There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

Multiwfn is a multifunctional program for wavefunction analysis. Its main functions are: (1) Calculating and visualizing real space function, such as electrostatic potential and electron localization function at point, in a line, in a plane or in a spatial scope. (2) Population analysis. (3) Bond order analysis. (4) Orbital composition analysis. (5) Plot density-of-states and spectrum. (6) Topology analysis for electron density. Some other useful utilities involved in quantum chemistry studies are also provided. The built-in graph module enables the results of wavefunction analysis to be plotted directly or exported to high-quality graphic file. The program interface is very user-friendly and suitable for both research and teaching purpose. The code of Multiwfn is substantially optimized and parallelized. Its efficiency is demonstrated to be significantly higher than related programs with the same functions. Five practical examples involving a wide variety of systems and analysis methods are given to illustrate the usefulness of Multiwfn. The program is free of charge and open-source. Its precompiled file and source codes are available from http://multiwfn.codeplex.com.

Multiwfn: a multifunctional wavefunction analyzer.

J. Appl. Cryst.の発刊に際して

The 11th edition of Harrison's Principles of Internal Medicine welcomes Anthony Fauci to its editorial staff, in addition to more than 85 new contributors. While the organization of the book is similar to previous editions, major emphasis has been placed on disorders that affect multiple organ systems. Important advances in genetics, immunology, and oncology are emphasized. Many chapters of the book have been rewritten and describe major advances in internal medicine. Subjects that received only a paragraph or two of attention in previous editions are now covered in entire chapters. Among the chapters that have been extensively revised are the chapters on infections in the compromised host, on skin rashes in infections, on many of the viral infections, including cytomegalovirus and Epstein-Barr virus, on sexually transmitted diseases, on diabetes mellitus, on disorders of bone and mineral metabolism, and on lymphadenopathy and splenomegaly. The major revisions in these chapters and many

