Quantum Mechanics in Chemistry

Hardcover | April 30, 1999

byJack Simons, Jeff Nichols

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Written for beginning graduate students and advanced undergraduates, this unique text combines both introductory and modern quantum chemistry in a single volume. Unlike similar texts, which concentrate on quantum physics and provide only brief examples of chemical applications, QuantumMechanics in Chemistry focuses on the topics a chemist needs to know. It provides an introduction to the fundamentals of quantum mechanics as they apply to chemistry, then moves on to the more modern aspects of the field, which are very important in industry and are not emphasized in any other text.It also includes introductions to molecular spectroscopy, chemical dynamics, and computational chemistry as applied to electronic structures. The authors' websites offer text-related computer programs and a large number of exercises, problems, and solutions to further enhance the flexibility andutility value of the text for students, instructors, and professionals in the field. The publisher's website is linked to the authors' websites: see Appendix H for WWW addresses.

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Written for beginning graduate students and advanced undergraduates, this unique text combines both introductory and modern quantum chemistry in a single volume. Unlike similar texts, which concentrate on quantum physics and provide only brief examples of chemical applications, QuantumMechanics in Chemistry focuses on the topics a chem...

Jack Simons and Jeff Nichols are both in the Department of Chemistry at the University of Utah.

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Format:HardcoverDimensions:640 pages, 7.13 × 10.2 × 1.3 inPublished:April 30, 1999Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0195082001

