Canonical Approaches to Interatomic Interactions

Chapter 1: The Born−Oppenheimer Approximation

• • 1.1: Definitions of key terms
• • 1.2: Underpinning knowledge (‘foundational’)

Chapter 2: Potential Energy Surfaces and Its Implications to Chemistry

• • 2.1: Molecular Structure
• • 2.2: Molecular Spectroscopy
• • 2.3: Reaction Dynamics

Chapter 3: Review of Modern Interpolations and Fitting Methods to Generate Potential Energy Surfaces.

• • 3.1: Definitions of key terms
• • 3.2: Underpinning knowledge (‘foundational’)
• • 3.3: Detailed methods/protocols
• • 3.4: Step-by-step guidance on key procedures/processes

Chapter 4: The Hellmann−Feynman and the Virial Theorems

• • 4.1: Definitions of key terms
• • 4.2: Underpinning knowledge (‘foundational’)

Chapter 5: Canonical Approaches to Pairwise Interatomic Interactions

• • 5.1: Introduction
• • 5.2: Methods
• • 5.2.1: Pointwise Force Method
• • 5.2.2: Average Force Method
• • 5.2.3: Structured vs Unstructured Methods
• • 5.3: Case studies
• • 5.3.1 Preliminaries
• • 5.3.2 Case Studies
• • 5.4: Computational Cost and Efficiency
• • 5.4.1: Approximation Accuracy
• • 5.4.2 Approximation Computational Cost
• • 5.4.3 Case Studies of Canonical Approximation Accuracy Versus Computational Cost
• • 5.5: Conclusions

Chapter 6: Canonical Approaches to Forces in Molecules

• • 6.1: Introduction
• • 6.2: Methods
• • 6.2.1 Computational Cost of Force Evaluations
• • 6.2.2 Piecewise Canonical Approximation Error
• • 6.3: Feynman Force Qualitative Properties
• • 6.4: Case studies and Results
• • 6.5: Conclusions

Chapter 7: Canonical Approaches and the Unification of Pairwise Interatomic Interactions

• • 7.1: Introduction
• • 7.2: Case studies and Results
• • 7.3: Discussion and Conclusion

Chapter 8: Canonical Approaches and the Born−Oppenheimer Approximation

• • 8.1: Introduction
• • 8.2: Methods
• • 8.3: Case studies and Results
• • 8.4: Discussion & Conclusions

Chapter 9: Canonical Approaches and the Virial Theorem

• • 9.1: Introduction
• • 9.2: Methods
• • 9.3: Case studies and Results
• • 9.4: Discussion & Conclusions

Chapter 10: Canonical Approaches to Multidimensional Potential Energy Surfaces

• • 10.1: Introduction
• • 10.2: Methods
• • 10.3: Case studies
• • 10.4: Discussion & Conclusion