"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.xlabel('Crmult value')\n",
"plt.plot(crmult,energies_c-emin,label='hgrid=0.55')\n",
"plt.plot(crmult,energies_hc-emin,label='varying hgrids+crmult')\n",
"plt.yscale('log')\n",
"plt.legend(loc='best')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Considerations\n",
"We see that _both_ the parameters `hgrids` and `rmult` have to be decreased and increased (respectively) in order to achieve convergence. Increasing only one of the two parameter will eventually lead to saturation of the absolute error on the energy."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"\n",
"HtoeV = 27.21138386 #Conversion Hartree to meV\n",
"\n",
"emin = HtoeV*results[-1].energy\n",
"ener = [ HtoeV*l.energy - emin for l in results ]\n",
"\n",
"ener2 = [ HtoeV*l.energy - emin for l in res2 ]\n",
"\n",
"plt.figure(figsize=(15,7))\n",
"# Plot with matplotlib\n",
"plt.plot(Hgrids, ener, marker='o', ls='-', color='#ff0000', label='varying hgrids+crmult') \n",
"plt.plot(Hgrids, ener2, marker='s', ls='-', color='#888888', label='crmult=3.5') \n",
"\n",
"plt.yscale('log')\n",
"plt.xlim(0.55,0.25)\n",
"plt.xlabel('Grid step (Bohr)')\n",
"plt.ylabel('Total energy precision (eV)')\n",
"plt.title('Total energy convergence versus the grid step for the CH$_4$ molecule')\n",
"plt.legend(loc=3)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fine tuning of the basis set\n",
"The multi-scale property of the wavelets is used in BigDFT and a two level grid is used for the calculation. \n",
"We've seen previously the coarse grid definition using the the multiplying factor `rmult`. \n",
"The second multiplying value on this line of the input file is used for the fine grid and is called `frmult`. \n",
"Like `crmult`, it defines a factor for the radii used to define the fine grid region where the number of degrees of freedom\n",
"is indeed eight times the one of the coarse grid. It allows to define region\n",
"near the atoms where the wavefunctions are allowed to vary more\n",
"quickly. Typical values for this factor are 8 to 10. It's worth to\n",
"note that even if the value of the multiplier is greater than `crmult` it defines a smaller region due to the fact that\n",
"the units which are associated to these radii are significantly different.\n",
"\n",
"The physical quantities used by `crmult` and `frmult` can be changed in the pseudo-potential by adding\n",
"an additional line with two values in bohr. The two values that the\n",
"code is using (either computed or read from the pseudo-potential files) are output in the following way in the screen output:\n",
" \n",
"\n",
" - Symbol : C #Type No. 01\n",
" No. of Electrons : 4\n",
" No. of Atoms : 1\n",
" Radii of active regions (AU):\n",
" Coarse : 1.58437\n",
" Fine : 0.30452\n",
" Coarse PSP : 1.30510\n",
" Source : Hard-Coded\n",
" - Symbol : H #Type No. 02\n",
" No. of Electrons : 1\n",
" No. of Atoms : 4\n",
" Radii of active regions (AU):\n",
" Coarse : 1.46342\n",
" Fine : 0.20000\n",
" Coarse PSP : 0.00000\n",
" Source : Hard-Coded"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Analysing the output\n",
"\n",
"The output of BigDFT is divided into four parts:\n",
"* Input values are printed out, including a summary of the\n",
" different input files (DFT calculation parameters, atom positions,\n",
" pseudo-potential values...);\n",
"* Input wavefunction creation, usually called \"input guess\";\n",
"* The SCF (Self-Consistent Field) loop itself;\n",
"* The post SCF calculations including the forces calculation and\n",
" other possible treatment like a finite size effect estimation or a\n",
" virtual states determination.\n",
"\n",
"### The system parameters output\n",
"All the read values from the different input files are printed\n",
"out at the program startup. Some additional values are provided there\n",
"also, like the memory consumption. Values are given for one process,\n",
"which corresponds to one core in an MPI environment."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import yaml\n",
"print yaml.dump(ch4.memory,default_flow_style=False)\n",
"\n",
"print 'Estimated Memory Peak',ch4.memory_peak,'MB'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The overall memory requirement needed for this calculation is thus: 39 MB (Estimated Memory Peak) which is provided by the`memory_peak` attribute.\n",
