I. Quantum mechanics of one-dimensional two-particle models. II. A quantum mechanical treatment of inelastic collisions

Part I

Solutions of Schrödinger’s equation for system of two particles bound in various stationary one-dimensional potential wells and repelling each other with a Coulomb force are obtained by the method of finite differences. The general properties of such systems are worked out in detail for the case of two electrons in an infinite square well. For small well widths (1-10 a.u.) the energy levels lie above those of the noninteresting particle model by as much as a factor of 4, although excitation energies are only half again as great. The analytical form of the solutions is obtained and it is shown that every eigenstate is doubly degenerate due to the “pathological” nature of the one-dimensional Coulomb potential. This degeneracy is verified numerically by the finite-difference method. The properties of the square-well system are compared with those of the free-electron and hard-sphere models; perturbation and variational treatments are also carried out using the hard-sphere Hamiltonian as a zeroth-order approximation. The lowest several finite-difference eigenvalues converge from below with decreasing mesh size to energies below those of the “best” linear variational function consisting of hard-sphere eigenfunctions. The finite-difference solutions in general yield expectation values and matrix elements as accurate as those obtained using the “best” variational function.

The system of two electrons in a parabolic well is also treated by finite differences. In this system it is possible to separate the center-of-mass motion and hence to effect a considerable numerical simplification. It is shown that the pathological one-dimensional Coulomb potential gives rise to doubly degenerate eigenstates for the parabolic well in exactly the same manner as for the infinite square well.

Part II

A general method of treating inelastic collisions quantum mechanically is developed and applied to several one-dimensional models. The formalism is first developed for nonreactive “vibrational” excitations of a bound system by an incident free particle. It is then extended to treat simple exchange reactions of the form A + BC →AB + C. The method consists essentially of finding a set of linearly independent solutions of the Schrödinger equation such that each solution of the set satisfies a distinct, yet arbitrary boundary condition specified in the asymptotic region. These linearly independent solutions are then combined to form a total scattering wavefunction having the correct asymptotic form. The method of finite differences is used to determine the linearly independent functions.

The theory is applied to the impulsive collision of a free particle with a particle bound in (1) an infinite square well and (2) a parabolic well. Calculated transition probabilities agree well with previously obtained values.

Several models for the exchange reaction involving three identical particles are also treated: (1) infinite-square-well potential surface, in which all three particles interact as hard spheres and each two-particle subsystem (i.e. BC and AB) is bound by an attractive infinite-square-well potential; (2) truncated parabolic potential surface, in which the two-particle subsystems are bound by a harmonic oscillator potential which becomes infinite for interparticle separations greater than a certain value; (3) parabolic (untruncated) surface. Although there are no published values with which to compare our reaction probabilities, several independent checks on internal consistency indicate that the results are reliable.

Part I. Coenzyme B12 as a hydroformylation-type catalyst. Part II. Mechanisms of hydrogen transfer in the methylmalonyl coenzyme a mutase reaction

Part I

The mechanism of the hydroformylation reaction was studied. Using cobalt deuterotetracarbonyl and 1-pentene as substrates, the first step in the reaction, addition of cobalt tetracarbonyl to an olefin, was shown to be reversible.

Part II

The role of coenzyme B₁₂ in the isomerization of methylmalonyl coenzyme A to succinyl coenzyme A by methylmalonyl coenzyme A mutase was studied. The reaction was allowed to proceed to partial completion using a mixture of methylmalonyl coenzyme A and 4, 4, 4-tri-²H-methylmalonyl coenzyme A as substrate. The deuterium distribution in the product, succinyl coenzyme A, was shown to best fit a model in which hydrogen is transferred from C-4 of methylmalonyl coenzyme A to C-5’ of the adenosyl moiety of coenzyme B₁₂ in the rate determining step. The three hydrogens at the 5’-adenosyl position of the coenzyme B₁₂ intermediate are then able to become enzymatically equivalent before hydrogen is transferred from the coenzyme B₁₂ intermediate to form succinyl coenzyme A.

Part I: Total yield measurements for the ^(21)Ne(α,n)^)(24)Mg reaction. Part II: A study of the ^(12)C(He,p)^(14)N reaction

PART I

The total cross-section for the reaction ²¹Ne(α, n)²⁴Mg has been measured in the energy range 1.49 Mev ≤ E_cm ≤ 2.6 Mev. The cross-section factor, S(O), for this reaction has been determined, by means of an optical model calculation, to be in the range 1.52 x 10¹² mb-Mev to 2.67 x 10¹² mb-Mev, for interaction radii in the range 5.0 fm to 6.6 fm. With S(O) ≈ 2 x 10¹² mb-Mev, the reaction ²¹Ne(α, n)²⁴Mg can produce a large enough neutron flux to be a significant astrophysical source of neutrons.

