Quantum and theoretical chemistry Books

Book SynopsisThis book distills the knowledge gained from research into atoms in molecules over the last 10 years into a unique, handy reference. Throughout, the authors address a wide audience, such that this volume may equally be used as a textbook without compromising its research-oriented character. Clearly structured, the text begins with advances in theory before moving on to theoretical studies of chemical bonding and reactivity. There follow separate sections on solid state and surfaces as well as experimental electron densities, before finishing with applications in biological sciences and drug-design. The result is a must-have for physicochemists, chemists, physicists, spectroscopists and materials scientists.Trade Review"…a handsome text that serves to create a one-stop reference point exploring the quantum theory of atoms and molecules in complete detail." (Electric Review, May 2007)Table of ContentsForeword vii Preface xix List of Abbreviations Appearing in this Volume xxvii List of Contributors xxxiii 1 An Introduction to the Quantum Theory of Atoms in Molecules 1Chérif F. Matta and Russell J. Boyd 1.1 Introduction 1 1.2 The Topology of the Electron Density 1 1.3 The Topology of the Electron Density Dictates the Form of Atoms in Molecules 5 1.4 The Bond and Virial Paths, and the Molecular and Virial Graphs 8 1.5 The Atomic Partitioning of Molecular Properties 9 1.6 The Nodal Surface in the Laplacian as the Reactive Surface of a Molecule 10 1.7 Bond Properties 10 1.7.1 The Electron Density at the BCP (pb) 11 1.7.2 The Bonded Radius of an Atom (rb), and the Bond Path Length 11 1.7.3 The Laplacian of the Electron Density at the BCP (∇2pb) 11 1.7.4 The Bond Ellipticity (є) 12 1.7.5 Energy Densities at the BCP 12 1.7.6 Electron Delocalization between Bonded Atoms: A Direct Measure of Bond Order 13 1.8 Atomic Properties 15 1.8.1 Atomic Electron Population [N(Ω)] and Charge [q(Ω)] 16 1.8.2 Atomic Volume [Vol.(Ω)] 16 1.8.3 Kinetic Energy [T(Ω)] 17 1.8.4 Laplacian [L(Ω)] 17 1.8.5 Total Atomic Energy [Ee(Ω)] 18 1.8.6 Atomic Dipolar Polarization [μ(Ω)] 20 1.8.7 Atomic Quadrupolar Polarization [Q(Ω)] 24 1.9 ‘‘Practical’’ Uses and Utility of QTAIM Bond and Atomic Properties 25 1.9.1 The Use of QTAIM Bond Critical Point Properties 25 1.9.2 The Use of QTAIM Atomic Properties 26 1.10 Steps of a Typical QTAIM Calculation 27 References 30 Part I Advances in Theory 35 2 The Lagrangian Approach to Chemistry 37Richard F. W. Bader 2.1 Introduction 37 2.1.1 From Observation, to Physics, to QTAIM 37 2.2 The Lagrangian Approach 38 2.2.1 What is The Lagrangian Approach and What Does it Do? 38 2.2.2 The Lagrangian and the Action Principle – A Return to the Beginnings 39 2.2.3 Minimization of the Action 40 2.2.4 Steps in Minimizing the Action 41 2.3 The Action Principle in Quantum Mechanics 42 2.3.1 Schrödinger’s Appeal to the Action 42 2.3.2 Schrödinger’s Minimization 42 2.3.2.1 Two Ways of Expressing the Kinetic Energy 43 2.3.3 Obtaining an Atom from Schrödinger’s Variation 44 2.3.3.1 The Role of Laplacian in the Definition of an Atom 45 2.3.4 Getting Chemistry from δG(Ψ, ∇Ψ; Ω) 46 2.4 From Schrödinger to Schwinger 48 2.4.1 From Dirac to Feynman and Schwinger 48 2.4.2 From Schwinger to an Atom in a Molecule 49 2.5 Molecular Structure and Structural Stability 52 2.5.1 Definition of Molecular Structure 52 2.5.2 Prediction of Structural Stability 53 2.6 Reflections and the Future 53 2.6.1 Reflections 53 2.6.2 The Future 55 References 57 3 Atomic Response Properties 61Todd A. Keith 3.1 Introduction 61 3.2 Apparent Origin-dependence of Some Atomic Response Properties 62 3.3 Bond Contributions to ‘‘Null’’ Molecular Properties 64 3.4 Bond Contributions to Atomic Charges in Neutral Molecules 70 3.5 Atomic Contributions to Electric Dipole Moments of Neutral Molecules 71 3.6 Atomic Contributions to Electric Polarizabilities 73 3.7 Atomic Contributions to Vibrational Infrared Absorption Intensities 78 3.8 Atomic Nuclear Virial Energies 82 3.9 Atomic Contributions to Induced Electronic Magnetic Dipole Moments 88 3.10 Atomic Contributions to Magnetizabilities of Closed-Shell Molecules 90 References 94 4 QTAIM Analysis of Raman Scattering Intensities: Insights into the Relationship Between Molecular Structure and Electronic Charge Flow 95Kathleen M. Gough, Richard Dawes, Jason R. Dwyer, and Tammy L. Welshman 4.1 Introduction 95 4.2 Background to the Problem 96 4.2.1 Conceptual Approach to a Solution 97 4.2.1.1 Experimental Measurement of Raman Scattering Intensities 97 4.2.1.2 Theoretical Modeling of Raman Scattering Intensities: What We Did and Why 99 4.3 Methodology 100 4.3.1 Modeling α and ∂α/∂r 101 4.3.2 Recouping α From the Wavefunction, With QTAIM 102 4.3.3 Recovering ∂α/∂r From QTAIM 103 4.4 Specific Examples of the Use of AIM2000 Software to Analyze Raman Intensities 103 4.4.1 Modeling α in H2 104 4.4.1.1 Modeling ∆α/∆r in H2 106 4.4.2 Modeling α and ∆α/∆r in CH4 106 4.4.3 Additional Exercises for the Interested Reader 108 4.5 Patterns in α That Are Discovered Through QTAIM 109 4.6 Patterns in ∂α/∂rCH That Apply Across Different Structures, Conformations, Molecular Types: What is Transferable? 111 4.6.1 Patterns in ∆α/∆rCH Revealed by QTAIM 111 4.6.1.1 QTAIM Analysis of ∆α/∆rCH in Small Alkanes 111 4.6.1.2 What Did We Learn From QTAIM That Can be Transferred to the Other Molecules? 113 4.7 What Can We Deduce From Simple Inspection of ∂α/∂rCH and ∂α/∂rCC From Gaussian? 