# Hartree-Fock Study of Helium Hydride

This is my final project for the Scientific Computation class at Reed (Physics 367), taught by Prof. Joel Franklin.

This project aims to find the equilibrium bond length of the helium hydride cation $\text{HeH}^+$ by calculating the molecular energy of $\text{HeH}^+$ over a range of internuclear distances using restricted, closed-shell Hartree-Fock calculation with the STO-3G basis set.

Hartree-Fock (HF), also known as the self-consistent field method, was the earliest and simplest method in electronic structure theory, which tries to describes the motion of electrons in atoms or molecules. Although it has been surpassed by many other more advanced and accurate methods, such as configuration interaction, density functional theory, HF remains useful as a starting point for many calculations. For example, many Quantum Monte Carlo (QMC) calculation use HF wave functions as trial wave functions. The vocabulary of HF, such as closed-shell, open-shell, restricted and unrestricted orbitals, lives on in the electronic structure literature today.

I want to use this project to get hands-on experience with HF as a first step to broaden my understanding of electronic structure theory beyond the niche of QMC (which is very distinct from the rest of the field). Understanding HF is a good springboard to understand other more currently relevant methods like configuration interaction, coupled-cluster and density functional theory, arguably the most popular of all electronic structure methods.

This project is also an opportunity for me to use Mathematica’s functional and rule-based style of programming as much as possible.