hf-tutorial: A Python repository from curiousprototype

Introduction

This is a tutorial on how to implement a simple program to solve the Hartree-Fock with SCF iterations.

Impement the SCF procedure

We start from step in the algorithm described in Szabo and Ostlund, 3.4.6, p. 146

Obtain a guess at the density matrix.
Calculate the exchange and coulomb matrices from the density matrix and the two-electron repulsion integrals.
Add exchange and coulomb matrices to the core-Hamiltonian to obtain the Fock matrix.
Diagonalize the Fock matrix.
Select the occupied orbitals and calculate the new density matrix.
Compute the energy
Compute the errors and check convergence
- If converged, return the energy
- If not converged, return to second step with new density matrix

You can first implement it for hydrogen molecule by running the following code:

    mol = "h2"
    r   = 1.0
    inp = f"{mol}-{r:.4f}"
    e = main(inp) # H2 molecule with bond length 1.0

then try some more complicated molecules, such as HeH+

    mol = "heh+"
    r   = 1.0
    inp = f"{mol}-{r:.4f}"
    e = main(inp) # HeH+ molecule with bond length 1.0

and H2O

    mol = "h2o"
    r   = 1.0
    inp = f"{mol}-{r:.4f}"
    e = main(inp) # water molecule with bond length 1.0

Potential Energy Surface

After implementing the SCF procedure, we can use it to compute the potential energy surface of the H$_2$ molecule. We can do this by varying the internuclear distance and computing the energy at each point.

    for r in numpy.linspace(0.5, 2.5, 21):
        inp = f"h2-{r:.4f}"
        e = main(inp)
        print(f"H2: r={r: 6.4f}, e={e: 12.8f}")

You may also try other molecules, such as HeH+ and H2O.

Unrestricted Hartree-Fock

Write a new function main_uhf to implement the unrestricted Hartree-Fock method. See what's the difference between the restricted and unrestricted Hartree-Fock potential energy surfaces.

Dependencies

numpy
scipy
If you wish to use ./data/gen_data.py to generate the integrals, pyscf is also required.

Reference