"\n",
"In this example, the memory requirement is given for one process run and the peak of memory will be in the initialisation during the Kernel calculation, while the SCF loop will reach 36MB during the Poisson solver calculation. For bigger systems, with more orbitals, the peak of memory is usually reached during the Hamiltonian application.\n",
"\n",
"### Exercise\n",
"\n",
"Run a script to estimate the memory requirement of a run before submitting it to the queue system of a super-computer\n",
"using the `dry_run` option.\n",
"\n",
"It reads the same input, and is thus convenient to validate inputs.\n",
"\n",
"Try several values from 1 to 6 and discuss the memory distribution."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"study = calc.SystemCalculator(dry_run=True) #Create a calculator\n",
"peak = []\n",
"for i in range(1,7):\n",
" study.set_global_option('dry_mpi',i)\n",
" dry = study.run(input=inp)\n",
" peak.append(dry.memory_peak)\n",
" print yaml.dump(dry.memory,default_flow_style=False)\n",
"for i,p in enumerate(peak):\n",
" print \"mpi=\",i+1,\"Estimated memory peak (MB)\",p"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"BigDFT distributes the orbitals over the available processes.\n",
"The value `All (distributed) orbitals` does not decrease anymore after 4 processes since there are only 4 bands in our example). \n",
"This means that running a parallel job with more processors than orbitals will result in a bad speedup. \n",
"The number of cores involved in the calculation might be however increased via OMP parallelisation, as it is indicated in [Scalability with MPI and OpenMP](./Tutorial-Scalability.ipynb) lesson.\n",
"\n",
"\n",
"## The input guess\n",
"The initial wavefunctions in BigDFT are calculated using the atomic orbitals for all the electrons of the s, p,\n",
"d shells, obtained from the solution of the PSP self-consistent equation for the isolated atom."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"print yaml.dump(ch4.log['Input Hamiltonian'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The corresponding hamiltonian is then diagonalised and the\n",
"n_band (``norb`` in the code notations) lower eigenfunctions are used to start the SCF loop. \n",
"BigDFT outputs the eigenvalues, in the following example, 8 electrons were used in the\n",
"input guess and the resulting first fourth eigenfunctions will be used\n",
"for a four band calculation.\n",
"\n",
"\n",
"Input Guess Overlap Matrices: {Calculated: true, Diagonalized: true}\n",
"Orbitals:\n",
"- {e: -0.6493539153869, f: 2.0}\n",
"- {e: -0.3625626366055, f: 2.0}\n",
"- {e: -0.3624675839372, f: 2.0}\n",
"- {e: -0.3624675839372, f: 2.0} -- Last InputGuess eval, H-L IG gap: 20.6959 eV\n",
"- {e: 0.3980916655348, f: 0.0} -- First virtual eval\n",
"- {e: 0.3983087771728, f: 0.0}\n",
"- {e: 0.3983087771728, f: 0.0}\n",
"- {e: 0.5993393223683, f: 0.0}\n",
"\n",
"\n",
"## The SCF loop\n",
"The SCF loop follows a direct minimisation scheme and is made of the following steps:\n",
"* Calculate the charge density from the previous wavefunctions.\n",
"* Apply the Poisson solver to obtain the Hartree potential from the\n",
" charges and calculate the exchange-correlation energy and the energy\n",
" of the XC potential thanks to the chosen functional.\n",
"* Apply the resulting hamiltonian on the current wavefunctions.\n",
"* Precondition the result and apply a steepest descent or a DIIS\n",
" history method. This depends on ``idsx``, not specified in the\n",
" present input. It is therefore set to the default\n",
" value, which is 6 (for an history of 6 previous set of vectors. To perform a SD \n",
" minimisation one should add \"``idsx: 0``\" to the *dft* dictionary of *inp*.\n",
"* Orthogonalise the new wavefunctions.\n",
"\n",
"Finally the total energy and the square norm of the residue\n",
"(gnrm) are printed out. The *gnrm* value is the stopping criterion. \n",
"It can be chosen using `gnrm_cv` in the *dft* dictionary. \n",
"The default value (1e-4) is used here and a good value can reach 1e-5."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"print 'gnrm_cv by default',ch4.gnrm_cv"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The minimisation scheme coupled with DIIS (and thanks to the good preconditioner) \n",
"is a very efficient way to obtain convergence for systems with a gap, even with a very small one. \n",
