Barry T. Pickup

A fast method of molecular shape comparison: A simple application of a Gaussian description of molecular shape

A Gaussian description of molecular shape is used to compare the shapes of two molecules by analytically optimizing their volume intersection. The method is applied to predict the relative orientation of ligand series binding to the proteins, thrombin, HIV protease, and thermolysin. The method is also used to quantify the degree of chirality of asymmetric molecules and to investigate the chirality of biphenyl and the amino acids. The shape comparison method uses the newly described shape multipoles that can also be used to describe the inherent shape of molecules. Some results of calculated shape quadrupoles are given for the ligands used in this work.

Quantum theory of molecular electronic structure

With the increasing availability of powerful computers, attempts to calculate the electronic structure and properties of molecules by the direct ab initio solution of a many-body Schrodinger equation have received a great stimulus. The authors review the mainstream developments in quantum chemistry and give a straightforward account of some of the many-body techniques borrowed, with appropriate modifications, from other areas of physics-field theory, nuclear theory and solid-state theory. After a historical introduction, the traditional approach based on the self-consistent field and the method of configuration interaction is developed in detail. This is followed by the introduction of the cluster expansion, various types of correlated electron-pair theory, and diagrammatic perturbation methods. Finally, propagator and Green function techniques are reviewed, not only as a means of calculating transition energies but also as an alternative approach to the determination of the electronic ground state.

A smooth permittivity function for Poisson–Boltzmann solvation methods

This work introduces a continuous smooth permittivity function into Poisson–Boltzmann techniques for continuum approaches to modeling the solvation of small molecules and proteins. The permittivity function is derived using a Gaussian method to describe volume exclusion. The new method allows a rigorous determination of solvent forces within a grid‐based technology. The generality of approach is demonstrated by considering a range of applications for small molecules and macromolecules. We also present a very complete statistical analysis of grid errors, and show that the accuracy of our Gaussian‐based method is improved over standard techniques. The method has been implemented in a new code called ZAP, which is freely available to academic institutions. 1

A new twist to molecular chirality: intrinsic chirality indices

We propose an intrinsic molecular chirality tensor based only on nuclear positions. The chirality tensor gives rise to two universal chirality indices, the first giving information about absolute chirality, and the second about the anisotropy chirality, i.e., the degree of chirality in different spatial directions. The formalism is derived using simple models obtained from the theory of optical activity. The indices are calculated analytically for a right angled tetrahedron, and numerically for a small selection of molecules.

The determination of individual rates from magnetization-transfer measurements

The rate equations for magnetization transfer between many sites have been solved for the general problem of one or many sites being perturbed by a selective pulse or pre-irradiation with a low power continuous wave frequency. Individual rate constants and relaxation times are derived, but no allowance is made for nuclear Overhauser effects. The analysis is applied to magnetization-transfer measurements made on the four-site 13C NMR problem, Cr(η6-C8H8(CO)3.

Plane wave and orthogonalized plane wave many-body Green's function calculations of photoionization intensities

General equations for the calculation of correlated single-channel photoionization cross-sections of randomly oriented molecules are presented. These equations, employing a plane wave orthogonalized to all (occupied and virtual) bound molecular orbitals as a wavefunction for the photoelectron, are derived in a many-body Greens function framework. Several decoupling approximations for the expansion of the one-particle propagator are then used to compute angle-averaged photoionization cross-sections for a Mg Kα photon source and for a representative set of molecules: CH4, H2O, C2H2, N2, and CO. Both orthogonality corrections to the continuum orbital and many-body corrections in the description of the ionization process are shown to be important for accurate simulations of soft X-ray ionization spectra.

The Gaussian Generalized Born model: application to small molecules

This work presents a Generalized Born model for the computation of the electrostatic component of solvation energies which is based on volume integration. An analytic masking function is introduced to remove Coulombic singularities. This approach leads to analytic formulae for the computation of Born radii, which are differentiable to arbitrary order, and computationally straightforward to implement.

Conduction in graphenes

It is shown that, within the tight-binding approximation, Fermi-level ballistic conduction for a perimeter-connected graphene fragment follows a simple selection rule: the zero eigenvalues of the molecular graph and of its subgraph minus both contact vertices must be equal in number, as must those of the two subgraphs with single contact vertices deleted. In chemical terms, the new rule therefore involves counting nonbonding orbitals of four molecules. The rule is initially derived within the source and sink potential scattering framework, but has equivalent forms that unify the molecular-orbital and valence-bond approaches to conduction. It is shown that the new selection rule can be cast in terms of Kekule counts, bond orders, and frontier-orbital coefficients. In particular, for a Kekulean graphene, conduction pathways are shown to be ranked in efficiency by a (nonmonotonic) function of Pauling bond order between the contact vertices. Frontier-orbital analysis of conduction approximates this function. For a monoradical graphene, the analogous function is shown to depend on Pauling spin densities at contact vertices.

A selection rule for molecular conduction

Conditions for transmission of a pi-conjugated molecular conductor are derived within the source and sink potential approach in terms of numbers of nonbonding levels of four graphs: The molecular graph G and the three vertex-deleted subgraphs obtained by removing one or both contact vertices. For all bipartite and most nonbipartite G, counting nonbonding levels gives a simple necessary and sufficient condition for conduction at the Fermi level. The exceptional case is where G is nonbipartite and all four graphs have the same number of nonbonding levels; then, an auxiliary requirement involving tail coefficients of the four characteristic polynomials must also be checked.

Fragment analysis of single-molecule conduction

In the tight-binding source and sink potential model of transmission in single-molecule pi-conjugated conductors, vanishing of the opacity polynomial defines a necessary condition for zero conductance at a given energy. Theorems are given for calculating opacity polynomials of composite devices in terms of opacity and characteristic polynomials of the subunits. These relations rationalize the positions and shapes of zeros in transmission curves for devices consisting of molecules with side chains or of units assembled in series and take an especially simple form for polymeric molecules with identical repeat units.