COMPOSITION OPERATOR ON BERS-TYPE SPACES

Necessary and sufficient conditions are established for a composition operator C f = fo to be bounded or compact on the Bers-type space Ha and the little Bers-type space Ha The boundedness and compactness of the composition operator C on A() are characterized, which generalize the case of C on Ha.     

An algorithm to delineate and integrate topological basins in a three-dimensional quantum mechanical density function

The growing activity in the area of Quantum Chemical Topology warrants a new algorithm to delineate topological basins in 3D scalar fields other than the electron density. A method based on the "octal tree search algorithm" of computer graphics is proposed to reach this goal. We illustrate the algorithm on the L(r) function, which is the negative of the Laplacian of the electron density. Because of its complicated topology, even in a simple test molecule such as water, it benefits from the octal tree algorithm as a robust, compact, and general technique to find the boundaries of topological basins. For the first time, we are able to compute the population and volume of the core and valence (bonding and nonbonding, i.e., lone pair) basins given by L(r)'s topology.     

Incorporation of local structure into kriging models for the prediction of atomistic properties in the water decamer

Machine learning algorithms have been demonstrated to predict atomistic properties approaching the accuracy of quantum chemical calculations at significantly less computational cost. Difficulties arise, however, when attempting to apply these techniques to large systems, or systems possessing excessive conformational freedom. In this article, the machine learning method kriging is applied to predict both the intra‐atomic and interatomic energies, as well as the electrostatic multipole moments, of the atoms of a water molecule at the center of a 10 water molecule (decamer) cluster. Unlike previous work, where the properties of small water clusters were predicted using a molecular local frame, and where training set inputs (features) were based on atomic index, a variety of feature definitions and coordinate frames are considered here to increase prediction accuracy. It is shown that, for a water molecule at the center of a decamer, no single method of defining features or coordinate schemes is optimal for every property. However, explicitly accounting for the structure of the first solvation shell in the definition of the features of the kriging training set, and centring the coordinate frame on the atom‐of‐interest will, in general, return better predictions than models that apply the standard methods of feature definition, or a molecular coordinate frame. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Teleportation via decay

We present a rare example of a decay mechanism playing a constructive role in quantum information processing. We show how the state of an atom trapped in a cavity can be teleported to a second atom trapped in a distant cavity by the joint detection of photon leakage from the cavities. The scheme, which is probabilistic, requires only a single three level atom in a cavity. We also show how this scheme can be modified to a teleportation with insurance.     

A fast algorithm to compute atomic charges based on the topology of the electron density

This work proposes a novel algorithm to compute atomic charges as defined by the theory of “atoms in molecules” (AIM). Using the divergence theorem it is possible to express the 3D volume integral over an atomic basin purely in terms of 2D surface integrals. Hence, it can be proven that an atomic charge is equal to the flux of the electric field of the whole molecule through the atom's complete boundary. This boundary consists of the interatomic surfaces and the so-called outeratomic surface, which is the open side of the atom. When fine-tuned the algorithm can generate atomic charges in the order of minutes without introducing any approximations. Moreover, the problem of the geometrical cusp occurring in atomic basins and that of multiple intersections is also eliminated. The computational overhead of computing the electric field (which is analytical) is compensated by the gain in computing time by eliminating one dimension of quadrature. The proposed algorithm opens an avenue to invalidate the oft-quoted drawback that AIM charges are computationally expensive. We explain the details of the implementation in MORPHY01 and illustrate the novel algorithm with a few examples. Received: 1 June 2000 / Accepted: 4 October 2000 / Published online: 23 January 2001     

FT-IR study of the effect of zinc exposure on the biochemical contents of the muscle of Labeo rohita

Heavy metal pollution is a major environmental problem in the modern world due to increasing human activities. Zinc is an essential element involved in a wide variety of cellular processes. However, it becomes toxic when elevated concentrations are introduced into the environment. The goal of the present study is to investigate the effect of zinc exposure on the biochemical contents of the muscle tissues of freshwater species Labeo rohita using Fourier transform infrared (FT-IR) spectroscopy. Since the muscle constitutes the greatest mass of the fish that is consumed, the present study has paid particular attention to muscle component. The result reveals that the zinc exposure causes significant changes in the biochemical contents of the L. rohita muscle tissues. In addition, it causes an alteration in the protein secondary structures by decreasing the α-helix and increasing the β-sheet contents of muscle tissues. Further, it has been observed that the administration of chelating agent D-penicillamine improves the protein and lipid contents in the muscle tissues compared to zinc exposed tissues. This result shows that D-penicillamine is the effective chelator of zinc in reducing the body burden of L. rohita fingerlings.     

Simulation of liquid imidazole using a high-rank quantum topological electrostatic potential

Rigid body molecular dynamics simulations were carried out on pure liquid imidazole at four different temperatures and at 1 atm. Imidazole, which is important both in life science and materials science, is one of the simplest molecules to possess both a lone pair and a π system. These two features are known to benefit from multipolar electrostatics. Here the electrostatic interaction is governed by atomic multipole moments obtained from topologically partitioned ab initio electron densities. The non-electrostatic terms are modeled with Lennard-Jones parameters adjusted to fit the experimental liquid density. All σ values are incrementally increased by one single scaling factor. We report on how the presence of multipolar electrostatics influences the local structure, dynamics and thermodynamics of the liquid compared to electrostatics by atomic point charges. The point charge force field exaggerates the number of π-stacked dimers in the liquid, and underestimates the number of hydrogen-bonded dimers. The effect of the temperature on the local structure of liquid imidazole was analysed using radial and spatial distribution functions.     

The prediction of atomic kinetic energies from coordinates of surrounding atoms using kriging machine learning

A novel design of a next-generation force field considers not only the electronic inter-atomic energy but also intra-atomic energy. This strategy promises a faithful mapping between the force field and the quantum mechanics that underpins it. Quantum chemical topology provides an energy partitioning in which atoms have well-defined electronic kinetic energies, and we are interested in capturing how they respond to changes in the positions of surrounding atoms. A machine learning method called kriging successfully creates models from a training set of molecular configurations that can then be used to predict the atomic kinetic energies occurring in previously unseen molecular configurations. We present a proof-of-concept based on four molecules of increasing complexity (methanol, N-methylacetamide, glycine and triglycine). We test how well the atomic kinetic energies can be modelled with respect to training set size, molecule size and elemental composition. For all atoms tested, the mean atomic kinetic energy errors fall below 1.5 kJ mol^?1, and far below this in most cases. This represents errors all under 0.5 % and thus the kinetic energies are well modelled using the kriging method, even when using modest-to-small training set sizes.