A geometric approach to direct minimization

The approach presented, geometric direct minimization (GDM), is derived from purely geometrical arguments, and is designed to minimize a function of a set of orthonormal orbitals. The optimization steps consist of sequential unitary transformations of the orbitals, and convergence is accelerated using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) approach in the iterative subspace, together with a diagonal approximation to the Hessian for the remaining degrees of freedom. The approach is tested by implementing the solution of the self-consistent field (SCF) equations and comparing results with the standard direct inversion in the iterative subspace (DIIS) method. It is found that GDM is very robust and converges in every system studied, including several cases in which DIIS fails to find a solution. For main group compounds, GDM convergence is nearly as rapid as DIIS, whereas for transition metal-containing systems we find that GDM is significantly slower than DIIS. A hybrid procedure where DIIS is used for the first several iterations and GDM is used thereafter is found to provide a robust solution for transition metal-containing systems.     

RING-OPENING PHOTOREACTIONS OF CYTOSINE AND 5-METHYLCYTOSINE WITH ALIPHATIC ALCOHOLS

Abstract Several reports in the late 1950s and early 1960s indicated that ultraviolet irradiation of dilute solutions of cytosine or 5-methylcytosine in aliphatic alcohols, such as methanol or ethanol, leads to reaction mixtures containing products with an absorption maximum around 300 nm. The present work reports the isolation and characterization of the products responsible for this absorption in the photochemical reactions of cytosine and 5-methylcytosine with methanol, ethanol and 2-propanol at concentrations in the neighborhood of 200 μM. Under these conditions the reactions have been shown, in each nucleobase/alcohol system, to give almost exclusively a single type of primary photopro-duct; each product shows an absorption maximum in the region of 300 nm. Structural analysis showed the products to be alcohol adducts with an ester linkage at C2 of the ring-opened base and an enamine structure at C6. For example, in the case of the reaction of cytosine with methanol, the product is N-carbomethoxy-3-aminoacrylamidine (IIIa). The occurrence of this type of photoreaction suggests a mode by which alcoholic functional groups on amino acid side chains could contribute to photoinduced DNA-protein cross-linking.     

On the Null-field Equations for Water-wave Scattering Problems

Consider a rigid body which is partially immersed in the freesurface of deep water, the body is fixed and a given time-harmonicwave is incident upon it. The corresponding linear boundary-valueproblem is solved using the null-field method and two systemsof null-field equations are obtained; each system is alwaysuniquely solvable—irregular frequencies do not occur.These results can be proved in two or three dimensions, forwater of infinite or finite depth, and for any incident wave.Next, it is assumed that the water is deep and that the incidentwave is a regular surface wave. With these assumptions, onesystem of null-field equations takes on a very simple form.This system is solved using the "method of projection" (Gregory& Gladwell, 1982), leading to a sequence of computable approximationsto the solution of the null-field equations; this sequence isguaranteed to converge. It seems worthwhile to establish thislast result, because (at present) there is a notable absenceof such convergence proofs in the general theory of the null-fieldmethod. As an example of this approach, the two-dimensionalproblem of the interaction between a regular surface wave anda fixed, half-immersed, elliptic cylinder is solved.     

PRODUCTS AND RELATIVE REACTION RATES OF THE OXIDATION OF TOCOPHEROLS WITH SINGLET MOLECULAR OXYGEN

Abstract— The relative reactivity of singlet molecular oxygen, 0₂(¹Δ_g), α-,β-,Γ-and δ with -tocopherol (vitamin E) was investigated using microwave discharge generation as a uniquely clean source of singlet oxygen and using a hydrocarbon solvent to approximate the membrane environment. The relative efficiencies of the tocopherols for O₂(¹Δg) were found to decrease in the order: D-α-tocopherol > D-β-tocopheroI > D–Γ-tocopherol > D-δ-tocopherol. The reaction products in all cases were found to be mixtures of quinone and quinone epoxides apparently resulting from decomposition of the primary product, the hydroperoxydienone.     

