Structural Chemistry (eBook)

Mihai V. Putz is currently an Associate Professor of theoretical and computational physical chemistry at the West University of Timisoara, Romania. He has an interdisciplinary training and research experience in physics, chemistry and spectroscopy and has been involved in numerous postdoctoral projects at the University of Calabria, Italy and in the Free University of Berlin, Germany. He has made valuable contributions to computational, quantum, and physical chemistry through seminal works published in numerous international journals. He is also a member of many professional societies and has received several national and international awards. In 2010 Mihai V. Putz was declared through a national competition the Best Researcher of Romania, while in 2013 he was recognized among the first Dr.-Habil. in Chemistry in Romania. From 2014 he became a full member of International Academy of Mathematical Chemistry.Fanica Cimpoesu graduated from the University of Bucharest. His PhD work, under the guidance of I. B. Bersuker, was dedicated to the orbital models of vibronic effects. Self-didactically, he approached several other topics such as organometallic stereochemistry and molecular magnetism, continuously enlarging his research area. The trademark of Fanica Cimpoesu's work is finding new methodological clues and heuristic viewpoints at the borderline between theory, computation and experimental chemistry. Research stages at the universities of Leuven (Prof. A. Ceulemans), Tokyo (Prof. K. Hirao) and Fribourg (Prof. C. A. Daul) are acknowledged as emulative events in his curriculum vitae.Marilena Ferbinteanu is an Associate professor at the University of Bucharest, Faculty of Chemistry, Inorganic Chemistry Department. She graduated and received her MS, PhD degrees in inorganic chemistry, at the same university. In 1999 she was awarded with the Alexander Von Humboldt fellowship (Prof. Herbert Roesky) and in 2004 with the Japan Society for Promotion Science fellowship (Prof. Masahiro Yamashita). She had several postdoctoral stages in Germany (Institute of Inorganic Chemistry, Göttingen, 2001) and in Japan (Ochanomizu University, Prof. Yutaka Fukuda, 2002; Tokyo Metropolitan University, Prof. Masahiro Yamashita and Hitoshi Miyasaka, 2003). In 2010 she won the first UEFISCDI-PCCE grant competition. She promoted advanced structural-property correlations combining the experiment, structural and applied coordinative chemistry, magnetic and optic properties with theory.

Foreword I 5
Foreword II 5
Preface 11
Acknowledgements 18
Contents 19
About the Authors 27
1 Atomic Structure and Quantum Mechanics 29
Abstract 29
1.1 The Long Road from Democritus to Bohr 30
1.1.1 Arcadian Antiquity 30
1.1.2 Along the Centuries, to the Positivist Era 32
1.1.3 Bohr’s Atomic Model: Natura Facit Saltus! 33
1.2 The Dawn of Quantum Theory and the Founding Fathers 39
1.2.1 The Revolutionary Milieu and Quantum Mechanics 39
1.2.2 Modus Operandi: Waves and Operators 40
1.2.3 The Schrödinger Equation and Schrödinger’s Cat 45
1.2.4 The Heisenberg Equations: Uncertainty and Matrix Mechanics 47
1.2.5 Hamiltonian Matrices, Non-orthogonal Bases, Variational Methods 51
1.3 Atomic Shell Structure and the Spherical Harmonics 55
1.3.1 Atomic Orbitals and Quantum Numbers: The Radial-Angular Factorization of the Atomic Wave Functions 55
