Status: this site is a work in progress. The introduction below, the Basis Sets page and the HF chapter are written. The MP2, CCSD and DFT chapter pages are placeholders with a one-line description and links; their content has not been written yet.

Foreword

Often I think about how could I have learned this subject better. I believe there may be numerous other students who also think the same. As a kinesthetic learner, I often wonder about the equation(s), how do they look and how they shaped the modern Quantum Chemistry from Quantum Mechanics. This is an ongoing project which I want to continue as long as I can. This is also a testament of my learning. As I learn, I write more to learn more.

At first, I will try to cover the Hartree-Fock approximation. It is imperative that all of us, students of computational chemistry to grasp this particular method. Then I will try to cover the basis-sets, different integrals and implement them with simple python codes.

Quantum Mechanics

The concept of finding approximate solution to the Schrödinger equation is central: Here, it also means that we try to find the solution of non-relativistic time-independent Schrödinger equation.

\[\hat{H} \Psi = E \Psi\]

where:

$\hat{H}$ is the Hamiltonian operator for a system of nuclei and electrons having position vector $\mathbf{R}_A$ and $\mathbf{r}_i$ respectively.
$\Psi$ is the wavefunction
$E$ is the energy

The electronic $\hat{H}$ for N electrons and M nuclei, in the Born-Oppenheimer approximation and in atomic units, is

\[\hat{H}_{\text{elec}} = -\sum_{i=1}^{N} \frac{1}{2}\nabla^{2}_{i} - \sum_{i=1}^{N}\sum_{A=1}^{M} \frac{Z_A}{r_{iA}} + \sum_{i=1}^{N}\sum_{j>i}^{N} \frac{1}{r_{ij}}\]

Where to go next

The chapters build on this introduction. Start with Basis sets, then Hartree-Fock.