Parallel algorithm for large scale electronic structure calculations

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Hardware and software aspects of parallel computing

Part 1 (Chapters 2,3 and 4) is concerned with the development of hardware for multiprocessor systems. Some of the concepts used in digital hardware design are introduced in Chapter 2. These include the fundamentals of digital electronics such as logic gates and flip-flops as well as the more complicated topics of rom and programmable logic. It is often desirable to change the network topology of a multiprocessor machine to suit a particular application. The third chapter describes a circuit switching scheme that allows the user to alter the network topology prior to computation. To achieve this, crossbar switches are connected to the nodes, and the host processor (a PC) programs the crossbar switches to make the desired connections between the nodes. The hardware and software required for this system is described in detail. Whilst this design allows the topology of a multiprocessor system to be altered prior to computation, the topology is still fixed during program run-time. Chapter 4 presents a system that allows the topology to be altered during run-time. The nodes send connection requests to a control processor which programs a crossbar switch connected to the nodes. This system allows every node in a parallel computer to communicate directly with every other node. The hardware interface between the nodes and the control processor is discussed in detail, and the software on the control processor is also described. Part 2 (Chapters 5 and 6) of this thesis is concerned with the parallelisation of a large molecular mechanics program. Chapter 5 describes the fundamentals of molecular mechanics such as the steric energy equation and its components, force field parameterisation and energy minimisation. The implementation of a novel programming (COMFORT) and hardware (the BB08) environment into a parallel molecular mechanics (MM) program is presented in Chapter 6. The structure of the sequential version of the MM program is detailed, before discussing the implementation of the parallel version using COMFORT and the BB08

Mass-resolved resonant two-photon ionisation spectroscopy of jet-cooled Cu2 and Ag2

Clusters of the transition metals were generated by laser vaporisation of a sample of the metal into the throat of a pulsed supersonic expansion. This allowed clusters with internal temperatures as low as 5 K to be routinely prepared. Mass-selective detection was accomplished by multi-photon ionisation of the clusters within the ion source of a time - of - flight mass spectrometer. Use of a tunable laser to carry out electronic excitation, prior to ionisation, allowed mass - resolved resonant two - photon ionisation spectra of the clusters to be recorded.Real time control of the experiment and automated data logging was achieved using software developed to run on an IBM PC - AT microcomputer. This allowed multiple ion signals to be recorded simultaneously whilst carrying out R2PI or time-resolved studies on the metal cluster species in the beam.Resonant two - photon ionisation spectroscopic studies were carried out on the ( 0 - 0 ) and ( 1 - 0 ) bands of the J X system of Cu9 and the A X system of Ag->. The 0.04 cm-1 bandwidth of the tunable dye laser used allowed rotationally resolved spectra to be recorded. The spectra recorded for these systems showed them both to be AA = 0 ( or AS2 = 0 ) transitions.The J state of CU2 was assigned to the 1 Zj state derived from the “P + atomic limit at Dg(X) + 45821 cm-1. Rotational analysis of the spectra yieldedl | lthe following constants for the Cu2 isotopomer: Bg = 0.1166(1) cm , ae = 0.0021(1) cm-1. This gave Rg = 2.138(1) A for the J state, shorter than the ground state bond length. Accordingly the transition was assigned to 3ditg -*•4piru, to give the above assignment.The rotational constants obtained, for the *®7Ag-, isotopomer, from analysisI _ | *of the spectra of the A X system of Ag-, were: Bg = 0.0447(3) cm , ae= 0.0004(2) cm'*, and Bq = 0.0490(18) cm"1. These gave bond lengths of Rg = 2.649(9) A and Rq = 2.530(46) A. The observed Ail = 0 transition agreed with the previous assignment of the A state as 0* arising from the 5sag -+ 5sau promotion

