Canonical approaches to interatomic interactions : theory and applications / Jay R. Walton, Luis A. Rivera-Rivera.

Format:

Book

Author/Creator:

Walton, Jay R., author.

Rivera-Rivera, Luis A., author.

Contributor:

ScienceDirect (Online service)

Language:

English

Subjects (All):

Chemistry, Physical and theoretical.

Potential energy surfaces.

Physical Description:

1 online resource (xiii, 252 pages) : illustrations

Place of Publication:

Amsterdam, Netherlands : Elsevier, 2025.

Contents:

Front Cover

Canonical Approaches to Interatomic Interactions

Canonical Approaches to Interatomic Interactions:Theory and Applications

Copyright

Dedication

Contents

Preface

Acknowledgments

1- Introduction to Potential Energy Surfaces

1

The Born-Oppenheimer Approximation

1.1 Definitions of Key Terms

1.2 Underpinning Knowledge ("Foundational")

References

2

Potential Energy Surfaces and Their Implications to Chemistry

2.1 Molecular Structure

2.2 Molecular Spectroscopy

2.3 Reaction Dynamics

3

Review of Modern Interpolation and Fitting Methods to Generate Potential Energy Surfaces

3.1 Definitions of Key Terms

3.1.1 Interpolating Moving Least-Squares

3.1.2 Reproducing Kernel Hilbert Space

3.1.3 Permutation Invariant Polynomial

3.1.4 Neutral Network

3.2 Underpinning Knowledge ("Foundational")

3.2.1 Interpolating Moving Least-Squares

3.2.2 Reproducing Kernel Hilbert Space

3.2.3 Permutation Invariant Polynomial

3.2.4 Neutral Network

3.3 Detailed Methods/Protocols

3.3.1 Interpolating Moving Least-Squares

3.3.2 Reproducing Kernel Hilbert Space

3.3.3 Permutation Invariant Polynomial

3.3.4 Neutral Network

3.4 Step-By-Step Guidance on Key Procedures/Processes

3.4.1 Interpolating Moving Least-Squares

3.4.2 Reproducing Kernel Hilbert Space

3.4.3 Permutation Invariant Polynomial

3.4.4 Neutral Network

4

The Hellmann-Feynman and the Virial Theorems

4.1 Definitions of Key Terms

4.2 Underpinning Knowledge ("Foundational")

2-Canonical Approaches

5

Canonical Approaches to Pairwise Interatomic Interactions

5.1 Introduction

5.2 Methods

5.2.1 Pointwise Force Method

Repulsive Branch

Attractive Branch

Unstable Potential Tails

Force Scaling

Concavity Scaling.

Canonical Optimization Scaling

5.2.2 Average Force Method

5.2.3 Structured Versus Unstructured Methods

5.3 Case Studies

5.3.1 Preliminaries

5.3.2 Case Studies

H2 Case Study

Algorithm for Estimating Rm

Algorithm for Estimating Re

H2+ Case Study

Estimate Rm

Estimate Re

Ar2 Case Study

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

Repulsive Side of the H2 Potential

Zeroth Order Canonical Approximation

First-Order Canonical Approximation

Second-Order Canonical Approximation

Third-Order Canonical Approximation

Attractive Side of the H2 Potential

Repulsive Side of the H2+ Potential

Zeroth Order Approximation Scheme

First-Order Approximation Scheme

Second-Order Approximation Scheme

Third Order Approximation Scheme

Attractive Side of the H2+ Potential

Repulsive Side of the Ar2 Potential

Zeroth Order Approximation

First-Order Approximation

Second-Order Approximation

Attractive Side of the Ar2 Potential

5.5 Conclusions

Further reading

6

Canonical Approaches to Forces in Molecules

6.1 Introduction

Discontinuity in Derivative of Piecewise Canonical Potential

6.2 Methods

6.2.1 Unstable Branch of the Feynman Force

6.2.2 Zeroth Order Canonical Approximation

6.2.3 First-Order Piecewise Canonical Force Approximation

6.2.4 Stable Branch of the Feynman Force.

Notes:

Electronic reproduction. Amsterdam Available via World Wide Web.

Online resource; title from PDF title page (Ebsco Books, viewed April 20, 2026)

Other Format:

Print version: Walton, Jay R. Canonical approaches to interatomic interactions.

ISBN:

9780323911610

0323911617

Publisher Number:

90104279455

Access Restriction:

Restricted for use by site license.