114 4.7.1 Variations in ∂α/∂rCH Among the Alkanes 114 4.7.2 ∆α/∆rCH in Cycloalkanes, Bicycloalkanes, and Hedranes 116 4.7.3 Patterns That Emerge in ∆α/∆rCC of Alkanes 116 4.7.4 Unsaturated Hydrocarbons and the Silanes: C-H, C=C, and Si-Si Derivatives 117 4.8 Conclusion 118 References 119 5 Topological Atom–Atom Partitioning of Molecular Exchange Energy and its Multipolar Convergence 121Michel Rafat and Paul L. A. Popelier 5.1 Introduction 121 5.2 Theoretical Background 123 5.3 Details of Calculations 128 5.4 Results and Discussion 130 5.4.1 Convergence of the Exchange Energy 130 5.4.2 Convergence of the Exchange Force 136 5.4.3 Diagonalization of a Matrix of Exchange Moments 136 5.5 Conclusion 139 References 139 6 The ELF Topological Analysis Contribution to Conceptual Chemistry and Phenomenological Models 141Bernard Silvi and Ronald J. Gillespie 6.1 Introduction 141 6.2 Why ELF and What is ELF? 142 6.3 Concepts from the ELF Topology 144 6.3.1 The Synaptic Order 145 6.3.2 The Localization Domains 145 6.3.3 ELF Population Analysis 147 6.4 VSEPR Electron Domains and the Volume of ELF Basins 149 6.5 Examples of the Correspondence Between ELF Basins and the Domains of the VSEPR Model 153 6.5.1 Octet Molecules 153 6.5.1.1 Hydrides (CH4, NH3, H2O) 153 6.5.1.2 AX4 (CH4, CF4, SiCl4) 154 6.5.1.3 AX3E and AX2E2 (NCl3, OCl2) 154 6.5.2 Hypervalent Molecules 155 6.5.2.1 PCl5 and SF6 155 6.5.2.2 SF4 and ClF3 155 6.5.2.3 AX7 and AX6E Molecules 155 6.5.3 Multiple Bonds 156 6.5.3.1 C2H4 and C2H2 156 6.5.3.2 Si2Me4 and Si2Me2 157 6.6 Conclusions 158 References 159 Part II Solid State and Surfaces 163 7 Solid State Applications of QTAIM and the Source Function – Molecular Crystals, Surfaces, Host–Guest Systems and Molecular Complexes 165Carlo Gatti 7.1 Introduction 165 7.2 QTAIM Applied to Solids – the TOPOND Package 166 7.2.1 QTAIM Applied to Experimental Densities: TOPXD and XD Packages 168 7.3 QTAIM Applied to Molecular Crystals 170 7.3.1 Urea 171 7.3.1.1 Urea: Packing Effects 172 7.4 QTAIM Applied to Surfaces 179 7.4.1 Si(111)(1*1) Clean and Hydrogen-covered Surfaces 180 7.4.2 Si(111)(2*1) Reconstructed Surface 184 7.5 QTAIM Applied to Host–Guest Systems 186 7.5.1 Type I Inorganic Clathrates A8Ga16Ge30 (A=Sr, Ba) 186 7.5.2 Sodium Electrosodalite 190 7.6 The Source Function: Theory 192 7.6.1 The Source Function and Chemical Transferability 194 7.6.2 Chemical Information from the Source Function: Long and Short-range Bonding Effects in Molecular Complexes 196 7.6.3 The Source Function: Latest Developments 201 References 202 8 Topology and Properties of the Electron Density in Solids 207Víctor Luaña, Miguel A. Blanco, Aurora Costales, Paula Mori-Sánchez, and Angel Martín Penda´s 8.1 Introduction 207 8.2 The Electron Density Topology and the Atomic Basin Shape 209 8.3 Crystalline Isostructural Families and Topological Polymorphism 213 8.4 Topological Classification of Crystals 215 8.5 Bond Properties – Continuity from the Molecular to the Crystalline Regime 217 8.6 Basin Partition of the Thermodynamic Properties 219 8.7 Obtaining the Electron Density of Crystals 222 References 227 9 Atoms in Molecules Theory for Exploring the Nature of the Active Sites on Surfaces 231Yosslen Aray, Jesus Rodríguez, and David Vega 9.1 Introduction 231 9.2 Implementing the Determination of the Topological Properties of p(r) from a Three-dimensional Grid 231 9.3 An Application to Nanocatalyts – Exploring the Structure of the Hydrodesulfurization MoS2 Catalysts 236 9.3.1 Catalyst Models 237 9.3.2 The Full p(r) Topology of the MoS2 Bulk 241 9.3.3 The p(r) Topology of the MoS2 Edges 245 References 254 Part III Experimental Electron Densities and Biological Molecules 257 10 Interpretation of Experimental Electron Densities by Combination of the QTAMC and DFT 259Vladimir G. Tsirelson 10.1 Introduction 259 10.2 Specificity of the Experimental Electron Density 261 10.3 Approximate Electronic Energy Densities 262 10.3.1 Kinetic and Potential Energy Densities 262 10.3.2 Exchange and Correlation Energy Densities 271 10.4 The Integrated Energy Quantities 275 10.5 Concluding Remarks 276 References 278 11 Topological Analysis of Proteins as Derived from Medium and Highresolution Electron Density: Applications to Electrostatic Properties 285Laurence Leherte, Benoȋt Guillot, Daniel P. Vercauteren, Virginie Pichon-Pesme, Christian Jelsch, Angélique Lagoutte, and Claude Lecomte 11.1 Introduction 285 11.2 Methodology and Technical Details 287 11.2.1 Ultra-high X-ray Resolution Approach 287 11.2.2 Medium-resolution Approach 289 11.2.2.1 Promolecular Electron Density Distribution Calculated from Structure Factors 289 11.2.2.2 Promolecular Electron Density Distribution Calculated from Atoms 290 11.2.3 A Test System – Human Aldose Reductase 291 11.3 Topological Properties of Multipolar Electron Density Database 294 11.4 Analysis of Local Maxima in Experimental and Promolecular Mediumresolution Electron Density Distributions 298 11.4.1 Experimental and Promolecular Electron Density Distributions Calculated from Structure Factors 299 11.4.2 Promolecular Electron Density Distributions Calculated from Atoms (PASA Model) 301 11.5 Calculation of Electrostatic Properties from Atomic and Fragment Representations of Human Aldose Reductase 305 11.5.1 Medium- and High-resolution Approaches of Electrostatic Potential Computations 307 11.5.2 Electrostatic Potential Comparisons 309 11.5.3 Electrostatic Interaction Energies 312 11.6 Conclusions and Perspectives 312 References 314 12 Fragment Transferability Studied Theoretically and Experimentally with QTAIM – Implications for Electron Density and Invariom Modeling 317Peter Luger and Birger Dittrich 12.1 Introduction 317 12.2 Experimental Electron-density Studies 318 12.2.1 Experimental Requirements 318 12.2.2 Recent Experimental Advances 319 12.2.2.1 Synchrotron