Typical pathways for modelling interatomic interactions involve the plotting of potential energy against radial displacement, but such approaches can be computationally costly. Canonical Approaches to Interatomic Interactions: Theory and Applications provides an overview of the field and presents a replicable, novel force-based approach that demonstrates accurate and quantitative interrelations between weakly bound and strong covalently bound intermolecular interactions.
Beginning with an introduction to Potential Energy Surfaces (PES) and modern approaches in Part 1, Part 2 goes on to describe Canonical Approaches in detail, including methodologies and data to allow replication. Part 3 then goes on to outline some key applications, before future directions are discussed in Part 4.
Sharing the insight of its progressive authors, Canonical Approaches to Interatomic Interactions: Theory and Applications is an informative guide for all those working with interatomic interactions and PES, including researchers in in chemical kinetics and bonding, molecular mechanics, quantum chemistry and molecular modelling.
1. Part 1. Introduction to Potential Energy Surfaces - p. P1 2. Chapter 1. The Born-Oppenheimer Approximation - p. 3 3. Chapter 2. Potential Energy Surfaces and Their Implications to Chemistry - p. 7 4. Chapter 3. Review of Modern Interpolation and Fitting Methods to Generate Potential Energy Surfaces - p. 17 5. Chapter 4. The Hellmann–Feynman and the Virial Theorems - p. 31 6. Part 2. Canonical Approaches - p. P2 7. Chapter 5. Canonical Approaches to Pairwise Interatomic Interactions - p. 41 8. 5.1 Introduction - p. 41 9. 5.2 Methods - p. 42 10. 5.2.1 Pointwise Force Method - p. 52 11. Repulsive Branch - p. 54 12. Attractive Branch - p. 60 13. Unstable Potential Tails - p. 63 14. Force Scaling - p. 64 15. Concavity Scaling - p. 65 16. Canonical Optimization Scaling - p. 67 17. 5.2.2 Average Force Method - p. 69 18. 5.2.3 Structured Versus Unstructured Methods - p. 74 19. 5.3 Case Studies - p. 82 20. 5.3.1 Preliminaries - p. 82 21. 5.3.2 Case Studies - p. 85 22. H2 Case Study - p. 87 23. Algorithm for Estimating Rm - p. 97 24. Algorithm for Estimating Re - p. 98 25. H2+ Case Study - p. 101 26. Estimate Rm - p. 103 27. Estimate Re - p. 104 28. Ar2 Case Study - p. 107 29. 5.4 Computational Cost and Efficiency - p. 109 30. 5.4.1 Approximation Accuracy - p. 110 31. 5.4.2 Approximation Computational Cost - p. 112 32. 5.4.3 Case Studies of Canonical Approximation Accuracy Versus Computational Cost - p. 112 33. H2 Case Study - p. 118 34. Repulsive Side of the H2 Potential - p. 118 35. Attractive Side of the H2 Potential - p. 123 36. H2+ Case Study - p. 128 37. Repulsive Side of the H2+ Potential - p. 128 38. Attractive Side of the H2+ Potential - p. 132 39. Ar2 Case Study - p. 135 40. Repulsive Side of the Ar2 Potential - p. 135 41. Attractive Side of the Ar2 Potential - p. 137 42. 5.5 Conclusions - p. 142 43. Chapter 6. Canonical Approaches to Forces in Molecules - p. 145 44. 6.1 Introduction - p. 145 45. 6.2 Methods - p. 147 46. 6.3 Feynman Force Qualitative Properties - p. 155 47. 6.4 Case Studies and Results - p. 158 48. 6.5 Conclusion - p. 169 49. Chapter 7. Canonical Approaches and the Unification of Pairwise Interatomic Interactions - p. 171 50. Part 3. Applications and Case Studies - p. P3 51. Chapter 8. Canonical Approaches and the Born-Oppenheimer Approximation - p. 201 52. Chapter 9. Canonical Approaches and the Virial Theorem - p. 213 53. Chapter 10. Canonical Approaches to Multidimensional Potential Energy Surfaces - p. 235 54. Index - p. 249
Typical pathways for modelling interatomic interactions involve the plotting of potential energy against radial displacement, but such approaches can be computationally costly. Canonical Approaches to Interatomic Interactions: Theory and Applications provides an overview of the field and presents a replicable, novel force-based approach that demonstrates accurate and quantitative interrelations between weakly bound and strong covalently bound intermolecular interactions.
