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

4.3. Fermionic creation and annihilation operators

In the previous section, we mentioned that the Fock space is a mathematical construction and does not represent a physical reality nor a chemical actuality. However, please keep in mind that in a molecule, each electron can occupy only one spin-orbit at a time and no two electrons can occupy the same spin-orbit.

Now we further consider a subspace of the Fock space, which is spanned by the occupation number of the spin-orbits, which is described by electronic basis states , where is the occupation number of orbital .

The spin-orbital state not occupied by an electron is represented by .

We define a set of fermionic annihilation operators and creation operators , which act on local electron modes, and which satisfy the following anti-commutation relations:

where is the Dirac delta function. The operators are called the occupation number operators and commute with one...