1.3.2 Intuitive Primer on the Pattern of Atomic Orbitals 57
1.3.3 Toward Setting the Schrödinger Equation in Atoms 62
1.3.4 The Schrödinger Equation for the One-Electron Atom: The Radial Part 64
1.3.5 A Qualitative Analysis of the Radial Nodal Structure of the Atomic Orbitals 68
1.3.6 The Complete Analytic Formulas of the Atomic Orbitals 70
1.3.7 A Philosophical Divagation 72
1.4 Elements of Relativistic Quantum Mechanics 73
1.4.1 The Electronic Spin, the Missing Link Between Atomic Shell Scheme and Chemical Systematics from the Periodic Table of Elements 73
1.4.2 First Principles of Relativistic Quantum Mechanics: Klein-Gordon and Dirac Equations 77
1.4.3 The Quantum Numbers of Dirac Relativistic Equations 80
1.4.4 The Two Quantum Worlds of Dirac Equations: Small and Large Spinor Components 81
1.4.5 Toward the Relativistic Atom: Electromagnetism Instead of Electrostatics 83
1.4.6 Concluding the Types of Relativistic Hamiltonian Terms: Zeeman, Spin–Orbit, Mass-Correction, Darwin, Breit, Breit-Pauli 86
1.4.7 The Spin–Orbit Coupling: A Term to Remember 88
1.5 Perturbation Theory Application: Quantum Polarizability 93
1.6 Atomic Stability: The Proof by Quantum Path Integrals 103
1.6.1 Schrodinger Equation by Quantum Path Integral 103
1.6.2 Feynman-Kleinert Effective Density Formalism 107
1.6.3 Quantum Smeared Effects and the Stability of Matter 112
1.6.4 Ground State (? ? ?, T ? 0 K) Case 118
1.7 Free and Observed Quantum Evolution: Extended Heisenberg Uncertainly Relationship (HUR) by Path Integrals 121
1.7.1 HUR by Periodic Paths 122
1.7.2 Wave-Particle Ratio Function 125
1.7.3 Extended HUR 127
1.8 Conclusions 131
References 132
2 Wave Function Theories and Electronic Structure Methods: Quantum Chemistry, from Atoms to Molecules 135
Abstract 135
2.1 Poly-electronic Wave Functions from Spin-Orbitals 136
2.1.1 Indiscernible Electrons and Anti-symmetric Wave Functions with Slater Determinants 136
2.1.2 Matrix Elements in a Basis of Slater Determinants: The Slater Rules 141
2.1.3 The Atomic Integrals: The Slater–Condon Symmetry Factorization of the Two-Electron Integrals 147
2.1.4 Orbital and Spin Quantum Numbers in the Poly-electronic Atom: The Spectral Terms 150
2.1.5 Slater Rules at Work: A Hands-On Example on the Helium Atom 157
2.2 Atoms with Many Electrons: A Guided Tour Through Selected Examples 165
2.2.1 Spectral Terms of Main Group Elements: The Li, B, C, N, O, F, Ne Series 165
2.2.2 Spectral Terms of Transition Metal Ions 172
2.2.3 Other Notes: Racah Parameters for Real-Type d Orbitals. Calculation of Slater–Condon Parameters. Approximate Ratios in the Series of Slater–Condon or Racah Parameters 176
2.3 Atomic Spectra in Practical Applications: From Neon Tubes to Warm White Light 180
2.3.1 Fiat Lux! Sunlight and Black Body Radiation 180
2.3.2 Generating Light from Atoms Excited in Plasma 181
2.3.3 Converting the Light Wavelength with Solid-State Phosphors 185
2.4 Back to the Basis! Atomic Basis Sets: Slater versus Gaussian Orbitals and Other Options 190
2.4.1 Deconstructing the Hydrogen-Type Analytic Atomic Orbitals and Recomposing the One-Electron Atom from Slater-Type Primitives 190
2.4.2 A Test with Slater-Type Orbitals (STOs) 198
2.4.3 The Gaussian-Type Orbitals (GTOs): The “Steel and Concrete” of the Massive Development of Quantum Chemistry 200