Beginning with an introduction to Potential Energy Surfaces (PES) and modern approaches in Part 1, Part 2 goes on to describe Canonical Approaches in detail, including methodologies and data to allow replication. Part 3 then goes on to outline some key applications, before future directions are discussed in Part 4.
Sharing the insight of its progressive authors, Canonical Approaches to Interatomic Interactions: Theory and Applications is an informative guide for all those working with interatomic interactions and PES, including researchers in in chemical kinetics and bonding, molecular mechanics, quantum chemistry and molecular modelling.
1. Part 1. Introduction to Potential Energy Surfaces - p. P1 2. Chapter 1. The Born-Oppenheimer Approximation - p. 3 3. Chapter 2. Potential Energy Surfaces and Their Implications to Chemistry - p. 7 4. Chapter 3. Review of Modern Interpolation and Fitting Methods to Generate Potential Energy Surfaces - p. 17 5. Chapter 4. The Hellmann–Feynman and the Virial Theorems - p. 31 6. Part 2. Canonical Approaches - p. P2 7. Chapter 5. Canonical Approaches to Pairwise Interatomic Interactions - p. 41 8. 5.1 Introduction - p. 41 9. 5.2 Methods - p. 42 10. 5.2.1 Pointwise Force Method - p. 52 11. Repulsive Branch - p. 54 12. Attractive Branch - p. 60 13. Unstable Potential Tails - p. 63 14. Force Scaling - p. 64 15. Concavity Scaling - p. 65 16. Canonical Optimization Scaling - p. 67 17. 5.2.2 Average Force Method - p. 69 18. 5.2.3 Structured Versus Unstructured Methods - p. 74 19. 5.3 Case Studies - p. 82 20. 5.3.1 Preliminaries - p. 82 21. 5.3.2 Case Studies - p. 85 22. H2 Case Study - p. 87 23. Algorithm for Estimating Rm - p. 97 24. Algorithm for Estimating Re - p. 98 25. H2+ Case Study - p. 101 26. Estimate Rm - p. 103 27. Estimate Re - p. 104 28. Ar2 Case Study - p. 107 29. 5.4 Computational Cost and Efficiency - p. 109 30. 5.4.1 Approximation Accuracy - p. 110 31. 5.4.2 Approximation Computational Cost - p. 112 32. 5.4.3 Case Studies of Canonical Approximation Accuracy Versus Computational Cost - p. 112 33. H2 Case Study - p. 118 34. Repulsive Side of the H2 Potential - p. 118 35. Attractive Side of the H2 Potential - p. 123 36. H2+ Case Study - p. 128 37. Repulsive Side of the H2+ Potential - p. 128 38. Attractive Side of the H2+ Potential - p. 132 39. Ar2 Case Study - p. 135 40. Repulsive Side of the Ar2 Potential - p. 135 41. Attractive Side of the Ar2 Potential - p. 137 42. 5.5 Conclusions - p. 142 43. Chapter 6. Canonical Approaches to Forces in Molecules - p. 145 44. 6.1 Introduction - p. 145 45. 6.2 Methods - p. 147 46. 6.3 Feynman Force Qualitative Properties - p. 155 47. 6.4 Case Studies and Results - p. 158 48. 6.5 Conclusion - p. 169 49. Chapter 7. Canonical Approaches and the Unification of Pairwise Interatomic Interactions - p. 171 50. Part 3. Applications and Case Studies - p. P3 51. Chapter 8. Canonical Approaches and the Born-Oppenheimer Approximation - p. 201 52. Chapter 9. Canonical Approaches and the Virial Theorem - p. 213 53. Chapter 10. Canonical Approaches to Multidimensional Potential Energy Surfaces - p. 235 54. Index - p. 249
