mirror of https://gitlab.com/QEF/q-e.git
add EXX example
git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@2794 c92efa57-630b-4861-b058-cf58834340f0
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degironc
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Hybrid Hartree-Fock-DFT functionals are an experimental feature in PWscf.
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Only few functionalities are implemented and it is possible (actually
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desirable, see later) that the implementation evolves in the future
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therefore its stability cannot be garanteed.
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HOW TO COMPILE :
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i) download the CVS version of QE and execute the ../configure step
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ii) edit file make.sys and add to variable DFLAGS the -DEXX option
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iii) issue "make pw" .
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Pay attention that ./configure re-creates make.sys so if the QE distributions
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is updated and ./configure run again also step ii) above has to be done again.
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WHICH FUNCTIONALS ARE IMPLEMENTED ?
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only a few hybrid functionals are implemented: Hartree-Fock, PBE0
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and B3LYP . Their labels in QE are "HF", "PBE0" and "B3LP" .
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This last one is not optimal but is needed to avoid conflict with LYP
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correlation when parsing the dft string. It might change in the future.
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Usually in PWscf the functional to be used is read from the
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pseudopotential files but we do not have so far a pseudopotential
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generator for hybrid functionals so one needs to use pseudopotentials
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generated with some other functionals (eg. PBE or LDA) and force the
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use of the hybrid functional in the PWscf input.
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This is done using the variable input_dft in system namelist; for instace
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input_dft="pbe0" will force the use of pbe0 unrespective of the functional
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used in the pseudopotential generation.
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HOW DOES THE SCF SEARCH PROCEED ?
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use of hybrid-functionals is VERY expensive (see later), moreover in
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more traditional DFT calculation the mixed quantity is the density while
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for HF of hybrid-functionals the density-matrix should be mixed which is
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not practical. The strategy used here is to consider (let's focus on HF
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for simplicity) an auxiliary set of wavefunctions psi in addition to the
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usual set phi and to minimize the auxiliary functional:
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E[phi,psi] = T[phi] + E_ext[phi] + E_Hartree[phi] +
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<phi|Vx[psi]|phi> - 0.5*<psi|Vx[psi]|psi>
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where Vx[psi] is the fock operator defined with the auxiliary function psi.
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Taking the functional derivatives w.r.t. phi it can be shown that the scf
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condition for phi are the HF equation with fixed Fock operator, so Vx does
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not enter in the scf procedure and one can mix density as usual. The
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minimum condition w.r.t. psi is simply psi=phi so when both psi and phi
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are minimized the standard HF energy is obtained.
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Actually one can show that the functional E[phi,psi] above is
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E[phi,psi] = E_HF[phi] + dexx[phi,psi]
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where dexx is a positive definite addition to E_HF .
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The scf procedure goes as follow.
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1) a normal scf (with LDA or other scheme is performed) then
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2) hybrid functional is switched on and psi = phi (the current best wfcs)
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3) a new scf is performed w.r.t phi, keeping fixed Vx[psi]
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4) dexx[phi,psi] is computed and if it exceeds the required tollerance
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the proceedure is repeated from point 2)
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HF may require several phi-scf cycles to reach full convergence. B3LYP
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and PBE0, due to the smaller fraction of HF exchange included, require
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usually a smaller number of phi-scf cycles
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HOW MUCH EXPENSIVE IS THE CALCULATION ?
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Very much.
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Applying the Fock operator on a single vawefunction (phi_k,v) requires
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the calculation of an integral over the whole BZ and all psi bands.
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For each needed pair psi_k+q,v' and phi_k,v an auxiliary charge density
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rho(-q+G) is built in real space and then FFT to reciprocal space where
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the corresponding Poisson equation is solved. This auxiliary potential is
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FFT back in real space where it is multiplied by psi_k+q,v' and added to
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Vx[psi]phi...
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The cost of the operation is therefore roughly NBND * NQS * ( 2 * FFT + ... )
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where NQS is the number of q-points chosen to represent the BZ integration,
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and depends in general on the localization of the Wannier functions of the
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system.
