Semiempirical methods of electronic structure calculation

Author(s)

• Segal, Gerald

Bibliographic Information

Semiempirical methods of electronic structure calculation

edited by Gerald A. Segal

（Modern theoretical chemistry, v. 7-8）

Plenum Press, c1977

• pt. A
• pt. B

Note

Includes bibliographies and indexes

Contents of Works

• pt. A. Techniques
• pt. B. Applications

Description and Table of Contents

Volume

pt. A ISBN 9780306335075

Description

If one reflects upon the range of chemical problems accessible to the current quantum theoretical methods for calculations on the electronic structure of molecules, one is immediately struck by the rather narrow limits imposed by economic and numerical feasibility. Most of the systems with which experimental photochemists actually work are beyond the grasp of ab initio methods due to the presence of a few reasonably large aromatic ring systems. Potential energy surfaces for all but the smallest molecules are extremely expensive to produce, even over a restricted group of the possible degrees of freedom, and molecules containing the higher elements of the periodic table remain virtually untouched due to the large numbers of electrons involved. Almost the entire class of molecules of real biological interest is simply out of the question. In general, the theoretician is reduced to model systems of variable appositeness in most of these fields. The fundamental problem, from a basic computational point of view, is that large molecules require large numbers of basis functions, whether Slater- type orbitals or Gaussian functions suitably contracted, to provide even a modestly accurate description of the molecular electronic environment. This leads to the necessity of dealing with very large matrices and numbers of integrals within the Hartree-Fock approximation and quickly becomes both numerically difficult and uneconomic.

Table of Contents

• 1. Huckel Theory and Topology.- 1. Introduction.- 2. Equivalence between Hiickel Theory and the Graph Spectral Theory of Conjugated Molecules.- 3. Two-Color Problem in Hiickel Theory.- 4. Relationship between the Topology of Conjugated Systems and Their Corresponding Characteristic Polynomials.- 4.1. Characteristic Polynomial of a Conj ugated Molecule.- 4.2. Coulson-Sachs Graphical Method for the Enumeration of Coefficients of the Characteristic Polynomial.- 4.3. Summary of Some Results Obtained from the Coulson-Sachs Method.- 5. Topological Formulas for Hiickel Energy and ?-Resonance Energy.- 5.1. Topological Formula for ?-ElectronEneigy.- 5.2. Topological Formula for ?-Resonance Energy.- 6. Conclusions.- References.- 2. The Neglect-of-Differential-Overlap Methods of Molecular Orbital Theory.- 1. Background.- 1.1. Methodology.- 1.2. The Central Field Approximation and the Self-Consistent Field Procedure.- 1.3. The Form of the Basis Set.- 1.4. The ZDO Approximation.- 2. The NDO Methods.- 2.1. The CNDO Methods.- 2.2. The (M)INDO Methods.- 2.3. The (P)NDDO Methods.- References.- 3. The PCILO Method.- 1. Main Features of the PCILO Method.- 1.1. Advantages of the Localized MOs.- 1.2. Perturbative CI.- 1.3. Keeping the Simplicity of the CNDO Hamiltonian at the CI Level.- 1.4. Comparison with the Valence Bond Method.- 2. Derivation of the PCILO-CNDO Energy Contributions.- 2.1. Choice of the Localized MOs.- 2.2. The Fully Localized Determinant Energy.- 2.3. Second-Order Contributions.- 2.4. Third-Order Contributions.- 2.5. Improvement of Bond Polarities.- 3. Efficiency and Limits of the Method