Radiation Compared with Laboratory Sources 319 12.2.2.2 Data Collection at Ultra-low Temperatures (10–20 K) 321 12.3 Studying Transferability with QTAIM – Atomic and Bond Topological Properties of Amino Acids and Oligopeptides 323 12.4 Invariom Modeling 328 12.4.1 Invariom Notation, Choice of Model Compounds, and Practical Considerations 330 12.4.2 Support for Pseudoatom Fragments from QTAIM 331 12.5 Applications of Aspherical Invariom Scattering Factors 334 12.5.1 Molecular Geometry and Anisotropic Displacement Properties 334 12.5.2 Using the Enhanced Multipole Model Anomalous Dispersion Signal 335 12.5.3 Modeling the Electron Density of Oligopeptide and Protein Molecules 336 12.6 Conclusion 338 References 339 Part IV Chemical Bonding and Reactivity 343 13 Interactions Involving Metals – From ‘‘Chemical Categories’’ to QTAIM, and Backwards 345Piero Macchi and Angelo Sironi 13.1 Introduction 345 13.2 The Electron Density in Isolated Metal Atoms – Hints of Anomalies 345 13.3 Two-center Bonding 349 13.3.1 The Dative Bond 350 13.3.1.1 Metal Carbonyls 351 13.3.1.2 Donor–Acceptor Interactions of Heavy Elements 352 13.3.2 Direct Metal–Metal Bonding 352 13.4 Three-center Bonding 356 13.4.1 π-Complexes 357 13.4.2 σ-Complexes 363 13.4.2.1 Dihydrogen and Dihydride Coordination 364 13.4.2.2 Agostic Interactions 364 13.4.2.3 Hydride Bridges 367 13.4.3 Carbonyl-supported Metal–Metal Interactions 370 13.5 Concluding Remarks 371 References 372 14 Applications of the Quantum Theory of Atoms in Molecules in Organic Chemistry – Charge Distribution, Conformational Analysis and Molecular Interactions 375Jesús Hernández-Trujillo, Fernando Cortés-Guzmn, and Gabriel Cuevas 14.1 Introduction 375 14.2 Electron Delocalization 375 14.2.1 The Pair-density 375 14.2.2 3JHH Coupling Constants and Electron Delocalization 378 14.3 Conformational Equilibria 380 14.3.1 Rotational barriers 380 14.3.1.1 Rotational Barrier of Ethane 380 14.3.1.2 Rotational Barrier of 1,2-Disubstituted Ethanes 382 14.3.2 Anomeric Effect on Heterocyclohexanes 386 14.4 Aromatic Molecules 391 14.4.1 Electronic Structure of Polybenzenoid Hydrocarbons 391 14.5 Conclusions 395 References 396 15 Aromaticity Analysis by Means of the Quantum Theory of Atoms in Molecules 399Eduard Matito, Jordi Poater, and Miquel Solà 15.1 Introduction 399 15.2 The Fermi Hole and the Delocalization Index 401 15.3 Electron Delocalization in Aromatic Systems 403 15.4 Aromaticity Electronic Criteria Based on QTAIM 404 15.4.1 The para-Delocalization Index (PDI) 404 15.4.2 The Aromatic Fluctuation Index (FLU) 406 15.4.3 The π-Fluctuation Aromatic Index (FLUπ) 407 15.5 Applications of QTAIM to Aromaticity Analysis 409 15.5.1 Aromaticity of Buckybowls and Fullerenes 409 15.5.2 Effect of Substituents on Aromaticity 412 15.5.3 Assessment of Clar’s Aromatic π-Sextet Rule 416 15.5.4 Aromaticity Along the Diels–Alder Reaction. The Failure of Some Aromaticity Indexes 418 15.6 Conclusions 419 References 421 16 Topological Properties of the Electron Distribution in Hydrogen-bonded Systems 425Ignasi Mata, Ibon Alkorta, Enrique Espinosa, Elies Molins, and José Elguero 16.1 Introduction 425 16.2 Topological Properties of the Hydrogen Bond 426 16.2.1 Topological Properties at the Bond Critical Point (BCP) 426 16.2.2 Integrated Properties 429 16.3 Energy Properties at the Bond Critical Point (BCP) 431 16.4 Topological Properties and Interaction Energy 435 16.5 Electron Localization Function, n(r) 438 16.6 Complete Interaction Range 440 16.6.1 Dependence of Topological and Energy Properties on the Interaction Distance 440 16.6.2 Perturbed Systems 448 16.7 Concluding Remarks 450 References 450 17 Relationships between QTAIM and the Decomposition of the Interaction Energy – Comparison of Different Kinds of Hydrogen Bond 453Sławomir J. Grabowski 17.1 Introduction 453 17.2 Diversity of Hydrogen-bonding Interactions 456 17.3 The Decomposition of the Interaction Energy 459 17.4 Relationships between the Topological and Energy Properties of Hydrogen Bonds 460 17.5 Various Other Interactions Related to Hydrogen Bonds 464 17.5.1 H+…π Interactions 464 17.5.2 Hydride Bonds 466 17.6 Summary 467 References 468 Part V Application to Biological Sciences and Drug Design 471 18 QTAIM in Drug Discovery and Protein Modeling 473Nagamani Sukumar and Curt M. Breneman 18.1 QSAR and Drug Discovery 473 18.2 Electron Density as the Basic Variable 474 18.3 Atom Typing Scheme and Generation of the Transferable Atom Equivalent (TAE) Library 476 18.4 TAE Reconstruction and Descriptor Generation 478 18.5 QTAIM-based Descriptors 480 18.5.1 TAE Descriptors 482 18.5.2 RECON Autocorrelation Descriptors 485 18.5.3 PEST Shape–Property Hybrid Descriptors 485 18.5.4 Electron Density-based Molecular Similarity Analysis 487 18.6 Sample Applications 489 18.6.1 QSAR/QSPR with TAE Descriptors 489 18.6.2 Protein Modeling with TAE Descriptors 491 18.7 Conclusions 492 References 494 19 Fleshing-out Pharmacophores with Volume Rendering of the Laplacian of the Charge Density and Hyperwall Visualization Technology 499Preston J. MacDougall and Christopher E. Henze 19.1 Introduction 499 19.2 Computational and Visualization Methods 501 19.2.1 Computational Details 501 19.2.2 Volume Rendering of the Laplacian of the Charge Density 501 19.2.3 The Hyperwall 505 19.2.4 Hyper-interactive Molecular Visualization 505 19.3 Subatomic Pharmacophore Insights 507 19.3.1 Hydrogen-bonding Donor Sites 507 19.3.2 Inner-valence Shell Charge Concentration (i-VSCC) Features in Transition-metal Atoms 509 19.3.3 Misdirected Valence in the Ligand Sphere of Transition-metal Complexes 511 19.4 Conclusion 513 References 514 Index 515