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For comparison non-local pseudopotentials in the KB formualtion (without
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exploiting the locality of the KB projetors) cost NKB * (2 * NPW) where
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NKB is tipically of the order of NBND but NPW cost at least an order
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of magnitude less than an FFT.
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Therefore even when one can take NQS=1 (for large non-metallic system
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should be ok) hybrid-functionals will require at least an order of
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magnitude more resources that a standard calculation.
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HOW CAN I CHOSE NQS IN INPUT ?
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In the system namelist there are three variables nqx1,nqx2,nqx3 that
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define the regular q-grid in the BZ in a way similar to the automatic
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k-points generation. Their vaule must be compatible with the k-points
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used (that is k+q must be equivalent to some other k in the k-points list)
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Their default value are nqx1=1,nqx2=1,nqx3=1 (BZ integration is
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approximated by gamma point value only).
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DIVERGENCE AT q->0
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The BZ integral to be performed has a diverging kernel when (q+G)->0.
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This is dealt with by adding and subtracting a term with the same
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divergence that can be integrated analytically and performing
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numerically the integration for the non divergent residue
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[Gygi-Baldereschi, PRB 34, 4405 (1986)].
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One problem is left: the now non divergent q=0 term is not easily determined
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since it is a 0/0 (non analytic) limit. Several options have been considered:
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1) just discard it ... this is not a good idea in general because it
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induces an error proportional to 1/(NQS*Omega) in the total energy
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where Omega is the Wigner-Seitze volume of the crystal. As one
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wish to keep NQS as small as possible this may be large.
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2) exploit the fact that the term has the above dependence and extract
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it from a calculation with a given nqx1,nqx2,nqx3 and the one with
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a grid twice as coarse in each direction. One does not really need to
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perform two calculations but can do it internally (even when nqx? are
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not even numbers...). This seems to work and it is set as the default.
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In order to disable this feature [and get back to option 1)] set
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x_gamma_extrapolation = .false.
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3) perform calcualtions in q-grids that are shifted away from gamma so that
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the 0/0 term is not needed. This create some extra complication in the
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coding and cannot be used with Gamma-only k-point integration.
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In some test does not seem to be superior to option 2) ... it has not
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been fully implemented and now it has been removed.
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4) use the value at small (q+G) to estimate the (q+G)->0 limit. This
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again has been tried and found to offer, for low order numerical
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differentiation, no better results that option 2). It is possible
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than higher order formulas can be better but this has not been explored.
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This option is currently not implemented but would be easy to resume it.
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OTHER LIMITATIONS
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So far only NORM-CONSERVING pseudopotentials are implemented.
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there is no fundametal problem in defining HF for US pseudopotentials
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but since some density-like object is required one would need to operate
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on the dense charge-density FFT grid anyway with no computational gain.
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Maybe this is not true and one can find ways to perform this integrals
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more efficently. So far I did not think to much to this point.
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PARALLEL IMPLEMENTATION ?
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yes (and no).
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At present only R-and-G parallelization has been implemented.
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This is what is needed for large systems ...
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For metals k-point parallelization is often useful but the need
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in hybrid-functionals for the BZ integration prevent its simple
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implementation, except when q-integration reduce to Gamma.
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In this case it should work.
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If the scratch area is common to all processors one could think about
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implementing it in general (one would needs a VERYBIG direct-access
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file that all processors can see) .. this feature is not implemented.
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WHAT PROPERTIES CAN I COMPUTE ?
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Energy and forces (thanks to Hellman-feynman theorem forces do not
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require extra calculations). In principle also stresses but the
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corresponding formulas have not been coded yet.
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So structural optimization is OK if the cell shape is kept fixed.
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Band structure ? yes and no. Obviously one compute wfc during the scf
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cycle and their eigenvalues are printed in output.