PART II

The reaction¹²C(³He, p)¹⁴N has been studied over the energy range 12 Mev ≤ E_lab ≤ 18 Mev. Angular distributions of the proton groups leading to the lowest seven levels in ¹⁴N were obtained.

Distorted wave calculations, based on two-nucleon transfer theory, were performed, and were found to be reliable for obtaining the value of the orbital angular momentum transferred. The present work shows that such calculations do not yield unambiguous values for the spectroscopic factors.

Structure of an unexpected trimer from the reaction of ageratochromene II with aluminum chloride

A new trimer from the reaction of ageratochromene [1] (6,7-dimethoxy-2,2-dimethyl-1-benzopyran) with anhydrous aluminum chloride was shown to be 3,4-dihydro-6,7-dimethoxy-2,2-dimethyl-3-(6',7'-dimethoxy-2',2'-di-methyl-2H-1-benzopyran-4'-yl)-4-(3" 4"-dihydro-6", 7"-dimethoxy-2",2"-dimethyl-2H-1-benzopyran-3"-yl)-2H-1-benzopyran. Its structure was confirmed by NMR (H-1, C-13, DEPT-135. COSY, HMBC, HSQC, TOCSY and NOESY), IR, mass spectra and elemental analysis. Copyright (C) 2002 John Wiley Sons, Ltd.

Synthesis and structure of new low dimensional polymeric haloplumbate(II) complexes [Pb4Br12(C40H40N8)] and [Pb4Cl12(C40H40N8)]center dot H2O

New low dimensional polymeric haloplumbate(II) complexes of the dication of (4,4'-bis(imidazolyl-ylmethyl)biphenyl) were synthesised and their crystal structures determined. Complex 1, [Pb4Br12(C40H40N8)], has cis-edge-shared, octahedral, lead bromide double chains. In compound 2 [Pb4Cl12(C40H40N8)]center dot H2O, the inorganic chains are corner-shared, square pyramidal chains of lead chloride. In both compounds the organic ammoniums form regular layers that alternate with the inorganic chains.

Theoretical studies on the reaction mechanism of oxidation of primary alcohols by Zn/Cu(II)-phenoxyl radical catalyst

The catalytic mechanism for the oxidation of primary alcohols catalyzed by the two functional models of galactose oxidase (GOase), M-II L (M = Cu, Zn; L = N,N'-bis(3,5-di-tert-butyl-2-hydroxyphenyl)1-2-diiminoquinone)), has been studied by use of the density functional method B3LYP The catalytic cycle of Cu- and Zn-catalysts consists of two parts, namely, substrate oxidation (primary alcohol oxidation) and O-2 reduction (catalyst regeneration). The catalytic mechanisms have been studied for the two reaction pathways (route 1 and route 2). The calculations indicate that the hydrogen atom transfer within the substrate oxidation part is the rate-determining step for both catalysts, in agreement with the experimental observation.

Effect of La3+ on structure and electrochemical reaction of microperoxidase-11 in imitated physiological solution

In this paper, the interaction mechanism between La3+ and microperoxidase-11 (MP-11) in the imitated physiological solution was investigated with the electrochemical and spectroscopic methods. It was found that when the molar ratio of La3+, and MP-11 is low, such as 2, La3+ can coordinate with oxygen in the propionic acid group of the heme group in the MP-11 molecule, forming the La-MP-11 complexes and leading to the increase in the non-planarity of the porphyrin cycle in the heme group and then the increase in the extent of exposure of the electrochemically active center, Fe(I I I) in the porphyrin cycle of the heme group. The increase in the extent of exposure of the electrochemically active center, Fe(III) in the porphyrin cycle of the heme group would increase the reversibility of the electrochemical reaction of the La-MP-11 complexes and its electrocatalytic activity for the reduction of H2O2. The results of the chromatographic analysis demonstrated that the average molar ratio of La3+ and MP-11 in the La-MP-11 complexes is 1.62.When the molar ratio of La3+ and MP-11 is high, such as 3, La3+ would shear some amino acid residues of the peptide of MP-11. Therefore, many La3+ ions can bind to the oxygen- and/or nitrogen-containing groups in the sheared amino acid residues except coordinating with the sheared and non-sheared MP-11 molecules.

