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

4.4. Molecular Hamiltonian in the Hartree-Fock orbitals basis

For mapping the original electronic structure Hamiltonian into the corresponding qubit Hamiltonian, we work in the second quantization formalism of quantum mechanics. Recall we introduced the first quantization in Section 4.1, Born-Oppenheimer approximation.

The Hartree-Fock (HF) method approximates an -body problem into one-body problems where each electron evolves in the mean field of the other electrons.

We can rewrite the electronic molecular Hamiltonian () as a linear combination of products of creation and annihilation operators (summarized in Figure 4.4):

where removes an electron from spin-orbital , and creates an electron in spin-orbital . The operation is the excitation operator, which excites an electron from the occupied spin-orbital into the unoccupied orbital . Constructing these were introduced in Section 2.1, Postulate 1 – Wave functions. The nuclear-nuclear ...