Calculated tautomeric equilibria and X-ray structures of 2-substituted N-methoxy-9-methyl-9H-purin-6-amines

Density Functional Theory calculations of nine 2-substituted N-methoxy-9-methyl-9H-purin-6-amines in the amino and imino tautomeric forms, as well as the complexes of the same with dimethyl sulfoxide (DMSO), were performed using two functionals (BP86 and B3LYP) and two basis sets (SV(P) and def2-TZVP). Solid-state structures of two of the compounds were obtained from single-crystal X-ray diffraction techniques. It was found that the inclusion of both an explicit hydrogen-bonding partner (DMSO) as well as continuum solvation effects, and vibrational corrections to energy, were necessary for qualitative and reasonable quantitative agreement with observed tautomeric ratios. The solution-optimized geometries and X-ray structures were found to be in good agreement. NMR spectroscopy confirmed the dependence of the tautomeric ratios on hydrogen-bonding abilities, in addition to the dipole moment of the solvent in question. Natural Bond Orbital charges on the N-7 nitrogen, as well as the tautomeric ratios were used to explain the observed reactivities of the compounds toward N-7 alkylation.     

On multiplicative maps

No abstract. November 15, 1999     

Hamilton's equations for constrained dynamical systems

We derive expressions for the conjugate momenta and the Hamiltonian for classical dynamical systems subject to holonomic constraints. We give an algorithm for correcting deviations of the constraints arising in numerical solution of the equations of motion. We obtain an explicit expression for the momentum integral for constrained systems.     

Neutral evolution in a biological population as diffusion in phenotype space: reproduction with local mutation but without selection

The process of "evolutionary diffusion," i.e., reproduction with local mutation but without selection in a biological population, resembles standard diffusion in many ways. However, evolutionary diffusion allows the formation of localized peaks that undergo drift, even in the infinite population limit. We relate a microscopic evolution model to a stochastic model which we solve fully. This allows us to understand the large population limit, relates evolution to diffusion, and shows that independent local mutations act as a diffusion of interacting particles taking larger steps.     

Microporous Molecular Materials from Dipeptides Containing Non‐proteinogenic Residues

Dipeptides with two hydrophobic side chains have proved to be an exceptional source of microporous organic materials, but since previous structures were limited to the incorporation of only proteinogenic residues, their full potential as adsorbents has remained unexplored. Single‐crystal XRD data for ten new compounds with non‐proteinogenic L ‐2‐aminobutanoic acid and/or L ‐2‐amino‐pentanoic acid are presented. The gas‐phase accessibility of their crystal pores, with cross‐sections of 2.3 to 5.1 Å, was monitored by CO₂ and CH₄ adsorption isotherms. Included CO₂ was also detected spectroscopically by 2D MAS NMR. An extensive conformational analysis reveals that the use of linear rather than branched side chains (such as L ‐valine and L ‐isoleucine) affords peptides with a greater degree of conformational freedom and yields more‐flexible channel surfaces that may easily adapt to a series of potential guest molecules.