Structure characterization and physical properties of a complex with supramolecular architectures Co-2(2,6-DPC2Co(H2O)5 center dot 2H(2)O (DPC=2,6-pyridinedicarboxylate)

Reaction of 2,6-pyridinedicarboxylic with CoCl2 . 6H(2)O in aqueous solution give rise to a three-dimensional Complex CO2(2,6-DPC)(2)Co(H2O)(5).2H(2)O (DPC = 2,6-pyridinedicarboxylate) 1. It has been characterized by elemental analyses, infrared spectra (IR) spectrum, thermogravimetric (TG) analysis, EPR spectrum, and single crystal X-ray diffraction. The complex crystallizes in the P2(1)/c space group with a = 8.3906(3) Angstrom, b = 27.4005(8) Angstrom, c = 9.6192(4) A, alpha = 90.00degrees, beta = 98.327(2)degrees, gamma = 90.00degrees, V = 2188.20(14) Angstrom(3), Z = 4. There are two types of cobalt environments: Co(1) is coordinated by four oxygen atoms from four carboxyl groups and two nitrogen 2 atoms which are all from pdc(2). Co(2) is coordinated by six oxygen atoms, five from coordinated water molecules and one from a carboxyl of pdc(2) - of which the other oxygen atom is linked to the Co(1). The extensive intermolecular hydrogen bonds are formed in the crystal by means of the five coordinated water molecules.

Synthesis, crystal structure and magnetic properties of a chain coordination polymer {[Cu4L2(H2O)] center dot H2O}(n)

A chain coordination polymer with the chemical formula {[Cu4L2(H2O)] (.) H2O)(n), has been synthesized by the assembly reaction of K(2)CuL(.)1.5H(2)O and Cu(OAC)(2)(H2O)-H-. with a 1:1 mole ratio in methanol., where H4L=2-hydroxy-3-[(E)-({2-[(2-hydroxybenzoyl)imino]ethyl I imino)methyl] benzoic acid, OAC(-) = CH3COO-. The crystal structure was determined by single-crystal X-ray diffraction analysis, the compound has chain molecular structure formed by dissymmetrical tetranuclear units. The magnetic measurements showed that Cu-Cu of the complex exhibit antiferromagnetic interactions, and satisfactory fittings to the observed magnetic susceptibility data were obtained by assuming a binuclear system, and further using molecular field approximation to deal with magnetic exchange interactions between binuclear systems.

Synthesis and characterization of (C5H9C9H6)(2)Yb(THF)(2)(II) (1) and [(C5H9C5H4)(2)Yb(THF)](2)O-2 (2), and ring-opening polymerization of lactones with 1

Reaction of YbI2 with two equivalents of cyclopentylindenyl lithium (C5H9C9H6Li) affords ytterbium(II) substituted indenyl complex (C5H9C9H6)(2)Yb(THF)(2) (1) which shows high activity to ring-opening polymerization (ROP) of lactones. The reaction between YbI2 and cyclopentylcyclopentadienyl sodium (C5H9C5H4Na) gives complex [(C5H9C5H4)(2)Yb(THF)](2)O-2 (2) in the presence of a trace amount of O-2, the molecular structure of which comprises two (C5H9C5H4)(2)Yb(THF) bridged by an asymmetric O-2 unit. The O-2 unit and ytterbium atoms define a plane that contains a C-i symmetry center.

Iron(II)-8-quinolinol/MCM-41-catalyzed phenol hydroxylation and reaction mechanism

Iron(II)-8-quinolino/MCM-41 is prepared. Its catalysis is studied in phenol hydroxylation using H2O2 (30%) as oxidant. The experiment shows that Iron(II)-8-quinolinol/MCM-41 has good catalytic activity and desired stability. Based on cyclic voltammetry, ESR, and UV-visible spectra studies of iron(II)-8-quinolinol complex in liquid phase, a radical substitution mechanism is proposed and used to demonstrate the experimental facts clearly. (C) 1997 Academic Press.

Phenol hydroxylation by iron(II) phenanthroline: The reaction mechanism

Phenol hydroxylation catalyzed by iron(II)-1,10-phenanthroline is investigated through kinetics, ESR, W-Vis as well as cyclic voltammogram studies. The optimum reaction conditions are obtained for diphenols production. Radical substitution mechanism is first proposed to explain the effects of pH, reaction medium and other factors on the phenol hydroxylation with H2O2 as oxidant, and found that the coexisting of iron(II)-1,10-phenanthroline and iron(III)-1,10-phenanthroline is the key for phenol hydroxylation to occur with H2O2 as oxygen donor.