Advances in Chemical Physics, Volume 147 E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Advances in Chemical Physics
• Sprache: Englisch

Seitenzahl: 614

Veröffentlichungsjahr: 2011

Beschreibung

The Advances in Chemical Physics series—the cutting edge of research in chemical physics

The Advances in Chemical Physics series provides the chemical physics and physical chemistry fields with a forum for critical, authoritative evaluations of advances in every area of the discipline. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series offers contributions from internationally renowned chemists and serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics.

This volume explores:

• Hydrogen Bond Topology and Proton Ordering in Ice and Water Clusters (Sherwin J. Singer and Chris Knight)
• Molecular Inner-Shell Spectroscopy, Arpis Technique and Its Applications (Eiji Shigemasa and Nobuhiro Kosugi)
• Geometric Optimal Control of Simple Quantum Systems: Geometric Optimal Control Theory (Dominique Sugny)
• Density Matrix Equation for a Bathed Small System and its Application to Molecular Magnets (D. A. Garanin)
• A Fractional Langevin Equation Approach to Diffusion Magnetic Resonance Imaging (Jennie Cooke)

Leseprobe

Contents

Cover

Editorial Board

Title Page

Copyright

Preface to the Series

Chapter 1: Hydrogen-Bond Topology and Proton Ordering in Ice and Water Clusters

I. Introduction: Hydrogen-Bond Connectivity and Physical Properties

II. Hydrogen-Bond Order–Disorder Transitions in Ice

III. Analysis of the Hydrogen-Bond Order–Disorder in Ice

IV. Enumeration of Hydrogen-Bond Configurations

V. Water Clusters

VI. Defects

VII. Conclusion

Acknowledgments

References

Chapter 2: Molecular Inner-Shell Spectroscopy. Arpis Technique and its Applications

I. Introduction

II. Angle-Resolved Photoion-Yield Spectroscopy

III. ARPIS of N2

IV. ARPIS of C2H2

V. ARPIS of O2

VI. ARPIS of SO2

VII. Some Extensions Related to ARPIS Technique

Acknowledgments

References

Chapter 3: Geometric Optimal Control of Simple Quantum Systems

I. Introduction

II. The Pontryagin Maximum Principle

III. Application to the Control of a Three-Level Quantum System

IV. Application to the Time-Optimal Control of Two-Level Dissipative Quantum Systems

V. Conclusion

References

Chapter 4: Density Matrix Equation for a Bathed Small System and its Application to Molecular Magnets

I. General Theory

II. The Density Matrix Equation

III. Time-Dependent Problems

IV. Application to Molecular Magnets

Acknowledgments

References

Chapter 5: A Fractional Langevin Equation Approach to Diffusion Magnetic Resonance Imaging

I. Overview

II. Phase Diffusion and Brownian Motion

III. A Langevin Equation Approach to Normal Diffusion

IV. Fractional Diffusion: Possible Explanations of the Stretched Exponential Behavior Using the Fractional Langevin Equation

V. Magnetic Resonance Imaging Methods

VI. Results of Experimental Investigation

VII.Discussion

Acknowledgments

Appendix A

Appendix B

References

Color Plates

Author Index

Subject Index

Editorial Board

Moungi G. Bawendi, Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

Kurt Binder, Condensed Matter Theory Group, Institut für Physik, Johannes Gutenberg- Universität Mainz, Mainz, Germany

William T. Coffey, Department of Electronics and Electrical Engineering, Trinity College, University of Dublin, Dublin, Ireland

Karl F. Freed, Department of Chemistry, James Franck Institute, University of Chicago, Chicago, Illinois, USA

Daan Frenkel, Department of Chemistry, Trinity College, University of Cambridge, Cambridge, United Kingdom

Pierre Gaspard, Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Brussels, Belgium

Martin Gruebele, School of Chemical Sciences and Beckman Institute, Director of Center for Biophysics and Computational Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA

Jean-Pierre Hansen, Department of Chemistry, University of Cambridge, Cambridge, United Kingdom

Gerhard Hummer, Chief, Theoretical Biophysics Section, NIDDK-National Institutes of Health, Bethesda, Maryland, USA

Ronnie Kosloff, Department of Physical Chemistry, Institute of Chemistry and Fritz Haber Center for Molecular Dynamics, The Hebrew University of Jerusalem, Israel

Ka Yee Lee, Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois, USA

Todd J. Martinez, Department of Chemistry, Stanford University, Stanford, California, USA

Shaul Mukamel, Department of Chemistry, University of California at Irvine, Irvine, California, USA