2.4.4 Caveats on Gaussian-Type Basis Sets 208
2.4.5 Other Options: Plane Waves and Numerical Bases 214
2.5 Ab Initio Methods 222
2.5.1 Hartree–Fock Method: The Simplest Level of Electronic Structure Calculations in Atoms and Molecules 222
2.5.2 Multi-configuration Self-consistent Field Methods: Closer to the Physical Truth and Chemical Realism 228
2.5.3 Valence Bond: A Tribute to the Historical Roots of Bond Theories and Yet a Promising Land 236
2.6 Conclusions 243
References 244
3 Density Functional Theory: From Conceptual Level Toward Practical Functionality 249
Abstract 249
3.1 Background and Principles 250
3.1.1 The Deep Roots of Density Functional Theory 250
3.1.2 The Hohenberg–Kohn Theorems and the Problem of Universals in Electronic Structure 251
3.1.3 A Bit of Maieutics on Exchange and Correlation Holes 255
3.1.4 An Illustration of Density Functional Issues 258
3.1.5 Methods and Concepts in DFT: Kohn–Sham Self-consistent Field, Fractional Occupations, Electronegativity and Chemical Hardness (Electrorigidity) 262
3.1.6 The Chemical Relevance of DFT: Electronegativity Equalization, Maximum Hardness Principle, Hard and Soft Acids and Bases (HSAB) 266
3.1.7 Ways to Approximated Density Functionals 269
3.1.8 Other Issues Related to Density Functional Theory: The DFT+U Methods and an Atomic Model Based on the Interpolation of Spectroscopic Configuration Energies 276
3.1.9 A Phenomenological Model: Energy of Atoms as Continuous Function of Valence Shell Populations 282
3.2 Density Functional Theory in More Detail 294
3.2.1 Density Functionals of Kinetic Energy 294
3.2.2 Density Functionals of Exchange Energy 297
3.2.3 Density Functionals of Correlation Energy 302
3.2.4 Density Functionals of Exchange-Correlation Energy 308
3.3 Conclusions 312
References 313
4 Bond! Chemical Bond: Electronic Structure Methods at Work 318
Abstract 318
4.1 Molecular Structure by Computational Chemistry: A Brief Synopsis 320
4.2 Hartree–Fock Versus Density Functional Theory Computation Simple Samples 324
4.3 Orbitals, the Building Blocks of Electronic Structure 331
4.4 The H2 Molecule: The Simplest Bond Prototype. Phenomenological Models and Calculation Methods 336
4.4.1 The Spin-Coupling Phenomenology of the Chemical Bond 336
4.4.2 Model Calculations on H2 340
4.5 Computational and Conceptual Valence Bond: The Spin Coupling Paradigm at Work 350
4.5.1 Overture to the Valence Bond Calculations 350
4.5.2 Benzene: Valence Bond Versus Complete Active Space 352
4.5.3 Playing with Graphic Rules for Setting a VB Modeling 359
4.6 Mobilis in Mobile: Electrons Moving Around Mobile Nuclei. Floppy Molecules, Unstable Systems, and Chemical Reactions 368
4.6.1 Jahn–Teller and Related Effects. Vibronic Coupling 368
4.6.2 A Simple Approach of the H3 Prototypic System. Example for Reaction Potential Energy Surfaces and E ? E-Type Jahn–Teller Effect 371
4.6.3 The Computational Approach of the Pseudo Jahn–Teller Effect (Second-Order Vibronic Coupling) 378
4.6.4 The Vibronic Orbitals 384
4.6.5 More on the Usage of Vibronic Modeling 389
4.6.5.1 Two State Models of Pseudo Jahn–Teller Effect 389
4.6.5.2 Vibronic Phenomenology of Mixed Valence Systems 392
4.6.5.3 The Use of Vibronic Models to Fit Potential Energy Curves, Surfaces and Hyper-Surfaces 395
4.7 Breaking Symmetry in Quantum Chemistry 400
