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

4.2. Fock space

The electronic wave function includes the spatial position for each electron () conditioned on the nuclear positions () and the spin directional coordinates for each electron (). The electronic wave function must be antisymmetric with respect to the exchange of pair particle labels because these particles are fermions. Please recall that this is the Pauli exclusion principle introduced in Section 2.1.3, General formulation of the Pauli exclusion principle.

Now, let's consider two electrons and in states and where the corresponding electronic wave function () representing the states of the two-electron system is antisymmetric () with respect to the exchange of identical pair particles :

Since a one-body electronic wave function as presented in Section 2.1, Postulate 1 – Wave functions, is a product of spatial () and spin components (), there are two...