Homology Modelling of the b Fraction of Factor B

The b domain of factor B (Bb) is found to be moderately homologous to the mammalian serine proteases. Sequence homology analysis showed that out of all the known serine protease structures, Bb was most homologous to bovine trypsin. Sequence alignment between Bb and bovine trypsin gave a sequence identity of the two sequences of between 17 - 21%. This meant that protein model building of Bb from a known serine protease structure, in this case bovine trypsin, could be attempted. The structure of bovine trypsin was taken from the Brookhaven Database. All the molecular modelling was carried out with the software package "COMMET" that was developed in our laboratory. In the first instance all of the substitutions necessary to computationally mutate the bovine trypsin structure into the Bb structure were carried out. Substitutions were carried out first as they are the least disruptive of the three modelling techniques used in homology modelling. Substitution only alters the side chain atoms of the residue that is being modified. No alterations to the backbone atoms are necessary at this stage. The software keeps the new side chain position as close to the original as possible. Where this is not feasible the side chain conformation is determined by a conformational search of the side chain's conformation space. The deletions from bovine trypsin were all small and accomplished by simple removal of the appropriate residues followed by energy minimisation to reposition and rejoin the main chain. Small insertions up to three residues long were built using the "insert" routine. After inserting a residue its side chain's torsion angles were defined by a conformational search. To ease steric strain at the site of small deletions and insertion a segment five residues either side of the insertion or deletion was run through the energy minimiser. There are a total of eight insertions of three residues in length or longer: Gin 30: 3 residues in length Ser 186: 3 residues in length Gly 129: 7 residues in length His 231: 8 residues in length Glu 101: 9 residues in length Leu 143: 9 residues in length Arg 170: 13 residues in length The conformation of these large insertions was calculated using a sophisticated conformational space sampling procedure which runs on a large parallel computer. The loop conformation generator searches through all of the conformational space and uses filters to eliminate unfavourable conformations. After all the modifications were carried out the entire protein was run through the energy minimiser. First polar hydrogens, then all hydrogens, and finally the water molecules from the bovine trypsin crystal structure were added to the model. Energy minimisation continued until the first derivatives from the Newton-Ralphson algorithm had become negligibly small

Towards Solving the Dopamine G Protein Coupled Receptor Modelling Problem

The overall aim of this work has been to furnish a model of the dopamine (DA) receptor D2. There are currently two sub-groups within the DA family of G protein coupled receptors (GPCRs): D1 sub-group (includes D1 and D5) and the D2 sub-group (includes D2, D3 and D4). Organon (UK) Ltd. supplied a disk containing the PDB atomic co-ordinates of the integral membrane protein bacteriorhodopsin (bRh; Henderson et al., 1975 and 1990) to use as a template to model D2 - the aim being to generate a model of D2 by simply mutating the side-residues of bRh. The assumption being that bRh had homology with members of the supergene class of GPCRs. However, using the GCG Wisconsin GAP algorithm (Devereux et al., 1984) no significant homology was detected between the primary structures of any member of the DA family of GPCRs and bRh. However, given the original brief to carry out homology modelling using bRh as a template (see appendix 1) I felt obliged to carry out further alignments using a shuffling technique and a standard statistical test to check for significant structural homology. The results clearly showed that there is no significant structural homology, on the basis of sequence similarity, between bRh and any member of the DA family of GPCRs. Indeed, the statistical analysis clearly demonstrated that while there is significant structural homology between every catecholamine binding GPCR, there is no structural homology what so ever between any catecholamine binding GPCR and bRh. Hydropathy analysis is frequently used to identify the location of putative transmembrane segments. However, is difficult to predict the end positions of each ptms. To this end a novel alignment algorithm (DH Scan) was coded to exploit transparallel supercomputer technology to provide a basis for identifying likely helix end points and to pinpoint areas of local homology between GPCRs. DH Scan clearly demonstrated characteristic transmembrane homology between different subtype DA GPCRs. Two further homology algorithms were coded (IH Scan and RH Scan) which provided evidence of internal homology. In particular IH Scan independently revealed a repeat region in the 3rd intracellular loop (iIII) of D4 and RH Scan revealed palindromic like short stretches of amino acids which were found to be particularly well represented in predicted ?-helices in each DA receptor subtype. In addition, the profile network prediction algorithm (PHD; Rost et al., 1994) predicted a short alpha-helix at greater than 80% probablility at each end of the third intracellular loop and between the carboxy terminal end of transmembrane VII and a conserved Cys residue in the forth intracellular loop. Fourier analysis of catecholamine binding GPCR primary structures in the form of a multiple-sequence file suggested that the consensus view that only those residues facing the protein interior are conserved is not entirely correct. In particular, transmembrane helices II and III do not exhibit residue conservancy characteristic of an amphipathic helix. It is proposed that these two helices undergo a form of helix interface shear to assist agonist binding to a Asp residue on helix II. This data in combination with information from a number of papers concerning helix shear interface mechanism and molecular dynamic studies of proline containing ?-helices suggested a physically plausible binding mechanism for agonists. While it was evident that homology modelling could not be scientifically justified, the combinatorial approach to protein modelling might be successfully applied to the transmembrane region of the D2 receptor. The probable arrangement of helices in the transmembrane region of GPCRs (Baldwin, 1993) which was based on a careful analysis of a low resolution projection map of rhodopsin (Gebhard et ah, 1993) was used as a guide to model the transmembrane region of D2. The backbone torsion angles of a helix with a middle Pro residue (Sankararamakrishnan et al., 1991) was used to model transmembrane helix V. Dopamine was successfully docked to the putative binding pocket of D2. Using this model as a template, models of D3 and D4 were produced. A separate model of Di was then produced and this in turn was used as a template to model D5