• Applications and Extensions.- 3.1. Nature of Possible Applications.- 3.2. Time and Memory Requirements
• the Differential Scheme.- 3.3. Limitations of the Method.- 3.4. Brief Review of Applications to Ground-State Conformational Problems.- 3.5. Extensions of the Method.- 4. Concluding Remarks.- References.- 4. The X? Method.- 1. Introduction.- 1.1. The Origins of the Xa Method.- 1.2. Early Applications of the Method.- 1.3. Advantages and Disadvantages.- 2. Derivation of the Equations.- 2.1. The Energy Functional.- 2.2. The Slater Transition State.- 2.3. The Virial and Hellmann-Feynman Theorems.- 2.4. The Choice of Parameters.- 2.5. The Spin-Polarized and Relativistic Modifications.- 3. Applications of the Method.- 3.1. Atomic Calculations.- 3.2. Molecular Calculations.- 4. Comparison with Other Methods.- References.- 5. The Consistent Force Field and Its Quantum Mechanical Extension.- 1. Introduction.- 1.1. Efficiency.- 1.2. Reliability.- 1.3. Flexibility.- 2. Empirical Potential Functions.- 3. The Consistent Force Field (CFF) Method.- 3.1. The Philosophy of the CFF Method.- 3.2. The Refinement of the Potential Function Parameters.- 3.3. The Advantage of the Cartesian Representation.- 4. Quantum Mechanical Extension of the CFF Method to Ground and Excited States of Conjugated Molecules.- 4.1. Potential Surf aces for Conjugated Molecules.- 4.2. The Refinement of the Empirical Integrals.- 5. Applications.- 5.1. Energies, Conformations, and Vibrations of Large Molecules.- 5.2. Crystal Packing, Crystal Geometry, Lattice Dynamics, and Excimer Formation.- 5.3. Excited-State Geometries, Vibronic Interactions, and Photochemistry.- 5.4. Resonance Raman Intensities of Biologically Important Molecules.- 5.5. Classical Trajectories and Molecular Dynamics.- 6. Concluding Remarks.- References.- 6. Diatomics-in-Molecules.- 1. Introduction.- 2. Formulationof the Method.- 2.1. Molecular Energies and Wave Functions.- 2.2. Polyatomic Basis Functions.- 2.3. Partitioning of the Hamiltonian.- 2.4. Fundamental Approximation of DIM.- 2.5. Ab Initio DIM Theory.- 2.6. Semiempirical DIM Theory.- 3. Application of the Method.- 3.1. Selection of Basis Functions.- 3.2. Spin Coupling.- 3.3. Fragment Information.- 3.4. Overlap.- 4. Assessmentof the Method.- 4.1. Practicality.- 4.2. Analysis of Basic Approximations.- 4.3. Comparison with Accurate Results.- 4.4. Transferability.- 5. Properties Other Than Energy.- 6. Polyatomics-in-Molecules.- 7. Conclusions.- References.- 7. Theoretical Basis for Semiempirical Theories.- 1. Introduction.- 1.1. Division between Semiempirical and Ab Initio Fields.- 1.2. Need for a Theoretical Basis of Semiempirical Theories.- 2. Semiempirical Theories: Background.- 2.1. Traditional Formulation.- 2.2. Ambiguities and Difficulties.- 2.3. Earlier Derivations.- 3. The True Effective Valence Shell Hamiltonian.- 3.1. Basic Concepts.- 3.2. Derivation of ?v.- 3.3. Properties of ?v.- 4. Extraction of True Parameters.- 4.1. The True Parameters.- 4.2. Nonclassical Terms.- 4.3. Dynamic Variable Electronegativity.- 4.4. Properties Other Than Energies.- 4.5. The Chemical Orbitals.- 4.6. Extraction of the ??.- 5. Approximate Evaluation of True Parameters.- 5.1. Ab Initio Evaluation of the Correlation Parts of ?v.- 5.2. Difiuseness of ?* Valence States.- 5.3. ?v for Twisted Olefins.- 6. Model Pseudopotentials.- 6.1. The Usual Pseudopotential Equations.- 6.2. Exact Equations for the Valence Electrons.- 6.3. The Many-Electron Case.- 7. Discussion.- References.- Author Index.- Molecule Index.

