Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. II. The two-shell nonzero shift ACCs and U(2n) generator MEs

This is the second in a series of articles whose ultimate goal is the evaluation of the matrix elements (MEs) of the U(2n) generators in a multishell spin-orbit basis. This extends the existing unitary group approach to spin-dependent configuration interaction (CI) and many-body perturbation theory calculations on molecules to systems where there is a natural partitioning of the electronic orbital space. As a necessary preliminary to obtaining the U(2n) generator MEs in a multishell spin-orbit basis, we must obtain a complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The zero-shift coefficients were obtained in the first article of the series. in this article, we evaluate the nonzero shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. We then demonstrate that the one-shell versions of these coefficients may be obtained by taking the Gelfand-Tsetlin limit of the two-shell formulas. These coefficients,together with the zero-shift types, then enable us to write down formulas for the U(2n) generator matrix elements in a two-shell spin-orbit basis. Ultimately, the results of the series may be used to determine the many-electron density matrices for a partitioned system. (C) 1998 John Wiley & Sons, Inc.

Computational chemistry on Fujitsu vector-parallel processors: Development and performance of applications software

In this and a preceding paper, we provide an introduction to the Fujitsu VPP range of vector-parallel supercomputers and to some of the computational chemistry software available for the VPP. Here, we consider the implementation and performance of seven popular chemistry application packages. The codes discussed range from classical molecular dynamics to semiempirical and ab initio quantum chemistry. All have evolved from sequential codes, and have typically been parallelised using a replicated data approach. As such they are well suited to the large-memory/fast-processor architecture of the VPP. For one code, CASTEP, a distributed-memory data-driven parallelisation scheme is presented. (C) 2000 Published by Elsevier Science B.V. All rights reserved.

Photodissociation of benzene under collision-free conditions: An ab initio/Rice-Ramsperger-Kassel-Marcus study

The ab initio/Rice-Ramsperger-Kassel-Marcus (RRKM) approach has been applied to investigate the photodissociation mechanism of benzene at various wavelengths upon absorption of one or two UV photons followed by internal conversion into the ground electronic state. Reaction pathways leading to various decomposition products have been mapped out at the G2M level and then the RRKM and microcanonical variational transition state theories have been applied to compute rate constants for individual reaction steps. Relative product yields (branching ratios) for C6H5+H, C6H4+H-2, C4H4+C2H2, C4H2+C2H4, C3H3+C3H3, C5H3+CH3, and C4H3+C2H3 have been calculated subsequently using both numerical integration of kinetic master equations and the steady-state approach. The results show that upon absorption of a 248 nm photon dissociation is too slow to be observable in molecular beam experiments. In photodissociation at 193 nm, the dominant dissociation channel is H atom elimination (99.6%) and the minor reaction channel is H-2 elimination, with the branching ratio of only 0.4%. The calculated lifetime of benzene at 193 nm is about 11 mus, in excellent agreement with the experimental value of 10 mus. At 157 nm, the H loss remains the dominant channel but its branching ratio decreases to 97.5%, while that for H-2 elimination increases to 2.1%. The other channels leading to C3H3+C3H3, C5H3+CH3, C4H4+C2H2, and C4H3+C2H3 play insignificant role but might be observed. For photodissociation upon absorption of two UV photons occurring through the neutral hot benzene mechanism excluding dissociative ionization, we predict that the C6H5+H channel should be less dominant, while the contribution of C6H4+H-2 and the C3H3+C3H3, CH3+C5H3, and C4H3+C2H3 radical channels should significantly increase. (C) 2004 American Institute of Physics.

Structure optimization combining soft-core interaction functions, the diffusion equation method, and molecular dynamics

Smoothing the potential energy surface for structure optimization is a general and commonly applied strategy. We propose a combination of soft-core potential energy functions and a variation of the diffusion equation method to smooth potential energy surfaces, which is applicable to complex systems such as protein structures; The performance of the method was demonstrated by comparison with simulated annealing using the refinement of the undecapeptide Cyclosporin A as a test case. Simulations were repeated many times using different initial conditions and structures since the methods are heuristic and results are only meaningful in a statistical sense.

