Free Boolean algebras with closure operators and a conjecture of Henkin, Monk, and Tarski

We characterize the nite-dimensional elements of a free cylindric algebra. This solve

Hydrogen Bonding in Proton Transfer Compounds of 5 Sulfosalicylic Acid With Ortho-Substituted Moocyclic Heteroaromatic Lewis Bases

The crystal structures of the 1:1 proton-transfer compounds of 5-sulfosalicylic acid with the ortho-substituted monocyclic heteroaromatic Lewis bases, 2-aminopyridine, 2- hydroxypyridine and 2-aminopyrimidine, viz. 2-aminopyridinium 5-sulfosalicylate (1), 2-hydroxypyridinium 5-sulfosalicylate monohydrate (2) and 2-aminopyrimidinium 5- sulfosalicylatemonohydrate (3) have been determined and their hydrogen-bonding patterns described. All compounds are monoclinic, space group P21/c, with Z=4 in cells with dimensions a=7.898(5), b=11.159(11), c=14.912(7) A° , β =96.849(11)◦ (1);=7.260(2), b=15.292(3), c=12.615(2) A° , β =102.45(5)◦ (2) and a=7.0430(7), b=12.1871(16), c=16.2825(12) A° , β =101.364(7)◦ (3). All three compounds show some molecular disorder, in 1 within the cation species and with both 2 and 3, a similar rotational disorder in the anion sulfonate group. Hydrogen bonding in all three compounds together with significant cation-anion or cation-cation inter-ring π–π interactions generate three-dimensional layered polymer structures

Structure, dynamics, and reactivity of hydrated electrons by ab initio molecular dynamics

Understanding the properties of hydrated electrons, which were first observed using pulse radiolysis of water in 1962, is crucial because they are key species in many radiation chemistry processes. Although time-resolved spectroscopic studies and molecular simulations have shown that an electron in water (prepared, for example, by water photoionization) relaxes quickly to a localized, cavity-like structure similar to 2.5 angstrom in radius, this picture has recently been questioned. In another experimental approach, negatively charged water clusters of increasing size were studied with photoelectron and IR spectroscopies. Although small clusters can bind an excess electron, their character is very different from bulk hydrated species. As data on electron binding in liquid water have become directly accessible experimentally, the cluster-to-bulk extrapolations have become a topic of lively debate. Quantum electronic structure calculations addressing experimental measurables have, until recently, been largely limited to small clusters; extended systems were approached mainly with pseudopotential calculations combining a classical description of water with a quantum mechanical treatment of the excess electron. In this Account, we discuss our investigations of electrons solvated in water by means of ab initio molecular dynamics simulations. This approach, applied to a model system of a negatively charged cluster of 32 water molecules, allows us to characterize structural, dynamical, and reactive aspects of the hydrated electron using all of the system's valence electrons. We show that under ambient conditions, the electron localizes into a cavity close to the surface of the liquid cluster. This cavity is, however, more flexible and accessible to water molecules than an analogous area around negatively charged ions. The dynamical process of electron attachment to a neutral water cluster is strongly temperature dependent. Under ambient conditions, the electron relaxes in the liquid cluster and becomes indistinguishable from an equilibrated, solvated electron on a picosecond time scale. In contrast, for solid, cryogenic systems, the electron only partially localizes outside of the cluster, being trapped in a metastable, weakly bound ``cushion-like'' state. Strongly bound states under cryogenic conditions could only be prepared by cooling equilibrated, liquid, negatively charged clusters. These calculations allow us to rationalize how different isomers of electrons in cryogenic clusters can be observed experimentally. Our results also bring into question the direct extrapolation of properties of cryogenic, negatively charged water clusters to those of electrons in the bulk liquid. Ab initio molecular dynamics represents a unique computational tool for investigating the reactivity of the solvated electron in water. As a prototype, the electron proton reaction was followed in the 32-water cluster. In accord with experiment, the molecular mechanism is a proton transfer process that is not diffusion limited, but rather controlled by a proton-induced deformation of the excess electron's solvent shell. We demonstrate the necessary ingredients of a successful density functional methodology for the hydrated electron that avoids potential pitfalls, such as self-interaction error, insufficient basis set, or lack of dispersion interactions. We also benchmark the density functional theory methods and outline the path to faithful ab initio simulations of dynamics and reactivity of electrons solvated in extended aqueous systems