diff --git a/notebook/band-theory/FFT_and_planewaves.ipynb b/notebook/band-theory/FFT_and_planewaves.ipynb index 28cca51..e5cb45b 100644 --- a/notebook/band-theory/FFT_and_planewaves.ipynb +++ b/notebook/band-theory/FFT_and_planewaves.ipynb @@ -7,11 +7,13 @@ "source": [ "# **Fourier Transforms and Plane-Wave Expansions**\n", "\n", + "Authors:Guoyuan Liu, Dou Du and Giovanni Pizzi\n", + "\n", " Go back to index\n", "\n", "**Source code:** https://github.com/osscar-org/quantum-mechanics/blob/master/notebook/band-theory/FFT_and_planewaves.ipynb\n", "\n", - "This notebook shows interactively how discrete Fourier series can represent a function with a limited amount of plane-wave components. A common way to represent a wavefunction when solving the Kohn-Sham equations is via its expansion in plane waves.\n", + "This notebook shows interactively how a discrete Fourier series can be used to represent a function with a limited number of plane-wave components. A common way to represent a wavefunction when solving the Kohn-Sham equations for a periodic solid is via its expansion in plane waves.\n", "This notebook focuses on a simple example (much simpler than a complete DFT calculation) in order to help the reader focus on the essential aspects of such a representation.\n", "\n", "
" @@ -25,7 +27,7 @@ "## **Goals**\n", "\n", "* Understand how a plane-wave basis is directly related to a Fourier series.\n", - "* Learn how to decompose a function using a FFT algorithm.\n", + "* Learn how to decompose a function using an FFT algorithm.\n", "* Examine how a function is reconstructed from a finite (possibly not complete) set of plane waves.\n", "* Understand the impact of the basis-set size on the convergence of the integral of the reconstructed function." ] @@ -51,7 +53,7 @@ "## **Tasks and exercises**\n", "\n", "
    \n", - "
  1. Prove that plane waves form an orthogonal basis set.\n", + "
  2. Background theory: prove that plane waves form an orthogonal basis set.\n", "
    \n", " Solution\n", " \n", @@ -59,26 +61,25 @@ "$$ \\langle w_N^j, w_N^k \\rangle = \\langle w_N^k, w_N^j \\rangle = \\int_{-\\pi}^{\\pi} e^{ijx} e^{-ikx}dx = \\int_{-\\pi}^{\\pi} e^{i(j-k)x} dx = \\frac 1 {i(j-k)} [e^{i(j-k)x}]_{-\\pi}^{\\pi} = \\begin{cases} 0 & \\text{if j $\\neq$ k} \\\\ 2\\pi & \\text{if j = k}\\end{cases}$$\n", "
  3. \n", "\n", - "
  4. How does the number of plane waves affect the approximation of the target function? Will a function with more \"oscillations\" require more components to be accurately represented?\n", + "
  5. How does the number of plane waves affect the approximation of the target function? Move the $N_{fft}$ slider to modify the number of Fourier components used in the approximation. Will a function with more \"oscillations\" require more components to be accurately represented? You can change the objective function (from a relatively smooth function to a more oscillatory one) via the drop-down menu.\n", "
    \n", " Solution\n", - "\n", - "Move the slider to try different numbers of Fourier components. Observe if the FFT interpolation approximates well the original function and if the integral of the square modulus is close to the convergence value. You can also change the objective function by the drop-down menu. Generally, more sampling yields more accurate representation. \n", + "Observe whether the FFT interpolation approximates well the original function and if the integral of the square modulus is close to the converged value indicated by the red horizontal line. Generally, increased sampling yields a more accurate representation of the objective function.\n", "For functions with more oscillations (higher frequency components), more Fourier components are needed to reach the same level of accuracy.\n", "
  6. \n", "\n", - "
  7. How can we reduce the number of plane waves needed in a DFT calculation, without sacrificing the accuracy of the representation?\n", + "
  8. Background theory: how can we reduce the number of plane waves needed in a DFT calculation, without sacrificing the accuracy of the representation?\n", "
    \n", " Solution\n", "\n", "Wavefunctions have the strongest oscillations near nucleus, and a very large number of plane waves is needed to accurately represent this region. Fortunately, core electrons are less relevant in chemical bonding, so we can simplify the problem and obtain a much smoother (pseudo)wavefunction by excluding the core electrons. To learn more about this approach, please check our notebook on pseudopotentials. In general, the combination of pseudopotentials and a plane-wave expansion enables fast and accurate calculation of materials and their properties.\n", "
  9. \n", "\n", - "
  10. In a DFT calculation, how can we control the number of plane waves used in the basis set?\n", + "
  11. Background theory: in a DFT calculation, how can we control the number of plane waves used in the basis set?\n", "