Harrison's Principles of Internal Medicine

The Quantum Theory of Atoms in Molecules

Foreword. Preface. List of Abbreviations Appearing in this Volume. List of Contributors. 1 An Introduction to the Quantum Theory of Atoms in Molecules (Cherif F. Matta and Russell J. Boyd). 1.1 Introduction. 1.2 The Topology of the Electron Density. 1.3 The Topology of the Electron Density Dictates the Form of Atoms in Molecules. 1.4 The Bond and Virial Paths, and the Molecular and Virial Graphs. 1.5 The Atomic Partitioning of Molecular Properties. 1.6 The Nodal Surface in the Laplacian as the Reactive Surface of a Molecule. 1.7 Bond Properties. 1.8 Atomic Properties. 1.9 "Practical" Uses and Utility of QTAIM Bond and Atomic Properties. 1.10 Steps of a Typical QTAIM Calculation. References. Part I Advances in Theory. 2 The Lagrangian Approach to Chemistry (Richard F. W. Bader). 2.1 Introduction. 2.2 The Lagrangian Approach. 2.3 The Action Principle in Quantum Mechanics. 2.4 From Schrodinger to Schwinger. 2.5 Molecular Structure and Structural Stability. 2.6 Re.ections and the Future. References. 3 Atomic Response Properties (Todd A. Keith). 3.1 Introduction. 3.2 Apparent Origin-dependence of Some Atomic Response Properties. 3.3 Bond Contributions to "Null" Molecular Properties. 3.4 Bond Contributions to Atomic Charges in Neutral Molecules. 3.5 Atomic Contributions to Electric Dipole Moments of Neutral Molecules. 3.6 Atomic Contributions to Electric Polarizabilities. 3.7 Atomic Contributions to Vibrational Infrared Absorption Intensities. 3.8 Atomic Nuclear Virial Energies. 3.9 Atomic Contributions to Induced Electronic Magnetic Dipole Moments. 3.10 Atomic Contributions to Magnetizabilities of Closed-Shell Molecules. References. 4 QTAIM Analysis of Raman Scattering Intensities: Insights into the Relationship Between Molecular Structure and Electronic Charge Flow (Kathleen M. Gough, Richard Dawes, Jason R. Dwyer, and Tammy L. Welshman). 4.1 Introduction. 4.2 Background to the Problem. 4.3 Methodology. 4.4 Speci.c Examples of the Use of AIM2000 Software to Analyze Raman Intensities. 4.5 Patterns in alpha That Are Discovered Through QTAIM. 4.6 Patterns in qa/qrCH That Apply Across Di.erent Structures, Conformations, Molecular Types: What is Transferable? 4.7 What Can We Deduce From Simple Inspection of &delta &alpha /&delta rCH and &delta &alpha /&delta rCC From Gaussian? 4.8 Conclusion. References. 5 Topological Atom-Atom Partitioning of Molecular Exchange Energy and its Multipolar Convergence (Michel Rafat and Paul L. A. Popelier). 5.1 Introduction. 5.2 Theoretical Background. 5.3 Details of Calculations. 5.4 Results and Discussion. 5.5 Conclusion. References. 6 The ELF Topological Analysis Contribution to Conceptual Chemistry and Phenomenological Models (Bernard Silvi and Ronald J. Gillespie). 6.1 Introduction. 6.2 Why ELF and What is ELF? 6.3 Concepts from the ELF Topology. 6.4 VSEPR Electron Domains and the Volume of ELF Basins. 6.5 Examples of the Correspondence Between ELF Basins and the Domains of the VSEPR Model. 6.6 Conclusions. References. Part II Solid State and Surfaces. 7 Solid State Applications of QTAIM and the Source Function - Molecular Crystals, Surfaces, Host-Guest Systems and Molecular Complexes (Carlo Gatti). 7.1 Introduction. 7.2 QTAIM Applied to Solids - the TOPOND Package. 7.3 QTAIM Applied to Molecular Crystals. 7.4 QTAIM Applied to Surfaces. 7.5 QTAIM Applied to Host-Guest Systems. 7.6 The Source Function: Theory. References. 8 Topology and Properties of the Electron Density in Solids (Victor Luana, Miguel A. Blanco, Aurora Costales, Paula Mori-Sanchez, and Angel Martin Pendas). 8.1 Introduction. 8.2 The Electron Density Topology and the Atomic Basin Shape. 8.3 Crystalline Isostructural Families and Topological Polymorphism. 8.4 Topological Classi.cation of Crystals. 8.5 Bond Properties - Continuity from the Molecular to the Crystalline Regime. 8.6 Basin Partition of the Thermodynamic Properties. 8.7 Obtaining the Electron Density of Crystals. References. 9 Atoms in Molecules Theory for Exploring the Nature of the Active Sites on Surfaces (Yosslen Aray, Jesus Rodriguez, and David Vega). 9.1 Introduction. 9.2 Implementing the Determination of the Topological Properties of p(r) from a Three-dimensional Grid. 9.3 An Application to Nanocatalyts - Exploring the Structure of the Hydrodesulfurization MoS2 Catalysts. References. Part III Experimental Electron Densities and Biological Molecules. 10 Interpretation of Experimental Electron Densities by Combination of the QTAMC and DFT (Vladimir G. Tsirelson). 10.1 Introduction. 10.2 Specificity of the Experimental Electron Density. 10.3 Approximate Electronic Energy Densities. 10.4 The Integrated Energy Quantities. 10.5 Concluding Remarks. References. 11 Topological Analysis of Proteins as Derived from Medium and Highresolution Electron Density: Applications to Electrostatic Properties (Laurence Leherte, Benoit Guillot, Daniel P. Vercauteren, Virginie Pichon-Pesme, Christian Jelsch, Ange'lique Lagoutte, and Claude Lecomte). 11.1 Introduction. 11.2 Methodology and Technical Details. 11.3 Topological Properties of Multipolar Electron Density Database. 11.4 Analysis of Local Maxima in Experimental and Promolecular Mediumresolution Electron Density Distributions. 11.5 Calculation of Electrostatic Properties from Atomic and Fragment Representations of Human Aldose Reductase. 11.6 Conclusions and Perspectives. References. 12 Fragment Transferability Studied Theoretically and Experimentally with QTAIM - Implications for Electron Density and Invariom Modeling (Peter Luger and Birger Dittrich). 12.1 Introduction. 12.2 Experimental Electron-density Studies. 12.3 Studying Transferability with QTAIM - Atomic and Bond Topological Properties of Amino Acids and Oligopeptides. 12.4 Invariom Modeling. 12.5 Applications of Aspherical Invariom Scattering Factors. 12.6 Conclusion. References. Part IV Chemical Bonding and Reactivity. 13 Interactions Involving Metals - From "Chemical Categories" to QTAIM, and Backwards (Piero Macchi and Angelo Sironi). 13.1 Introduction. 13.2 The Electron Density in Isolated Metal Atoms - Hints of Anomalies. 13.3 Two-center Bonding. 13.4 Three-center Bonding. 13.5 Concluding Remarks. References. 14 Applications of the Quantum Theory of Atoms in Molecules in Organic Chemistry - Charge Distribution, Conformational Analysis and Molecular Interactions (Jesus Hernandez-Trujillo, Fernando Cortes-Guzman, and Gabriel Cuevas). 14.1 Introduction. 14.2 Electron Delocalization. 14.3 Conformational Equilibria. 14.4 Aromatic Molecules. References. 15 Aromaticity Analysis by Means of the Quantum Theory of Atoms in Molecules (Eduard Matito, Jordi Poater, and Miquel Sola ). 15.1 Introduction. 15.2 The Fermi Hole and the Delocalization Index. 15.3 Electron Delocalization in Aromatic Systems. 15.4 Aromaticity Electronic Criteria Based on QTAIM. 15.5 Applications of QTAIM to Aromaticity Analysis. 15.6 Conclusions. References. 16 Topological Properties of the Electron Distribution in Hydrogen-bonded Systems (Ignasi Mata, Ibon Alkorta, Enrique Espinosa, Elies Molins, and Jose Elguero). 16.1 Introduction. 16.2 Topological Properties of the Hydrogen Bond. 16.3 Energy Properties at the Bond Critical Point (BCP). 16.4 Topological Properties and Interaction Energy. 16.5 Electron Localization Function, n(r). 16.6 Complete Interaction Range. 16.7 Concluding Remarks. References. 17 Relationships between QTAIM and the Decomposition of the Interaction Energy - Comparison of Different Kinds of Hydrogen Bond (Stawomir J. Grabowski). 17.1 Introduction. 17.2 Diversity of Hydrogen-bonding Interactions. 17.3 The Decomposition of the Interaction Energy. 17.4 Relationships between the Topological and Energy Properties of Hydrogen Bonds. 17.5 Various Other Interactions Related to Hydrogen Bonds. 17.6 Summary. References. Part V Application to Biological Sciences and Drug Design. 18 QTAIM in Drug Discovery and Protein Modeling (Nagamani Sukumar and Curt M. Breneman). 18.1 QSAR and Drug Discovery. 18.2 Electron Density as the Basic Variable. 18.3 Atom Typing Scheme and Generation of the Transferable Atom Equivalent (TAE) Library. 18.4 TAE Reconstruction and Descriptor Generation. 18.5 QTAIM-based Descriptors. 18.6 Sample Applications. 18.7 Conclusions. References. 19 Fleshing-out Pharmacophores with Volume Rendering of the Laplacian of the Charge Density and Hyperwall Visualization Technology (Preston J. MacDougall and Christopher E. Henze). 19.1 Introduction. 19.2 Computational and Visualization Methods. 19.3 Subatomic Pharmacophore Insights. 19.4 Conclusion. References. Index.