4.7.1 The Symmetry Breaking of Chemical Field Generation 400
4.7.2 The Inverse Quantum Chemical Problem 404
4.8 Conclusions 409
References 411
5 New Keys for Old Keywords: Hybridization and Aromaticity, Graphs and Topology 416
Abstract 416
5.1 Introduction 417
5.2 The Concept of Hybridization 418
5.2.1 Hybrids with s and p Orbitals: A Good Basis of Discussion 418
5.2.2 The Natural Hybrids Orbitals from Natural Bond Orbital Analysis of Electronic Density 423
5.2.3 Are the Hybrids with s, p, and d Composition Realistic? 426
5.2.4 Hybrids in the Isolobal Analogy 430
5.3 Aromaticity as Resonance 435
5.3.1 Criteria of Aromaticity 435
5.3.2 Iconic Prototypes: Aromaticity in Benzene Versus Anti-aromaticity in Cyclobutadiene, from Valence Bond Perspective 438
5.3.3 Resonance Structures Without a Valence Bond Frame 450
5.3.4 The Spherical Aromaticity in Inorganic Clusters: The Icosahedral Borane 456
5.3.5 Aromaticity and Anti-aromaticity in Non-organic Systems 460
5.4 Aromaticity by Chemical Reactivity 463
5.4.1 Modeling Molecular Aromaticity with Electronegativity and Chemical Hardness 463
5.4.2 Modeling Absolute Aromaticity of Atoms-in-Molecules 467
5.4.3 Modeling Compact Aromaticity of Atoms-in-Molecules 474
5.5 Chemical Bonding by Coloring Reactivity 491
5.5.1 Reactivity Coloring of Topological Distance Matrix 491
5.5.2 Reactivity Coloring of Topological Adjacency Matrix 502
5.6 Conclusions 521
References 522
6 Coordination Bonding: Electronic Structure and Properties 529
Abstract 529
6.1 The Ligand Field Theory: An Evergreen Field 530
6.1.1 The Puzzle of Supra-valent Coordination Numbers and Werner’s Clear Cut Theory 530
6.1.2 Generalities on Ligand Field Modeling 531
6.1.3 The Effective Electrostatic Formalism of Ligand Field Theory 534
6.1.4 The General Formulation of the Ligand Field Potential in Spherical Harmonics Basis 536
6.1.5 Particular Ligand Field Hamiltonians in Selected Symmetries 541
6.1.6 Limitations of Ligand Field Modeling: The Holohedrization Effect 548
6.1.7 Ligand Field Potential Maps: A Picturesque Representation of Multi-parametric Systems 552
6.2 The Angular Overlap Model (AOM): Angling for Chemical Meaning in Ligand Field Parameterization 555
6.2.1 Principles and Techniques of AOM: Chemists Believe in Orbital Overlapping 555
6.2.2 The AOM Parameterization in Prototypic Cases 559
6.2.3 Meaning and Estimation of AOM Parameters 561
6.3 Bonding Schemes and Ligand Field Stabilization Energy in Transition Metal Complexes 565
6.4 Modeling  Electronic Spectroscopy of Transition Metal Complexes 569
6.4.1 Taking a Case Study: The [Ni(Phen)3]2+ Complex. Preamble: Molecular Geometry of the Complex Electronic Structure of the Free Metal Ions 569
6.4.2 Calculation of the Ligand Field Spectra by Multi-configuration Methods 571
6.4.3 The Advanced Level: Guiding the Calculations and Handling the Results to Meet the Ligand Field Phenomenology 573
6.4.4 The Time Dependent Density Functional Theory (TD-DFT) Calculation of Electronic Spectra in Coordination Compounds: Limitations and Advantages 584
6.5 The Thermochromism of Coordination Compounds 590
6.5.1 A Colorful Topic 590
6.5.2 Thermochromic Behavior by Linkage Isomerism: The Nitro-nitrito Isomerization 592
6.5.3 The Thermochromism of the Tetrahalocuprates: Tetrahedral-Square Planar Switching 597