Brownian dynamics simulation of gelation in soft sphere systems with irreversible bond formation

Brownian dynamics simulation is used to study the structure and small-deformation shear rheology of three-dimensional particle gels formed from a model of soft spherical particles incorporating a combination of flexible, irreversible bond formation and non-bonded interparticle interactions. An essential feature of the model is the restriction of angular reorganization of cross-linked aggregates during and after gelation. Numerical data relating to the fractal structure and porosity of the gels are compared with those from some related particle gel simulation models in two and three dimensions. Stress relaxation and frequency dependent rheological properties are determined as a function of the strength and nature of the interparticle interactions, and the results are discussed in relation to structural properties. A linear relationship is demonstrated between the high-frequency modulus and the number of bonds in the gel network.     

The structure of 12C

The nucleus ¹²C has a rather significant role in modern nuclear physics, but whose influence can be traced to the work of Hoyle in the 1950s, when it was concluded that there should be a state close to 7.68 MeV responsible for the synthesis of carbon in stellar nucleosynthesis. Although a state at 7.65 MeV was subsequently discovered, its properties have remained something of a mystery until rather recently. This paper explores our current understanding of the structure of ¹²C, in particular the nature of the Hoyle state.     

Tunnelling splittings in the high resolution microwave and UV spectra of the benzonitrile—water complex: modelling the internal motion in its S0 and S1 states

Refined values of the barriers to internal motion in the 1:1 complex between benzonitrile and water in the gas phase have been determined from analyses of its fully resolved microwave and ultraviolet spectra. Both spectra exhibit tunnelling splittings associated with this motion. Modelling this behaviour using a semi-rigid Hamiltonian for an internal rotation of water around its C ₂ axis yields values of V ₂ = 440 ± 30 cm^?1 and 450 ± 30 cm^?1 in the ground and excited electronic states, respectively. These relatively high barriers are a consequence of two hydrogen bonds between the interacting species.     

VIBRATIONAL MODES OF TRUMPET BELLS

We report on an investigation of the normal modes of vibration of the bells of several modern trumpets. We describe the results of experiments using electronic speckle-pattern interferometry to visualize the modal structure and we show that the mode frequencies follow a generalized version of Chladni's law.     

Molecular orbital study of polarity and hydrogen bonding effects on the g and hyperfine tensors of site directed NO spin labelled bacteriorhodopsin

Semiempirical molecular orbital methods (PM3, INDO, ZINDO/S) have been used to calculate the effects of local electric fields and of hydrogen bonding on the g and hyperfine tensors of a nitroxide spin label model system. The results yield a linear correlation between the two principal tensor components g _xx and A ^N _zz at label sites of varying polarity. Hydrogen bonding with a single water molecule produces a constant shift of Δg _xx ? ?4 × 10^?4. These theoretical results are used to interpret recent high field (3.4 T, 95 GHz) electron paramagnetic resonance investigations on site-directed spin labelled bacteriorhodopsin. This protein reveals a close correlation between proticity and polarity at the various label sites. The slope of the g _xx versus A ^N _zz dependence is affected strongly by polarity induced structural strains of the spin label.     

The computation of Karplus equation coefficients and their components using self-consistent field and second-order polarization propagator methods

The Karplus equation has been investigated by ab initio computation of the spin-spin coupling constants for a series of rotated ethane geometries. The couplings have been calculated at the self-consistent field (SCF) level as well as using the second-order polarization propagator approximation (SOPPA) and the second-order polarization propagator approximation with coupled cluster singles and doubles amplitudes (SOPPA(CCSD)) and have been compared with results of previous calculations. The four principal components of the coupling constants rather than just the Fermi-contact have been calculated, and the common supposition that the Fermi-contact term is totally dominant has been confirmed. The derivatives of the orbital paramagnetic and orbital diamagnetic terms are significant but opposite in sign for the case of this rotation in ethane. It is found that the coefficients in the Karplus equation are largely overestimated at the SCF level, whereas the SOPPA(CCSD) results are in good agreement with coefficients derived from experimental coupling constant data or the results of multi-configurational self-consistent field (MCSCF) calculations. It is further observed that extending the Fourier series in the Karplus equation to include cos(3θ) and cos(4θ) terms neither significantly improves the quality of the fit nor significantly changes the values of the other coefficients. In order to simulate the Abraham and Pachler equation, calculations varying the nuclear charge on hydrogen have been performed. These will allow an abstract but flexible prediction of the effect of electronegative substituents.