Boundary conditions in quantum field theories

Several interesting and important quantum field theories must contain the coupling constant in the boundary conditions. The theories considered include quantum electrodynamics of spin-1/2 fermions and gauge field theories.     

The cyclodimerisation of 3-methyl-2-butenenitrile

3-Methyl-2-butenenitrile (1) cyclodimerised on treatment with lithium diisopropylamide in dimethoxyethane at temperatures between ?78°C and 0°C to 3-amino-4-cyano-1,5,5-trimethyl-1,3-cyclohexadiene (2) the structure of which was established by acid hydrolysis to the known 4-cyano-1,5,5-trimethyl-1-cyclohexene-3-one (3).     

Modeling of serine protease prototype reactions with the flexible effective fragment potential quantum mechanical/molecular mechanical method

A complete cycle of chemical transformations for the serine protease prototype reaction is modeled following calculations with the flexible effective fragment quantum mechanical/molecular mechanical (QM/MM) method. The initial molecular model is based on the crystal structure of the trypsin–bovine pancreatic trypsin inhibitor complex including all atoms of the enzyme within approximately 15–18 Å of the oxygen center O of the catalytic serine residue. Several selections of the QM/MM partitioning are considered. Fractions of the side chains of the residues from the catalytic triad (serine, histidine and aspartic acid) and a central part of a model substrate around the C–N bond to be cleaved are included into the QM subsystem. The remaining part, or the MM subsystem, is represented by flexible chains of small effective fragments, whose potentials explicitly contribute to the Hamiltonian of the QM part, but the corresponding fragment–fragment interactions are described by the MM force fields. The QM/MM boundaries are extended over the C–C bonds of the peptides assigned to the QM subsystem in the enzyme, C–C and C–N bonds in model substrates. Multiple geometry optimizations have been performed by using the RHF/6-31G method in the QM part and OPLSAA or AMBER sets of MM parameters, resulting in a series of stationary points on the complex potential-energy surfaces. All structures generally accepted for the serine protease catalytic cycle have been located. Energies at the stationary points found have been recomputed at the MP2/6-31+G^* level for the QM part in the protein environment. Structural changes along the reaction path are analyzed with special attention to hydrogen-bonding networks. In the case of a model substrate selected as a short peptide CH₃(NHCO-CH₂)₂ – HN–CO–(CH₂–NHCO)CH₃ the computed energy profile for the acylation step shows too high activation energy barriers. The energetics of this rate-limiting step is considerably improved, if more realistic model for the substrate is considered, following the motifs of the ThrI11–GlyI12–ProI13-–CysI14–LysI15–AlaI16–ArgI17–IleI18–IleI19 sequence of the bovine pancreatic trypsin inhibitor.     

De novo structural prediction of transition metal complexes: application to technetium

De novo structural prediction of transition metal complexes is investigated. Technetium complexes are chosen given their importance in medical imaging and nuclear waste remediation and for the chemical diversity they display. A new conformational searching algorithm (LIGB) for transition metals is described that allows one to search for different conformational and geometric isomers within a single simulation. In the preponderance of cases, both conformational searching techniques (LIGB and high-temperature molecular dynamics/simulated annealing) provide comparable results, while LIGB is superior for macrocyclic complexes. A genetic algorithm-optimized PM3(tm) parametrization for Tc is compared with the standard implementation and found to yield a significant improvement in predictive ability for the most prevalent Tc structural motifs. The utility of a coupled molecular mechanics-semiempirical quantum mechanics protocol is demonstrated for very rapid, efficient, and effective de novo prediction of transition metal complex geometries.     

Triazene proton affinities: A comparison between density functional,Hartree–Fock,and post-Hartree–Fock methods

The consistency of three density functional computational implementations (DMol, DGauss, and deMon) are compared with high-level Hartree–Fock and Møller–Plesset (MP) calculations for triazene (HN?NNH₂) and formyl triazene (HN?NNHCOH). Proton affinities on all electronegative sites are investigated as well as the geometries of the neutral and protonated species. Density functional calculations employing the nonlocal gradient corrections show agreement with MP calculations for both proton affinities and geometries of neutral and protonated triazenes. Local spin density approximation DMol calculations using numerical basis sets must employ an extended basis to agree with other density functional codes using analytic Gaussian basis sets. The lowest energy conformation of triazene was found to be nonplanar; however, the degree of nonplanarity, as well as some bond lengths, is dependent on the basis set, electron correlation treatment, and methods used for the calculation. © 1994 by John Wiley & Sons, Inc.