ISBN - 13:9780195082005

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Table of Contents

Section 1 The Basic Tools of Quantum Mechanics1. Quantum Mechanics describes matter in terms of wavefunctions and energy levels. Physical measurements are described in terms of operators acting on wavefunctions.I. Operators, Wavefunctions, and the Schrodinger EquationII. Examples of Solving the Schrodinger EquationIII. The Physical Relevance of Wavefunctions, Operators, and Eigenvalues2. Approximation methods can be used when exact solutions to the Schrodinger equation can not be found.I. The Variational MethodII. Perturbation TheoryIII. Example Applications of Variational and Perturbation Methods3. The Application of the Schrodinger equation to the motions of electrons and nuclei in a molecule lead to the chemists' picture of electronic energy surfaces on which vibration and rotation occurs and among which transitions take place.I. The Born-Oppenheimer Separation of Electronic and Nuclear MotionsII. Rotation and Vibration of Diatomic MoleculesIII. Rotation of Polyatomic MoleculesIV. SummarySummarySection 1 Exercises and Problems and SolutionsSection 2 Simple Molecular Orbital Theory4. Valence atomic orbitals on neighboring atoms combine to form bonding, non-bonding, and antibonding molecular orbitals.I. Atomic OrbitalsII. Molecular Orbitals5. Molecular orbitals possess specific topology, symmetry, and energy-level patterns.I. Orbital Interaction TopologyII. Orbital Symmetry6. Along "reaction paths", orbitals can be connected one-to-one according to their symmetries and energies. This is the origin of the Woodward-Hoffman rules.I. Reduction in Symmetry Along Reaction PathsII. Orbital Correlation Diagrams - Origins of the Woodward-Hoffman Rules7. The most elementary molecular orbital models contain symmetry, nodal pattern, and approximate energy information.I. The LCAO-MO Expansion and the Orbital-Level Schrodinger EquationII. Determining the Effective Potential VSection 2 Exercises and Problems and SolutionsSection 3 Electronic Configurations, Term Symbols, and States8. Electrons are placed into orbital to form configurations, each of which can be labeled by its symmetry. The configurations may "interact" strongly if they have similar energies. The mean-field model, which forms the basis of chemists' pictures of electronic structure of molecules, is not veryaccurate.I. Orbitals Do Not Provide the Complete Picture; Their Occupancy by the N-Electrons Must Be SpecifiedII. Even N-Electron Configurations Are Not Mother Nature's True Energy StatesIII. Mean-Field ModelIV. Configuration Interaction (CI) Describes the Correct Electronic States9. Electronic wavefunctions must be constructed to have permutational antisymmetry because the N-electrons are indistinguishable Fermions.I. Electronic ConfigurationsII. Antisymmetric Wavefunctions10. Electronic wavefunctions must also possess proper symmetry. These include angular momoentum and point group symmetries.I. Angular Momentum Symmetry and Strategies for Angular Momentum CouplingII. Atomic Term Symbols and WavefunctionsIII. Linear Molecule Term Symbols and WavefunctionsIV. Non-linear Molecule Term Symbols and WavefunctionsV. Summary11. One must be able to evaluate the matrix elements among properly symmetry adapted N-electron configuration functions for any operator, the electronic Hamiltonian in particular. The Slater-Condon rules provide this capability.I. CSF's Are Used to Express the Full N-Electron WavefunctionII. The Slater-Condon Rules Give Expressions for the Operator Matrix Elements Among the CSF'sIII. Examples of Applying the Slater-Condon RulesIV. Summary12. Along "reaction paths", configurations can be connected one-to-one according to their symmetries and energies. This is another part of the Woodward-Hoffmann rules.I. Concepts of Configuration and State EnergiesII. Mixing of Covalent and Ionic ConfigurationsIII. Various Types of Configuration MixingSection 3 Exercises and Problems and SolutionsSection 4 Molecular Rotation and Vibration13. Treating the full internal nuclear-motion dynamics of a polymatomic molecule is complicated. It is conventional to examine the rotational movement of a hypothetical "rigid" molecule as well as the vibrational motion of a non-rotating molecule, and to then treat the rotation-vibration couplingsusing perturbation theory.I. Rotational Motions of Rigid MoleculesII. Vibrational Motion Within the Harmonic ApproximationIII. AnharmonicitySection 5 Time Dependent Processes14. The interaction of a molecular species with electromagnetic fields can cause transitions to occur among the available molecular energy levels (electronic, vibrational, rotational, and nuclear spin). Collisions among molecular species likewise can cause transitions to occur. Time-dependentperturbation theory and the methods of molecular dynamics can be employed to treat such transitions.I. The Perturbation Describing Interactions with Electromagnetic RadiationII. Time-Dependent Perturbation TheoryIII. The Kinetics of Photon Absorption and Emission15. The tools of time-dependent perturbation theory can be applied to transitions among electronic, vibrational, and rotational states of molecules.I. Rotational TransitionsII. Vibration-Rotation TransitionsIII. Electronic-Vibration-Rotation TransitionsIV. Time Correlation Function Expressions for Transition Rates16. Collisions among molecules can also be viewed as a problem in time-dependent quantum mechanics. The perturbation is the "interaction potential", and the time dependence arises from the movement of the nuclear positions.I. One Dimensional ScatteringII. Multichannel ProblemsIII. Classical Treatment of Nuclear MotionIV. WavepacketsSection 6More Quantitative Aspects of Electronic Structure Calculations17. Electrons interact via pairwise Coulomb forces; within the "orbital picture" these interactions are modelled by less difficult to treat "averaged" potentials. The difference between the true Coulombic interactions and the averaged potential is not small, so to achieve reasonable (ca. 1 kcal/mol)chemical accuracy, high-order corrections to the orbital picture are needed.I. Orbitals, Configurations, and the Mean-Field PotentialII. Electron Correlation Requires Moving Beyond a Mean-Field ModelIII. Moving from Qualitative to Quantitative ModelsIV. Atomic Units18. The Single Slater determinant wavefunction (properly spin and symmetry adapted) is the starting point of the most common mean-field potential. It is also the origin of the molecular orbital concept.I. Optimization of the Energy for a Multiconfiguration WavefunctionII. The Single Determinant WavefunctionIII. The Unrestricted Hartree-Fock Spin Impurity ProblemIV. The LCAO-MO ExpansionV. Atomic Orbital Basis SetsVI. The Roothaan Matrix SCF ProcessVII. Observations on Orbitals and Orbital Energies19. Corrections to the mean-field model are needed to describe the instantaneous Coulombic interactions among the electrons. This is achieved by including more than one Slater determinant in the wavefunction.I. Different MethodsII. Strengths and Weaknesses of Various ModelsIII. Further Details on Implementing Multiconfigurational Methods20. Many physical properties of a molecule can be calculated as expectation values of a corresponding quantum mechanical operator. The evaluation of other properties can be formulated in terms of the "response" (i.e., derivative) of the electronic energy with respect to the application of anexternal field perturbation.I. Calculations of Properties Other Than the EnergyII. Ab Initio, Semi-Empirical, and Empirical Force FieldsSection 6 Exercises and Problems and SolutionsUseful Information and DataAppendicesMathematics Review AThe Hydrogen Atom Orbitals BQuantum Mechanical Operators and Commutation CTime Independent Perturbation Theory DPoint Group Symmetry EQualitative Orbital Picture and Semi-Empirical MethodsAngular Momentum Operator Identities G