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Book SynopsisDas Verständnis der quantentheoretischen Ursachen der Moleküleigenschaften steht im Mittelpunkt dieser Einführung. Kompakt und verständlich gelingt es dem Autor, den Leser von den mathematischen und physikalischen Grundlagen der Quantenmechanik hin zu einem grundlegenden Verständnis der Moleküleigenschaften zu führen. Zahlreiche Beispiele machen die Darstellung anschaulich und helfen dem Leser bei der Erarbeitung des Stoffes. Table of Contents

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Book SynopsisMathematik für Chemiker ist eine gut verständliche, didaktisch klare Einführung in die mathematische Behandlung naturwissenschaftlicher Probleme. Das Buch bietet das mathematische Basisrepertoire für den Studenten der Chemie und anderer naturwissenschaftlicher Fachrichtungen. Es vermittelt das nötige mathematische Grundwissen und geht auf die Rolle ein, die die Mathematik in der Begriffs- und Theorienbildung spielt. Auf strenge mathematische Herleitungen wird dabei weitgehend verzichtet, die anschauliche Begründung vorgezogen.Table of ContentsEinleitung: Über das Verhältnis von Mathematik und Naturwissenschaften.- 1. Vom Meßwert zum funktionalen Zusammenhang.- 1.1 Einiges über Meßgrößen als Zahlen und als Skalare oder Vektoren.- 1.1.1 Zahlen.- 1.1.2 Skalare und Vektoren.- 1.2 Meßwerte und Meßfehler.- 1.2.1 Streuung von Meßwerten durch statistische Einflüsse: Theoretische Betrachtungen.- 1.2.2 Streuung von Meßwerten durch statistische Einflüsse: Praktische Handhabun.- 1.3 Statistische Fehler in Meßreihen geringen Umfangs.- 1.3.1 Einiges über Stichproben.- 1.3.2 Beurteilung von Mittelwert und Standardabweichung bei angenäherter Normalverteilung.- 1.3.3 Nicht-normale Verteilungen.- 1.4 Stochastische und funktionale Zusammenhänge zwischen zwei Variablen.- 1.4.1 Korrelation und Korrelationsanalyse.- 1.4.2 Lineare Regression und Allgemeines über Ausgleichsrechnung.- 1.4.3 Der funktionale Zusammenhang als Abstraktion.- 2. Funktionen.- 2.1 Über mathematische Funktionen und ihre Darstellung.- 2.1.1 Allgemeines und Terminologisches.- 2.1.2 Die graphische Darstellung von Funktionen.- 2.1.3 Transformation von Ortskoordinaten.- 2.2 Einige wichtige Funktionen einer Variablen.- 2.2.1 Algebraische Funktionen.- 2.2.2 Trigonometrische Funktionen.- 2.2.3 Exponentialfunktion und Logarithmusfunktion.- 2.2.4 Zwei spezielle, stückweise definierte Funktionen.- 2.2.5 Modifikation gegebener Funktionen durch multiplikative oder additive Zusätze.- 2.3 Die Stetigkeit von Funktionen.- 2.3.1 Grenzwerte und Stetigkeit.- 2.3.2 Einige Eigenschaften stetiger Funktionen.- 2.3.3 Stetige Funktionen in naturwissenschaftlichen Zusammenhängen.- 2.4 Vermischtes zu Funktionen mehrerer Variablen.- 2.4.1 Erweiterung einiger Begriffe.- 2.4.2 Kugelflächenfunktionen.- 2.4.3 Bemerkungen über vektorielle Ortsfunktionen (Vektorfelder).- 3. Differentialrechnung von Funktionen einer Variablen.- 3.1 Der Differentialquotient einer Funktion.- 3.1.1 Der Differentialquotient als Lösung des Tangentenproblems.- 3.1.2 Der Differentialquotient als abgeleitete Funktion.- 3.1.3 Differentiale.- 3.1.4 Naturwissenschaftliche Anwendungen?.- 3.2 Das Differenzieren.- 3.2.1 Die Differentiation analytisch gegebener Funktionen; allgemeine Differentiationsregeln.- 3.2.2 Die Differentiation numerisch gegebener Funktionen.- 3.2.3 Die Differentiation graphisch gegebener Funktionen.- 3.3 Höhere Ableitungen.- 3.4 Einige praktische Anwendungen der Differentialrechnung.- 3.4.1 Lineare Approximation von Funktionen und Fehlerdiskussion.- 3.4.2 Ableitungen als Hilfsmittel der Kurvendiskussion.- 3.4.3 Variation von Parametern; Anpassung und Ausgleichsrechnung.- 3.4.4 Behebung von Unbestimmtheiten.- 3.5 Potenzreihenentwicklung einer Funktion.- 3.5.1 Beschreibung von Meßergebnissen durch ganze rationale Funktionen.- 3.5.2 Entwicklung einer analytisch gegebenen Funktion in eine Potenzreihe.- 3.5.3 Einiges über unendliche Reihen.- 3.5.4 Beispiele.- 4. Differentialrechnung von Funktionen zweier (und mehrerer) Variablen.- 4.1 Neue Gesichtspunkte bei der Erweiterung der Differentialrechnung.- 4.1.1 Die verschiedenen Differentialquotienten und das Rechnen damit.- 4.1.2 Wechsel der Variablen.- 4.1.3 Funktionaldeterminanten als Rechenhilfsmittel.- 4.2 Einige Anwendungen.- 4.3 Differentialrechnung mit vektoriellen Größen.- 5. Integralrechnung von Funktionen einer Variablen.- 5.1 Stammfunktion und Integral einer Funktion.- 5.1.1 Die Stammfunktion einer Funktion.- 5.1.2 Das Integral als Lösung des Flächenproblems.- 5.1.3 Der Zusammenhang zwischen Stammfunktion und Integral.- 5.2 Das Integrieren.- 5.2.1 Die Integration analytisch gegebener Funktionen; allgemeine Integrationsregeln.- 5.2.2 Die Integration numerisch gegebener Funktionen.- 5.2.3 Die Integration graphisch gegebener Funktionen.- 5.3 Definition von Funktionen durch Integrale.- 5.4 Die Integration einfacher Differentialgleichungen.- 5.4.1 Allgemeine Vorbemerkungen.- 5.4.2 Einige Lösungsschemata und Lösungsbeispiele.- 5.4.3 Differentialgleichungen spezieller Funktionen.- 6. Integralrechnung von Funktionen zweier (und mehrerer) Variablen.- 6.1 Anschauliche Einführung.- 6.2 Linienintegrale.- 6.2.1 Das allgemeine Kurvenintegral und seine Berechnung.- 6.2.2 Wegunabhängige Kurvenintegrale.- 6.3 Flächenintegrale.- 6.4 Integralrechnung mit vektoriellen Größen.- 7. Ein Blick auf die Funktionentheorie.- 7.1 Funktionen einer komplexen Variablen und ihre Darstellung.- 7.2 Differential- und Integralrechnung im Falle einer komplexen Variablen.- Zwischenbemerkung.- 8. Vektortransformationen im Dreidimensionalen.- 8.1 Koordinatentransformation bei Drehung der Basis.- 8.2 Vektortransformation in fester Basis.- 8.2.1 Transformation eines Vektors durch Drehung.- 8.2.2 Lineare Transformation eines Vektors.- 8.2.3 Einiges über Tensoren.- 9. Matrizen und Determinanten.- 9.1 Matrizen.- 9.1.1 Matrizenrechnung.- 9.1.2 Transformation von Matrizen.- 9.2 Determinanten und weitere Charakteristika von Matrizen.- 9.2.1 Die Determinante und ihre Berechnung.- 9.2.2 Der Rang einer Matrix.- 9.2.3 Zwei Exempel: Reziproke Matrizen, orthogonale Matrizen.- 9.3 Einiges über lineare Gleichungssysteme.- 9.4 Eigenwerte von Matrizen.- 9.4.1 Diagonalisierung einer symmetrischen Matrix.- 9.4.2 Eigenwerte und Eigenvektoren einer symmetrischen Matrix.- 9.4.3 Gleichzeitige Diagonalisierung und gemeinsame Eigenvektoren zweier Matrizen.- 9.4.4 Ergänzungen zum Thema Matrizentransformation.- 9.4.5 Physikalisch-chemische Fragen: Ausblick auf Anwendungen.- 10. Gruppen.- 10.1 Die Gruppe als algebraische Struktur.- 10.1.1 Erste Beispielgruppe.- 10.1.2 Gruppenaxiome und ergänzende Begriffe.- 10.2 Darstellungen von Gruppen.- 10.2.1 Die Darstellung durch Matrizensysteme.- 10.2.2 Irreduzible Darstellungen.- 10.2.3 Zweite Beispielgruppe.- 10.2.4 Charaktere.- 10.2.5 Zum Begriff „Produkt„ in der Gruppentheorie.- 10.3 Einige Bemerkungen über Symmetriegruppen.- 11. Vektorräume höherer Dimension.- 11.1 Die Verallgemeinerung des Vektorbegriffs.- 11.1.1 Der lineare Vektorraum.- 11.1.2 Vektorraum mit Skalarprodukt.- 11.1.3 Ergänzungen.- 11.2 Funktionen als Vektoren.- 11.2.1 Die Interpretation einer Funktion als Vektor.- 11.2.2 Transformation von Vektoren, die Funktionen sind.- 12. Orthogonale Funktionensysteme.- 12.1 Entwicklung nach orthogonalen Funktionen.- 12.2 Entwicklung von Funktionen einer Variablen nach trigonometrischen Funktionen (Fourierentwicklung).- 12.2.1 Basisfunktionen und Entwicklungskoeffizienten der Fourierreihe.- 12.2.2 Fourierreihe als Spektrum.- 12.2.3 Das Spektrum nichtperiodischer Funktionen (Fourierintegral).- 12.3 Entwicklung von Funktionen zweier Variablen nach Kugelflächenfunktionen.- 13. Differentialgleichungen.- 13.1 Eigenwerte bei Differentialgleichungen.- 13.2 Lineare Differentialgleichungen.- 13.2.1 Einiges zur Integration einer gewöhnlichen linearen Differentialgleichung.- 13.2.2 Einiges über Systeme von linearen Differentialgleichungen.- 13.3 Partielle Differentialgleichungen.- 13.3.1 Die Wellengleichung.- 13.3.2 Die Schrödingergleichung.