1 This article is a U.S. Government work and, as such, is in the public domain in the United States of America.

     

Scanning electrochemical microscopy as a probe of Ag+ binding kinetics at Langmuir phospholipid monolayers

A new method has been developed for measuring local adsorption rates of metal ions at interfaces based on scanning electrochemical microscopy (SECM). The technique is illustrated with the example of Ag+ binding at Langmuir phospholipid monolayers formed at the water/air interface. Specifically, an inverted 25 microm diameter silver disc ultramicroelectrode (UME) was positioned in the subphase of a Langmuir trough, close to a dipalmitoyl phosphatidic acid (DPPA) monolayer, and used to generate Ag+ via Ag electro-oxidation. The method involved measuring the transient current-time response at the UME when the electrode was switched to a potential to electrogenerate Ag+. Since the Ag+/Ag couple is reversible, the response is highly sensitive to local mass transfer of Ag+ away from the electrode, which, in turn, is governed by the interaction of Ag+ with the monolayer. The methodology has been used to determine the influence of surface pressure on the adsorption of Ag+ ions at a phospholipid (dipalmitoyl phosphatidic acid) Langmuir monolayer. It is shown that the capacity for metal ion adsorption at the monolayer increased as the density of surface adsorption sites increased (by increasing the surface pressure). A model for mass transport and adsorption in this geometry has been developed to explain and characterise the adsorption process.     

Theoretical studies on the hydrolysis of mono-phosphate and tri-phosphate in gas phase and aqueous solution

Phosphate hydrolysis by GTPases plays an important role as a molecular switch in signal transduction and as an initiator of many other biological processes. Despite the centrality of this ubiquitous reaction, the mechanism is still poorly understood. As a first step to understand the mechanisms of this process, the nonenzymatic hydrolysis of mono-phosphate and tri-phosphate esters were systematically studied in gas phase and aqueous solution using hybrid density functional methods. The dielectric effect of the environment on the energetics of these processes was also explored. Theoretical results show that for mono-phosphate ester, the dissociative pathway is much more favorable than the associative pathway. However, the reaction barriers for the dissociative and associative pathways of tri-phosphate hydrolysis are very close in aqueous solution, though the dissociative pathway is more favorable in the gas phase. High dielectric solvents, such as water, significantly lower the activation barrier of the associative pathway due to the greater solvation energy of the associative transition states than that of the reactant complex. By contrast, the barrier of the dissociative pathway, with respect to the gas phase, is less sensitive to the surrounding dielectric. In the associative hydrolysis pathway of the tri-phosphate ester, negative charge is transferred from the gamma-phosphate to beta-phosphate through the bridging ester oxygen and results in Pgamma-O bond dissociation. No analogous charge transfer was observed in the dissociative pathway, where Pgamma-O bond dissociation resulted from proton transfer from the gamma-phosphate to the bridge oxygen. Finally, the active participation of local water molecules can significantly lower the activation energy of the dissociative pathway for both mono-phosphate and tri-phosphate.     

Worldsheet instantons,torsion curves and non-perturbative superpotentials

As a first step towards computing instanton-generated superpotentials in heterotic standard model vacua, we determine the Gromov–Witten invariants for a Calabi–Yau threefold with fundamental group π₁(X)=Z₃×Z₃${\pi }_1(X)={\mathbb{Z}}_3\times {\mathbb{Z}}_3$. We find that the curves fall into homology classes in H₂(X,Z)=Z³⊕(Z₃⊕Z₃)$H_2(X,\mathbb{Z})={\mathbb{Z}}^3\oplus ({\mathbb{Z}}_3\oplus {\mathbb{Z}}_3)$. The unexpected appearance of the finite torsion subgroup in the homology group complicates our analysis. However, we succeed in computing the complete genus-0 prepotential. Expanding it as a power series, the number of instantons in any integral homology class can be read off. This is the first explicit calculation of the Gromov–Witten invariants of homology classes with torsion. We find that some curve classes contain only a single instanton. This ensures that the contribution to the superpotential from each such instanton cannot cancel.     

A Study of Possible Morphine Complexes Formed with Calcium and Magnesium

Morphine fluorescence spectra were obtained for morphine sulfate in distilled water, in KRP solution, and in KRP solutions with various concentrations of Ca⁺⁺ and Mg⁺⁺. No evidence of fluorescence shifting indicative of complex formation was observed. Similar solutions were used in a potentiometric study, and no evidence for complex formation was observed.