Resonance Raman scattering amplitude calculations for diatomic molecules

A direct procedure for calculating resonance Raman scattering amplitudes for diatomic molecules is presented and compared with other calculational procedures. An extension of the present procedure is outlined for cases where there is more than one excited intermediate state and these states interact with one another.     

Ground state alternative for <Emphasis Type="Italic">p</Emphasis>-Laplacian with potential term

Let Ω be a domain in , d ≥ 2, and 1 < p < ∞. Fix . Consider the functional Q and its Gateaux derivative Q′ given by If Q ≥ 0 on, then either there is a positive continuous function W such that for all, or there is a sequence and a function v > 0 satisfying Q′ (v) = 0, such that Q(u _k ) → 0, and in . In the latter case, v is (up to a multiplicative constant) the unique positive supersolution of the equation Q′ (u) = 0 in Ω, and one has for Q an inequality of Poincaré type: there exists a positive continuous function W such that for every satisfying there exists a constant C > 0 such that . As a consequence, we prove positivity properties for the quasilinear operator Q′ that are known to hold for general subcritical resp. critical second-order linear elliptic operators.     

Negombins A-I, new chlorinated polyfunctional diterpenoids from the marine sponge Negombata species

Nine novel compounds designated negombins A-I (1-9) were isolated, together with latrunculin, from the Tanzanian sponge Negombata sp. The nine are sacculatane type diterpenes, previously only known from liverworts. The structures of the compounds were elucidated by interpretation of MS and 1D and 2D NMR spectra. A possible biogenesis initiated by the naturally rare chloronium ion is suggested, possibly hinting to a guest microorganism as the source of the compounds. Compound 4 is toxic to brine shrimp larvae.     

Towards experimental determination of conical intersection properties: a twin state based comparison with bound excited states

The energy and approximate structure of certain S(0)/S(1) conical intersections (CI) are shown computationally to be deducible from those of two bound states: the first triplet (T(1)), which is iso-energetic with the CI, and the second excited singlet state (S(2)). This is demonstrated for acepentalene (I) and its perfluoro derivative (II) using the twin state concept for three states systems and based on the fact that the triplet T(1) is almost degenerate with the CI. The stable S(2) (C(3v) configuration) state exhibits unusual exaltation of Jahn-Teller active degenerate mode-ν(JT) = 2058 cm(-1) (～500 cm(-1) higher than analogous e-mode of the symmetric (C(3v)) T(1) and the dianion I(-2) or any C-C vibration of the Jahn-Teller distorted (C(s)) ground state minimum). The acepentalene molecule, whose rigid structure and possibility to attain the relatively high symmetry C(3v) configuration, is a particularly suitable candidate for this purpose.     

Density-dependent liquid nitromethane decomposition: molecular dynamics simulations based on ReaxFF

The decomposition mechanism of hot liquid nitromethane at various compressions was studied using reactive force field (ReaxFF) molecular dynamics simulations. A competition between two different initial thermal decomposition schemes is observed, depending on compression. At low densities, unimolecular C-N bond cleavage is the dominant route, producing CH(3) and NO(2) fragments. As density and pressure rise approaching the Chapman-Jouget detonation conditions (～30% compression, >2500 K) the dominant mechanism switches to the formation of the CH(3)NO fragment via H-transfer and/or N-O bond rupture. The change in the decomposition mechanism of hot liquid NM leads to a different kinetic and energetic behavior, as well as products distribution. The calculated density dependence of the enthalpy change correlates with the change in initial decomposition reaction mechanism. It can be used as a convenient and useful global parameter for the detection of reaction dynamics. Atomic averaged local diffusion coefficients are shown to be sensitive to the reactions dynamics, and can be used to distinguish between time periods where chemical reactions occur and diffusion-dominated, nonreactive time periods.     

Spectral properties of Schrödinger operators on radial N-dimensional infinite trees

We study the discreteness of the spectrum of Schrödinger operators which are defined on a class of radial N-dimensional rooted trees of a finite or infinite volume, and are subject to a certain mixed boundary condition. We present a method to estimate their eigenvalues using operators on a one-dimensional tree. These operators are called width-weighted operators, since their coefficients depend on the section width or area of the N-dimensional tree. We show that the spectrum of the width-weighted operator tends to the spectrum of a one-dimensional limit operator as the sections width tends to zero. Moreover, the projections to the one-dimensional tree of eigenfunctions of the N-dimensional Laplace operator converge to the corresponding eigenfunctions of the one-dimensional limit operator.     

The photo-dissociation of the pyrrole-ammonia complex--the role of hydrogen bonding in Rydberg states photochemistry

The photochemistry of the pyrrole-ammonia cluster is analyzed theoretically. Whereas in neat pyrrole the dominant photochemical reaction is H-atom cleavage, recent experiments show that in pyrrole-ammonia clusters the major reaction is H-transfer to form the NH(4) radical (solvated by ammonia molecules in the case of large clusters) and the pyrrolyl radical. A mechanism involving the hydrogen-bonded Rydberg state is offered to account for these results and verified computationally. Two minima are located on the lowest excited singlet PES. Both of them are Rydberg states, one leads to the formation of NH(4) and pyrrolyl radicals, the other is connected to the πσ* state through a relatively high barrier, leading to a 3-body dissociation reaction to form a pyrrolyl radical, ammonia and an H-atom. The former is the energetically and statistically preferred one.     

Idiotypic network dysregulation

The pathogenesis of autoimmune disease is still an enigma. Whereas the diverse clinical manifestations of many autoimmune diseases cannot be explained by the existence of autoantibodies, idiotypic dysregulation may provide an alternative explanation. Experimental models, serum level changes of pathogenic idiotypes during exacerbation and remission, and the increased expression of pathogenic idiotypes following common infections all support this notion. In this article we review experimental models of autoimmune disease induction (systemic lupus erythematosus, antiphospholipidsyn drome, Goodpasture's syndrome, autoimmune thyroiditis, and vasculitis) by manipulation of the idiotypic network and discuss the utilization of idiotypes for the immunotherapy of autoimmune diseases and other conditions that involve the immune system (e.g., atherosclerosis).     

Maximum and anti-maximum principlesand eigenfunctions estimates via perturbation theory of positive solutions of elliptic equations

In this paper we discuss some new results concerning perturbation theory for second order elliptic partial differential equations related to positivity properties of such equations. We continue the study of some different notions of “small” perturbations and discuss their relations to comparisons of Green's functions, refined maximum and anti-maximum principles, ground state, and the decay of eigenfunctions. In particular, we show that if V is a positive function which is a semismall perturbation of a subcritical Schr?dinger operator H defined on a domain , and are the (Dirichlet) eigenfunctions of the equation , then for any , the function is bounded and has a continuous extension up to the Martin boundary of the pair , where is the ground state of H with a principal eigenvalue . Received: 29 November 1998