Asymmetric MRI magnet design using a hybrid numerical method

This paper describes a hybrid numerical method for the design of asymmetric magnetic resonance imaging magnet systems. The problem is formulated as a field synthesis and the desired current density on the surface of a cylinder is first calculated by solving a Fredholm equation of the first kind. Nonlinear optimization methods are then invoked to fit practical magnet coils to the desired current density. The field calculations are performed using a semi-analytical method. A new type of asymmetric magnet is proposed in this work. The asymmetric MRI magnet allows the diameter spherical imaging volume to be positioned close to one end of the magnet. The main advantages of making the magnet asymmetric include the potential to reduce the perception of claustrophobia for the patient, better access to the patient by attending physicians, and the potential for reduced peripheral nerve stimulation due to the gradient coil configuration. The results highlight that the method can be used to obtain an asymmetric MRI magnet structure and a very homogeneous magnetic field over the central imaging volume in clinical systems of approximately 1.2 m in length. Unshielded designs are the focus of this work. This method is flexible and may be applied to magnets of other geometries. (C) 1999 Academic Press.

A two-dimensional analytical solution of groundwater responses to tidal loading in an estuary and ocean

Previous studies on tidal dynamics of coastal aquifers have focussed on the inland propagation of oceanic tides in the cross-shore direction, a configuration that is essentially one-dimensional. Aquifers at natural coasts can also be influenced by tidal waves in nearby estuaries, resulting in a more complex behaviour of head fluctuations in the aquifers. We present an analytical solution to the two-dimensional depth-averaged groundwater flow equation for a semi-infinite aquifer subject to oscillating head conditions at the boundaries. The solution describes the tidal dynamics of a coastal aquifer that is adjacent to a cross-shore estuary. Both the effects of oceanic and estuarine tides on the aquifer are included in the solution. The analytical prediction of the head fluctuations is verified by comparison with numerical solutions computed using a standard finite-difference method. An essential feature of the present analytical solution is the interaction between the cross- and along-shore tidal waves in the aquifer area near the estuary's entry. As the distance from the estuary or coastline increases, the wave interaction is weakened and the aquifer response is reduced, respectively, to the one-dimensional solution for oceanic tides or the solution of Sun (Sun H. A two-dimensional analytical solution of groundwater response to tidal loading in an estuary, Water Resour Res 1997;33:1429-35) for two-dimensional non-interacting tidal waves. (C) 2000 Elsevier Science Ltd. All rights reserved.

Finite element modeling of fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins

In order to use the finite element method for solving fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins effectively and efficiently, we have presented, in this paper, the new concept and numerical algorithms to deal with the fundamental issues associated with the fluid-rock interaction problems. These fundamental issues are often overlooked by some purely numerical modelers. (1) Since the fluid-rock interaction problem involves heterogeneous chemical reactions between reactive aqueous chemical species in the pore-fluid and solid minerals in the rock masses, it is necessary to develop the new concept of the generalized concentration of a solid mineral, so that two types of reactive mass transport equations, namely, the conventional mass transport equation for the aqueous chemical species in the pore-fluid and the degenerated mass transport equation for the solid minerals in the rock mass, can be solved simultaneously in computation. (2) Since the reaction area between the pore-fluid and mineral surfaces is basically a function of the generalized concentration of the solid mineral, there is a definite need to appropriately consider the dependence of the dissolution rate of a dissolving mineral on its generalized concentration in the numerical analysis. (3) Considering the direct consequence of the porosity evolution with time in the transient analysis of fluid-rock interaction problems; we have proposed the term splitting algorithm and the concept of the equivalent source/sink terms in mass transport equations so that the problem of variable mesh Peclet number and Courant number has been successfully converted into the problem of constant mesh Peclet and Courant numbers. The numerical results from an application example have demonstrated the usefulness of the proposed concepts and the robustness of the proposed numerical algorithms in dealing with fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins. (C) 2001 Elsevier Science B.V. All rights reserved.