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Book SynopsisThis book presents the basic theory and application of the Monte Carlo method to the electronic structure of atoms and molecules. It assumes no previous knowledge of the subject, only a knowledge of molecular quantum mechanics at the first-year graduate level. A working knowledge of traditional ab initio quantum chemistry is helpful, but not essential.Some distinguishing features of this book are:Table of ContentsReview of ab initio quantum chemistry; introduction to Monte Carlo methods; the variational Monte Carlo method; quantum Monte Carlo; exact Green's function methods; released node methods; excited states; properties other than energy; determination of interaction potentials, stationary geometries, energy derivatives; valence-electron and acceleration methods.

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Book SynopsisThis book presents the basic theory and application of the Monte Carlo method to the electronic structure of atoms and molecules. It assumes no previous knowledge of the subject, only a knowledge of molecular quantum mechanics at the first-year graduate level. A working knowledge of traditional ab initio quantum chemistry is helpful, but not essential.Some distinguishing features of this book are:Table of ContentsReview of ab initio quantum chemistry; introduction to Monte Carlo methods; the variational Monte Carlo method; quantum Monte Carlo; exact Green's function methods; released node methods; excited states; properties other than energy; determination of interaction potentials, stationary geometries, energy derivatives; valence-electron and acceleration methods.

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Book SynopsisThis book addresses the problem of teaching the Electronic Structure and Chemical Bonding of atoms and molecules to high school and university students. It presents the outcomes of thorough investigations of some teaching methods as well as an unconventional didactical approach which were developed during a seminar for further training organized by the University of Bordeaux I for teachers of the physical sciences.The text is the result of a collective effort by eleven scientists and teachers: physicists and chemists doing research at the university or at the CRNS, university professors, and science teachers at high-school or university level.While remaining wide open to the latest discoveries of science, the text also offers a large number of problems along with their solutions and is illustrated by several pedagogic suggestions. It is intended for the use of teachers and students of physics, chemistry, and of the physical sciences in general.Table of ContentsPart 1 Historical survey: main events in the history of chemical bonding. Part 2 Theoretical bases for the description of molecular electronic structure and chemical bonding - quantum mechanics and molecular symmetry: quantum bases of chemical bonding; molecular symmetry, its description and consequences. Part 3 Two complementary descriptions of chemical bonding - mechanical treatment of chemical bonding: fundamentals; applications. Part 4 Orbitals in chemical bonding - applications and limits: one-electron treatment of many-electron particles; MOs and chemical bonding; beyond the one-electron description.

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Book SynopsisThis volume focuses on the use of quantum theory to understand and explain experiments in organic chemistry. High level ab initio calculations, when properly performed, are useful in making quantitative distinctions between various possible interpretations of structures, reactions and spectra. Chemical reasoning based on simpler quantum models is, however, essential to enumerating the likely possibilities. The simpler models also often suggest the type of wave function likely to be involved in ground and excited states at various points along reaction paths. This preliminary understanding is needed in order to select the appropriate higher level approach since most higher level models are designed to describe improvements to some reasonable zeroth order wave function. Consequently, most of the chapters in this volume begin with experimental facts and model functions and then progress to higher level theory only when quantitative results are required.In the first chapter, Zimmerman discusses a wide variety of thermal and photochemical reactions of organic molecules. Gronert discusses the use of ab initio calculations and experimental facts in deciphering the mechanism of β-elimination reactions in the gas phase. Bettinger et al focus on carbene structures and reactions with comparison of the triplet and singlet states. Next, Hrovat and Borden discuss more general molecules with competitive triplet and singlet contenders for the ground state structure. Cave explains the difficulties and considerations involved with many of the methods and illustrates the difficulties by comparing with the UV spectra of short polyenes. Jordan et al discuss long-range electron transfer using model compounds and model Hamiltonians. Finally, Hiberty discusses the breathing orbital valence bond model as a different approach to introducing the crucial σπ correlation that is known to be important in organic reactions.

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Book SynopsisThis book provides a detailed presentation of modern quantum theories for treating the reaction dynamics of small molecular systems. Its main focus is on the recent development of successful quantum dynamics theories and computational methods for studying the molecular reactive scattering process, with specific applications given in detail for a number of benchmark chemical reaction systems in the gas phase and the gas surface. In contrast to traditional books on collision in physics focusing on abstract theory for nonreactive scattering, this book deals with both the development and the application of the modern reactive or rearrangement scattering theory, and is written in a fashion in which the development of the reactive scattering theory is closely coupled with its computational aspects for practical applications for realistic molecular reactions. The volume includes such topics as methods for calculating rovibrational states of molecules, fundamental quantum theory for scattering (nonreactive and reactive), modern time-independent computational methods for reactive scattering, general time-dependent wave packet methods for reactive scattering, dynamics theory of chemical reactions, dynamics of molecular fragmentation, semiclassical description of quantum mechanics, and also some useful appendices.The book is intended for the reader to not only understand the molecular reaction dynamics from the fundamental scattering theory, but also utilize the provided computational methodologies in their practical applications. It should benefit graduate students and researchers in the field of chemical physics.

