Quantum Theory of Polymers as Solids

The goal of this monograph is to summarize the different quantum- mechanical methods developed in the last 20 years to treat the electronic structure of polymers. Owing to the nature of the problem, these methods consist of a mixture of quantum-chemical and solid-state physical tech- niques. The theory described in Part I treats, besides the Hartree-Fock problem, the* electron correlation, and it has also been developed for disordered polymeric systems. Though for obvious reasons the book could not include all the existing calculations, each new method des- cribed is illustrated by a few applications, with a discussion of the numerical results obtained. Far more details see the Introduction to Part I. The second part contains the theoretical calculation of different properties of polymers based on the methods systematically introduced in the first part. The properties calculated include the electronic and vibrational spectra of polymers, and the computation of their transport, magnetic, and mechanical properties. In cases where reliable ex- perimental data are available, the theoretical results are compared with them.

Table of Contents:
I. Quantum Theory of Polymeric Electronic Structure.- 1. Hartree-Fock Crystal-Orbital Theory of Periodic Polymers.- 1.1. Simple Translation.- 1.1.1. Block Diagonalization of the Hamiltonian Matrix.- 1.1.2. Elimination of the Overlap Matrix.- 1.1.3. Hartree-Fock-Roothaan Crystal-Orbital Formalism.- 1.2. Combined Symmetry Operation.- 1.3. Methods to Treat Many-Neighbor Interactions.- 1.4. Different Orbitals for Different Spin Formalisms.- 1.5. Relativistic Formulation.- 1.5.1. Introductory Remarks.- 1.5.2. Derivation of the Relativistic Hartree-Fock-Roothaan Equations for Molecules and Crystals.- 1.5.3. Concluding Remarks.- References.- 2. Examples of Ab Initio Calculations on Quasi-One-Dimensional Polymers.- 2.1. Some Polymers Used for the Production of Plastics: Polyethylene and Its Fluoro Derivatives.- 2.1.1. The Energy-Band Structure of Polyethylene.- 2.1.2. Band Structures of Fluorinated Polyethylenes.- 2.2. Highly Conducting Polymers: (CH)x, (SN)x, TCNQ and TTF Stacks.- 2.2.1. Hartree-Fock Calculations on cis- and trans-Polyacetylenes (Polyenes).- 2.2.2. The Energy-Band Structure of (SN)x.- 2.2.3. Ab Initio Calculation of Infinite TCNQ and TTF Stacks.- 2.3. Periodic Biopolymers: Homopolynucleotides and Homopolypeptides.- 2.3.1. Homopolynucleotides.- 2.3.2. Homopolypeptides.- References.- 3. Semiempirical Band-Structure Calculations.- 3.1. Semiempirical Crystal-Orbital Methods.- 3.1.1. The Pariser-Parr-Pople Crystal-Orbital Method.- 3.1.2. Semiempirical All-Valence Electron Crystal-Orbital Schemes.- 3.2. Applications to Highly Conducting Polymers and Biopolymers.- 3.2.1. Trans-Polyacetylene.- 3.2.2. TCNQ and TTF Stacks.- 3.2.3. Periodic DNA and Protein Models.- References.- 4. The Treatment of Aperiodicity in Polymers.- 4.1. Elementary Green Function Theory.- 4.1.1. Solution of Inhomogeneous Differential Equation by Means of Green Functions.- 4.1.2. Application of Green Functions to the Solution of the Time-Independent Schrodinger Equation.- 4.1.3. Simple Derivation of the Dyson Equation.- 4.2. Demonstration of the Effects of Aperiodicity on the Electronic Structure of Polymers.- 4.2.1. Effect of Side-Chain Disorder on the Electronic Structure of Proteins.- 4.2.2. Localization of Wave Functions in a Disordered Hydrogen Ring.- 4.3. Single-Site Coherent Potential Approximation and Its Application to (SN)x with Hydrogen Impurities.- 4.3.1. Derivation of the Single-Site CPA Equation.- 4.3.2. Application of the Single-Site CPA Method to (SN)xwith Hydrogen Impurities.- 4.4. The Negative Factor Counting (NFC) Technique and Its Application to Aperiodic DNA and Proteins.- 4.4.1. The Negative Factor Counting Technique in Its One Band (Simple Tight-Binding) Form.- 4.4.2. The NFC Method in Its Ab Initio (Matrix-Block) Form.- 4.4.3. Application of the NFC Method to Aperiodic Polypeptides and Polynucleotides.- 4.5. Investigation of the Localization of the Orbitals in Disordered Chains.