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

4.5. Basis sets

The spatial wave functions, , in the integrals of Section 4.4, Molecular Hamiltonian in the Hartree-Fock orbitals basis, are approximated by linear combinations of several independent basis functions. The form of these functions is inspired by the atomic orbitals of hydrogen-like systems that we introduced in Section 2.1.1, Spherical harmonic functions, which have a radial part as shown in Section 2.2.1, Computing the radial wave functions.

Two classes of approximate basis orbitals that are commonly used are Slater-type orbitals (STOs) based on the Slater determinant introduced in Section 4.2, Fock space, and Cartesian Gaussian-type orbitals (GTOs). These two types of basis functions can be combined as STO-nG, where n is the number of Gaussians used to make the approximation. Ab Initio electronic structure computations are conducted numerically using a basis set of orbitals.

We now detail the structure of these two classes and illustrate them with Python plots...