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Book SynopsisThis study guide aims at explaining theoretical concepts encountered by practitioners applying theory to molecular science. This is a collection of short chapters, a manual, attempting to walk the reader through two types of topics: (i) those that are usually covered by standard texts but are difficult to grasp and (ii) topics not usually covered, but are essential for successful theoretical research. The main focus is on the latter. The philosophy of this book is not to cover a complete theory, but instead to provide a set of simple study cases helping to illustrate main concepts. The focus is on simplicity. Each section is made deliberately short, to enable the reader to easily grasp the contents. Sections are collated in themed chapters, and the advantage is that each section can be studied separately, as an introduction to more in-depth studies. Topics covered are related to elasticity, electrostatics, molecular dynamics and molecular spectroscopy, which form the foundation for many presently active research areas such as molecular biophysics and soft matter physics. The notes provide a uniform approach to all these areas, helping the reader to grasp the basic concepts from a common set of theoretical tools.Table of ContentsVectors and Tensors; Electrostatics; Classical Mechanics; Quantum Mechanics; Statistical Mechanics; Liquids; Diffusion; Molecular Hydrodynamics; Elasticity; Solutions and Electrolytes; Spectra; Solvation;

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Book SynopsisThis study guide aims at explaining theoretical concepts encountered by practitioners applying theory to molecular science. This is a collection of short chapters, a manual, attempting to walk the reader through two types of topics: (i) those that are usually covered by standard texts but are difficult to grasp and (ii) topics not usually covered, but are essential for successful theoretical research. The main focus is on the latter. The philosophy of this book is not to cover a complete theory, but instead to provide a set of simple study cases helping to illustrate main concepts. The focus is on simplicity. Each section is made deliberately short, to enable the reader to easily grasp the contents. Sections are collated in themed chapters, and the advantage is that each section can be studied separately, as an introduction to more in-depth studies. Topics covered are related to elasticity, electrostatics, molecular dynamics and molecular spectroscopy, which form the foundation for many presently active research areas such as molecular biophysics and soft matter physics. The notes provide a uniform approach to all these areas, helping the reader to grasp the basic concepts from a common set of theoretical tools.Table of ContentsVectors and Tensors; Electrostatics; Classical Mechanics; Quantum Mechanics; Statistical Mechanics; Liquids; Diffusion; Molecular Hydrodynamics; Elasticity; Solutions and Electrolytes; Spectra; Solvation;

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Book SynopsisWhat Arieh Warshel and fellow 2013 Nobel laureates Michael Levitt and Martin Karplus achieved — beginning in the late 1960s and early 1970s when computers were still very primitive — was the creation of methods and programs that describe the action of biological molecules by 'multiscale models'. In this book, Warshel describes this fascinating, half-century journey to the apex of science.From Kibbutz Fishponds to The Nobel Prize is as much an autobiography as an advocacy for the emerging field of computational science. We follow Warshel through pivotal moments of his life, from his formative years in war-torn Israel in an idealistic kibbutz that did not encourage academic education; to his time in the army and his move to the Technion where he started in his obsession of understanding the catalytic power of enzymes; to his eventual scientific career which took him to the Weizmann Institute, Harvard University, Medical Research Council, and finally University of Southern California. We read about his unique contributions to the elucidation of the molecular basis of biological functions, which are combined with instructive stories about his persistence in advancing ideas that contradict the current dogma, and the nature of his scientific struggle for recognition, both personal and for the field to which he devoted his life. This is, in so many ways, more than just a memoir: it is a profoundly inspirational tale of one man's odyssey from a kibbutz that did not allow him to go to a university to the pinnacle of the scientific world, highlighting that the correct mixture of persistence, talent and luck can lead to a Nobel Prize.

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Book SynopsisWhat Arieh Warshel and fellow 2013 Nobel laureates Michael Levitt and Martin Karplus achieved — beginning in the late 1960s and early 1970s when computers were still very primitive — was the creation of methods and programs that describe the action of biological molecules by 'multiscale models'. In this book, Warshel describes this fascinating, half-century journey to the apex of science.From Kibbutz Fishponds to The Nobel Prize is as much an autobiography as an advocacy for the emerging field of computational science. We follow Warshel through pivotal moments of his life, from his formative years in war-torn Israel in an idealistic kibbutz that did not encourage academic education; to his time in the army and his move to the Technion where he started in his obsession of understanding the catalytic power of enzymes; to his eventual scientific career which took him to the Weizmann Institute, Harvard University, Medical Research Council, and finally University of Southern California. We read about his unique contributions to the elucidation of the molecular basis of biological functions, which are combined with instructive stories about his persistence in advancing ideas that contradict the current dogma, and the nature of his scientific struggle for recognition, both personal and for the field to which he devoted his life. This is, in so many ways, more than just a memoir: it is a profoundly inspirational tale of one man's odyssey from a kibbutz that did not allow him to go to a university to the pinnacle of the scientific world, highlighting that the correct mixture of persistence, talent and luck can lead to a Nobel Prize.

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Book Synopsis'Clary's account makes for fascinating reading, not least because of its clear style and copious citation of primary sources and original scientific articles. The author provides a compelling narrative of … Schrödinger's departure in 1933 from a highly eminent position at the University of Berlin to a precarious, untenured position at Magdalen College … with political and scientific considerations deftly woven together.' [Read Full Review]ScienceErwin Schrödinger was one of the greatest scientists of all time but it is not widely known that he was a Fellow at Magdalen College, Oxford in the 1930s. This book is an authoritative account of Schrödinger's time in Oxford by Sir David Clary, an expert on quantum chemistry and a former President of Magdalen College, who describes Schrödinger's remarkable life and scientific contributions in a language that can be understood by all. Through access to many unpublished manuscripts, the author reveals in unprecedented detail the events leading up to Schrödinger's sudden departure from Berlin in 1933, his arrival in Oxford and award of the Nobel Prize, his dramatic escape from the Nazis in Austria to return to Oxford, and his urgent flight from Belgium to Dublin at the start of the Second World War.The book presents many acute observations from Schrödinger's wife Anny and his daughter Ruth, who was born in Oxford and became an acquaintance of the author in the last years of her life. It also includes a remarkable letter sent to Schrödinger in Oxford from Adolf Hitler, thanking him for his services to the state as a professor in Berlin. Schrödinger's intense interactions with other great scientists who were also refugees during this period, including Albert Einstein and Max Born, are examined in the context of the chaotic political atmosphere of the time. Fascinating anecdotes of how this flamboyant Austrian scientist interacted with the President and Fellows of a highly traditional Oxford College in the 1930s are a novel feature of the book.A gripping and intimate narrative of one of the most colourful scientists in history, Schrödinger in Oxford explains how his revolutionary breakthrough in quantum mechanics has become such a central feature in 21st century science.

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Book Synopsis'Clary's account makes for fascinating reading, not least because of its clear style and copious citation of primary sources and original scientific articles. The author provides a compelling narrative of … Schrödinger's departure in 1933 from a highly eminent position at the University of Berlin to a precarious, untenured position at Magdalen College … with political and scientific considerations deftly woven together.' [Read Full Review]ScienceErwin Schrödinger was one of the greatest scientists of all time but it is not widely known that he was a Fellow at Magdalen College, Oxford in the 1930s. This book is an authoritative account of Schrödinger's time in Oxford by Sir David Clary, an expert on quantum chemistry and a former President of Magdalen College, who describes Schrödinger's remarkable life and scientific contributions in a language that can be understood by all. Through access to many unpublished manuscripts, the author reveals in unprecedented detail the events leading up to Schrödinger's sudden departure from Berlin in 1933, his arrival in Oxford and award of the Nobel Prize, his dramatic escape from the Nazis in Austria to return to Oxford, and his urgent flight from Belgium to Dublin at the start of the Second World War.The book presents many acute observations from Schrödinger's wife Anny and his daughter Ruth, who was born in Oxford and became an acquaintance of the author in the last years of her life. It also includes a remarkable letter sent to Schrödinger in Oxford from Adolf Hitler, thanking him for his services to the state as a professor in Berlin. Schrödinger's intense interactions with other great scientists who were also refugees during this period, including Albert Einstein and Max Born, are examined in the context of the chaotic political atmosphere of the time. Fascinating anecdotes of how this flamboyant Austrian scientist interacted with the President and Fellows of a highly traditional Oxford College in the 1930s are a novel feature of the book.A gripping and intimate narrative of one of the most colourful scientists in history, Schrödinger in Oxford explains how his revolutionary breakthrough in quantum mechanics has become such a central feature in 21st century science.

