{ "cells": [ { "cell_type": "markdown", "source": [ "# Tutorial using recipes\n", "\n", "Recipes are scripted functions that cover probably 90% of cases. They read and save all information to disk using the HDF5 format and have sensible defaults. If you need more flexibility for your calculation, you can run in full control mode instead. \n", "\n", "In a production run, each one of these cells would most likely best be executed as a job. In that case, you would want to separate the computationally intensive runs from the analysis.\n", "\n", "You will need to install `pyscf`, `ase`, `matplotlib`, `h5py`, `pandas` and `pyqmc` to use these routines. These all can be installed using `pip`. " ], "metadata": {} }, { "cell_type": "code", "execution_count": 1, "source": [ "import os\n", "os.environ[\"MKL_NUM_THREADS\"] = \"1\"\n", "os.environ[\"NUMEXPR_NUM_THREADS\"] = \"1\"\n", "os.environ[\"OMP_NUM_THREADS\"] = \"1\"\n", "import numpy as np\n", "import pandas as pd\n", "from pyscf import gto, scf\n", "import pyqmc.api as pyq\n", "import h5py\n", "import matplotlib.pyplot as plt\n", "from ase.data.pubchem import pubchem_atoms_search\n", "import pyscf.pbc.tools.pyscf_ase as pyscf_ase\n", "# Here we reset the files \n", "for fname in ['mf.hdf5','optimized_wf.hdf5','vmc_data.hdf5','dmc.hdf5']:\n", " if os.path.isfile(fname):\n", " os.remove(fname) " ], "outputs": [ { "output_type": "stream", "name": "stderr", "text": [ "/opt/homebrew/Caskroom/miniforge/base/envs/python3.9/lib/python3.9/site-packages/pyscf/lib/misc.py:46: H5pyDeprecationWarning: Using default_file_mode other than 'r' is deprecated. Pass the mode to h5py.File() instead.\n", " h5py.get_config().default_file_mode = 'a'\n" ] } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "This function computes the mean-field solution and saves the results to the file specified. We recommend using the ccecp pseudopotentials for high accuracy and efficiency.\n", "\n", "Here we search up the atomic positions of water to reduce errors. " ], "metadata": {} }, { "cell_type": "code", "execution_count": 2, "source": [ "def mean_field(chkfile):\n", " atoms = pubchem_atoms_search(name='water')\n", " mol = gto.M(\n", " atom=pyscf_ase.ase_atoms_to_pyscf(atoms),\n", " basis=\"ccECP_cc-pVDZ\", ecp=\"ccecp\",\n", " )\n", " mf = scf.RHF(mol)\n", " mf.chkfile = chkfile\n", " mf.kernel()\n", "mean_field(\"mf.hdf5\")" ], "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "converged SCF energy = -16.9321257267691\n" ] } ], "metadata": { "tags": [] } }, { "cell_type": "markdown", "source": [ "Now we wish to construct a Slater-Jastrow wave function and optimize its energy. This is done using the OPTIMIZE function in pyq. It's often helpful to do the first optimization with only a few configurations, to get close to the minimum cheaply.\n", "\n", "By default, `OPTIMIZE` uses 10 VMC blocks of 10 steps each, so this is 10x10x100=10,000 VMC samples per iteration. \n", "\n", "To increase precision, it is usually best to increase the number of configurations. " ], "metadata": {} }, { "cell_type": "code", "execution_count": 3, "source": [ "pyq.OPTIMIZE(\"mf.hdf5\", #Construct a Slater-Jastrow wave function from the pyscf output\n", " \"optimized_wf.hdf5\", #Store optimized parameters in this file.