Expression, purification, crystallization, and NMR studies of the helicase interaction domain of Escherichia coli DnaG primase

in Escherichia coli, the DnaG primase is the RNA polymerase that synthesizes RNA primers at replication forks. It is composed of three domains, a small N-terminal zinc-binding domain, a larger central domain responsible for RNA synthesis, and a C-terminal domain comprising residues 434-581 [DnaG(434-581)] that interact with the hexameric DnaB helicase. Presumably because of this interaction, it had not been possible previously to express the C-terminal domain in a stably transformed E coli strain. This problem was overcome by expression of DnaG(434-581) under control of tandem bacteriophage gimel-promoters, and the protein was purified in yields of 4-6 mg/L of culture and studied by NMR. A TOCSY spectrum of a 2 mM solution of the protein at pH 7.0, indicated that its structured core comprises residues 444-579. This was consistent with sequence conservation among most-closely related primases. Linewidths in a NOESY spectrum of a 0.5 mM sample in 10 mM phosphate, pH 6.05, 0.1 M NaCl, recorded at 36 degreesC, indicated the protein to be monomeric. Crystals of selenomethionine-substituted DnaG(434-581) obtained by the hanging-drop vapor-diffusion method were body-centered tetragonal, space group I4(1)22, with unit cell parameters a = b 142.2 Angstrom, c = 192.1 Angstrom, and diffracted beyond 2.7 Angstrom resolution with synchrotron radiation. (C) 2003 Elsevier Inc. All rights reserved.

A new integrable model of strongly correlated electrons with Hubbard-like interaction

A new completely integrable model of strongly correlated electrons is proposed which describes two competitive interactions: one is the correlated one-particle hopping, the other is the Hubbard-like interaction. The integrability follows from the fact that the Hamiltonian is derivable from a one-parameter family of commuting transfer matrices. The Bethe ansatz equations are derived by algebraic Bethe ansatz method.

Control of chaotic instabilities in a spinning spacecraft with dissipation using Lyapunov's method

Control of chaotic instability in a simplified model of a spinning spacecraft with dissipation is achieved using an algorithm derived using Lyapunov's second method. The control method is implemented on a realistic spacecraft parameter configuration which has been found to exhibit chaotic instability for a range of forcing amplitudes and frequencies when a sinusoidally varying torque is applied to the spacecraft. Such a torque, may arise in practice from an unbalanced rotor or from vibrations in appendages. Numerical simulations are performed and the results are studied by means of time history, phase space, Poincare map, Lyapunov characteristic exponents and bifurcation diagrams. (C) 2002 Elsevier Science Ltd. All rights reserved.

Recombinant expression of Munc18c in a baculovirus system and interaction with syntaxin4

Two protein families that are critical for vesicle transport are the Syntaxin and Munc18/Sec1. families of proteins. These two molecules form a high affinity complex and play an essential role in vesicle docking and fusion. Munc18c was expressed as an N-terminally His-tagged fusion protein from recombinant baculovirus in Sf9 insect cells. His-tagged Munc18c was purified to homogeneity using both cobalt-chelating affinity chromatography and gel filtration chromatography. With this simple two-step protocol, 3.5 mg of purified Munc18c was obtained from a 1 L culture. Further, the N-terminal His-tag could be removed by thrombin cleavage while the tagged protein was bound to metal affinity resin. Recombinant Munc18c produced in this way is functional, in that it forms a stable complex with the SNARE interacting partner, syntaxin4. Thus we have developed a method for producing and purifying large amounts of functional Munc18c-both tagged and detagged-from a baculovirus expression system. We have also developed a method to purify the Munc18c:syntaxin4 complex. These methods will be employed for future functional and structural studies. Crown copyright (C) 2003 Published by Elsevier Inc. All rights reserved.