Jose Onuchic, Department of Physics, Co-Director Center for Theoretical Biological Physics, University of California at San Diego, La Jolla, California, USA

Steven Quake, Department of Physics, Stanford University, Stanford, California, USA

Mark Ratner, Department of Chemistry, Northwestern University, Evanston, Illinois, USA

David Reichmann, Department of Chemistry, Columbia University, New York, New York, USA

George Schatz, Department of Chemistry, Northwestern University, Evanston, Illinois, USA

Norbert Scherer, Department of Chemistry, James Franck Institute, University of Chicago, Chicago, Illinois, USA

Steven J. Sibener, Department of Chemistry, James Franck Institute, University of Chicago, Chicago, Illinois, USA

Andrei Tokmakoff, Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

Donald G. Truhlar, Department of Chemistry, University of Minnesota, Minneapolis, Minnesota, USA

John C. Tully, Department of Chemistry, Yale University, New Haven, Connecticut, USA

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Published by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

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Library of Congress Catalog Number: 58-9935

ISBN: 978-1-118-12234-1

Preface to the Series

Advances in science often involve initial development of individual specialized fields of study within traditional disciplines, followed by broadening and overlapping, or even merging, of those specialized fields, leading to a blurring of the lines between traditional disciplines. The pace of that blurring has accelerated in the last few decades, and much of the important and exciting research carried out today seeks to synthesize elements from different fields of knowledge. Examples of such research areas include biophysics and studies of nanostructured materials. As the study of the forces that govern the structure and dynamics of molecular systems, chemical physics encompasses these and many other emerging research directions. Unfortunately, the flood of scientific literature has been accompanied by losses in the shared vocabulary and approaches of the traditional disciplines, and there is much pressure from scientific journals to be ever more concise in the descriptions of studies, to the point that much valuable experience, if recorded at all, is hidden in supplements and dissipated with time. These trends in science and publishing make this series, Advances in Chemical Physics, a much needed resource.

The Advances in Chemical Physics is devoted to helping the reader obtain general information about a wide variety of topics in chemical physics, a field that we interpret very broadly. Our intent is to have experts present comprehensive analyses of subjects of interest and to encourage the expression of individual points of view.We hope that this approach to the presentation of an overview of a subject will both stimulate new research and serve as a personalized learning text for beginners in a field.

Stuart A. Rice

Aaron R. Dinner

Chapter 1

Hydrogen-Bond Topology and Proton Ordering in Ice and Water Clusters

Sherwin J. Singer and Chris Knight

Department of Chemistry, Ohio State University, Columbus OH

I. Introduction: Hydrogen-Bond Connectivity and Physical Properties

Water is a unique substance. Most small molecules (nitrogen, oxygen, carbon dioxide, methane, e.g.,) exist only as gases under ambient conditions. In contrast, water is commonly found as a vapor, liquid, or solid. The uniqueness of water arises because of the strong hydrogen bonds (H-bonds) between water molecules. Not only are H-bonds unusually strong intermolecular bonds, they are directional. A water molecule prefers to accept two H-bonds and donate two other H-bonds in tetrahedral directions (Fig. 1. Understanding the properties of ice and the structure of many water clusters is an exercise in working out the ramifications of building water H-bonds according to this pattern. A good illustration is H-bond order–disorder phenomena in ice, which will be the major concern in this chapter. In the known phases of ice at pressures less than 10 GPa, water molecules donate and accept two H-bonds with four neighbors, as shown in Fig. 1. The previous statements express what is known as the Bernal–Fowler “ice rules” [1].

Figure 1. The central water donates a H-bond to the two upper molecules, and accepts a H-bond from the lower molecules. The directionality of the H-bonds in indicated by the arrows on the right.