\n", " nconfig=100, #Optimize using this many Monte Carlo samples/configurations\n", " max_iterations=10, #10 optimization steps\n", " verbose=False)" ], "outputs": [], "metadata": { "tags": [] } }, { "cell_type": "markdown", "source": [ "The API contains functions such as `read_opt` which assist in reading the output files. Here we print out the energy and uncertainty as the optimization proceeds. You should see that the energy is decreasing (within uncertainty). " ], "metadata": {} }, { "cell_type": "code", "execution_count": 4, "source": [ "df = pyq.read_opt(\"optimized_wf.hdf5\")\n", "df" ], "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ " energy iteration error fname\n", "0 -16.991545 0 0.017707 optimized_wf.hdf5\n", "1 -17.080173 1 0.018693 optimized_wf.hdf5\n", "2 -17.126727 2 0.010658 optimized_wf.hdf5\n", "3 -17.116194 3 0.009721 optimized_wf.hdf5\n", "4 -17.109356 4 0.011984 optimized_wf.hdf5\n", "5 -17.123817 5 0.010352 optimized_wf.hdf5\n", "6 -17.150079 6 0.011616 optimized_wf.hdf5\n", "7 -17.148353 7 0.010380 optimized_wf.hdf5\n", "8 -17.158911 8 0.009709 optimized_wf.hdf5\n", "9 -17.170465 9 0.008196 optimized_wf.hdf5" ], "text/html": [ "
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" ] }, "metadata": {}, "execution_count": 4 } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "The output is stored as a standard HDF5 file. You can use `h5py` or other utilities to inspect their contents. Here we print out the 2-body Jastrow coefficients. Overall, these should be negative, since electrons repel each other.\n", "\n", "Since we did not request orbital optimization, only the Jastrow was optimized, and only the Jastrow parameters are saved in the output file. \n" ], "metadata": {} }, { "cell_type": "code", "execution_count": 5, "source": [ "with h5py.File(\"optimized_wf.hdf5\") as f:\n", " print(\"keys\", list(f.keys()))\n", " print(\"wave function parameters\", list(f['wf'].keys()))\n", " print(f['wf/wf2bcoeff'][()])" ], "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "keys ['configs', 'energy', 'energy_error', 'est_min', 'iteration', 'nconfig', 'pgradient', 'tau', 'wf', 'x', 'yfit']\n", "wave function parameters ['wf2acoeff', 'wf2bcoeff']\n", "[[-0.25 -0.5 -0.25 ]\n", " [ 0.05606749 0.04630514 0.06288114]\n", " [-0.10519429 -0.20769824 -0.09778117]\n", " [-0.13156762 -0.24253197 -0.13787106]]\n" ] } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "To evaluate the properties of the wave function, we use the `VMC` function. " ], "metadata": {} }, { "cell_type": "code", "execution_count": 6, "source": [ "pyq.VMC(\"mf.hdf5\", #Construct a Slater-Jastrow wave function from this file\n", " \"vmc_data.hdf5\", #Store Monte Carlo data in this file\n", " load_parameters=\"optimized_wf.hdf5\", #Load optimized parameters from this file\n", " nblocks=30, #Run for 30 blocks. By default, there are 10 steps per block and 1000 configurations\n", " verbose=False)" ], "outputs": [], "metadata": { "tags": [] } }, { "cell_type": "markdown", "source": [ "The uncertainty in the final energy is much lower than in the optimization above, since we sampled many more Monte Carlo configurations. With the above settings, there are 30x1000x10 = 300,000 Monte Carlo samples generated. \n", "\n", "* `energytotal` should match the final step in optimization to within uncertainties\n", "* `energygrad2` should be twice `energyke` within uncertainties\n", "* `energytotal` should be quite a lot lower than the Hartree-Fock energy\n", "* The uncertainties should be lowered (versus the optimization steps above) by a factor $\\frac{\\sqrt{M_{OPT}}}{\\sqrt{M_{VMC}}}$" ], "metadata": {} }, { "cell_type": "code", "execution_count": 7, "source": [ "pyq.read_mc_output(\"vmc_data.hdf5\")" ], "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "{'fname': 'vmc_data.hdf5',\n", " 'warmup': 1,\n", " 'reblock': None,\n", " 'acceptance': 0.5971488764044944,\n", " 'acceptance_err': 0.0006122970977467954,\n", " 'block': 45.0,\n", " 'block_err': 2.7386127875258306,\n", " 'energyecp': 