Riccati-based preconditioner for computing invariant subspaces of large matrices

Summary. This paper introduces and analyzes the convergence properties of a method that computes an approximation to the invariant subspace associated with a group of eigenvalues of a large not necessarily diagonalizable matrix. The method belongs to the family of projection type methods. At each step, it refines the approximate invariant subspace using a linearized Riccati's equation which turns out to be the block analogue of the correction used in the Jacobi-Davidson method. The analysis conducted in this paper shows that the method converges at a rate quasi-quadratic provided that the approximate invariant subspace is close to the exact one. The implementation of the method based on multigrid techniques is also discussed and numerical experiments are reported. Received June 15, 2000 / Revised version received January 22, 2001 / Published online October 17, 2001     

Excess partial molar enthalpies,entropies, Gibbs energies,and volumes in aqueous dimethylsulfoxide

The excess partial molar enthalpies, the vapor pressures, and the densities of dimethylsulfoxide (DMSO)–H₂O mixtures were measured and the excess partial molar Gibbs energies and the partial molar volumes were calculated for DMSO and for H₂O. The values of the excess partial molar Gibbs energies for both DMSO and H₂O are negative over the entire composition range. The results for the water-rich region indicated that the presence of DMSO enhances the hydrogen bond network of H₂O. Unlike monohydric alcohols, however, the solute-solute interaction is repulsive in terms of the Gibbs energy. This was a result of the fact that the repulsion among solutes in terms of enthalpy surpassed the attraction in terms of entropy. The data in the DMSO-rich region suggest that DMSO molecules form clusters which protect H₂O molecules from exposure to the nonpolar alkyl groups of DMSO.     

Determination of the solubility of vinyl stearate in water by a monolayer technique

Summary The surface activity of vinyl stearate has provided a method for determining its solubility in water to be 0,7±0,2×10^–6 mole/litre. The methods described above could be used to determine the solubility in water of any sparingly soluble surface active compound, such as stearic acid or cetyl alcohol, which formed a stable monolayer at theA/W interface. Method A could be used for compounds with a solubility as low as 10^–5 mole/litre where as for Method B solubilities as low as 10^–7 mole/litre could be measured.     

Systematic control of photochemistry: the dynamics of photoisomerization of a model cyanine dye

On-the-fly CASSCF nonadiabatic dynamics have been used to model the trans-cis isomerization of a model cyanine dye. Our results show that the photochemical generation of the trans versus cis product is dynamically controlled by the presence of an extended cis-trans conical intersection seam that persists along all torsional angles. This in turn suggests that the photochemistry could be completely controlled by controlling the distribution of momentum components in a wave packet excited by laser photolysis in a coherent control experiment.     

Regulation of SV40-induced cell division and tumor antigen by dibutyryl adenosine 3'-5'-monophosphate.

Simian virus 40 (SV40) induces cell division in microcultures of sparsely plated nongrowing mouse BALB/3T3 cells during acute infection at moderate multiplicities of infection (MOI = 10-100). The infected cells are killed when a MOI of 1,000 is used. SV40 tumor (T) antigen is synthesized in the infected cells, but viral DNA, virion antigen, and progeny virions are not synthesized (abortive infection). The addition of exogenous dibutyryl adenosine 3'-5'-monophosphate (dbcAMP) at the time of infection stimulates the SV40-induced cell division at all MOI and inhibits SV40-induced cell death at high MOI. The percentage of T antigen-positive cells, as monitored by immunofluorescence, is also increased by the addition of dbcAMP at the time of infection. This regulation of SV40-induced cell division and T antigen formation by exogenous dbcAMP occurs within the first 6 hr after infection at 37 degrees C and is dependent upon both the MOI and the concentration of added dbcAMP. The addition of dbcAMP to productively infected TC7 monkey cells has litte effect on the SV40-induced cell death or T antigen formation.     

A multi-residue cation-exchange clean up procedure for basic drugs in produce of animal origin

There is considerable interest in maximising the amount of information obtained from animal product analyses, when screening for the presence of veterinary drug residues. One of the barriers to effective multi-residue analysis to date has been a lack of effective clean up procedures to isolate a wide range of residues from the potential interferents, which may be present in both simple and complex (including processed) foods. A cation-exchange clean up has, therefore, been developed for use with acetonitrile extracts of foods, when analysing for several basic drug groups (sulfonamides, benzimidazoles, levamisole, nitroimidazoles, tranquillisers and fluroquinolones). The clean up procedure has also been shown to be effective using a modified extraction solvent for malachite green and leucomalachite green in fish.Several of the key parameters that influence analyte recovery have been investigated and in an optimised procedure, tissue/biofluid samples containing sulfonamides, benzimidazoles, levamisole, nitroimidazoles, tranquillisers and fluoroquinolones are first extracted with acetonitrile. The extract is then dried with sodium sulfate and acidified with glacial acetic acid before loading onto a Bond Elut, strong cation-exchange (SCX) solid phase extraction (SPE) cartridge. Extracts from fish containing malachite green and leucomalachite green can be cleaned up using the same SCX SPE procedure following extraction with citrate buffer/acetonitrile. Typical recoveries of drugs from low level fortified tissues using the optimised procedure lie in the range 53-104% with the exception of carazolol from pig kidney (31%), malachite green from trout (42-51%) and ciprofloxacin from chicken muscle (44%) and from egg (21%).     

A simple approach for improving the hybrid MMVB force field: application to the photoisomerization of s-cis butadiene

MMVB is a QM/MM hybrid method, consisting of a molecular mechanics force field coupled to a valence bond Heisenberg Hamiltonian parametrized from ab initio CASSCF calculations on several prototype molecules. The Heisenberg Hamiltonian matrix elements Q(ij) and K(ij), whose expressions are partitioned here into a primary contribution and second-order correction terms, are calculated analytically in MMVB. When the original MMVB force field fails to produce potential energy surfaces accurate enough for dynamics calculations, we show that significant improvements can be made by refitting the second-order correction terms for the particular molecule(s) being studied. This "local" reparametrization is based on values of K(ij) extracted (using effective Hamiltonian techniques) from CASSCF calculations on the same molecule(s). The method is demonstrated for the photoisomerization of s-cis butadiene, and we explain how the correction terms that enabled a successful MMVB dynamics study [Garavelli, M.; Bernardi, F.; Olivucci, M.; Bearpark, M. J.; Klein, S.; Robb, M. A. J Phys Chem A 2001, 105, 11496] were refitted.     

Vertical proton affinities of CH2O and CH2OH+ in their ground singlet,excited triplet and ionized doublet states

Vertical proton affinities were calculated with closed and open shell direct SCF-MO methods for the ground, excited triplet and ionized doublet states of CH₂O and CH₂OH⁺.The computed gas phase basicity of CH₂O follows the order: CH₂O(¹ A ₁) > CH₂O*(³ A ₁ or ³ A ₂) > CH₂O⁺(² B ₂ or ² B ₁).     

The computation of the representation matrices of the generators of the unitary group

A method is presented for the efficient computation of the representation matrices of the unitary group, U(n) in the Gelfand—Tsetlin basis (corresponding to the usual spin-symmetry adapted basis for an N electron CI). The present scheme is conceptually and computationally attractive in that it is formulated directly in terms of Weyl tableaux and also that it permits simultaneous basis vector generation and matrix element evaluation. In addition the basis vectors are ordered so that subsequent restriction to the three dimensional rotation group is facilitated. An illustrative example is also presented.Taken in part from a thesis submitted to the University of London in partial fulfilment of the requirements for the degree of PhD.