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

4.1. Born-Oppenheimer approximation

Recall that the atomic orbital of an electron in an atom and the molecular orbital of an electron in a molecule are time-independent stationary states. In Section 2.4, Postulate 4 – Time-independent stationary states, we introduced the time-independent Schrödinger equation:

where is the non-relative Hamiltonian operator obtained by quantizing the classical energy in Hamilton form (first quantization), and it represents the total energy () of all its particles; electrons and nuclei. For a molecular system, the electric charge of two nuclei and are and with masses and . The position of the particles in the molecule is determined by using a laboratory (LAB) frame coordinate system, as shown in Figure 4.2, where the origin of the coordinate system is outside the molecule. The origin of the coordinate system can be placed anywhere in free space.

Figure 4.2 – LAB frame coordinates

The Hamiltonian...