Chapter
6. LRM Treatment of the Vibrational Isotope Effect in the Harmonic Approximation
6.1. Out-Of-Plane Vibrations of Planar Molecules
6.2. Interlacing Rule for out-of-Plane Vibrations of Planar Molecules
6.3. Single Isotopic Substitutions
6.5. Interlacing of Out-of-Plane Vibrational Frequencies of Thiophene and Deuterated Thiophenes
6.6. Out-of-Plane Vibrations of Ethylene Isotopomers
6.7. Out-of-Plane Vibrations of Benzene Isotopomers
6.8. Equality of LRM and DFT out-of-Plane Frequencies of Benzene (H,D)-Isotopomers
6.9. Comparison of LRM, Frequency Scaled DFT and Experimental out-of-Plane Frequencies of Benzene (H,D)-Isotopomers
7. External Modification as a Special Case of Internal Modification
8. Infinite Dimensional Systems
9. Description of an Infinite-Dimensional System
10. External Modifications of Infinite-Dimensional Systems
11. General Properties of The Solutions to the Infinite-Dimensional Combined System
11.2. Description of the Open System that Interacts with an Infinite System
12. Characteristic and Derived Operators
12.1. Calculation of the Derived Operators
13. Isolated Solutions of the Infinite-Dimensional Combined System
13.2. Probabilities Associated with Isolated Cardinal Eigenstates
14. Embeded Solutions of the Combined System
14.1. Embedded Cardinal Solutions
14.1.1. Basic Properties of the Solutions to the Fractional Shift Eigenvalue Equation
14.1.2. Probabilities Associated with Embedded Cardinal Eigenstates
14.1.3. Emergence of Resonance in the Case of the Weak Coupling
14.1.4. Anomal Points and Isolated Solutions
14.2. Embedded Singular Solutions
15. Completeness Relations
16. One Dimensional Open Systems
17.3. Example E3: Interaction of a Single State with one-Dimensional Solid in The Nearest-Neighbor Tight-Binding Approximation
17.3.1. The Case of Weak Coupling
18. Time-Dependent Systems
19. One Dimensional Open Systems – Time Dependent Case
19.1. Decay of a Local State in the Weak Coupling Limit
19.2. Transitions of the State Θ to The Eigenstates of the System ∞A
19.3. Transition of the Local State to The System ∞A in the Weak Coupling Limit
Chapter 2 MOLECULAR SYMMETRY AND FUZZY SYMMETRY
2.1. Generalized Parity in the Environment Space with Point GroupSymmetry
2.2. Generalized Parity in the Intrinsic Reaction Space
2.3. Generalized Parity in the Environment Space with Space PeriodicSymmetry
3. Molecular Fuzzy Symmetry Characteristics
3.1. The Membership Function of Molecular Fuzzy Symmetry
3.2. The Fuzzy Representation and Representation Component of MolecularOrbital
4. The Fuzzy Symmetry Characteristicsof Linear Small Molecule
4.1. The Fuzzy Symmetry Characteristics of Diatomic Molecule
4.1.1. The Non-hydride Diatomic Molecule
4.1.2. The Hydride Diatomic Molecule
4.2. The Fuzzy Symmetry Characteristics of Tri-Atomic Linear Molecule
5. The Fuzzy Symmetry Characteristics of Planar Molecule
5.1. The Fuzzy D2h Symmetry Characteristics – Ethylene Tetra-HalidMolecules
5.1.1. The Membership Functions and Representation Components of EthyleneTetra-Halide
5.1.2. The MO Fuzzy Correlation Diagram of Ethylene Tetra-Halide
5.2. The Fuzzy D6h Symmetry Characteristics --Azines Molecules
5.2.1. The Fuzzy Symmetry of Benzene and Pyridine
5.2.2. The Fuzzy Symmetry of Diazine
