Domain‐Averaged Exchange‐Correlation Energies as a Physical Underpinning for Chemical Graphs

A novel solution to the problem of assigning a molecular graph to a collection of nuclei (i.e. how to draw a molecular structure) is presented. Molecules are universally understood as a set of nuclei linked by bonds, but establishing which nuclei are bonded and which are not is still an empirical matter. Our approach borrows techniques from quantum chemical topology, which showed for the first time the construction of chemical graphs from wave functions, shifting the focus on energetics. This new focus resolves issues surrounding previous topological analyses, in which domain‐averaged exchange‐correlation energies (V_xc), quantities defined in real space between each possible atom pair, hold the key. Exponential decay of V_xc in non‐metallic systems as the intercenter distance increases guarantees a well‐defined hierarchy for all possible V_xc values in a molecule. Herein, we show that extracting the set of atom pairs that display the largest V_xc values in the hierarchy is equivalent to retrieving the molecular graph itself. Notably, domain‐averaged exchange‐correlation energies are transferable, and they can be used to calculate bond strengths. Fine‐grained details resulted to be related to simple stereoelectronic effects. These ideas are demonstrated in a set of simple pilot molecules.     

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     

The effect of titanium dioxide exposure on the thermal properties of Zebrafish (<Emphasis Type="Italic">Danio rerio</Emphasis>) bones

This article presents the changes in the thermal properties of the control and titanium dioxide (TiO₂), both nano and bulk exposed Zebrafish bones by using thermo analytical techniques. The result shows that the mass loss due to the thermal decomposition occurs in three distinct steps due to loss of water, organic and inorganic materials. The titanium dioxide exposed bones present a different thermal behaviour compared to the control bones. The residue masses are found to be increased due to titanium dioxide exposure. In particular, nano titanium dioxide exposure increases the residue mass level significantly (three fold) when compared to titanium dioxide bulk exposure. These thermal characteristics can be used as a qualitative method to check the metal oxide intoxication in biological samples.     

SOME POSTERIOR DISTRIBUTIONS FOR THE LAPLACE MEAN

Two posterior distributions for the mean of the Laplace distribution are obtained by deriving the distributions of the product XY and the ratio X/Y when X and Y are Student＇s t and Laplace random variables distributed independently of each other. Tabulations of the associated percentage points are given along with computer programs for generating them.     

Realistic sampling of amino acid geometries for a multipolar polarizable force field

The Quantum Chemical Topological Force Field (QCTFF) uses the machine learning method kriging to map atomic multipole moments to the coordinates of all atoms in the molecular system. It is important that kriging operates on relevant and realistic training sets of molecular geometries. Therefore, we sampled single amino acid geometries directly from protein crystal structures stored in the Protein Databank (PDB). This sampling enhances the conformational realism (in terms of dihedral angles) of the training geometries. However, these geometries can be fraught with inaccurate bond lengths and valence angles due to artefacts of the refinement process of the X‐ray diffraction patterns, combined with experimentally invisible hydrogen atoms. This is why we developed a hybrid PDB/nonstationary normal modes (NM) sampling approach called PDB/NM. This method is superior over standard NM sampling, which captures only geometries optimized from the stationary points of single amino acids in the gas phase. Indeed, PDB/NM combines the sampling of relevant dihedral angles with chemically correct local geometries. Geometries sampled using PDB/NM were used to build kriging models for alanine and lysine, and their prediction accuracy was compared to models built from geometries sampled from three other sampling approaches. Bond length variation, as opposed to variation in dihedral angles, puts pressure on prediction accuracy, potentially lowering it. Hence, the larger coverage of dihedral angles of the PDB/NM method does not deteriorate the predictive accuracy of kriging models, compared to the NM sampling around local energetic minima used so far in the development of QCTFF. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Prediction of conformationally dependent atomic multipole moments in carbohydrates

The conformational flexibility of carbohydrates is challenging within the field of computational chemistry. This flexibility causes the electron density to change, which leads to fluctuating atomic multipole moments. Quantum Chemical Topology (QCT) allows for the partitioning of an “atom in a molecule,” thus localizing electron density to finite atomic domains, which permits the unambiguous evaluation of atomic multipole moments. By selecting an ensemble of physically realistic conformers of a chemical system, one evaluates the various multipole moments at defined points in configuration space. The subsequent implementation of the machine learning method kriging delivers the evaluation of an analytical function, which smoothly interpolates between these points. This allows for the prediction of atomic multipole moments at new points in conformational space, not trained for but within prediction range. In this work, we demonstrate that the carbohydrates erythrose and threose are amenable to the above methodology. We investigate how kriging models respond when the training ensemble incorporating multiple energy minima and their environment in conformational space. Additionally, we evaluate the gains in predictive capacity of our models as the size of the training ensemble increases. We believe this approach to be entirely novel within the field of carbohydrates. For a modest training set size of 600, more than 90% of the external test configurations have an error in the total (predicted) electrostatic energy (relative to ab initio) of maximum 1 kJ mol^?1 for open chains and just over 90% an error of maximum 4 kJ mol^?1 for rings. © 2015 Wiley Periodicals, Inc.     

Flux line lattice symmetries in the borocarbide superconductor LuNi2B2C

We compare the results of small angle neutron scattering on the flux line lattice (FLL) obtained in the borocarbide superconductor LuNi₂B₂C with the applied field along the c- and a-axes. For H‖c the temperature dependence of the FLL structural phase transition from square to hexagonal symmetry was investigated. Above 10 K the transition onset field. H ₂(T), rises sharply, bending away from H _c2(T) in contradiction to theoretical predictions of the two merging. For H‖a a first order FLL reorientation transition is observed at H _tr=3–3.5 kOe. Below H _tr the FLL nearest neighbor direction is parallel to the b-axis, and above H _tr to the c-axis. This transition cannot be explained using nonlocal corrections to the London model.     

Multipolar electrostatics for proteins: Atom–atom electrostatic energies in crambin

Accurate electrostatics necessitates the use of multipole moments centered on nuclei or extra point charges centered away from the nuclei. Here, we follow the former alternative and investigate the convergence behavior of atom‐atom electrostatic interactions in the pilot protein crambin. Amino acids are cut out from a Protein Data Bank structure of crambin, as single amino acids, di, or tripeptides, and are then capped with a peptide bond at each side. The atoms in the amino acids are defined through Quantum Chemical Topology (QCT) as finite volume electron density fragments. Atom‐atom electrostatic energies are computed by means of a multipole expansion with regular spherical harmonics, up to a total interaction rank of L = ?_A+ ?_B + 1 = 10. The minimum internuclear distance in the convergent region of all the 15 possible types of atom‐atom interactions in crambin that were calculated based on single amino acids are close to the values calculated from di and tripeptides. Values obtained at B3LYP/aug‐cc‐pVTZ and MP2/aug‐cc‐pVTZ levels are only slightly larger than those calculated at HF/6‐31G(d,p) level. This convergence behavior is transferable to the well‐known amyloid beta polypeptide Aβ_1–42. Moreover, for a selected central atom, the influence of its neighbors on its multipole moments is investigated, and how far away this influence can be ignored is also determined. Finally, the convergence behavior of AMBER becomes closer to that of QCT with increasing internuclear distance. © 2013 Wiley Periodicals, Inc.