Comparative study of Li, Na, and K adsorptions on graphite by using ab initio method

A comprehensive study has been conducted to compare the adsorptions of alkali metals (including Li, Na, and K) on the basal plane of graphite by using molecular orbital theory calculations. All three metal atoms prefer to be adsorbed on the middle hollow site above a hexagonal aromatic ring. A novel phenomenon was observed, that is, Na, instead of Li or K, is the weakest among the three types of metal atoms in adsorption. The reason is that the SOMO (single occupied molecular orbital) of the Na atom is exactly at the middle point between the HOMO and the LUMO of the graphite layer in energy level. As a result, the SOMO of Na cannot form a stable interaction with either the HOMO or the LUMO of the graphite. On the other hand, the SOMO of Li and K can form a relatively stable interaction with either the HOMO or the LUMO of graphite. Why Li has a relatively stronger adsorption than K on graphite has also been interpreted on the basis of their molecular-orbital energy levels.

GCMC-surface area of carbonaceous materials with N-2 and Ar adsorption as an alternative to the classical BET method

In this paper we apply a new method for the determination of surface area of carbonaceous materials, using the local surface excess isotherms obtained from the Grand Canonical Monte Carlo simulation and a concept of area distribution in terms of energy well-depth of solid–fluid interaction. The range of this well-depth considered in our GCMC simulation is from 10 to 100 K, which is wide enough to cover all carbon surfaces that we dealt with (for comparison, the well-depth for perfect graphite surface is about 58 K). Having the set of local surface excess isotherms and the differential area distribution, the overall adsorption isotherm can be obtained in an integral form. Thus, given the experimental data of nitrogen or argon adsorption on a carbon material, the differential area distribution can be obtained from the inversion process, using the regularization method. The total surface area is then obtained as the area of this distribution. We test this approach with a number of data in the literature, and compare our GCMC-surface area with that obtained from the classical BET method. In general, we find that the difference between these two surface areas is about 10%, indicating the need to reliably determine the surface area with a very consistent method. We, therefore, suggest the approach of this paper as an alternative to the BET method because of the long-recognized unrealistic assumptions used in the BET theory. Beside the surface area obtained by this method, it also provides information about the differential area distribution versus the well-depth. This information could be used as a microscopic finger-print of the carbon surface. It is expected that samples prepared from different precursors and different activation conditions will have distinct finger-prints. We illustrate this with Cabot BP120, 280 and 460 samples, and the differential area distributions obtained from the adsorption of argon at 77 K and nitrogen also at 77 K have exactly the same patterns, suggesting the characteristics of this carbon.

Is the method of signal analysis and test selection important for measuring standing balance in subjects with persistent whiplash?

Dizziness and or unsteadiness, associated with episodes of loss of balance, are frequent complaints in those suffering from persistent problems following a whiplash injury. Research has been inconclusive with respect to possible aetiology, discriminative tests and analyses used. The aim of this pilot research was to identify the test conditions and the most appropriate method for the analysis of sway that may differentiate subjects with persistent whiplash associated disorders (WAD) from healthy controls. The six conditions of the Clinical Test for Sensory Interaction in Balance was performed in both comfortable and tandem stance in 20 subjects with persistent WAD compared to 20 control subjects. The analyses were carried out using a traditional method of measurement, total sway distance, to results obtained from the use of wavelet analysis. Subjects with WAD were significantly less able to complete the tandem stance tests on a firm surface than controls. In comfortable stance, using wavelet analysis, significant differences between subjects with WAD and the control group were evident in total energy of the trace for all test conditions apart from eyes open on the firm surface. In contrast, the results of the analysis using total sway distance revealed no significant differences between groups across all six conditions. Wavelet analysis may be more appropriate for detecting disturbances in balance in whiplash subjects because the technique allows separation of the noise from the underlying systematic effect of sway. These findings will be used to direct future studies on the aeitiology of balance disturbances in WAD. (c) 2004 Elsevier B.V. All rights reserved.