    \n", " Solution\n", " \n", - "The kinetic energy of a plane wave of momentum $\\mathbf G$ is given by $\\frac {\\hbar^2}{2m} \\lvert \\mathbf G \\rvert^2$. By setting a cutoff energy, we can limit the size of the plane-wave basis set. The value of the cutoff depends on the system under investigation and the pseudopotential used, and convergence tests are normally required. To have a suggestion of a converged cutoff value based on the choice of pseudopotentials, you can check the standard solid-state pseudopotentials (SSSP) library on Materials Cloud.\n", + "The kinetic energy of a plane wave of momentum $\\mathbf G$ is given by $\\frac {\\hbar^2}{2m} \\lvert \\mathbf G \\rvert^2$. By setting a cutoff energy, we can limit the size of the plane-wave basis set. The value of the required cutoff depends on the system under investigation and the pseudopotential used. Convergence tests are normally required to gain confidence in the value of the cutoff employed. To have a suggestion of a converged cutoff value based on the choice of pseudopotentials, you can check the standard solid-state pseudopotentials (SSSP) library on Materials Cloud.\n", "
  12. \n", "
" ] @@ -96,7 +97,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "id": "a34187d0", "metadata": {}, "outputs": [], @@ -112,7 +113,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "id": "e85c3b8b", "metadata": {}, "outputs": [], @@ -129,7 +130,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "id": "c463b6d5", "metadata": {}, "outputs": [], @@ -147,7 +148,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "id": "48d2b850", "metadata": {}, "outputs": [], @@ -188,7 +189,7 @@ " N_rfft += 1\n", "\n", " ax2.axes.yaxis.set_ticks([]) # remove y ticks\n", - " ax2.set_title('Expansion Components')\n", + " ax2.set_title('Basis functions')\n", "\n", "CONVERGE_SMOOTH = get_integral_resampled(N_fft=200, function=periodic_f)\n", "CONVERGE_ROUGH = get_integral_resampled(N_fft=200, function=periodic_f2)\n", @@ -265,10 +266,36 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "id": "300944ff", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "2a4e66bb71e2403b90d321de1de984be", + "version_major": 2, + "version_minor": 0 + }, + "image/png": 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", + "text/html": [ + "\n", + "
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\n", + " Figure\n", + "
\n", + " \n", + "
\n", + " " + ], + "text/plain": [ + "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# define layout by gridspec\n", "fig = plt.figure(constrained_layout=True, figsize=(7, 6))\n", @@ -279,7 +306,6 @@ "\n", "# interactive plot 2 for line picking\n", "cid = fig.canvas.mpl_connect('button_press_event', on_plot_click)\n", - "\n", "# show plots\n", "plot_update(None)\n", "plt.show()\n", @@ -288,10 +314,39 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "id": "2f7c5461", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "814874cad20d4d928bb0f9f785681dda", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "HBox(children=(IntSlider(value=6, continuous_update=False, description='$N_{\\\\text{fft}}$', layout=Layout(marg…" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "c33cda02e0f84d048d0e2fc5ec32dc07", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "HBox(children=(Button(description='Show all', icon='redo', layout=Layout(margin='0px 20px 0px 60px', width='22…" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# display widgets\n", "display(ipw.HBox([N_slider, func_dropdown]))\n", @@ -303,15 +358,17 @@ "id": "17052811", "metadata": {}, "source": [ - "## Legend\n", + "## Interactive Figures\n", "\n", "The target function, sampling points and the reconstructed function are shown in the top left plot. The real part (cosine functions) and the constant term of the discrete Fourier series are shown in the top right panel.\n", " \n", "Note that the components are shifted vertically for clarity. The integral of the square of the functions reconstructed from truncated Fourier series with different numbers of plane waves $N_{\\text{fft}}$ is shown in the bottom panel, where the current choice of sampling is indicated with a red dot. The converged value is also shown with a red horizontal line, obtained with a large number (200) of FFT components. \n", "\n", - "The number of FFT components $N_{\\text{fft}}$ can be set by the slider. Two target functions can be chosen from the drop-down menu.\n", + "## Controls\n", "\n", - "By clicking one of the expansions in the top-right panel, the contribution of that component will be shown in the top left panel. Click the reset button to display all expansion coefficients again." + "The number of FFT components $N_{\\text{fft}}$ can be set by the slider. \n", + "Two target functions can be chosen from the drop-down menu.\n", + "By clicking on one of the basis functions in the top-right panel, the contribution of that basis function will be shown in the top left panel. One can click the reset button to display all basis functions again." ] }, { @@ -342,7 +399,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.10.12" }, "voila": { "authors": "Guoyuan Liu, Dou Du and Giovanni Pizzi"