1.0427315791047875,\n", " 'energyecp_err': 0.006711132061017259,\n", " 'energyee': 17.014264728785488,\n", " 'energyee_err': 0.008604562456597334,\n", " 'energyei': -55.72503351189938,\n", " 'energyei_err': 0.025886049026138145,\n", " 'energygrad2': 26.987968519107632,\n", " 'energygrad2_err': 0.19301283541097783,\n", " 'energyke': 13.597633594791404,\n", " 'energyke_err': 0.01795711497868946,\n", " 'energytotal': -17.170490001013118,\n", " 'energytotal_err': 0.001961047903916406,\n", " 'nconfig': 10000.0,\n", " 'nconfig_err': 0.0}" ] }, "metadata": {}, "execution_count": 7 } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "Finally we run diffusion Monte Carlo. In this example, we have run with many configurations so the convergence of DMC would be very clear. If you want to reduce the computational cost, you can run it with 10x fewer (1000) configurations.\n" ], "metadata": {} }, { "cell_type": "code", "execution_count": 8, "source": [ "pyq.DMC(\"mf.hdf5\",\n", " \"dmc.hdf5\", #Initialize the Slater-Jastrow wave function using pyscf\n", " load_parameters=f\"optimized_wf.hdf5\", #Load the optimized parameters\n", " verbose=False, \n", " tstep=.1, #timestep of 0.1 Hartrees^-1\n", " nsteps=int(50/.1), #propagate for 50 Hartrees^-1\n", " branchtime=1, #Efficiency parameter; these are 'mini-blocks'\n", " nconfig=10000) #Use 1,000 configurations" ], "outputs": [], "metadata": { "tags": [ "outputPrepend" ] } }, { "cell_type": "markdown", "source": [ "We can read the energy directly from the HDF5 file. \n", "\n", "You should see that the first few steps are higher in energy than the average. These are the warmup steps." ], "metadata": {} }, { "cell_type": "code", "execution_count": 12, "source": [ "with h5py.File(\"dmc.hdf5\") as f:\n", " en = f['energytotal'][...]\n", "plt.plot(en, marker='o')\n", "plt.xlabel(\"DMC step\")\n", "plt.ylabel(\"Energy (Hartree)\")" ], "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "Text(0, 0.5, 'Energy (Hartree)')" ] }, "metadata": {}, "execution_count": 12 }, { "output_type": "display_data", "data": { "text/plain": [ "
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" }, "metadata": { "needs_background": "light" } } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "Since the DMC samples are correlated due to the timestepping, it is important to do two things: \n", "1) Remove the warmup steps. \n", "2) Reblocking analysis to estimate the statistical uncertainties correctly. \n", "\n", "The `read_mc_output` function has two parameters that help with this:\n", "* `warmup`: remove the first `warmup` steps from the data, before reblocking\n", "* `reblock`: bin the data into `reblock` blocks.\n" ], "metadata": {} }, { "cell_type": "code", "execution_count": 13, "source": [ "block_sizes = np.linspace(2,len(en)//16, 10, dtype=int)\n", "reblocks = [len(en)//s for s in block_sizes]\n", "print(reblocks)\n", "print(block_sizes)\n", "df = pd.DataFrame([pyq.read_mc_output(\"dmc.hdf5\", warmup=100, reblock=reblock) for reblock in reblocks])\n", "df['block_size'] = block_sizes\n", "plt.plot(\"block_size\",'energytotal_err',data=df, marker='o')\n", "plt.xlabel(\"Block size\")\n", "plt.ylabel(\"Estimated uncertainty (Ha)\")" ], "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "[250, 100, 62, 45, 35, 27, 23, 20, 18, 16]\n", "[ 2 5 8 11 14 18 21 24 27 31]\n" ] }, { "output_type": "execute_result", "data": { "text/plain": [ "Text(0, 0.5, 'Estimated uncertainty (Ha)')" ] }, "metadata": {}, "execution_count": 13 }, { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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" 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