Interior- and Surface-Bound Excess Electron States in Large Water Cluster Anions

We present the results of mixed quantum/classical simulations on relaxed thermal nanoscale water cluster anions,(H_2O)^-_n, with n=200, 500, 1000 and 8000. By using initial equilibration with constraints, we investigate stable/metastable negatively charged water clusters with both surface-bound and interior-bound excess electron states. Characterization of these states is performed in terms of geometrical parameters, energetics, and optical absorption spectroscopy of the clusters. The calculations provide data characterizing these states in the gap between previously published calculations, and experiments, on smaller clusters and the limiting cases of either an excess electron in bulk water, or an excess electron at an infinite water/air interface. The present results are in general agreement with previous simulations and provide a consistent picture of the evolution of the physical properties of water cluster anions with size over the entire size range, including results for vertical detachment energies and absorption spectra that would signify their presence. In particular, the difference in size dependence between surface-bound and interior-bound state absorption spectra is dramatic, while for detachment energies the dependence is qualitatively the same

Excess Electron Relaxation Dynamics at Water/Air Interfaces

We have performed mixed quantum-classical molecular dynamics simulations of the relaxation of a ground state excess electron at interfaces of different phases of water with air. The investigated systems included ambient water/air, supercooled water/air, Ih ice/air and an amorphous solid water/air interfaces. The present work explores the possible connections of the examined interfacial systems to finite size cluster anions, and the three-dimensional infinite, fully hydrated electron. Localization site analyses indicate that in the absence of nuclear relaxation the electron localizes in a shallow potential trap on the interface in all examined systems in a diffuse, surface-bound (SB) state. With relaxation, the weakly bound electron undergoes an ultrafast localization and stabilization on the surface with the concomitant collapse of its radius. In the case of the ambient liquid interface the electron slowly (on the 10 ps timescale) diffuses into the bulk to form an interior-bound (IB) state. In each other case, the excess electron persists on the interface in surface-bound (SB) states. The relaxation dynamics occur through distinct SB structures which are easily distinguishable by their energetics, geometries, and interactions with the surrounding water bath. The systems exhibiting the most stable SB excess electron states (supercooled water/air and Ih ice/air interfaces) are identified by their characteristic hydrogen-bonding motifs which are found to contain double acceptor type water molecules in the close vicinity of the electron. These surface states correlate reasonably with those extrapolated to infinite size from simulated water cluster anions

Excess Electron Localization Sites in Neutral Water Clusters

We present approximate pseudopotential quantum mechanical calculations of the excess electron states of equilibrated neutral water clusters sampled by classical molecular dynamics simulations. The internal energy of the clusters are representative of those present at temperatures of 200 K and 300 K. Correlated electronic structure calculations are used to validate the pseudopotential for this purpose. We find that the neutral clusters support localized, bound excess electron ground states in about 50 % of the configurations for the smallest cluster size studied (n=20), and in almost all configurations for larger clusters (n>66). The state is always exterior to the molecular frame, forming typically a diffuse surface state. Both cluster size and temperature dependence of energetic and structural properties of the clusters and the electron distribution are explored. We show that the stabilization of the electron is strongly correlated with the pre-existing instantaneous dipole moment of the neutral clusters, and its ground state energy is reflected in the electronic radius. The findings are consistent with electron attachment via an initial surface state. The hypothetical spectral dynamics following such attachment is also discussed

Vienna Circle and Logical Analysis of Relativity Theory

In this paper we present some of our school's results in the area of building up relativity theory (RT) as a hierarchy of theories in the sense of logic. We use plain first-order logic (FOL) as in the foundation of mathematics (FOM) and we build on experience gained in FOM. The main aims of our school are the following: We want to base the theory on simple, unambiguous axioms with clear meanings. It should be absolutely understandable for any reader what the axioms say and the reader can decide about each axiom whether he likes it. The theory should be built up from these axioms in a straightforward, logical manner. We want to provide an analysis of the logical structure of the theory. We investigate which axioms are needed for which predictions of RT. We want to make RT more transparent logically, easier to understand, easier to change, modular, and easier to teach. We want to obtain deeper understanding of RT. Our work can be considered as a case-study showing that the Vienna Circle's (VC) approach to doing science is workable and fruitful when performed with using the insights and tools of mathematical logic acquired since its formation years at the very time of the VC activity. We think that logical positivism was based on the insight and anticipation of what mathematical logic is capable when elaborated to some depth. Logical positivism, in great part represented by VC, influenced and took part in the birth of modern mathematical logic. The members of VC were brave forerunners and pioneers.Comment: 25 pages, 1 firgure

Axiomatizing relativistic dynamics without conservation postulates

A part of relativistic dynamics (or mechanics) is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein's famous $E=mc^2$. The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.Comment: 21 pages, 7 figure

Testing definitional equivalence of theories via automorphism groups

Two first-order logic theories are definitionally equivalent if and only if there is a bijection between their model classes that preserves isomorphisms and ultraproducts (Theorem 2). This is a variant of a prior theorem of van Benthem and Pearce. In Example 2, uncountably many pairs of definitionally inequivalent theories are given such that their model categories are concretely isomorphic via bijections that preserve ultraproducts in the model categories up to isomorphism. Based on these results, we settle several conjectures of Barrett, Glymour and Halvorson

Twin Paradox and the logical foundation of relativity theory

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization SpecRel of special relativity from the literature. SpecRel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in SpecRel. As it turns out, this is practically equivalent to asking whether SpecRel is strong enough to "handle" (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to SpecRel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of SpecRel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that the Twin Paradox becomes provable in AccRel, but it is not provable without IND.Comment: 24 pages, 6 figure

A logic road from special relativity to general relativity

We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist

Comparing theories: the dynamics of changing vocabulary. A case-study in relativity theory

There are several first-order logic (FOL) axiomatizations of special relativity theory in the literature, all looking essentially different but claiming to axiomatize the same physical theory. In this paper, we elaborate a comparison, in the framework of mathematical logic, between these FOL theories for special relativity. For this comparison, we use a version of mathematical definability theory in which new entities can also be defined besides new relations over already available entities. In particular, we build an interpretation of the reference-frame oriented theory SpecRel into the observationally oriented Signalling theory of James Ax. This interpretation provides SpecRel with an operational/experimental semantics. Then we make precise, "quantitative" comparisons between these two theories via using the notion of definitional equivalence. This is an application of logic to the philosophy of science and physics in the spirit of Johan van Benthem's work.Comment: 27 pages, 8 figures. To appear in Springer Book series Trends in Logi