tamuhey/python_1d_dft

1D density functional theory code in Python

DFT (Density Functional Theory) tutorial code in Python

• Jupyter Notebook (Japanese)

• Run in browser (Japanese)

• Simplified Chinese

• Goal: write our own Kohn-Sham (KS) DFT code

  • Target: a harmonic oscillator including kinetic energy, electrostatic repulsion between the electrons, and the local density approximation for electronic interactions, ignoring correlation.

Refs.

• http://dcwww.camd.dtu.dk/~askhl/files/python-dft-exercises.pdf

python_1d_dft's Issues

The boundary condition?

I found this wonderful repo very useful to understand DFT.

I wrote a short code snippet to calculate the Hydrogen atom energy levels here using finite difference method, which is pretty naive, and your repo may be very helpful for me to improve my code.

I am just confused about the treatment of boundary conditions. It seems your code doesn't take account of PBC(Periodic Boundary Condition). What should we do to include the PBC?

Here is what I know for now.

For the second derivative operator, we should use D2[0,-1] = D2[0, 1] and D2[-1, 0] = D2[-1, -2] to make sure the operator be symmetric like this:

$$\begin{bmatrix} -2 & 1 & \cdots & \cdots & 1 \\ 1 & -2 & 1 & \cdots & \cdots \\ \cdots & 1 & -2 & 1 & \cdots \\ \cdots & \cdots & 1 & -2 & 1 \\ 1 & \cdots & \cdots & 1 & -2 \end{bmatrix}$$

And what about the potential part? The potential part is added to the diagonal part of Hamiltonian and how to include PBC?

Thanks very much in advance.