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This can be enough to draw a band structure or a DOS, however the
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problem is when one wish non-scf calculations in k-points different
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from those computed during the scf cycle. At present it is not possible
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because it would require the knowledge of all bands at k+q that we do
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not have. I do not know how to by-pass this problem.
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ELECTRIC FIELD
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I did not dig into this issue but Paolo Umari is using EXX with
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electric field. For details it would be better to ask him directly.
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AN EXAMPLE
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run_example script in this directory performs two series of calculations:
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1) total energy of Silicon using different values for nq,
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2) calculation of binding energy of o2,co,n2 from calculations in a
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12 au cubic box and gamma sampling.
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Running it will generate directory "results" to be compared with directory
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"reference"
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Please report problems and suggestions to Stefano de Gironcoli
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(degironc@sissa.it) and keep in mind that this feature is still
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experimetal..
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@ -0,0 +1,403 @@
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#!/bin/sh
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# run from directory where this script is
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cd `echo $0 | sed 's/\(.*\)\/.*/\1/'` # extract pathname
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EXAMPLE_DIR=`pwd`
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# check whether echo has the -e option
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if test "`echo -e`" = "-e" ; then ECHO=echo ; else ECHO="echo -e" ; fi
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$ECHO
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$ECHO "$EXAMPLE_DIR : starting"
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$ECHO
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$ECHO "This example shows how to use pw.x to calculate the total energy and"
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$ECHO "of silicon and a few small molecules using hybrid functionals."
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# set the needed environment variables
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. ../environment_variables
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# required executables and pseudopotentials
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BIN_LIST="pw.x"
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PSEUDO_LIST="Si.vbc.UPF"
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$ECHO
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$ECHO " executables directory: $BIN_DIR"
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$ECHO " pseudo directory: $PSEUDO_DIR"
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$ECHO " temporary directory: $TMP_DIR"
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$ECHO " checking that needed directories and files exist...\c"
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# check for directories
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for DIR in "$BIN_DIR" "$PSEUDO_DIR" ; do
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if test ! -d $DIR ; then
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$ECHO
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$ECHO "ERROR: $DIR not existent or not a directory"
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$ECHO "Aborting"
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exit 1
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fi
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done
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for DIR in "$TMP_DIR" "$EXAMPLE_DIR/results" ; do
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if test ! -d $DIR ; then
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mkdir $DIR
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fi
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done
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cd $EXAMPLE_DIR/results
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# check for executables
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for FILE in $BIN_LIST ; do
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if test ! -x $BIN_DIR/$FILE ; then
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$ECHO
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$ECHO "ERROR: $BIN_DIR/$FILE not existent or not executable"
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$ECHO "Aborting"
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exit 1
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fi
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done
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# check for pseudopotentials
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for FILE in $PSEUDO_LIST ; do
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if test ! -r $PSEUDO_DIR/$FILE ; then
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$ECHO
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$ECHO "ERROR: $PSEUDO_DIR/$FILE not existent or not readable"
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$ECHO "Aborting"
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exit 1
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fi
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done
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$ECHO " done"
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# how to run executables
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PW_COMMAND="$PARA_PREFIX $BIN_DIR/pw.x $PARA_POSTFIX"
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$ECHO
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$ECHO " running pw.x as: $PW_COMMAND"
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$ECHO
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# clean TMP_DIR
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$ECHO " cleaning $TMP_DIR...\c"
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rm -rf $TMP_DIR/*
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$ECHO " done"
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$ECHO
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$ECHO " running PBE0 calculation for Si with nq=1,2,4 \c"
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$ECHO
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for nq in 1 2 4 ; do
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# self-consistent calculation
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cat > si.in << EOF
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&control
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calculation = 'scf'
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restart_mode='from_scratch',
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prefix='silicon',
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pseudo_dir = '$PSEUDO_DIR/',
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outdir='$TMP_DIR/'
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/
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&system
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ibrav= 2, celldm(1) =10.20, nat= 2, ntyp= 1,
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ecutwfc =12.0, nbnd = 8,
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input_dft='pbe0', nqx1 = $nq, nqx2 = $nq, nqx3 = $nq,
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/
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&electrons
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mixing_beta = 0.7
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/
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ATOMIC_SPECIES
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Si 28.086 Si.vbc.UPF