- 4.5.1. Green Matrix Method for the Study of the Localization Properties of the States Belonging to a Disordered Chain.- 4.5.2. Application to a Model Hamiltonian.- 4.6. Treatment of a Cluster of Impurities Imbedded in a Periodic Chain.- 4.6.1. Green Matrix Formulation of the Problem.- 4.6.2. Application to a Hydrogen Impurity in a Lithium Chain.- References.- 5. Electronic Correlation in Polymers.- 5.1. Construction of Wannier Functions.- 5.2. Second-Order Moller-Plesset Many-Body Perturbation Theory for Infinite Systems.- 5.3. The Electronic Polaron Model and the Quasi-Particle Band Structure of Polymers.- 5.4. Selected Correlation Energy Calculations on Polymers.- 5.4.1. Ground-State Energy of an Infinite Metallic Hydrogen Chain.- 5.4.2. The Quasi-Particle Energy Gap of Alternating trans-Polyacetylene.- 5.4.3. Correlation Energy and Quasi-Particle Gap in a Cytosine Stack.- 5.5. Correlation in Polymers with Large Unit Cells.- 5.6. Remarks on Correlation in Disordered Chains.- References.- 6. Interaction between Polymers.- 6.1. Perturbation Theoretical Considerations.- 6.2. The Mutually Consistent Field (MCF) Method.- 6.2.1. The MCF Method in the Point-Charge Representation of the Potentials.- 6.2.2. The MCF Method in the Pseudopolarization Tensor Formulation.- 6.3. Application to DNA-Protein Interactions.- 6.3.1. Models for B-DNA and Polyglycine and Methods of Calculation.- 6.3.2. Results of B-DNA-Polygly Calculations and Their Discussion.- References.- 7. The Effect of Environment on the Band Structure of Polymers.- 7.1. Generation of an Effective Potential Field of the Environment.- 7.2. Results for a Cytosine Stack.- References.- II. Theoretical Calculation of the Different Physical Properties of Polymers.- 8. Excited and Ionized States of Polymers.- 8.1. Intermediate Exciton Theory with Correlation.- 8.2. Application of Intermediate Exciton Theory to UV Spectra of Different Polymers.- 8.2.1. Applications to Polydiacetylenes and to Polyethylenes.- 8.2.2. Applications to a Cytosine Stack and to Polyglycine.- 8.2.3. The Exciton Spectrum of Polyglycine and Polyalanine.- 8.3. Ionized States of Polymers and Their X-Ray Photoelectron Spectra.- 8.3.1. Theoretical Calculation of the Ionized States of Simple Periodic Polymer Chains.- 8.3.2. Interpretation of the Photoelectron Spectra of Polymers.- References.- 9. Vibrational Spectra and Transport Properties of Polymers.- 9.1. Methods for the Calculation of Vibrational Spectra of Polymers.- 9.2. Phonon Calculations for Selected Ordered and Disordered Polymer Chains.- 9.2.1. Polymethineimine.- 9.2.2. Polyethylene.- 9.2.3. Bent Chain of Hydrogen Fluoride Molecules.- 9.2.4. Periodic and Nonperiodic Alternating trans-Polyacetylene.- 9.3. Transport Properties of Polymers.- 9.3.1. The Theory of Bloch-Type Electric Conduction in Polymers and Its Applications.- 9.3.2. Calculation of Bloch Conduction for Narrow-Band Polymers.- 9.3.3. Theory of Hopping Conduction in Very Narrow Band Polymers and in Disordered Polymers with Applications.- References.- 10. Magnetic, Electrical, and Mechanical Properties of Polymers.- 10.1. Hartree-Fock Equations for Periodic Polymer Chains in a Magnetic Field.- 10.1.1. Static Magnetic Field.- 10.1.2. Some General Remarks about the Theory of the Effects of Magnetic Fields on Polymers.- 10.2. Electric Polarizabilities of Polymers.- 10.2.1. Theoretical Methods.- 10.2.2. Numerical Applications.- 10.3. Mechanical Properties of Polymers.- 10.3.1. Theoretical Considerations.- 10.3.2. Application to Polyethylene.- References.- 11. The Possible Role of Solid-State Physical Properties of Biopolymers in Their Biological Functions.- 11.1. Mutation and Aging.- 11.1.1. Theory of Point Mutation.- 11.1.2. Remarks about Aging.- 11.2. Carcinogenesis Caused by Chemicals and Different Radiations.- 11.2.1. Different Biochemical Mechanisms of Oncogene Activation through Chemical Carcinogens.- 11.2.2. Different Long-Range Physical Mechanisms of Carcinogen Binding to DNA.- 11.2.3. Remarks on the Effect of UV and Particle Radiation and the Initiation of Carcinogenesis.- References.