From 4aa46e72a7508e9d9096ca649b4c332316dc5e4d Mon Sep 17 00:00:00 2001
From: ialcon <160740748+ialcon@users.noreply.github.com>
Date: Thu, 8 Aug 2024 13:00:46 +0200
Subject: [PATCH] Changes to S_02

---
 S_02/run.ipynb | 31 +++++++++++++++++--------------
 1 file changed, 17 insertions(+), 14 deletions(-)

diff --git a/S_02/run.ipynb b/S_02/run.ipynb
index 4ab3af0..f2502cf 100644
--- a/S_02/run.ipynb
+++ b/S_02/run.ipynb
@@ -16,17 +16,17 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Analysing output from Siesta makes analysis much easier since many things are intrinsically enabled through `sisl`, i.e. orbital numbering etc. may easily be handled with `sisl`.\n",
+    "Analysing output from Siesta makes analysis much easier since many things are intrinsically enabled through `sisl` - i.e. orbital numbering etc. may easily be handled with `sisl`.\n",
     "\n",
-    "In this example we will use Siesta to calculate the *heavy* part, i.e. the projected density of states for a fine $k$-point sampling. The formula used to calculate the projected density of states is:\n",
+    "In this example we will use Siesta to calculate the *heavy* part, i.e. the projected density-of-states for a fine $k$-point sampling. The formula used to calculate the projected density-of-states is:\n",
     "\\begin{align}\n",
-    "  \\mathrm{PDOS}_\\nu(E) &= \\int \\mathrm d k \\sum_i \\psi^*_{i,k,\\nu} [\\mathbf S(k) | \\psi_{i,k}\\rangle]_\\nu D(E-\\epsilon_i),\n",
+    "  \\mathrm{PDOS}_\\nu(E) &= \\int \\mathrm d k \\sum_i \\psi^*_{i,k,\\nu} [\\mathbf S(k) | \\psi_{i,k}\\rangle]_\\nu D(E-\\epsilon_{i}(k)),\n",
     "  \\\\\n",
-    "  \\mathrm{DOS}(E) &= \\int \\mathrm d k \\sum_i D(E-\\epsilon_i) = \\sum_\\nu \\mathrm{PDOS}_\\nu(E),\n",
+    "  \\mathrm{DOS}(E) &= \\int \\mathrm d k \\sum_i D(E-\\epsilon_{i}(k)) = \\sum_\\nu \\mathrm{PDOS}_\\nu(E),\n",
     "\\end{align}\n",
-    "with $D(\\Delta E)$ being the distribution function (in Siesta, this is the Gaussian distribution function).\n",
-    "Finally, we will also compare with the same calculation using `sisl` to ensure that correctness of both methods.\n",
-    "Note that `sisl` is (for now) not MPI parallelized and thus for large systems it may be *way* more efficient to use Siesta to calculate PDOS, but use `sisl` to post-process the PDOS data.\n",
+    "Where *E* is the energy, $D(\\Delta E)$ is the distribution function (in Siesta, this is the Gaussian distribution function) and $\\epsilon_{i}(k)$ and $\\mathbf S(k)$ are the ith eigenvalue and overlap matrix, respectively, at a given **k**-point. $\\psi_{i,k}$ is the ith **k**-resolved eigenstate, and $\\psi^*_{i,k,\\nu}$ is the corresponding complex-conjugate resolved for a concrete atomic orbital $\\nu$. \n",
+    "Finally, we will do the same calculation using `sisl` to ensure the correctness of both methods.\n",
+    "Note that `sisl` is (for now) not MPI parallelized and thus for large systems it may be *way* more efficient to use Siesta to calculate PDOS, and then use `sisl` to post-process the PDOS data.\n",
     "\n",
     "The system will again be graphene."
    ]
@@ -85,8 +85,8 @@
     "     siesta RUN.fdf | tee RUN.out\n",
     "\n",
     "Subsequently, we will read in the PDOS information and post-process it.  \n",
-    "First we will data found in the `siesta.PDOS.xml` file, 3 quantities will be returned:\n",
-    "1. The geometry (as found in the XML file), this also contains all atomic species etc.\n",
+    "First we will extract data found in the `siesta.PDOS.xml` file. Three quantities will be returned:\n",
+    "1. The geometry (as found in the XML file) - this also contains all atomic species etc.\n",
     "2. The energy grid used\n",
     "3. Orbital and energy resolved DOS\n",
     "\n",
@@ -124,12 +124,15 @@
     "4. Read in the Hamiltonian (as done in [S 1](../S_01/run.ipynb)) and create a Monkhorst-Pack grid as the one in Siesta input. Use this snippet to calculate the PDOS using `sisl`\n",
     "\n",
     "       mp = sisl.MonkhorstPack(H, [nx, ny, 1])\n",
-    "       mp_avg = mp.apply.average\n",
-    "       pdos = mp_avg.PDOS(E, eta=True)\n",
+    "       def wrap_multiple(eigenstate):\n",
+    "           DOS = eigenstate.DOS(E)\n"
+    "           PDOS = eigenstate.PDOS(E)\n"
+    "           return sisl.oplist([DOS, PDOS])\n",
+    "       DOS, PDOS = mp.apply.average.eigenstate(wrap=wrap_multiple, eta=True)\n",
     "\n",
-    "    Search the API documentation for the `MonkhorstPack.apply.average` method and figure out what it does. Note, there are other `MonkhorstPack.apply.*` methods, these are all extremely useful when calculating many quantities of data in a Brillouin-zone object.\n",
+    "    Search the API documentation for the `MonkhorstPack.apply.average` method and figure out what it does. Note, there are other `MonkhorstPack.apply.*` methods - these are all extremely useful when calculating many quantities of data in a Brillouin-zone object.\n",
     "5. Compare the Siesta PDOS with sisl PDOS, why are they different?  \n",
-    "   *HINT*: $\\sigma$. Check the API for the `PDOS` method."
+    "   *HINT*: $\\sigma$. Check the API for the `PDOS` method in the Siesta manual (https://siesta-project.org/SIESTA_MATERIAL/Docs/Manuals/siesta-4.1.5.pdf)."
    ]
   },
   {
@@ -152,7 +155,7 @@
  ],
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   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
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