6.6 The Specifics and Subtleties of the Electronic Structure of Lanthanide Complexes. Ligand Field + Spin-Orbit = Magnetic Anisotropy 611
6.6.1 The Puzzle of the f Orbitals in Molecule 611
6.6.2 An Intermezzo on Magnetic Anisotropy 612
6.6.3 The Non-aufbau Nature of the f-Shell in the Molecular Orbital Pictures 614
6.6.4 The Multi-configurational Methods of the f-Element Complexes: The First-Principles Route to Ligand Field Phenomenology and ab initio Magnetic Anisotropy 616
6.6.5 Other Ways of LF Modeling: Stevens Equivalent Operators Technique, Exemplified in Axial Symmetry 627
6.7 Conclusions 632
References 634
7 The Modeling in Molecular Magnetism 639
Abstract 639
7.1 Phenomenological Models in Magnetochemistry 641
7.1.1 The Spin Coupling Hamiltonian 641
7.1.2 Other Effective Magnetic Components: Zeeman Hamiltonian and Zero Field Splitting 643
7.1.3 Magnetic Susceptibility 645
7.2 Fit to Experiment of Spin Coupling Parameters: Some Non-trivial Issues 648
7.3 The CASSCF and Broken Symmetry DFT Methods, Face to Face, in the Estimation of Exchange Coupling Parameters 652
7.4 The Broken Symmetry Approach to Poly-nuclear Systems 655
7.5 The Complexity of Structure-Property Relationships Poly-nuclear Systems Within Lanthanide Ions: Spin Coupling, Ligand Field, and Spin-Orbit Factors 659
7.5.1 Generic Mechanisms for Ferromagnetic and Antiferromagnetic d-f Exchange Couplings. The Case of Cu–Gd Complexes 659
7.5.2 Exchange Coupling in d-f Complexes with Degenerate Ground Terms of Lanthanide Ions 664
7.5.3 The Ligand Field Analysis of the CASSCF Results 667
7.5.4 The Angular Overlap Modeling of the Ligand Field in Lanthanide Complexes 672
7.5.5 Magnetic Anisotropy of the Lanthanide Ions in Ground and Excited States. State-Specific Magnetization Polar Maps. The Ab Initio Simulation of the Magnetic Properties 674
7.6 The Spin Crossover Phenomena 682
7.6.1 Generalities 682
7.6.2 A Simple Modeling of the Ligand Field Versus Spin Coupling Balance 684
7.6.3 Adding the Vibrational Factors 688
7.6.4 Illustration of the Spin Crossover in Prototypic Fe(II) Complexes 691
7.6.5 The Rare Cases of Spin Crossover in Mn(III) Complexes 696
7.7 Conclusions 700
References 702
8 Bonding in Rings and Clusters 706
Abstract 706
8.1 Clues for Heuristic Insight in the Structure of Quasi-symmetric Systems 707
8.1.1 Symmetry as Ancillary Tool 707
8.1.2 Point Groups in a Nutshell 708
8.1.3 Orbital Symmetry in Ring Systems 711
8.2 Tensor Surface Harmonics (TSH) Theory 714
8.2.1 Orbital Patterns in Quasi-spherical Clusters 714
8.2.2 Modeling Clusters by Vector Surface Harmonics 729
8.2.3 Complex Structures MO Diagrams by TSH Theory 735
8.3 Special Bonding in Adjacencies by Topological Isomers 738
8.4 Conclusions 746
References 746
9 Add on. The Bondon: A New Theory of Electron Effective Coupling and Density Ensembles 749
Abstract 749
9.1 The Need for Bondonic Theory in Quantum Chemistry 750
9.2 The Analytical Roots of Bondonic Theory 752
9.3 The Gravitational Side of Bondonic Theory 761
9.4 Modeling Graphene Systems by Bondonic Theory 776
9.5 Bondons on Graphene by Symmetry Breaking Modeling 790
9.5.1 Symmetry Breaking Phenomenology in Quantum Nanochemistry 790
9.5.2 Bondons by Symmetry Breaking 793
9.5.3 Goldstone Bondons on Graphene with Topological Defects 798
9.6 Conclusions 802
References 803
Appendix: Atomic Two-Electron Integrals 807
Index 822