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The Quantum theory of atoms in molecules : from solid state to DNA and drug design

Bond paths linking two bonded hydrogen atoms that bear identical or similar charges are found between the ortho-hydrogen atoms in planar biphenyl, between the hydrogen atoms bonded to the C1–C4 carbon atoms in phenanthrene and other angular polybenzenoids, and between the methyl hydrogen atoms in the cyclobutadiene, tetrahedrane and indacene molecules corseted with tertiary-tetra-butyl groups. It is shown that each such H–H interaction, rather than denoting the presence of “nonbonded steric repulsions”, makes a stabilizing contribution of up to 10 kcal mol−1 to the energy of the molecule in which it occurs. The quantum theory of atoms in molecules—the physics of an open system—demonstrates that while the approach of two bonded hydrogen atoms to a separation less than the sum of their van der Waals radii does result in an increase in the repulsive contributions to their energies, these changes are dominated by an increase in the magnitude of the attractive interaction of the protons with the electron density distribution, and the net result is a stabilizing change in the energy. The surface virial that determines the contribution to the total energy decrease resulting from the formation of the H–H interatomic surface is shown to account for the resulting stability. It is pointed out that H–H interactions must be ubiquitous, their stabilization energies contributing to the sublimation energies of hydrocarbon molecular crystals, as well as solid hydrogen. H–H bonding is shown to be distinct from “dihydrogen bonding”, a form of hydrogen bonding with a hydridic hydrogen in the role of the base atom.

Hydrogen-hydrogen bonding: a stabilizing interaction in molecules and crystals.

We report on several weak interactions in nucleic acids, which, collectively, can make a nonnegligible contribution to the structure and stability of these molecules. Fragments of DNA were obtained from previously determined accurate experimental geometries and their electron density distributions calculated using density functional theory (DFT). The electron densities were analyzed topologically according to the quantum theory of atoms in molecules (AIM). A web of closed-shell bonding interactions is shown to connect neighboring base pairs in base-pair duplexes and in dinuleotide steps. This bonding underlies the well-known π-stacking interaction between adjacent nucleic acid bases and is characterized topologically for the first time. Two less widely appreciated modes of weak closed-shell interactions in nucleic acids are also described:  (i) interactions between atoms in the bases and atoms belonging to the backbone (base−backbone) and (ii) interactions among atoms within the backbone itself (backbone−...

Extended Weak Bonding Interactions in DNA: π-Stacking (Base−Base), Base−Backbone, and Backbone−Backbone Interactions†

The observation that some properties attributed to atoms and functional groups are transferable from one molecule to another has played a key role in the development of chemistry. This observation provides a basis for group additivity schemes and is exemplified by the constancy of group contributions to thermodynamic and spectroscopic properties. But what is the electronic basis of this empirical transferability? The quantum theory of atoms in molecules (QTAIM) [1], developed by Professor Richard F. W. Bader and his coworkers, relies on quantum observables such as the electron density rðrÞ and energy densities to answer such a question. Other important (related) questions addressed by QTAIM include: What is an atom in a molecule or a crystal? How can an atom or a group of atoms be transferable sometimes in very different external potentials? Can one define bonding in molecules unambiguously especially in borderline cases?

Chérif F. Matta

Papers

The Quantum Theory of Atoms in Molecules

The Quantum theory of atoms in molecules : from solid state to DNA and drug design

Hydrogen-hydrogen bonding: a stabilizing interaction in molecules and crystals.

Extended Weak Bonding Interactions in DNA: π-Stacking (Base−Base), Base−Backbone, and Backbone−Backbone Interactions†

An Introduction to the Quantum Theory of Atoms in Molecules