An improved algorithm to locate critical points in a 3D scalar field as implemented in the program MORPHY

A new algorithm for location of the critical points in general scalar fields is described. The new method has been developed as part of an on-going process to exploit the topologic analysis of general 3D scalar fields. Part of this process involves the use of topologic information to seed the critical point search algorithm. The continuing move away from topologic studies of just the electron density requires more general algorithms and the ability to easily "plug in" new functions, for example, the Laplacian of the electron density ( triangle down (2)rho), the Electron Localisation Function (ELF), the Localised Orbital Locator (LOL), the Lennard-Jones function (LJF), as well as any new functions that may be proposed in the future. Another important aspect of the current algorithm is the retention of all possible intermediate information, for example, the paths describing the connectivity of critical points, as well as an ability to restart searches, something that becomes increasingly important when analysing larger systems. This new algorithm represents a core part of a new local version of the MORPHY code. We distinguish nine universal types of gradient paths.     

Theoretical Definition of a Functional Group and the Molecular Orbital Paradigm

It is the purpose of this review to demonstrate that the empirical classification of the observations of chemistry in terms of the properties assigned to functional groups is a consequence of and is predicted by physics. This is accomplished by showing that the atoms and functional groups of chemistry can be identified with bounded space-filling objects whose properties are defined by quantum mechanics. The quantum mechanical definition of a group is combined with a new pictorial representation of its form to obtain a unified picture which should make it eminently recognizable to chemists. This picture, when combined with the demonstrated ability of these groups to recover the measured properties of atoms in molecules, is offered as one which meets the expectations a chemist associates with the concept of a functional group. The manner in which this physical definition of a group differs fundamentally from models of functional groups based upon molecular orbital theory is discussed.     

Spectral and scattering theory for a Schrödinger operator with a class of momentum-dependent long-range potentials

Let be the selfadjoint operator for the static electromagnetic field where W _j for 0, 1, 2, ..., n is a sum of (i) a short-range potential and (ii) a smooth long-range potential decreasing at as |x|^- with in (0, 1]. Then for >1/2, asymptotic completeness holds for the scattering system (H, H ₀).     

Thermodynamic and kinetic effects of Lewis acid complexation on a Schiff base present in two tautomeric forms

The effect of complexation with Lewis acids on the tautomeric equilibrium of a derivative of pyridoxal has been explored using density functional theory. Three complexation sites (pyridine nitrogen, aromatic ring, and carbonyl group) have been considered. The tautomeric equilibrium can be modulated with the formation of complexes at the different sites. The changes observed in the geometric, energetic and electronic properties of the tautomers and transition states have been analyzed. Relationships have been found between those parameters, including a relationship between energetic and geometric parameters in agreement with the Hammond postulate. Copyright © 2010 John Wiley & Sons, Ltd.     

Raman spectroscopic investigation on the microenvironment of the liver tissues of Zebrafish (Danio rerio) due to titanium dioxide exposure

Nano titanium dioxide (nTiO₂), generally considered to be toxicologically inert, is manufactured in large quantities and extensively applied in consumer products. The small size and large surface area endow them with an active group or intrinsic toxicity. Advances in instrumentation are making Raman spectroscopy the tool of choice for an increasing number of (bio) chemical applications. One of the great advantages of this technique is its ability to provide information on the concentration, structure and interaction of biochemical molecules in their microenvironments within intact cells and tissues, non-destructively. Zebrafish (Danio rerio), one of the most important vertebrate model organisms used in developmental biology, are increasingly used in biomedical research, particularly as a model of human disease. In the present work, an attempt is made to study the effect of titanium dioxide, both nano and bulk, on the microenvironment of the liver tissues of Zebrafish using FT-Raman spectroscopy. The results of the present study suggest that TiO₂ exposure demonstrate a marked influence on the microenvironments of the liver tissues of Zebrafish. A shift to a higher wavenumber and an increase in the intensity of the band at ∼1087 cm⁻¹ in the TiO₂ exposed tissues suggest that some of the conformational changes resulting from the alkali recovery process takes place due to TiO₂ exposure. The decreased intensity ratio (I₃₂₂₀/I₃₄₀₀) observed in the titanium-exposed tissues suggests a decreased water domain size, which could be interpreted in terms of weaker hydrogen-bonded molecular species of water in the TiO₂ exposed tissues. The observed shift of COO⁻ bands to higher frequencies shows the disruption of salt bridges as a result of a change in the oppositely charged partners and due to the enhanced random coil conformation. The variation in the intensity ratio of the tyrosyl doublet (I₈₅₈/I₈₂₅) indicates variation in the hydrogen bonding of the phenolic hydroxyl group due to TiO₂ exposure. The results further suggest that the microenvironments are greatly altered due to titanium nano exposure when compared to titanium bulk. In conclusion, the results indicate that FT-Raman spectroscopy might be a useful tool for rapid assessment of nano particle biological interactions.     

pKa prediction from an ab initio bond length: part 3--benzoic acids and anilines

The prediction of pK(a) from a single ab initio bond length has been extended to provide equations for benzoic acids and anilines. The HF/6-31G(d) level of theory is used for all geometry optimisations. Similarly to phenols (Part 2 of this series of publications), the meta-/para-substituted benzoic acids can be predicted from a single model constructed from one bond length. This model had an impressive RMSEP of 0.13 pK(a) units. The prediction of ortho-substituted benzoic acids required the identification of high-correlation subsets, where the compounds in the same subset have at least one of the same (e.g. halogens, hydroxy) ortho substituent. Two pK(a) equations are provided for o-halogen benzoic acids and o-hydroxybenzoic acids, where the RMSEP values are 0.19 and 0.15 pK(a) units, respectively. Interestingly, the bond length that provided the best model differed between these two high-correlation subsets. This demonstrates the importance of investigating the most predictive bond length, which is not necessarily the bond involving the acid hydrogen. Three high-correlation subsets were identified for the ortho-substituted anilines. These were o-halogen, o-nitro and o-alkyl-substituted aniline high-correlation subsets, where the RMSEP ranged from 0.23 to 0.44 pK(a) units. The RMSEP for the meta-/para-substituted aniline model was 0.54 pK(a) units. This value exceeded our threshold of 0.50 pK(a) units and was higher than both the m-/p-benzoic acids in this work and the m-/p-phenols (RMSEP = 0.43) of Part 2. Constructing two separate models for the meta- and para- substituted anilines, where RMSEP values of 0.63 and 0.33 pK(a) units were obtained respectively, revealed it was the meta-substituted anilines that caused the large RMSEP value. For unknown reasons the RMSEP value increased with the addition of a further twenty meta-substituted anilines to this model. The C-N bond always produced the best correlations with pK(a) for all the high-correlation subsets. A higher level of theory and an ammonia probe improved the statistics only marginally for the hydroxybenzoic acid high-correlation subsets.     

Some relations between additive functions,II

Aequationes mathematicae -