Volume

pt. B ISBN 9780306335082

Description

If one reflects upon the range of chemical problems accessible to the current quantum theoretical methods for calculations on the electronic structure of molecules, one is immediately struck by the rather narrow limits imposed by economic and numerical feasibility. Most of the systems with which experimental photochemists actually work are beyond the grasp of ab initio methods due to the presence of a few reasonably large aromatic ring systems. Potential energy surfaces for all but the smallest molecules are extremely expensive to produce, even over a restricted group of the possible degrees of freedom, and molecules containing the higher elements of the periodic table remain virtually untouched due to the large numbers of electrons involved. Almost the entire class of molecules of real biological interest is simply out of the question. In general, the theoretician is reduced to model systems of variable appositeness in most of these fields. The fundamental problem, from a basic computational point of view, is that large molecules require large numbers of basis functions, whether Slater- type orbitals or Gaussian functions suitably contracted, to provide even a modestly accurate description of the molecular electronic environment. This leads to the necessity of dealing with very large matrices and numbers of integrals within the Hartree-Fock approximation and quickly becomes both numerically difficult and uneconomic.

Table of Contents

• 1. Ground-State Potential Surfaces and Thermochemistry.- 1. Introduction.- 2. Macroscopic Properties from Molecular Calculations.- 2.1. A Scheme for Thermodynamic Parameters.- 2.2. The Need for Geometry Calculations.- 2.3. Statistical Thermodynamic Formalism.- 2.4. Activation Parameters.- 2.5. The Zero-Point Vibrational Correction.- 2.6. The Partition Function.- 3. Semiempirical Molecular Orbital Theory for Closed Shells.- 3.1. The Nature of Semiempirical Theory.- 3.2. Parametrization.- 3.3. Strengths and Limitations for Potential Surface Calculations.- 4. Exploring Potential Energy Surfaces.- 4.1. The Size and Shape of Potential Surfaces.- 4.2. Geometry Optimization.- 4.3. Force Constants.- 5. Selected Results and Comparisons.- 5.1. Introduction.- 5.2. Molecular Geometries.- 5.3. Energies of Equilibrium States.- 5.4. Activation Parameters.- 5.5. Vibrational Frequencies.- 6. Conclusions and an Opinion.- References.- 2. Electronic Excited States of Organic Molecules.- 1. Introduction.- 2. The Hamiltonian Operator.- 3. The Zeroth-Order Approximation.- 4. The Electronic Wave Function.- 4.1. The All-Valence-Electron Approximation.- 4.2. The SCF Procedure.- 4.3. The Trial Functions.- 4.4. The ZDO Approximation.- 4.5. The Semiempirical Approximations.- 4.6. Comparison of Various Methods.- 5. The Interaction of Matter and Electromagnetic Fields.- 5.1. Transition Moments.- 5.2. Photoelectron Cross Sections.- 6. Spin-Orbit and Spin-Spin Coupling.- 6.1. Spin-Orbit Coupling.- 6.2. Spin-Spin Coupling.- 7. Vibrationally Induced Transitions.- 7.1. Herzberg-Teller Theory.- 7.2. Born-Oppenheimer Breakdown Theory.- 8. Application of ZDO Methods.- 8.1. Simple Organic Compounds.- 8.2. Inorganic Compounds.- 8.3. Interacting Nonplanar 7r-Electron Systems.- 8.4. TripletStates.- 8.5. Free Radicals and Doublet States
• Photoelectron Spectra.- 8.6. Rydberg Transitions.- 8.7. Treatment of d Orbitals.- 8.8. Geometry of Excited States.- 8.9. Spin-Orbit, Spin-Spin, and Vibronic Coupling.- 8.10. Ionization Potentials.- 8.11. Dipole Moments and Polarizabilities.- 8.12. Miscellaneous Studies.- 9. Conclusions.- References.- 3. Photochemistry Josef Michl.- 1. Introduction.- 2. Photochemical Processes.- 3. Semiempirical Methods.- 3.1. Model Hamiltonians.- 3.2. Solving the Models.- 4. Examples of Application.- 4.1. Phototautomerism.- 4.2. Electrocyclic Reactions.- 5. Summary and Outlook.- References.- 4. Approximate Methods for the Electronic Structures of Inorganic Complexes.- 1. Inorganic Complexes Contrasted to Organic Molecules.- 2. TheOrbitals.- 3. The Ligand Field and the Crystal Field Methods.- 4. Koopmans' Theorem.- 5. Spin-Orbit Coupling.- 6. NonempiricalCNDO and INDO Methods.- 7. Semiempirical CNDO and INDO Methods.- 8. The Excited States.- 9. The Crystal Field Theory.- 10. Extended Huckel Theory. Angular Overlap Model.- 11. An Example, Ni(CN)4~. Conclusions.- References.- 5. Approximate Molecular Orbital Theory of Nuclear and Electron Magnetic Resonance Parameters.- 1. Introduction.- 2. Magnetic Resonance Parameters.- 3. Molecular Quantum Mechanics.- 3.1. Molecular Orbital Theory.- 3.2. Approximate Molecular Orbital Theory.- 3.3. Perturbation Theory.- 4. NMR Shielding Constants and Chemical Shifts.- 4.1. Quantum Mechanical Development of ?N.- 4.2. Calculation of Shielding Constants.- 5. NMR Nuclear Spin Coupling Constants.- 5.1. Quantum Mechanical Development of KMN.- 5.2. The Fermi Contact Term.- 5.3. The Orbital and Dipolar Terms.- 5.4. Calculations of JMN.- 6. ESRg-Tensors.- 7. ESR Electron-Nuclear Hyperfine Tensors.- 7.1. Quantum Mechanical Development of TN.- 7.2. Isotropic Hyperfine Coupling.- 7.3. Calculations of Isotropic Hyperfine Constants.- 7.4. Anisotropic Hyperfine Coupling.- 7.5. Calculations of Anisotropic Hyperfine Constants.- References.- 6. The Molecular Cluster Approach to Some Solid-State Problems.- 1. Introduction.- 1.1. Perfect Crystalline Solids and the Bloch Theorem.- 1.2. Imperfect Solids and the Breakdown of B loch's Theorem.- 2. Solid-State Theory Approaches to Surface Problems.- 2.1. The Perfect Surface.- 2.2. Surf ace-Adsorbate Interactions.- 3. Molecular Cluster Approach to Surface Problems.- 3.1. Nonmetals.- 3.2. MetalClusters.- 3.3. Metals and Adsorbates.- 4. Summary.- References.- 7. Electron Scattering Donald G. Truhlar.- 1. Introduction.- 2. Explicit Inclusion of Electronic Excitations.- 2.1. Expansions Including Free Waves.- 2.2. L2 Expansions.- 3. Neglect of Electronic Excitation Except for Final State.- 3.1. Strong-Coupling, Static-Exchange, and Distorted-Wave Approximations.- 3.2. High-Energy Approximations.- 4. Inclusion of Effect of Omitted Electronic States by Approximate Polarization Potentials.- References.- Author Index.- Molecule Index.

by "Nielsen BookData"

Details

• NCID: BA06718580
• ISBN:
  • 0306335077
  • 0306335085
• LCCN: 76048060
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: New York
• Pages/Volumes: 2 v.
• Size: 26 cm
• Classification:
  • LCC : QD461
  • DC : 541/.28
• Subject Headings:
  • LCSH : Molecular orbitals
  • LCSH : Quantum chemistry
• Parent Bibliography ID:
  • BA0007310X