism yields quantum chemical analogs for the classic concepts and thereby gives an additional insight into their nature. The scope of validity of these concepts also is discussed. Applicability of the approach suggested to specific chemical problems is illustrated by a brief consideration of the S_N2 and Ad_E2 reactions. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 302–316, 2003     

Modeling three-dimensional network formation with an atomic lattice model: application to silicic acid polymerization

We present an atomic lattice model for studying the polymerization of silicic acid in sol-gel and related processes for synthesizing silica materials. Our model is based on Si and O atoms occupying the sites of a body-centered-cubic lattice, with all atoms arranged in SiO(4) tetrahedra. This is the simplest model that allows for variation in the Si-O-Si angle, which is largely responsible for the versatility in silica polymorphs. The model describes the assembly of polymerized silica structures starting from a solution of silicic acid in water at a given concentration and pH. This model can simulate related materials-chalcogenides and clays-by assigning energy penalties to particular ring geometries in the polymerized structures. The simplicity of this approach makes it possible to study the polymerization process to higher degrees of polymerization and larger system sizes than has been possible with previous atomistic models. We have performed Monte Carlo simulations of the model at two concentrations: a low density state similar to that used in the clear solution synthesis of silicalite-1, and a high density state relevant to experiments on silica gel synthesis. For the high concentration system where there are NMR data on the temporal evolution of the Q(n) distribution, we find that the model gives good agreement with the experimental data. The model captures the basic mechanism of silica polymerization and provides quantitative structural predictions on ring-size distributions in good agreement with x-ray and neutron diffraction data.     

Molecular-scale model for the mass density of electrolyte solutions bound by clay surfaces: application to bentonites

A model to simulate the density of solutions adsorbed onto clay mineral surfaces is proposed. In this model, the alteration of the ionic distribution caused by the electric field associated with the surface charge of clay platelets is accounted for using an electrical triple-layer model with an overlapping diffuse layer. The combined effects of ion hydration and the electric field on the structure of water are introduced through their influence on the partial molar volume of water. This model, applied to Na-montmorillonite, simulates the distribution of the interplatelet solution density as a function of the distance to the mineral surface. High densities in the direct vicinity of the surface and slightly lower density (a few percent) than the normal density in the diffuse layer are obtained. These results show good consistency with the available data on bentonite and with the densities that can be inferred from molecular dynamics simulations. This model shows that the interplatelet distance plays an important role in the distribution of the mass density of the solution in the pore space of clay rocks.     

Ratio control variate method for efficiently determining high-dimensional model representations

The High-Dimensional Model Representation (HDMR) technique is a family of approaches to efficiently interpolate high-dimensional functions. RS(Random Sampling)-HDMR is a practical form of HDMR based on randomly sampling the overall function, and utilizing orthonormal polynomial expansions to approximate the RS-HDMR component functions. The determination of the expansion coefficients for the component functions employs Monte Carlo integration, which controls the accuracy of the RS-HDMR interpolation. The control variate method is an established approach to improve the accuracy of Monte Carlo integration. However, this method is often not practical for an arbitrary function f(x) because there is no general way to find the analytical control variate function h(x), which needs to be very similar to f(x). In this article, we show that truncated RS-HDMR expansions can be used as h(x) for arbitrary f(x), and a more stable iterative ratio control variate method was developed for the determination of the expansion coefficients for the RS-HDMR component functions. As the asymptotic error (standard deviation) of the estimator given by the ratio control variate method is proportional to 1/N(sample size), it is more efficient than the direct Monte Carlo integration, whose error is proportional to 1/square root(N). In an illustration of a four-dimensional atmospheric model a few hundred random samples are sufficient to construct an RS-HDMR expansion by the ratio control variate method with an accuracy comparable to that obtained by direct Monte Carlo integration with thousands of samples.     

Coarse grained protein-lipid model with application to lipoprotein particles

A coarse-grained model for molecular dynamics simulations is extended from lipids to proteins. In the framework of such models pioneered by Klein, atoms are described group-wise by beads, with the interactions between beads governed by effective potentials. The extension developed here is based on a coarse-grained lipid model developed previously by Marrink et al., although future versions will reconcile the approach taken with the systematic approach of Klein and other authors. Each amino acid of the protein is represented by two coarse-grained beads, one for the backbone (identical for all residues) and one for the side-chain (which differs depending on the residue type). The coarse-graining reduces the system size about 10-fold and allows integration time steps of 25-50 fs. The model is applied to simulations of discoidal high-density lipoprotein particles involving water, lipids, and two primarily helical proteins. These particles are an ideal test system for the extension of coarse-grained models. Our model proved to be reliable in maintaining the shape of preassembled particles and in reproducing the overall structural features of high-density lipoproteins accurately. Microsecond simulations of lipoprotein assembly revealed the formation of a protein-lipid complex in which two proteins are attached to either side of a discoidal lipid bilayer.     

Pair density related to one‐electron information for the ground state of spin‐compensated two‐electron systems

The recent study by Joubert on effects of Coulomb repulsions in a many‐electron system has focused attention on an integral identity involving the pair density. This has motivated the derivation presented here of a vectorial differential form related to this integral result. Our differential identity is then illustrated explicitly by using (i) an exact ground‐state wave function for the so‐called Hookean atom having external potential energy (1/2)kr², with k = 1/4, and (ii) Moshinsky's model in which both the interparticle interaction and the external potential are of harmonic type. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

A note on atomic density

In atomic systems, electron density has a simple finite expansion in spherical harmonics times radial factors. The difficulties in the calculation of some radial factors are illustrated in the low‐lying states of the carbon atom. Single‐particle methods such as Hartree–Fock and approximate density functional theory cannot ensure the correct expansion of the density in spherical harmonics. Wave‐function methods are appropriate but, as some expansion terms are entirely due to correlation, these methods only will give correct results for high‐quality variational functions. Using full‐configuration integration (CI), all the terms predicted by the theory appear and are not negligible but the convergence of the term due to correlation toward its correct value is uncertain even for very large CI spaces. © 2012 Wiley Periodicals, Inc.     

The Physical Basis of the VSEPR Model

The VSEPR model is a consequence of the correlation of same-spin electrons resulting from the operation of the Pauli exclusion principle. Although the VSEPR rules can be interpreted in terms of an orbital model they do not provide the physical basis for the model.     

Novel properties from experimental charge densities: an application to the zwitterionic neurotransmitter taurine

The charge distribution of taurine (2-aminoethane-sulfonic acid) is revisited by using an orbital-based method that describes the density in a fixed molecular orbital basis with variable orbital occupation numbers. A new neutron data set is also employed to explore whether this improves the deconvolution of thermal motion and charge density. A range of molecular properties that are novel for experimentally determined charge densities are computed, including Weinhold population analysis, Mayer bond orders, and local kinetic energy densities, in addition to charge topological analysis and quantum theory of atoms-in-molecules (QTAIM) integrated properties. The ease with which a distributed multipole analysis can be performed on the fitted density matrix makes it straightforward to compute molecular moments, the lattice energy, and the electrostatic interaction energies of molecules removed from the crystal. Results are compared with high-level (QCISD) gas-phase calculations and band structure calculations employing density functional theory. Finally, the avenues available for extending the range of molecular properties that can be calculated from experimental charge densities still further using this approach are discussed.