AN INTRODUCTION TO MOLECULAR ORBITALS

Transcription

1 AN INTRODUCTION TO MOLECULAR ORBITALS by YVES JEAN and FRANCOIS VOLATRON translated and edited by Jeremy Burdett New York Oxford OXFORD UNIVERSITY PRESS 1993

2 Contents Introduction, xiii I INTRODUCTION TO ATOMIC AND MOLECULAR STRUCTURE 1. From the periodic table to molecules, The periodic Classification, Short description of the first three periods, Core and valence electrons, Systems with eight valence electrons, The electronegativity concept, Lewis' theory and Lewis structures, Bond pairs and lone pairs, The octet rule, Formal charges, Classification of reactants, Dipole moments of diatomic molecules, Resonance or mesomerism, Exampies of mesomeric structures: carbonate ion (C0 3 2 ~) and benzene (C 6 H 6 ), Selection of mesomeric or resonance structures, Application to the structure of aniline, Molecular geometry, Spatial representation of molecules: Cram's model, VSEPR theory, Extensions of VSEPR theory, Dipole moments of polyatomic molecules, Conclusion, 25 Exercises, Properties of atoms, Elements of quantum mechanics, Schrödinger's equation, Some important properties of the eigenfunctions, The hydrogen atom, Solutions of the Schrödinger equation, Description of the eigenfunctions, 37

3 Vlll CONTENTS Electron spin, Hydrogen-like atoms, Many-electron atoms, The orbital approximation, Mathematical description and nomenclature of atomic orbitals, Atomic orbital energies, The electronic configuration of atoms, Hund's rule, Core and valence electrons, The periodic Classification of the elements, Organization by rows, Organization by column: chemical families, Electronic parameters of many-electron atoms, Screening, The effective charge: Slater's rules, Orbital radii and atomic size, Evolution of atomic properties, Atomic orbital parameters, Relationship with measurable properties, Electronegativity scales, Electronegativity, orbital energy and orbital radius, 68 Exercises, 69 II BUILDING UP MOLECULAR ORBITALS AND ELECTRONIC STRUCTURE 3. Interaction of two atomic orbitals on different centers, Basic approximations, The Born-Oppenheimer approximation, The orbital approximation, The form of the MOs: the LCAO approximation, Construction of MOs, Interaction of two identical AOs, Interaction of two different AOs, Orbitals with zero overlap, Application to some simple diatomic molecules, Level Alling rules, Systems with two or four electrons, Total energy of the molecule: the Morse curve for H 2, Systems with one or three electrons, Overlap and symmetry, ls/ls overlap, Overlap between 'parallel' 2p orbitals (rc-type overlap), ls/2p overlap, Symmetry ideas, 90

4 3.5. Application of symmetry ideas to some polyatomic molecules, a/n Separation, The n MOs of ethylene, n System of formaldehyde, A comparison between ethylene and formaldehyde, The n orbitals of acetylene, Conclusions, 97 Exercises, 99 CONTENTS IX 4. The fragment orbital method; application to some model Systems, Molecular orbitals of some model Systems, H, Square planar H 4, Rectangular H 4, Linear H 3, Linear H 4, Triangulär H 3, Tetrahedral H 4, HexagonalH 6, Influence of electronegativity on the form and energy of the molecular orbitals, 120 Exercises, 123 Appendix: Degenerate orbitals, Interactions between two fragment orbitals: linear AH 2, trigonal AH 3 and tetrahedral AH 4, Linear AH 2 molecules, Symmetry properties of the fragment orbitals, MOs for linear AH 2 molecules, Application to BeH 2, Trigonal planar molecules, Symmetry properties of the fragment orbitals, Molecular orbitals of trigonal planar AH 3, Application to the electronic structure of BH 3, Tetrahedral AH 4 molecules, Symmetry properties of the fragment orbitals, MOs of tetrahedral AH 4 molecules, Application to the electronic structure of CH 4, 143 Exercises, 145 Appendix: Analogous orbitals, Interactions between three fragment orbitals: AH, bent AH 2 and pyramidal AH 3, Rules for the interaction of three orbitals, Outline of the problem, Rules for the construction of the MOs, 150

