Eugene Babaev "Intuitive Chemical Topology Concepts" (c)

Table of contents

1. Introduction

2. Some Useful Concepts of Visual Topology

2.1. Graphs

2.2. Hypergraphs

2.3. Surfaces

2.4. Euler Characteristic

2.5. Surfaces and Polygons

2.6. Graphs and Surfaces

3. Explicit Concepts of Molecular Topology

3.1. Classical Chemical Models

Molecular graph

Molecular surface

Homeomorphism in C_nH_{2n+x series}

3.2. Graphs and Surfaces in Physical Models

Molecular graphs in physical models

Molecular 2D surfaces in physical models

4. Intuitive Chemical Concepts Related to Topology

Intuitive cut-and-paste

Double bond

Free radicals and open-shell molecules

Lone pairs and vacancies

5. Topology of Lewis Formula: Pseudographs, Graphoids and Topoids

5.1. Molecular Pseudograph

(i) Cycles and electron count

(ii) Invariance of valency

(iii) Isomorphism and similarity

(iv) Octet rule and resonance

5.2. Molecular Graphoid

5.3. Concept of Molecular Topoid

6. Some Properties of Molecular Topoids

6.1. Overview and Manipulations with Topoids

6.2. The Cut-and-Paste Procedure

6.3. Virtual Handle and Self-crossing in 2D Surfaces

7. Invariance of the Euler Characteristic in Chemical Reactions

Loss of connectedness (case of boa and elephant)

Formation of cycle (Uroboros paradox)

Topological balance equations

8. Homeomorphism of Topoids

CH₂ group

CH⁺ group

BH group

NH₃ group

Aromaticity and homeomorphism

9. Surfaces with Jordan Curves as Exact Images of Graphs

9.1. Idea and Algorithm of Representing Graph by Labeled Surface

9.2. Dual Graphs for Labeled Surface

9.3. Labeled Sphere and Trees

9.4. Labeled Torus and Monocycles

10. Chemical Applications of Surfaces with Embedded Jordan Curves

10.1. Chemical Isomerism and Homology: a Novel Viewpoint

10.2. Homeomorphism and Isotopy: Lone Pair and Double Bond

10.3. Isotopy and Delocalization in Cycles

11. Delocalized Bonds and Hypertopoids

11.1. Attempts to Use Molecular Graphs and Hypergraphs

11.2. Pseudomanifolds and Their Euler Characteristic

11.3. Molecular Hypertopoids and their Homeomorphism

11.4. Interconversion of Molecular Hypertopoids

Heterolytic processes

Homolytic processes

Topological design of reaction mechanisms

Curved arrows, resonance, and topology

Expanded 2D images of delocalized molecules

12. Orientation, Spin and Nonorientable Surfaces of Free Radicals

Conclusion

References