Book Image

Quantum Chemistry and Computing for the Curious

By : Keeper L. Sharkey, Alain Chancé
Book Image

Quantum Chemistry and Computing for the Curious

By: 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)
8
Chapter 8: References
9
Chapter 9:Glossary
Appendix B: Leveraging Jupyter Notebooks on the Cloud
Appendix C: Trademarks

2.4. Postulate 4 – Time-independent stationary states

A quantum state is a time-independent stationary state if all its observables are independent of time. These states are very important in quantum chemistry. The atomic orbital of an electron and the molecular orbital of an electron in a molecule are time-independent stationary states.

The time-independent Schrödinger equation can be written as follows, that is, static: where is the energy eigenvalue, and is the state vector of the quantum system not as a function of time.

This postulate implies that the wave function must be an eigenfunction for all measurements and corresponding operations that represent the energy. An eigenfunction is a function that remains unchanged when acted upon it by an operator or when a measurement is made.

We use this concept more in Chapter 4, Molecular Hamiltonians.