Book Image

Quantum Chemistry and Computing for the Curious

By : Alex Khan, Keeper L. Sharkey, Alain Chancé
Book Image

Quantum Chemistry and Computing for the Curious

By: Alex Khan, Keeper L. Sharkey, Alain Chancé

Overview of this book

Explore quantum chemical concepts and the postulates of quantum mechanics in a modern fashion, with the intent to see how chemistry and computing intertwine. Along the way you’ll relate these concepts to quantum information theory and computation. We build a framework of computational tools that lead you through traditional computational methods and straight to the forefront of exciting opportunities. These opportunities will rely on achieving next-generation accuracy by going further than the standard approximations such as beyond Born-Oppenheimer calculations. Discover how leveraging quantum chemistry and computing is a key enabler for overcoming major challenges in the broader chemical industry. The skills that you will learn can be utilized to solve new-age business needs that specifically hinge on quantum chemistry
Table of Contents (14 chapters)
Chapter 8: References
Chapter 9:Glossary
Appendix B: Leveraging Jupyter Notebooks on the Cloud
Appendix C: Trademarks

6.1. Non-Born-Oppenheimer molecular Hamiltonian

Recall from Section 4.1, Born-Oppenheimer approximation, the expression of the Hamiltonian in the laboratory frame coordinates :

where in atomic units, the mass of the electron and the reduced Planck constant () are set to the value 1. The LAB Hamiltonian comprises the sum of the kinetic energy of all particles and the potential energy between all particles with the following definitions:

  • and are the second derivative operator with respect to the position coordinates for electrons and nuclei, that is, and likewise for the electron.
  • , , and are the distances between electrons and , electron and nucleus , and nuclei and determined by the Euclidean norm.

The list of the operators of the LAB Hamiltonian has been presented in Figure 4.3.

In the LAB Hamiltonian, the energy of the molecular system is continuous, not discrete. The center-of-mass (COM) motion does not yield any change to...