Examples

Included in the DFT_1d download is an example folder including several scripts

demonstrating possible uses of DFT_1d.

Hartree-Fock Self-Consistent Field Example

Summary:

Generates Hartree-Fock (HF) a tabel from the [Baker2015] paper which includes Li atom and Li, Be, He, and H atoms.

examples.hf_scf_example.hf_scf_atom(grids, N_e, Z)

Example HF-SCF calculation for a 1D atom with

exponential interactions, see ext_potentials.exp_hydrogenic.

Parameters

• grids – grids: numpy array of grid points for evaluating 1d potential.

• (num_grids –

• ) –

• N_e – the number of electrons in the atom.

• Z – the nuclear charge Z of the atom.

Returns

HF-SCF solver class.

examples.hf_scf_example.get_latex_table_atoms(grids)

Example Reproduce HF results in table 2 of [Baker2015].

Parameters

• grids – grids: numpy array of grid points for evaluating 1d potential.

• (num_grids –

• ) –

Prints:

copyable latex-formatted table.

examples.hf_scf_example.single_atom(grids, N_e, Z)

Kohn-Sham DFT Example

Summary:

Generates LDA DFT values from a tabel from the [Baker2015] paper which includes Li atom and Li, Be, He, and H atoms.

examples.ks_dft_example.lda_ks_dft_atom(grids, N_e, Z)

local density approximation (LDA) KS-DFT calculation for a 1D atom with

exponential interactions, see ext_potentials.exp_hydrogenic.

Parameters

• grids – grids: numpy array of grid points for evaluating 1d potential.

• (num_grids –

• ) –

• N_e – the number of electrons in the atom.

• Z – the nuclear charge Z of the atom.

Returns

KS-DFT solver class.

examples.ks_dft_example.get_latex_table_atoms(grids)

Reproduce LDA results in table 2 of [Baker2015].

Parameters

• grids – grids: numpy array of grid points for evaluating 1d potential.

• (num_grids –

• ) –

Prints:

copyable latex-formatted table.

examples.ks_dft_example.single_atom(grids, N_e, Z)

Poschl-Teller potentials

Summary:

Calculates a system with two Poschl-Teller wells

examples.two_poschl_teller.get_plotting_params()

Initialize figure for plots.

Returns

a Figure object with initialized parameters. ax: an Axes object with initialized parameters.

Return type

fig

examples.two_poschl_teller.plot_and_save(x_list, y_list, x_label, y_label, name, xlim=(None, None), ylim=(None, None), folder=None)

Plot a single curve on a graph and save it as .png file.

Parameters

• x_list – list (or array), specify the x-axis points.

• y_list – list (or array), specify the y-axis points.

• x_label – label for x-axis.

• y_label – label for y-axis.

• name – str, name of the image saved (without .png).

• folder – str, the path to the folder to save the image in. Does not need to pre-exist before running.

examples.two_poschl_teller.plot_multiple_and_save(plot_list, name, xlim=(None, None), ylim=(None, None), folder=None)

Plot mutiple curves on a single graph and save it as .png file.

Parameters

• plot_list – list of lists, specify plotting parameters for each curve in the form of [label, x_list, y_list, linestyle, color].

• name – str, name of the image saved (without .png).

• xlim – tuple, xlim[0] == left limit, xlim[1] == right limit; setting to None means flexible ranges.

• ylim – tuple, ylim[0] == bottom limit, ylim[1] == top limit; setting to None means flexible ranges.

• folder – str, the path to the folder to save the image in. Does not need to pre-exist before running.

examples.two_poschl_teller.two_poschl_teller(grids, d, lam=1.0, a=1.0)

Two Poschl-Teller potential wells seperated by distance d.

Parameters

• grids – numpy array of grid points for evaluating 1d potential. (num_grids,)

• d – float, distance seperated by two Poschl-Teller potential wells.

• lam – float, lambda in the Poschl-Teller potential function.

• a – float, coefficient in the Poschl-Teller potential function.

• center – float, the center of the potential.

Returns

Potential on grid with shape (num_grid,)

Raises

ValueError – If lam is not positive.