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ATOMIC_POSITIONS
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Si 0.00 0.00 0.00
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Si 0.25 0.25 0.25
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K_POINTS
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10
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0.1250000 0.1250000 0.1250000 1.00
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0.1250000 0.1250000 0.3750000 3.00
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0.1250000 0.1250000 0.6250000 3.00
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0.1250000 0.1250000 0.8750000 3.00
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0.1250000 0.3750000 0.3750000 3.00
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0.1250000 0.3750000 0.6250000 6.00
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0.1250000 0.3750000 0.8750000 6.00
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0.1250000 0.6250000 0.6250000 3.00
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0.3750000 0.3750000 0.3750000 1.00
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0.3750000 0.3750000 0.6250000 3.00
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EOF
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$ECHO " running the scf calculation for Si with nq = $nq ...\c"
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$PW_COMMAND < si.in > si.PBE0_nq=${nq}.out
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$ECHO " done"
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grep -e ! si.PBE0_nq=${nq}.out | tail -1
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rm -f si.in
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done
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$ECHO
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$ECHO " running now a few molecules with Gamma sampling ...\c"
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$ECHO
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PSEUDO_DIR=../Pseudo
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$ECHO " pseudo directory cahnged to: $PSEUDO_DIR"
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xc=pbe0
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ps=1nlcc
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ecut=80
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rm -fr $TMP_DIR/*
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cat > o.inp << EOF
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&CONTROL
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calculation = 'scf' ,
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restart_mode = 'from_scratch' ,
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outdir = '$TMP_DIR/' ,
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pseudo_dir = '$PSEUDO_DIR/',
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prefix = 'o',
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disk_io = 'minimal' ,
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iprint = 1
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tprnfor = .true.
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/
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&SYSTEM
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ibrav = 1,
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celldm(1) = 12.0,
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nat = 1,
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ntyp = 1,
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ecutwfc = $ecut ,
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input_dft='$xc'
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nspin = 2
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starting_magnetization(1) = 0.2,
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nbnd = 4
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nelec = 6.0
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nelup = 4.0
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neldw = 2.0
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/
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&ELECTRONS
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conv_thr = 0.5d-3
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/
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ATOMIC_SPECIES
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O 16.0 OPBE$ps.RRKJ3
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ATOMIC_POSITIONS angstrom
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O 0.1 0.2 0.3
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K_POINTS gamma
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#automatic
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#1 1 1 0 0 0
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EOF
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$ECHO " running oxygen atom..\c"
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$PW_COMMAND < o.inp > o.$xc.$ps.out-$ecut
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$ECHO " done"
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rm -fr $TMP_DIR/*
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cat > c.inp << EOF
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&CONTROL
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calculation = 'scf' ,
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restart_mode = 'from_scratch' ,
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outdir = '$TMP_DIR/' ,
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pseudo_dir = '$PSEUDO_DIR/',
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prefix = 'o2',
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disk_io = 'minimal' ,
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iprint = 1
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tprnfor = .true.
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/
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&SYSTEM
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ibrav = 1,
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celldm(1) = 12.0,
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nat = 1,
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ntyp = 1,
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ecutwfc = $ecut ,
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input_dft='$xc'
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nspin = 2
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starting_magnetization(1) = 0.2,
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nbnd = 4
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nelec = 4.0
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nelup = 3.0
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neldw = 1.0
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/
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&ELECTRONS
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conv_thr = 0.5d-3
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/
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ATOMIC_SPECIES
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C 16.0 CPBE$ps.RRKJ3
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ATOMIC_POSITIONS angstrom
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C 0.1 0.2 0.3
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K_POINTS gamma
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#automatic
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#1 1 1 0 0 0
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EOF
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$ECHO " running carbon atom..\c"
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$PW_COMMAND < c.inp > c.$xc.$ps.out-$ecut
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$ECHO " done"
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rm -fr $TMP_DIR/*
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cat > n.inp << EOF
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&CONTROL
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calculation = 'scf' ,
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restart_mode = 'from_scratch' ,
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outdir = '$TMP_DIR/' ,
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pseudo_dir = '$PSEUDO_DIR/',
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prefix = 'o2',
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disk_io = 'minimal' ,
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iprint = 1
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tprnfor = .true.