While the oxygen atoms form a periodic lattice, the hydrogen atoms are disordered in ices Ih, III, V, VI, VII, and XII, which undergo a phase transition to ices XI, IX, XIII, XV, VIII, and XIV, respectively, as temperature is lowered. The origin of the disorder is easily seen in Fig. 1, where the central water molecule is shown donating to the two upper neighbors. In the disordered ice phases, the water molecules may donate to any two among its four neighbors. Hence, a water molecule constrained to orient hydrogen atoms in two of four possible tetrahedral directions may be found in 4·3/2=6 different configurations. Several possible unit cells of ice Ih are shown in Fig. 2. Of course, the orientation of the neighboring molecules are partially constrained if the central molecule is fixed, so the number of available H-bond configurations is considerably less than 6N, where N is the number of water molecules. In 1935, Linus Pauling [2] estimated that there are different ways to arrange the H-bonds of N water molecules subject to the ice rules in the lattice of ice Ih, the phase of ice formed when water freezes under ambient pressures. The contribution to the entropy would be . Pauling's estimate would prove to be remarkably accurate compared with more powerful solutions of the counting problem [3, 4]. Earlier in 1932, based on the measurements of others, Giauque and Ashley [5] had calculated the residual entropy of ice Ih near 0K to be in the range of 0.87–0.96 calK−1mol−1, and attributed the entropy at 0K to “the persistence of rotation of water in ice below 10°K”. In 1936, Giauque and Stout [6] measured the heat capacity of ice. Combining their results with known thermodynamic properties of the liquid and vapor and a spectroscopic estimate of the absolute entropy of water vapor, they estimated the residual entropy of ice to be 0.82calK−1mol−1, which is within their experimental error of 0.05calK−1mol−1. The experiment confirmed that the H-bonds in ice are in a nearly random arrangement, (i.e., the H-bonds are disordered). Thus, somewhere between the freezing temperature of water and 0 K, ice falls out of equilibrium.

Figure 2. Four possible arrangements of H-bonds within a 16-water-molecule orthorhombic unit cell of ice Ih. Here, cis and trans bonds are defined as whether protons lie on the same or opposite side of the H-bond, respectively, as indicated for structure (a). The H-bond isomers are summarized mathematically by directed graphs in which directional bonds point from H-bond donor to H-bond acceptor, as illustrated for the isomer (b).

While the origin of the residual entropy of ice seemed settled, it was recognized that an ordered phase of ice Ih could exist if a suitable experimental means was available to allow equilibration [7]. Little progress was made concerning a possible low-temperature form of ice until the 1980s, when calorimetry experiments on samples doped with impurities, particularly potassium hydroxide (KOH), exhibited a clear signature of a proton-ordering transition at 72 K [8-10]. The transition temperature was independent of the KOH concentration, indicating that KOH acts like a catalyst. This proton-ordered structure suggested by subsequent diffraction experiments, [10-15] is called ice XI. It is structure (a) of space group symmetry Cmc21 in Fig. 2, where ice XI can be seen to be ferroelectric on account of the ordered c-axis bonds. The mechanism by which KOH induces the proton-ordering transition in ice Ih is unclear. Furthermore, the ferroelectric structure of ice XI is unexpected. There has been continued debate and research as to whether the H-bond arrangements in the high-temperature phase of ice are actually random or partially ordered [16, 17], whether a phase transition to a fully H-bond ordered structure exists [15, 18-20], and if so, its identity. Hydrogen-bond order–disorder transitions in other parts of the ice phase diagram have been long known [21], and new examples continue to emerge [22-24].

Like the phases of ice, water clusters can be grouped into families among which the oxygen atoms occupy nearly the same position, and that differ in the direction of the H-bonds between those oxygens. Unlike ice structures, where the energy difference per water between different H-bond structures is on the order of 0.1kcalmol−1, the energy difference between H-bond isomers in water clusters can amount to several kilocalories per mole per water. As a result, the H-bond disordered ice phases tend toward nearly complete disorder while only the lowest energy isomer or isomers of water clusters are typically observed in cluster beam experiments. The properties of the cubic water clusters (Fig. 3) illustrate this behavior. There are 14 symmetry-distinct ways to connect waters in a cubic arrangement [25]. Among those, the D2d and S4 clusters (structures 1 and 2 of Fig. 3) are the lowest energy isomers [26], and the only ones observed experimentally [27].

Figure 3. The 14 symmetry-distinct H-bond arrangements possible when the oxygen atoms of eight waters form a cubic structure. The point group symmetry is indicated when it is higher than

C1.

While the molecular coordinates completely specify the unit cells of Fig. 2 or clusters of Fig. 3, it is natural to distill the H-bond topology from the molecular geometry and ask to what extent physical properties can be predicted on the basis of the H-bond topology alone, as first conceived by Radhakrishnan and Herndon [28]. The abstraction from full atomic coordinates to the H-bond topology can be described in several ways. The topology can be summarized using directed graphs [29, 30], either for ice crystals () or finite clusters (), in which each vertex corresponds to a water oxygen and an arrow connecting two vertices indicates the presence of a H-bond and the direction from H-bond donor to H-bond acceptor. The ice rules require that all vertices in defect-free ice have two incoming and two outgoing bonds. Another language to describe the mapping of deep local minima of the potential surface to patterns of H-bond connectivity abstraction is to describe a mapping to a spin-lattice model [31, 32]. In fact, there exist magnetic compounds, known as spin ices, in which the electronic spins obey ice rules [33-35].