"Usual run should reach the 1e-4 stop criterion within 15 to 25 iterations. \n",
"Otherwise, there is an issue with the system, either there is no gap, \n",
"or the input guess is too symmetric due to the LCAO diagonalization, specific spin polarization..."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"ch4.wfn_plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The post-SCF treatments\n",
"At the end of the SCF loop, a diagonalisation of the current hamiltonian is done to obtain Kohn-Sham eigenfunctions. The\n",
"corresponding eigenvalues are also given."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"print ch4.evals"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The forces are then calculated."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"print yaml.dump(ch4.forces,default_flow_style=False)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some other post-SCF may be done depending on the parameters in the *dft* dictionary of *inp*.\n",
"\n",
"### Exercise\n",
"Run `bigdft` when varying the DIIS history length and discuss the memory consumption.\n",
"\n",
"Reducing the DIIS history is a good way to reduce the memory consumption when one cannot increase the\n",
"number of processes. Of course this implies more iterations in SCF loops."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Adding a charge\n",
"BigDFT can treat charged system without the requirement to add a compensating background like in plane waves.\n",
"The additional charge to add to the system is set in the *dft* dictionary with the *qcharge* key. \n",
"In the following example an electron has been added (-1):"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"inp3 = {}\n",
"inp3['dft'] = { 'hgrids': 0.55, 'nrepmax': 'accurate' }\n",
"inp3['posinp'] = 'CH3-_posinp.xyz'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise \n",
"Remove the last hydrogen atom in the previous methane example and modify to add an electron. \n",
"Then run BigDFT for an electronic convergence.\n",
"\n",
"One can notice that the total charge in the system is indeed -8 thanks to the additional charge. \n",
"The convergence rate is still good for this CH$_3^-$ radical since it is a closed shell system."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"study = calc.SystemCalculator() #Use a new calculator)\n",
"ch3m = study.run(input=inp3)\n",
"print ch3m\n",
"ch3m.wfn_plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Running a geometry optimisation\n",
"In the previous charged example the geometry of the radical is kept the same than for the methane molecule, while it is likely to\n",
"change. One can thus optimize the geometry with BigDFT.\n",
"\n",
"To run geometry calculations (molecular dynamics, structure\n",
"optimisations...) one should add another dictionary *geopt* in the input which contains the method to use.\n",
"\n",
"In the log file, all input variables are indicated with their default value.\n",
"\n",
"Here, we look for a local minimum so we can use the keyword `LBFGS`.\n",
"We can add also the stopping criteria.\n",
"There are two stopping criteria: the first `ncount_cluster_x` being the number of loops (force evaluations) and the second `forcemax` is the maximum on forces. For isolated systems, the first criterion is well adapted\n",
"while the second is good for periodic boundary conditions."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"inpg = {}\n",
"inpg['dft'] = { 'hgrids': 0.55, 'nrepmax': 'accurate' }\n",
"inpg['posinp'] = 'CH4_posinp.xyz'\n",
"inpg['geopt'] = { 'method': 'LBFGS', 'ncount_cluster_x': 20}\n",
"study = calc.SystemCalculator() #Use a new calculator)\n",
"ch4geopt = study.run(input=inpg)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"ch4geopt.geopt_plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise\n",
"Take the CH$_3^-$ radical [**CH3-_posinp.xyz**](./CH3-_posinp.xyz) file and run a geometry optimisation.\n",
"\n",
"The evolution of the forces during relaxation can be easily obtained using the `geop_plot` function to the result of the calculation.\n",
"\n",
"At each iteration, BigDFT outputs a file **posout_XXXX.xyz** in the directory **data** with the geometry of the iteration\n",
"XXX. You can visualize it using v_sim (select all files in the \"Browser\" tab)."
]
}
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