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/
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&SYSTEM
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ibrav = 1,
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celldm(1) = 12.0,
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nat = 1,
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ntyp = 1,
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ecutwfc = $ecut ,
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input_dft='$xc'
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nspin = 2
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starting_magnetization(1) = 0.2,
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nbnd = 4
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nelec = 5.0
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nelup = 4.0
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neldw = 1.0
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/
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&ELECTRONS
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conv_thr = 0.5d-4
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/
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ATOMIC_SPECIES
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N 16.0 NPBE$ps.RRKJ3
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ATOMIC_POSITIONS angstrom
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N 0.1 0.2 0.3
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K_POINTS gamma
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#automatic
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#1 1 1 0 0 0
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EOF
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$ECHO " running nitrogen atom..\c"
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$PW_COMMAND < n.inp > n.$xc.$ps.out-$ecut
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$ECHO " done"
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rm -fr $TMP_DIR/*
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b=0.3169
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cat > n2.inp << EOF
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&CONTROL
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calculation = 'scf' ,
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restart_mode = 'from_scratch' ,
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outdir = '$TMP_DIR/' ,
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pseudo_dir = '$PSEUDO_DIR/',
|
||||
prefix = 'o2',
|
||||
disk_io = 'minimal' ,
|
||||
iprint = 1
|
||||
tprnfor = .true.
|
||||
/
|
||||
&SYSTEM
|
||||
ibrav = 1,
|
||||
celldm(1) = 12.0,
|
||||
nat = 2,
|
||||
ntyp = 1,
|
||||
ecutwfc = $ecut ,
|
||||
input_dft='$xc'
|
||||
nbnd = 8
|
||||
/
|
||||
&ELECTRONS
|
||||
conv_thr = 1.d-4
|
||||
/
|
||||
&IONS
|
||||
/
|
||||
ATOMIC_SPECIES
|
||||
N 16.0 NPBE$ps.RRKJ3
|
||||
ATOMIC_POSITIONS angstrom
|
||||
N $b $b $b
|
||||
N -$b -$b -$b
|
||||
K_POINTS gamma
|
||||
#automatic
|
||||
#1 1 1 0 0 0
|
||||
EOF
|
||||
$ECHO " running n2 molecule..\c"
|
||||
$PW_COMMAND < n2.inp > n2.$xc.$ps.out-$ecut
|
||||
$ECHO " done"
|
||||
|
||||
rm -fr $TMP_DIR/*
|
||||
|
||||
b=0.3256
|
||||
cat > co.inp << EOF
|
||||
&CONTROL
|
||||
calculation = 'scf' ,
|
||||
restart_mode = 'from_scratch' ,
|
||||
outdir = '$TMP_DIR/' ,
|
||||
pseudo_dir = '$PSEUDO_DIR/',
|
||||
prefix = 'o2',
|
||||
disk_io = 'minimal' ,
|
||||
iprint = 1
|
||||
tprnfor = .true.