Molecular Mechanics Force Field Optimisation Using Parallel Computers

Ever since the discovery that the bond lengths and angles between the same atomic types vary little between different molecules chemists have been using models of molecules to aid them in their research. This technique is known as molecular modelling and is now usually performed with the aid of computers. One of the main areas of interest in molecular modelling is that of molecular mechanics calculations. Molecular mechanics (MM) is the use of empirical equations and their associated parameter to determine the energy of any particular molecular conformation and the use of that energy in helping to predict such things as the minimum energy conformation. The equations and the parameters are together described as the MM force field. One drawback of molecular mechanics is that in certain situations where its application would be useful there is an absence of reliable parameters so giving rise to the situation where calculations are often performed using 'guesstimates' for parameter values. To improve this situation an investigation into the possible forms of a general purpose compact force field was undertaken. There exist several force fields that reduce the number of parameters required by simplification of the situations where a parameter may be applied, for example a torsional barrier would be defined in terms of the central two atom types only rather than the more rigorous case where the atom types of all four atoms in the torsion angle would be used to decide which parameter is to be used. Some work had also already been done on reducing the number of parameters by calculating some by using other empirical formulae, an example of this being the calculation of bond stretch constants from their associated bond length parameters. These equations usually require some optimisable 'constants' but, in general, the technique resulted in an overall reduction in the number of parameters that are required to be optimised. What is not obvious is which of these methods are best at reducing the number of parameters without having an excessive effect on the accuracy of the results produced by the final force field. For each of these published force fields it is possible to adapt an energy minimisation program to calculate the minimum energy structures of known molecules and then compare the calculated results with experimental data. This will give us an overview of the accuracy for that force field but will not show which of the methods used within that force field have been the most effective. As MM is an empirical approach there are force fields which have basically the same form but have different parameters and it is usually unwise to interchange the parameters between them without reoptimising the whole force field. At the start of the project the methods used to optimise force fields were slow and the production of even an optimised force field for alkanes could take many years even after the form of the equations had been decided. It was obvious that using normal methods of optimisation it would take far too long to implement a system to vary the methods of parameter reduction and then reoptimise the force field in each case to see its effects. To overcome this problem it was decided to produce the required force fields by computer optimisation. This was made possible in mainly by the recently available parallel computing power of the Inmos transputer chip. The method chosen the controlling computer program to alter the parameters and so could be left for long periods to produce an optimised force field in a fraction of the time that would previously have been required. The first studies were done on small sets of alkene data as initially the processing power was limited. These initial studies culminated in investigations using a set of 50 alkene structures. These showed that a highly reduced force field is a viable option for alkenes, however alkenes are not very representative of all the atom types that will be needed so it was decided to introduce some more atom types before deciding on the final form of the force field. To this end a set of 109 structures was constructed which contained the following atom types: H, Csp2, Csp3, Osp2, Cl, Br and F. After considering the results of optimisations with this set of structures the form of a highly reduced parameter force field was decided upon. This force field was used in a limited study using a set of 243 structures with 25 different atom types. The following table summarises the results of this optimisation. Conformer refers to energy difference measures between conformers, 'Average Diff' is the average difference between the experimental value and that predicted by the force field and 'Average Error' is the average experimental error for that property type. Although not totally conclusive this study indicated that a highly reduced force field would be a valuable addition to the range of force fields available to the molecular modeller, as while being not as accurate a fuller force field it would have the significant advantage of covering, with reasonable accuracy, those situations that are not parameterised in the more specific force fields