6. The Fuzzy Symmetry Characteristics of Dynamic MolecularSystem
6.1. The Fuzzy Symmetry for Simple Tri-Atomic Dynamic System
6.1.1. The Fuzzy Symmetry of B…A…C (with the same B and C) System
6.1.2. The Fuzzy Symmetry of B…A…C (with the various B and C) System
6.2. The Fuzzy Symmetry for Internal-Rotation of Allene and Its 1.3-Dihalide
6.2.1. The Fuzzy Symmetry for Internal-Rotation of Allene
6.2.2. The Fuzzy Symmetry for Chiral Transition of Allene 1,3-Dihalide
7. The One-Dimensional Space Periodic FuzzySymmetry of Some Molecules
7.1. The Fuzzy G11 Symmetry of Polyynes and Their Cyano-Compounds
7.1.1. The Fuzzy Symmetry of Molecular Skeletons
7.1.2. The Membership Function of MO
7.1.3. The Representation Component of MO
7.2. The Fuzzy G12 Symmetry of Cis-Trans-Conjugate Polyenes
7.2.1. The Fuzzy Symmetry of Molecular Skeleons
7.2.2. The Fuzzy Symmetry of MOs
Chapter 3 INFORMATION PERSPECTIVE ON MOLECULAR ELECTRONIC STRUCTURE
2. Entropy, Information and Communication Systems
2.1. Alternative Measures of Information
2.2. Dependent Probability Distributions
2.3. Communication Systems
2.4. Several Probability Schemes
2.5. Variational Principles
3. Schrödinger Equation as Information Principle
4. Electron Probabilities as Carriers of Information in Molecules
5. Bonded Atoms from Information Theory
5.2. Information-Theoretic Justification
5.3. Information Densities of Bonded Atoms
6. Importance of Non-Additive Information Measures
6.1. Electron Localization Function
6.2. Contra-Gradience Criterion of Bond Localization
7. Molecular Communication Systems
7.1. Information Channels in Atomic Orbital Resolution
7.2. Many-Orbital Extension
7.3. Localized Bonds in Diatomic Fragments
8. Additive and Non-Additive Componentsof Information Channels
Chapter 4 THE CHEMISTRY AND MATHEMATICS OF DNA POLYHEDRA
2. Building Polyhedra with DNA
2.2. When DNA Meets Polyhedra
3.2.1. DNA Truncated Octahedron
3.2.2. DNA Truncated Icosahedron
3.3. More Complicated Polyhedra
3.3.1. DNA Prisms and Bipyramid
3.3.2. Goldberg Polyhedra
4. Polyhedral Links – Novel Structures from DNA Polyhedra
4.1. Platonic Polyhedral Links
4.1.1. Type I Platonic Polyhedral Links and Knot Invariants
4.1.2. Type II Platonic Polyhedral Links and Dual Transformation
4.2. Truncated Platonic Polyhedral Links, Archimedean Polyhedral Linksand Chirality
4.3. Goldberg Polyhedral Links
4.3.1. Goldberg Polyhedral Links
4.3.2. Extended Goldberg Polyhedra and Polyhedral Links
Chapter 5 HIGH-GAIN OBSERVERS FOR ESTIMATION OF KINETICS IN BATCH AND CONTINUOUS BIOREACTORS
2. Nonlinear Dynamical Models of Bioprocesses
2.1. The General Dynamical State-Space Model of Bioprocesses
2.2. Pseudo Bond Graph Modeling Procedure for Simple Bioprocesses
Continuous Bioreactor Case
2.3. The Model of a Wastewater Biodegradation Process inside a CSTB
2.4. Models of Activated Sludge Bioprocesses
The Model of an Activated Sludge Bioprocess inside a CSTB
The Model of an Activated Sludge Bioprocess inside a SBR
2.5. The Model of a Lipase Production Bioprocess Taking Placeinside a FBB
3. High-Gain Observers for on-Line Estimation of Kinetics
3.1. The Design of High-Gain Observers
3.2. High-Gain Observers for the Wastewater Biodegradation Processinside CSTB
3.3. High-Gain Observers for Activated Sludge Processes
The Activated Sludge Bioprocess inside a CSTB