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Book SynopsisComputational spectroscopy and computational quantum chemical dynamics is a vast field in physical chemistry. Significant part of this field is developed based on the concepts of time-dependent quantum mechanics and its numerical implementations.This book gives an introduction to the Time-Dependent Quantum Chemistry for use with any introductory college/university course in optics, spectroscopy, kinetics, dynamics, or experimental physical chemistry or chemical physics of the kind usually taken by undergraduate and graduate students in physical chemistry. In this book, different concepts of time-dependent quantum mechanics are systematically presented by first giving emphasis on the contrasting viewpoint of classical and quantum mechanical motion of a particle, then by demonstrating the ways to find classical flavour in quantum dynamics, thereafter by formally defining the wavepacket which represents a quantum particle and finally by demonstrating numerical methods to explore the wavepacket dynamics in one dimension. Along with the analytical theory, accompanying Python chapters in this book take readers to a hands-on tour with Python programming by first giving them a quick introduction to the Python programming, then by introducing the position-space grid representation of the wavefunction, thereafter, by making them familiarized with the Fourier transform to represent the discretized wavefunction in momentum space, subsequently by showing the Python-based methodologies to express Hamiltonian operator in matrix form and finally by demonstrating the entire Python program which solves the wavepacket dynamics in one dimension under influence of time-independent Hamiltonian following split-operator approach.Rigorous class-testing of the presented lecture notes at the Indian Institute of Science, GITAM University and at NPTEL platform reveals that physical chemistry students, after thoroughly going through all chapters, not only develop an in-depth understanding of the wavepacket dynamics and its numerical implementations, but also start successfully writing their own Python code for solving any one dimensional wavepacket dynamics problem.

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Book SynopsisThis is a textbook on thermodynamics of materials for junior/senior undergraduate students and first-year graduate students as well as a reference book for researchers who would like to refresh their understanding of thermodynamics.The textbook employs a plain language to explain the thermodynamic concepts and quantities. It embraces the mathematical beauty and rigor of Gibbs thermodynamics through the fundamental equation of thermodynamics from which all thermodynamic properties of a material can be derived. However, a reader with basic first-year undergraduate calculus skills will be able to get through the book without difficulty. One unique feature of this textbook is the descriptions of the step-by-step procedures for computing all the thermodynamic properties from the fundamental equation of thermodynamics and all the thermodynamic energies from a set of common, experimentally measurable thermodynamic properties, supplemented with ample numerical examples.Another unique feature of this textbook is its emphasis on the concept of chemical potential and its applications to phase equilibria in single component systems and binary solutions, chemical reaction equilibria, and lattice and electronic defects in crystals. The concept of chemical potential is introduced at the very beginning of the book together with temperature and pressure. It avoids or minimizes the use of terms such as molar Gibbs free energy, partial molar Gibbs free energy, or Gibbs potential because molar Gibbs free energy or partial molar Gibbs free energy is precisely the chemical potential of a material or a component. It is the chemical potential that determines the stability of chemical species, compounds, and phases and their tendency to chemically react to form new species, transform to new physical state, and migrate from one spatial location to another. Therefore, it is the chemical potential differences or gradients that drive essentially all materials processes of interest. A reader after finishing reading the book is expected to not only achieve a high-level fundamental understanding of thermodynamics but also acquire the analytical skills of applying thermodynamics to determining materials equilibrium and driving forces for materials processes.Table of ContentsIntroduction and Definitions.- First and Second Laws of Thermodynamics.- Fundamental Equation of Thermodynamics.- Thermodynamic Properties.- Internal Energy.- Enthalpy.- Entropy.- Gibbs Free Energy.- Chemical Potential.- Thermodynamic Equilibrium and Stability Conditions.- Thermomechanical Equilibria: Phase Equilibria with Respect to Temperature and Pressure.- Chemical Equilibria: Thermodynamics of Chemical Species Mixing to Form Solutions.- Phase Equilibria in Binary Systems and Graphical Representations.- Chemical Reaction Equilibria and Graphical Representations.- Defect Equilibria: Chemical Potentials of Electronic and Atomic Defects.- Energy Conversions: Electrochemical energy conversion.

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Book SynopsisThis book covers recent advances of the fragment molecular orbital (FMO) method, consisting of 5 parts and a total of 30 chapters written by FMO experts. The FMO method is a promising way to calculate large-scale molecular systems such as proteins in a quantum mechanical framework. The highly efficient parallelism deserves being considered the principal advantage of FMO calculations. Additionally, the FMO method can be employed as an analysis tool by using the inter-fragment (pairwise) interaction energies, among others, and this feature has been utilized well in biophysical and pharmaceutical chemistry. In recent years, the methodological developments of FMO have been remarkable, and both reliability and applicability have been enhanced, in particular, for non-bio problems. The current trend of the parallel computing facility is of the many-core type, and adaptation to modern computer environments has been explored as well. In this book, a historical review of FMO and comparison to other methods are provided in Part I (two chapters) and major FMO programs (GAMESS-US, ABINIT-MP, PAICS and OpenFMO) are described in Part II (four chapters). dedicated to pharmaceutical activities (twelve chapters). A variety of new applications with methodological breakthroughs are introduced in Part IV (six chapters). Finally, computer and information science-oriented topics including massively parallel computation and machine learning are addressed in Part V (six chapters). Many color figures and illustrations are included. Readers can refer to this book in its entirety as a practical textbook of the FMO method or read only the chapters of greatest interest to them.Table of ContentsPart 1: Positioning of FMO.- Fragment molecular orbital method as cluster expansion.- Comparison of various fragmentation methods for quantum chemical calculations of large molecular systems.- Part 2: Programs.- Recent development of the fragment molecular orbital method in GAMESS.- The ABINIT-MP program.- PAICS: Development of An Open-Source Software of Fragment Molecular Orbital Method for Biomolecule.- Open-Architecture Program of Fragment Molecular Orbital Method for Massive Parallel Computing (OpenFMO) with GPU Acceleration.- Part 3: Pharmaceutical activities.- How to perform FMO calculation in Drug Discovery.- FMO drug design consortium.- Development of an automated FMO calculation protocol to construction of FMO database.- Application of FMO to ligand design: SBDD, FBDD, and protein–protein interaction.- Drug Discovery Screening by Combination of X-ray Crystal Structure Analysis and FMO Calculation .- Cooperative study combining X-ray crystal structure analysis and FMO calculation: Interaction analysis of FABP4 inhibitors.- Application of FMO for protein-ligand binding affinity prediction.- Recent Advances of In Silico Drug Discovery: Integrated Systems of Informatics and Simulation.- Pharmaceutical Industry - Academia Cooperation.- Elucidating the efficacy of clinical drugs using FMO.- Application of Fragment Molecular Orbital Calculations to Functional Analysis of Enzymes.- AnalysisFMO toolkit: A PyMOL plugin for 3D-visualization of interaction energies in proteins (3D-VIEP) calculated by the FMO method.- Part 4: New methods and applications.- FMO interfaced with Molecular Dynamics simulation.- Linear Combination of Molecular Orbitals of Fragments (FMO-LCMO) Method: Its Application to Charge Transfer Studies.- Modeling of solid and surface.- Development of the analytic second derivatives for the fragment molecular orbital method .- The FMO-DFTB Method.- Self-consistent treatment of solvation structure with electronic structure based on 3D-RISM theory.- New methodology and framework.- New methodology and framework Information science-assisted analysis of FMO results for Drug Design.- Extension to multiscale simulations.- FMO-based investigations of excited-state dynamics in molecular aggregates.- Application of the fragment molecular orbital method to organic charge transport materials in xerography: a feasibility study and a charge mobility analysis.- Group molecular orbital method and Python-based programming approach.- Multi-level parallelization of the fragment molecular orbital method in GAMESS.

