Matrix element factorization in the unitary group approach for configuration interaction calculations

Techniques of diagrammatic spin algebra are employed to derive segment factorization formulas for spin-adapted matrix elements of one- and two-electron excitation operators. The spin-adapted basis is formed by the Yamanouchi–;Kotani geneological coupling method, and therefore constitutes an irreducible basis of the unitary group U(N), as prescribed by Gel'fand and Tsetlin. Several features distinguish this paper from similar work that has recently been published. First, intermediate steps in the derivation of each segment factor are fully documented. Comprehensive tables list the spin diagrams and phases that contribute to the possible segment factors. Second, a special effort has been made to distinguish between those parts of a segment factor that can be ascribed to a spin diagram and those parts which arise from the orbitals. The results of this paper should thus be useful for those who wish to extend diagrammatic spin algebra to evaluation of matrix elements for states built from nonorthogonal orbitals. Third, a novel graphical method has been introduced to keep track of phase changes that are induced by line up permutations of creation and annihilation operators. This technique may be useful for extension of our analysis to higher excitations. The necessary concepts of second quantization and diagrammatic spin algebra are developed in situ, so the present derivation should be accessible to those who have little prior knowledge of such methods.     

Design and synthesis of aromatic inhibitors of anthranilate synthase

Aromatic analogues of chorismate were synthesised as potential inhibitors of anthranilate synthase. Molecular modelling using GOLD2.1 showed that these analogues docked into the active site of Serratia marcescens anthranilate synthase in the same conformation as chorismate. Most compounds were found to be micromolar inhibitors of S. marcescens anthranilate synthase. The most potent analogue, 3-(1-carboxy-ethoxy)-4-hydroxybenzoate (K(I) 3 microM), included a lactyl ether side chain. This appears to be a good replacement for the enol-pyruvyl side chain of chorismate.     

A genetic algorithm for the automated generation of molecules within constraints

Summary A genetic algorithm has been designed which generates molecular structures within constraints. The constraints may be any useful function, for example an enzyme active site, a pharmacophore or molecular properties from pattern recognition or rule-induction analyses. The starting point may be random or may utilise known molecules. These are modified to grow into families of structures which, using the evolutionary operators of selection, crossover and mutation evolve to better fit the constraints. The basis of the algorithm is described together with some applications in lead generation, 3D database construction and drug design. Genetic algorithms of this type may have wider applications in chemistry, for example in the design and optimisation of new polymers, materials (e.g. superconducting materials) or synthetic enzymes.     

The water rise in front of a model planing hull

It is known that the water “splashes-up” or rises above the undisturbed surface immediately in front of a planing surface. This rise is greatest in front of a flat planing plate and a number of attempts have been made to reduce the experimental measurements of this phenomenon to some kind of order. Since it was first independently proposed by both Schnitzer and Smiley in 1952, all attempts to correlate the flat plate splash-up have started with the assumption that splash is only a function of the immersed length of the plate and is independent of trim angle at least below about 20°. In part, this was because the three early studies which compared this hypothesis with experimental data omitted those portions of the data which did not support the hypothesis. The present paper concludes that this forty year old hypothesis is fallacious and that the water rise in front of any prismatic planing surface is best approximated by $$\frac{d}{{\sqrt {bl} }} = k\sin ^2 {\mathbf{\tau }}$$ whered is the vertical water rise at the water/keel intersection;b is the beam;l is the submerged length of the keel;τ is the trim angle;k: is a constant determined from experiment, approximated by,k = 2e ^?2.5β , whereβ is the deadrise angle in radians. It might be thought that this is a slight contribution, of little practical import, but for one thing. Starting in the 1950's most towing tank experimenters in the United States abandoned the difficult measurement of model draft and obtained only the “actually wetted length” from underwater photographs. But theoretical planing force calculations require a knowledge of the relationship between a hull and the undisturbed water plane. Thus if modern experimental data is to be compared with theory, it is necessary to estimate what the undefined splash-up or water rise was during each experiment, in order to estimate the model's true position in space. The paper concludes by criticizing the format of some modern reports of experiments with model planing hulls and suggests that, in addition to the usual graphical presentations, measured data should always be reported numerically. Also, that when relevant data is omitted from a plot, the facts of such omission should be clearly stated.