The Activated Sludge Bioprocess inside a SBR
3.4. High-Gain Observers for the Lipase Production Bioprocess
Chapter 6 REMARKS ON NOVEL EXACT SOLUTION METHODOLOGIES IN WAVEFUNCTION ANALYSIS
Some Selected HOA Example Calculations
Example 1. 1 dim Simple Harmonic Oscillator
Example 2. Schrödinger Hamiltonian with SHOs having N-Arbitrary Massesin Pairwise Anisotropic Interaction
Example 3. Schrödinger Molecular Hamiltonian with Pairwise CoulombInteraction
Example 4. Dirac and Majorana Equations with Minimum-CoupledElectromagnetic Gauge Field
Example 5. Dirac Molecular Hamiltonian with PairwiseCoulomb-Breit Interaction
Example 6. Exact Quadrature Solution of Linear Eigenvalue Problem forGeneral Class of Variable Coefficient Differential Operators
Example 7. Exact Quadrature Solution of General Class of Variable-Coefficient Differential Equations
Chapter 7 ON THE ENUMERATION OF VARIOUS NETWORKS
II. Structure of the Archetypal Closoglitter Lattice
III. On the Topology of the Glitter Series Networks
IV. Enumeration of Crystalline Networks in 3-Dimensions
Chapter 8 CHEMICAL PHYSICS OF PHONONS AND SUPERCONDUCTIVITY: A HEURISTIC APPROACH
I. Superconductivity and the Gas Laws
II. Superconductivity and the Electron-Phonon CouplingParameter, λ
III. Superconductivity and the Morse Potential & Badger’s Rule
Chapter 9 AN INTENSITY-ENHANCED 2D GRAPHICAL REPRESENTATION OF DNA AND RNA SEQUENCE
2. Intensity-Enhanced Graphical Representation
Chapter10LAGUERREFUNCTIONSWITHAPPLICATIONSFROMMATHEMATICALCHEMISTRY
MatrixFormulationoftheMainOperators
4.2.SingularLinearProblems
4.3.EigenvectorsandEigenvalues
4.3.1.TheFokker-PlanckEquation
4.4.NonlinearSteadyProblems
4.4.1.Thomas-FermiEquation
4.4.2.TheGross-PitaevskiiEquation
4.5.NonlinearEvolutionProblems
4.6.2.TheLotka-VolterraModel
Chapter 11 STABILITY OF CHEMICAL AND PHASE EQUILIBRIUM: ALTERNATIVE FORMS OF EQUATIONS FOR THERMODYNAMIC ANALYSIS
2. Traditional Approach to the Analysis of ThermodynamicStability
3. Le Chatelier – Braun Principle as an Alternative Approachto the Stability Criteria
4. Thermodynamic Inequalities for the Case of Phase Transitionsin Multicomponent Systems without Chemical Reactions
5. Thermodynamic Inequalities for the Systems with ChemicalInteractions
6. The General System of Thermodynamic Inequalities
7. Transformations of the Stability Matrix
8. The Use of Stability Criteria to Characterise NonequilibriumSystems and Processes
Chapter12LIMITATIONSINUSINGTHESANDERSON’SPRINCIPLETOESTIMATEGLOBALREACTIVITY
2.TheoreticalBackgroundandComputationalMethods
2.1.TheoreticalBackground
3.1.BuildingtheChemicalPotential
3.2.BuildingtheMolecularHardness
3.3.BuildingtheElectrophilicity
4.DeviationsinUsingtheAdditivitySchemesinEthylenePolymerizationCatalyzedbyMetallocenes.
Chapter13AGENERALMETHODFORCENTRALPOTENTIALSINQUANTUMMECHANICS
1.BackgroundandMotivation
3.TheGeneralizedPseudospectralMethod
4.1.SpikedHarmonicOscillator
4.2.ScreenedCoulombPotentials
4.3.Power-lawandLogarithmicPotentials
4.5.ApplicationtoAtomicRydbergandHollowResonances
Chapter14AREVIEWOFREDUCTIONMETHODSFORMULTIPLETIMESCALESTOCHASTICREACTIONNETWORKS
1.RecentResultsonReductionMethods
Mathematical Chemistry
( Chemistry Research and Applications )
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