Biomedical subjects

Nathaniel O J Malcolm

Publications and source records attributed to Nathaniel O J Malcolm.

3 recordsLinked to original sources

PubMed2003

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.

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PubMed2003

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.

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PubMed2003

The full topology of the Laplacian of the electron density: scrutinising a physical basis for the VSEPR model.

Within the framework of quantum chemical topology (QCT) the function L(r), which equals the negative of the Laplacian of the electron density, has been proposed before as a physical basis for the valence shell electron pair repulsion (VSEPR) model. The availability of a new algorithm to integrate property densities over the basins of L(r) enabled a re-evaluation of this physical basis. We optimised a set of nine molecules at B3LYP/6-311+G(2d,p) level and partitioned the corresponding L(r) function for each molecule into basins. For the first time we visualise these basins in L(r), by directly showing their boundaries. We identify the basins in L(r) with the domains of the VSEPR model. Observations drawn from the populations and volumes of L-basins are contrasted with the three subsidiary VSEPR postulates. We find unexpectedly small populations, nearer to one than to two, for non-hydrogen cores and bonding domains, and populations much larger than two for non-bonding domains. We conclude that non-bonding or lone pairs have larger domains than bonding pairs in the same valence shell, in accordance with VSEPR. We also confirm that double and triple bond domains are larger than single-bond domains. However we cannot substantiate the effect of the electronegativity of central atom or ligand on the volume of bonding domains. In summary, the full topology of L(r) supports two out of three subsidiary VSEPR postulates.

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