Canonical Approaches to Interatomic Interactions - Theory and Applications

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.

List of contents

Part 1: Introduction to Potential Energy Surfaces

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’)

Part 2: Canonical Approaches
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

Part 3: Applications and Case Studies
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

About the author

Luis A. Rivera-Rivera is an Associate Professor at the Department of Physical Sciences, Ferris State University, USA. After completing his B.S. degree in chemistry at the University of Puerto Rico, Dr. Rivera went on to do an M.S. degree in inorganic chemistry, finally completing his Ph.D. in physical chemistry at Texas A&M University. After his Ph.D., he carried out postdoctoral research in theoretical chemistry and has published well over forty papers and given multiple presentations in this area.
Jay R. Walton is Professor Emeritus at the Department of Mathematics, Texas A&M University, USA. He earned his Ph.D. from Indiana University, and was previously also Professor of Aerospace Engineering and Deputy Director of the Institute for Applied Mathematics and Computational Science at the university. He has published over 90 research papers.

Product details

• Authors: Jay R. Walton, Luis A. Rivera-Rivera, Luis A Rivera-Rivera, Jay R Walton
• Publisher: Elsevier
• Languages: English
• Release: 01.10.2025
• EAN: 9780323911559
• ISBN: 978-0-323-91155-9
• Subjects: Natural sciences, medicine, IT, technology > Chemistry > Physical chemistry; SCIENCE / Chemistry / Physical & Theoretical, Physical Chemistry