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Book SynopsisThis book is a stop-gap contribution to the science and technology of carbon plasmas and carbon vapors. It strives to cover two strongly related fields: the molecular quantum theory of carbon plasmas and carbon nanostructures; and the molecular and atomic spectroscopy of such plasmas and vapors. These two fields of research are strongly intertwined and thus reinforce one another.Even though the use of carbon nanostructures is increasing by the day and their practical uses are emerging, there is no modern review on carbon plasmas, especially from molecular theoretical and spectroscopic viewpoints. The importance of the present book is therefore great from both educational and practical aspects. This review might be the first step towards bringing such textbooks into existence for university education. Similarly, for applied and engineering works in carbon nanostructures, the book provides a theoretical salient point for technologists in the field.Table of ContentsKinetic and Diagnostic Studies of Carbon-Containing Plasmas Using Laser Absorption Techniques; Optical Emission Spectroscopy of C2 and C3 Molecules in Laser Ablation Carbon Plasma; Spectroscopic Studies on Laser-Prouced Carbon Vapor; Spectroscopy of Carbon Nanotube Production Processes; Electronic Spectra of Small Carbon Clusters in the Gas Phase; Carbon Stars; Laser Spectroscopy of Transient Carbon Species in the Context of Soot Formation; Dynamics of Laser-Ablated Carbon Plasma for Thin Film Deposition: Spectroscopic and Imaging Applications; Spectroscopy of Carbon Clusters at Heavy Ion Storage Rings.

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Book SynopsisHyperspherical harmonics are extremely useful in nuclear physics and reactive scattering theory. However, their use has been confined to specialists with very strong backgrounds in mathematics. This book aims to change the theory of hyperspherical harmonics from an esoteric field, mastered by specialists, into an easily-used tool with a place in the working kit of all theoretical physicists, theoretical chemists and mathematicians. The theory presented here is accessible without the knowledge of Lie-groups and representation theory, and can be understood with an ordinary knowledge of calculus. The book is accompanied by programs and exercises designed for teaching and practical use.

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Book SynopsisThis is a comprehensive overview of state-of-the-art computational methods based on orbital-free formulation of density functional theory completed by the most recent developments concerning the exact properties, approximations, and interpretations of the relevant quantities in density functional theory.The book is a compilation of contributions stemming from a series of workshops which had been taking place since 2002. It not only chronicles many of the latest developments but also summarises some of the more significant ones. The chapters are mainly reviews of sub-domains but also include original research.Table of ContentsPart 1: Density Functional for the Kinetic Energy and Its Applications in Orbital-Free DFT Simulations: From the Hohenberg-Kohn Theory to the Kohn-Sham Equations (Y A Wang & P Xiang); Accurate Computation of the Non-Interacting Kinetic Energy from Electron Densities (F A Bulat & W Yang); The Single-Particle Kinetic Energy of Many-Fermion Systems: Transcending the Thomas-Fermi plus Von Weizsacker Method (G G N Angilella & N H March); An Orbital Free ab initio Method: Applications to Liquid Metals and Clusters (A Aguado, D J Gonzalez, L E Gonzalez, J M Lopez, S Nunez & M J Stott); Electronic Structure Calculations at Macroscopic Scales Using Orbital-Free DFT (B G Radhakrishnan & V Gavini); Properties of Hot and Dense Matter by Orbital-Free Molecular Dynamics (F Lambert, J Clerouin, J-F Danel, L Kazandjian & S Mazevet); Shell-Correction and Orbital-Free Density-Functional Methods for Finite Systems (C Yannouleas & U Landman); Finite Element Approximations in Orbital-Free Density Functional Theory (H Chen & A Zhou); Part 2: The Functional for the Non-Additive Kinetic Energy and Its Applications in Numerical Simulations: Non-Additive Kinetic Energy and Potential in Analytically Solvable Systems and Their Approximated Counterparts (T A Wesolowski & A Savin); Towards the Description of Covalent Bonds in Subsystem Density-Functional Theory (Ch R Jacob & L Visscher); Orbital-Free Embedding Calculations of Electronic Spectra (J Neugebauer); On the Principal Difference Between the Exact and Approximate Frozen-Density Embedding Theory (O V Gritsenko); Part 3: Kinetic Energy Functional and Information Theory: Analytic Approach and Monte Carlo Sampling for Electron Correlations (L M Ghiringhelli & L Delle Site); Kinetic Energy and Fisher Information (A Nagy); Quantum Fluctuations, Dequantization, Information Theory and Kinetic-Energy Functionals (I P Hamilton, R A Mosna & L Delle Site); Part 4: Appendix: Semilocal Approximations for the Kinetic Energy (F Tran & T A Wesolowski).

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Book SynopsisThis unique volume offers a clear perspective of the relevant methodology relating to the chemical theory of the next generation beyond the Born-Oppenheimer paradigm. It bridges the gap between cutting-edge technology of attosecond laser science and the theory of chemical reactivity. The essence of this book lies in the method of nonadiabatic electron wavepacket dynamic, which will set a new foundation for theoretical chemistry.In light of the great progress of molecular electronic structure theory (quantum chemistry), the authors show a new direction towards nonadiabatic electron dynamics, in which quantum wavepackets have been theoretically and experimentally revealed to bifurcate into pieces due to the strong kinematic interactions between electrons and nuclei.The applications range from nonadiabatic chemical reactions in photochemical dynamics to chemistry in densely quasi-degenerated electronic states that largely fluctuate through their mutual nonadiabatic couplings. The latter is termed as “chemistry without the potential energy surfaces” and thereby virtually no theoretical approach has been made yet.Restarting from such a novel foundation of theoretical chemistry, the authors cast new light even on the traditional chemical notions such as the Pauling resonance theory, proton transfer, singlet biradical reactions, and so on.Table of ContentsBasic Framework of Theoretical Chemistry; Nuclear Dynamics on Adiabatic Electronic Potential Energy Surfaces; Breakdown of the Born-Oppenheimer Approximation; Classic Theories of Nonadiabatic Transitions and Ideas Behind; Direct Observation of the Wavepacket Bifurcation due to Nonadiabatic Transitions; Nonadiabatic Electron Wavepacket Dynamics in Path Branching Representation; Dynamical Electron Theory for Chemical Reactions; Molecular Electron Dynamics in Laser Fields;

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