5 X CONTENTS 6.2. Electronic structure of AH molecules, Outline of the problem, Form of the MOs, Electronic structure of LiH, Electronic structure of BH, Electronic structure of FH, Conclusions for AH molecules, Bent AH 2 molecules, Symmetry of the fragment orbitals, Interaction diagram and form of the MOs: H 2 0 as an example, Electronic structure of H 2 0, Pyramidal AH 3 molecules, Symmetry of the fragment orbitals, Interaction diagram and form ofthe MOs: the example ofnh 3, Electronic structure of NH 3, 171 Exercises, Interactions between four fragment orbitals: the diatomic molecules A 2 and AB, Homonuclear diatomics, A 2, Outline of the problem, Construction of the rc-type MOs, Construction of the cx-type MOs, MO diagrams for A 2 molecules (A = Li,..., Ne), Electronic structure of the A 2 molecules (A = Li,..., Ne), Bond lengths and bond energies, Heteronuclear diatomic molecules, AB, Construction of the n MOs, Construction of the <x MOs, MOs and electronic structure of CO, 192 Exercises, 195 Appendix: The number of bonds (bond order) in diatomic molecules, Large molecules, MOs of acetylene, ethylene and ethane, MOs and electronic structure of acetylene, MOs and electronic structure of ethylene, MOs and electronic structure of ethane, Conjugated polyenes, MOs and electronic structure of allyl, MOs and electronic structure of butadiene, MOs and electronic structure of cyclopropenyl, MOs and electronic structure of cyclobutadiene, MOs and electronic structure of benzene, 212

6 CONTENTS XI Aromatic and antiaromatic Compounds and Hückel's rule, 213 Exercises, 215 Appendix: Bond localization, 218 III INTRODUCTION TO THE STUDY OF THE GEOMETRY AND REACTIVITY OF MOLECULES 9. Orbital correlation diagrams: the model Systems H 3 + and H 3 ~, Rules for drawing orbital correlation diagrams, Stabilization or destabilization of the MOs, Conservation of orbital symmetry, The non-crossing rule for MOs of the same symmetry, Orbital correlation diagram for bending H 3, Geometrical model, Symmetry of the MOs, Energetic evolution of the MOs, Geometry ofh 3 +, Geometry of H 3 ~ and the rule of the highest occupied MO, Rule of the highest occupied MO (HOMO), Geometry ofh 3 ~, The Jahn-Teller effect, Conclusion, 232 Exercises, Geometry of AH 2 and AH 3 molecules, AH 2 molecules, MOs of linear AH 2, Orbital correlation diagram, linear to bent AH 2, Geometry of AH 2 molecules, AH 3 molecules, MOs of trigonal planar AH 3, Orbital correlation diagram for trigonal planar to pyramidal AH 3, Planar or pyramidal geometries?, Extension to more complex molecules, The geometries of AX 2 and AX 3 molecules, 249 Exercises, Molecular geometry using fragment molecular Orbitals, Two- and four-electron interactions, Energetic consequences, Electron transfer, Model examples of H 3 + and H 3 ~, Geometry ofh 3 +, 256

7 Xll CONTENTS Geometry ofh 3 ~, Hyperconjugation, Conformation of the C 2 H 4 2+ dication, The ethyl cation CH 3 CH 2 +, The s-cis and s-trans conformations of butadiene, 265 Exercises, An introduction to the study of chemical reactivity, Description of a chemical reaction, The reaction scheme and elementary processes, Reaction mechanism, Reaction coordinate, Energy profiles, transition states and reaction intermediates, The frontier orbital approximation, The method, Electrophilic and nucleophilic reactants, The validity of the approximation, Cycloaddition reactions, The [4s + 2s] thermal cycloaddition: the Diels-Alder reaction, Thermal [2s + 2s] cycloaddition: the dimerization of ethylene, Generalization to [ms + ns] cycloadditions, Further aspects of the [2 + 2] cycloaddition, Concerted mechanisms, Non-concerted mechanisms, Examples of ionic reactions, The S N 2 mechanism, Markovnikov's rule, 288 Exercises, 292 IV PROBLEMS Problem 1. Stabilization of a planar tetravalent carbon atom via n effects, 297 Problem 2. Nucleophilic attack on a carbonyl group, 300 Problem 3. Structure and reactivity of substituted cyclopropanes, 304 Problem 4. Conformational consequences of hyperconjugation, 307 Bibliography, 311 Answers to Exercises, 313 Index, 333