Methods for the atomistic simulation of ultrasmall semiconductor devices

As the feature sizes in VLSI technology shrink to less than 100 nm the effects due to the quantisation of electronic charge begin to emerge. There are a small number of carriers and impurities and the statistical variation in their number have significant effects on the threshold characteristics of the devices that hamper their large scale integration into future ULSI.The complex potential landscape arising from the Coulomb force, with its sharp localised peaks and troughs, faces problems due to band limiting in meshes and places heavy burdens on the integration techniques. A computationally efficient solution to the problem of band-limiting is presented and is shown to provide an accurate description of the electrostatics. This work also introduces a highly efficient and numerically stable multigrid solver, for Poisson's equation, that can cope with the complex potential distributions on large meshes.The study of ionised impurity scattering is used to validate these molecular dynamics simulations. Results have shown that the Brownian method - despite precluding the use of adaptive integration schemes - gives a good approximation to the standard results and has the advantage of smoothing away errors that can build up during the integration of motion and drives the system towards thermal equilibrium.The greatest hurdle to be cleared before these three-dimensional simulations can be practicable is the sheer computational effort that is required. The implementation of the problem on parallel architectures has been explored and discussed.The methods developed in this work are demonstrated through the simulation of an 80 nm dual-gate MESFET. The results were verified by comparing them with those from a commercial drift-diffusion simulator.The threshold behaviour of devices has been investigated through the study of the formation of conduction channels in blocks. The percolation threshold gives the point when conductive paths form across the gate barrier. The results from the FET simulation were found to be in agreement with the earlier studies on the blocks

Molecular Mechanics Force Field Optimisation Using Parallel Computers

Ever since the discovery that the bond lengths and angles between the same atomic types vary little between different molecules chemists have been using models of molecules to aid them in their research. This technique is known as molecular modelling and is now usually performed with the aid of computers. One of the main areas of interest in molecular modelling is that of molecular mechanics calculations. Molecular mechanics (MM) is the use of empirical equations and their associated parameter to determine the energy of any particular molecular conformation and the use of that energy in helping to predict such things as the minimum energy conformation. The equations and the parameters are together described as the MM force field. One drawback of molecular mechanics is that in certain situations where its application would be useful there is an absence of reliable parameters so giving rise to the situation where calculations are often performed using 'guesstimates' for parameter values. To improve this situation an investigation into the possible forms of a general purpose compact force field was undertaken. There exist several force fields that reduce the number of parameters required by simplification of the situations where a parameter may be applied, for example a torsional barrier would be defined in terms of the central two atom types only rather than the more rigorous case where the atom types of all four atoms in the torsion angle would be used to decide which parameter is to be used. Some work had also already been done on reducing the number of parameters by calculating some by using other empirical formulae, an example of this being the calculation of bond stretch constants from their associated bond length parameters. These equations usually require some optimisable 'constants' but, in general, the technique resulted in an overall reduction in the number of parameters that are required to be optimised. What is not obvious is which of these methods are best at reducing the number of parameters without having an excessive effect on the accuracy of the results produced by the final force field. For each of these published force fields it is possible to adapt an energy minimisation program to calculate the minimum energy structures of known molecules and then compare the calculated results with experimental data. This will give us an overview of the accuracy for that force field but will not show which of the methods used within that force field have been the most effective. As MM is an empirical approach there are force fields which have basically the same form but have different parameters and it is usually unwise to interchange the parameters between them without reoptimising the whole force field. At the start of the project the methods used to optimise force fields were slow and the production of even an optimised force field for alkanes could take many years even after the form of the equations had been decided. It was obvious that using normal methods of optimisation it would take far too long to implement a system to vary the methods of parameter reduction and then reoptimise the force field in each case to see its effects. To overcome this problem it was decided to produce the required force fields by computer optimisation. This was made possible in mainly by the recently available parallel computing power of the Inmos transputer chip. The method chosen the controlling computer program to alter the parameters and so could be left for long periods to produce an optimised force field in a fraction of the time that would previously have been required. The first studies were done on small sets of alkene data as initially the processing power was limited. These initial studies culminated in investigations using a set of 50 alkene structures. These showed that a highly reduced force field is a viable option for alkenes, however alkenes are not very representative of all the atom types that will be needed so it was decided to introduce some more atom types before deciding on the final form of the force field. To this end a set of 109 structures was constructed which contained the following atom types: H, Csp2, Csp3, Osp2, Cl, Br and F. After considering the results of optimisations with this set of structures the form of a highly reduced parameter force field was decided upon. This force field was used in a limited study using a set of 243 structures with 25 different atom types. The following table summarises the results of this optimisation. Conformer refers to energy difference measures between conformers, 'Average Diff' is the average difference between the experimental value and that predicted by the force field and 'Average Error' is the average experimental error for that property type. Although not totally conclusive this study indicated that a highly reduced force field would be a valuable addition to the range of force fields available to the molecular modeller, as while being not as accurate a fuller force field it would have the significant advantage of covering, with reasonable accuracy, those situations that are not parameterised in the more specific force fields