|
||||
/
|
||||
&SYSTEM
|
||||
ibrav = 1,
|
||||
celldm(1) = 12.0,
|
||||
nat = 2,
|
||||
ntyp = 2,
|
||||
ecutwfc = $ecut ,
|
||||
input_dft='$xc'
|
||||
nbnd = 8
|
||||
/
|
||||
&ELECTRONS
|
||||
conv_thr = 0.5d-3
|
||||
/
|
||||
&IONS
|
||||
/
|
||||
ATOMIC_SPECIES
|
||||
C 16.0 CPBE$ps.RRKJ3
|
||||
O 16.0 OPBE$ps.RRKJ3
|
||||
ATOMIC_POSITIONS angstrom
|
||||
C $b $b $b
|
||||
O -$b -$b -$b
|
||||
K_POINTS gamma
|
||||
#automatic
|
||||
#1 1 1 0 0 0
|
||||
EOF
|
||||
$ECHO " running co molecule..\c"
|
||||
$PW_COMMAND < co.inp > co.$xc.$ps.out-$ecut
|
||||
$ECHO " done"
|
||||
|
||||
rm -fr $TMP_DIR/*
|
||||
b=0.3478
|
||||
cat > o2.inp << EOF
|
||||
&CONTROL
|
||||
calculation = 'scf' ,
|
||||
restart_mode = 'from_scratch' ,
|
||||
outdir = '$TMP_DIR/' ,
|
||||
pseudo_dir = '$PSEUDO_DIR/',
|
||||
prefix = 'o2',
|
||||
disk_io = 'minimal' ,
|
||||
iprint = 1
|
||||
tprnfor = .true.
|
||||
/
|
||||
&SYSTEM
|
||||
ibrav = 1,
|
||||
celldm(1) = 12.0,
|
||||
nat = 2,
|
||||
ntyp = 1,
|
||||
ecutwfc = $ecut ,
|
||||
input_dft='$xc'
|
||||
nspin = 2
|
||||
starting_magnetization(1) = 0.2,
|
||||
nbnd = 8
|
||||
nelec = 12.0
|
||||
nelup = 7.0
|
||||
neldw = 5.0
|
||||
/
|
||||
&ELECTRONS
|
||||
conv_thr = 0.5d-3
|
||||
/
|
||||
&IONS
|
||||
/
|
||||
ATOMIC_SPECIES
|
||||
O 16.0 OPBE$ps.RRKJ3
|
||||
ATOMIC_POSITIONS angstrom
|
||||
O $b $b $b
|
||||
O -$b -$b -$b
|
||||
K_POINTS gamma
|
||||
#automatic
|
||||
#1 1 1 0 0 0
|
||||
EOF
|
||||
$ECHO " running o2 molecule..\c"
|
||||
$PW_COMMAND < o2.inp > o2.$xc.$ps.out-$ecut
|
||||
$ECHO " done"
|
||||
$ECHO " summarize"
|
||||
cat > summarize << EOF
|
||||
grep -e ! n.$xc.$ps.out-$ecut | tail -1 | awk '{print \$5}' > N
|
||||
grep -e ! n2.$xc.$ps.out-$ecut | tail -1 | awk '{print \$5}' > N2
|
||||
paste N2 N | awk '{be= (\$1-\$2*2.0) * 13.6058 * 23.06; print "N2 : ",be}'
|
||||
grep -e ! o.$xc.$ps.out-$ecut | tail -1 | awk '{print \$5}' > O
|
||||
grep -e ! o2.$xc.$ps.out-$ecut | tail -1 | awk '{print \$5}' > O2
|
||||
paste O2 O | awk '{be= (\$1-\$2*2.0) * 13.6058 * 23.06 ; print "O2 : ",be}'
|
||||
grep -e ! c.$xc.$ps.out-$ecut | tail -1 | awk '{print \$5}' > C
|
||||
grep -e ! co.$xc.$ps.out-$ecut | tail -1 | awk '{print \$5}' > CO
|
||||
paste CO O C | awk '{be= (\$1-\$2-\$3) * 13.6058 * 23.06; print "CO : ",be}'
|
||||
rm C N O CO O2 N2
|
||||
EOF
|
||||
sh summarize
|
||||
|
||||
rm -f *.inp
|
||||
rm -fr $TMP_DIR/*
|
||||
$ECHO "$EXAMPLE_DIR : done"
|
||||
Loading…
Reference in New Issue