Liege Caliste Bigdft

8/6/2019 Liege Caliste Bigdft

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BigDFT - anew ABINIT

library

PSolverdescription

Interpolets

Separability

Performances

PSolver inABINIT

02poisson

Real space

Results

BigDFT inABINIT

Outlines

Structure

Results

Outlook

3rd International ABINIT Developer Workshop

LIÈGE - BELGIUM

Introducing wavelet basis sets inside ABINIT via

the BigDFT project

Damien Caliste & Luigi Genovese

PCPM - UCL / L_Sim - CEA Grenoble

30 January 2007

EU Nest Adventure - BigDFT project www.abinit.org




library

PSolverdescription

Interpolets

Separability

Performances

PSolver inABINIT

02poisson

Real space

Results

BigDFT inABINIT

Outlines

Structure

Results

Outlook

Outline

1 Poisson Solver for free BCInterpolating scaling functions

SeparabilityPerformances

2 Computing Hartree’s potential in ABINIT for isolatedsystems

The 02poisson interfaceComputing potentials in real spaceEffects on sample potentials

3 Inclusion of a wavelet basis set into ABINIT, the BigDFTproject

A quick view into BigDFT machineryInterface between BigDFT and ABINITConvergence and results

4 Summary and outlook





library

PSolverdescription

Interpolets

Separability

Performances

PSolver inABINIT

02poisson

Real space

Results

BigDFT inABINIT

Outlines

Structure

Results

Outlook

Poisson Solver with interpolating scaling functions

Calculation of the self-consistent potential

Poisson Equation for isolated systems∇2V H (r) = −4πρ(r) =⇒ V H (r) =

Z Ω

K (|r− r|)ρ(r)d r

The kernel K (r) = 1/r with Ω = R3

This equation is usually solved using plane waves. Theirdelocalization results in problems for isolated systems.How to remove long-distance interactions?

Most commonly used methods (Hockney, Martina-Tuckerman)

Modify the kernel operator K = K short + K long

Does not implement well short-distance behaviour

We must consider a size that is larger than the size ofthe original system





library

PSolverdescription

Interpolets

Separability

Performances

PSolver inABINIT

02poisson

Real space

Results

BigDFT inABINIT

Outlines

Structure

Results

Outlook

Using a localized function set

Interpolating Scaling Functions (from wavelet theory)

Localized in real and Fourier space

Undergo multi-scale relations

The expansion coefficients coincide with the values on a(uniform) grid

Separable basis functions φj(r) = φ j x (x )φ j y

(y )φ j z (z )

Optimal for isolated systems

The potential is obtained via a discrete convolution

V (i) =

∑jK i−j ρ(j)

K i =Z

K (|r|)Φi(r)d r =Z

1

r φi x

(x )φi y (y )φi z

(z )d r

Given K i, we can calculate convolution using zero-padded

FFT (O (N log(N ) scaling)EU Nest Adventure - BigDFT project www.abinit.org




library

PSolverdescription

Interpolets

Separability

Performances

PSolver inABINIT

02poisson

Real space

Results

BigDFT inABINIT

Outlines

Structure

Results

Outlook

Gaussian tensor product decomposition

The calculation of the kernel K i can be improved thanks toseparability of the basis

Approximation with gaussians(Beylkin et al.)

1

r ∑

k

ωk e −p k r 2

with very high accuracy89 terms, p k , ωk suitably chosen.The sum in gaussians allows us to write the tensordecomposition of the kernel:

The computational cost is reduced N 3 → 89×N

K j =89

∑k =1

ωk K j x (p k )K j y

(p k )K j z (p k )

K j (p ) = R φ0(x )e −p (x − j )2dx





library

PSolverdescription

Interpolets

Separability

Performances

PSolver inABINIT

02poisson

Real space

Results

BigDFT inABINIT

Outlines

Structure

Results

Outlook

Features

Very fast with moderate memory occupation:

Elapsed Time on a Cray XT3,1283 grid

np 1 2 4 8 16 32 64

s .92 .55 .27 .16 .11 .08 .09

More precise than other existing Poisson Solvers:

1e-11

1e-10

1e-09

1e-08

1e-07

1e-06

1e-05

1e-04

0.001

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6

M a x

E r r o r

Grid step

HockneyTuckerman

8th14th20th30th40th50th60th

100th





library

PSolverdescription

Interpolets


PSolver inABINIT

02poisson

Real space

Results

BigDFT inABINIT

Outlines

Structure

Results

Outlook

Overview

In summary, we have developed a technique

Free boundary conditions

Very high accuracy

Good computational performance, easy to parallelize

Based on a real space grid, can be used independently

Allows for MultiResolution Analysis (adaptivity)

Paper published

L. Genovese, T. Deutsch, A. Neelov,S. Goedecker, G. Beylkin

Efficient solution of Poisson’s equation with free boundary conditions , [arXiv: cond-mat/0605371],J. Chem. Phys. 125, 074105 (2006)





library

PSolverdescription

Interpolets


PSolver inABINIT

02poisson

Real space

Results

BigDFT inABINIT

Outlines

Structure

Results

Outlook

The 02poisson interface

ABINIT BigDFT

included from 02poisson directory

PSolver_hartree()

Branching into rhohxc_coll() between hartre() andPSolver_hartree()

if (dtset%icoultrtmt == 1) thencall PSolver_hartree(dtset, 1, nfft, ngfft, rhor, rprimd, vhartr)elsecall hartre(cplex,gmet,gsqcut,izero,mpi_enreg,nfft,ngfft,qphon,rhog,vhartr)

end if

Two new input variablesicoultrtmt that controls the computation of Coulomb’spotential ;nscforder which commands the degree ofinterpolating scaling functions used in the kernel.





library

PSolverdescription

Interpolets


PSolver inABINIT

02poisson

Real space

Results

BigDFT inABINIT

Outlines

Structure

Results

Outlook

Realspace potentials within E total

With icoultrtmt == 1, all local potentials are computed inrealspace.

Real space Reciprocal space

E kin

E hart PSolver_hartree() hartre()

E psp _ nl

E psp _ loc branched inside mklocl()

mklocl_realspace()† mklocl_recipspace()

E ewald simple ion/ion interaction

∑λ,κ ;λ=κ

Z λionZ κ ion

τλ−τκ ionion_realspace() ewald()

† Computation of E psp _ loc in real space requires a description of

pseudo-potentials in RS, currently implemented for GTH and HGH

only.





library

PSolverdescription

Interpolets


PSolver inABINIT

02poisson

Real space

Results

BigDFT in

ABINITOutlines

Structure

Results

Outlook

Better estimated potentials for isolated systems

The local part from pseudo-potentials

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

-20 -15 -10 -5 0 5 10 15 20

I o n i c p o t e n t i a l ( H a

r t r e e . B o h r -

1 )

Distance in [111] axis (Bohr)

Centered SiH4

molecule: calculation of the ionic potential (Ec=20Ht)

Gaussian charges on originPeriodic conditions, box size = 10BohrPeriodic conditions, box size = 20BohrPeriodic conditions, box size = 30Bohr

Isolated conditions

the potentials are correct in the boundary regions ;

the 1r

behavior is valid whatever the supercell size.


B i d i l f i l d




library

PSolverdescription

Interpolets


PSolver inABINIT

02poisson

Real space

Results

BigDFT in

ABINITOutlines

Structure

Results

Outlook

Better estimated potentials for isolated systems

The Hartree’s potential

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25 30

H a r t r e e

p o t e n t i a l ( H

a r t r e e . B o h r

- 1 )

Distance in demi [111] axis (Bohr)

Centered SiH4

molecule: calculation of the Hartree potential (Ec=20Ht)

Gaussian charges on originDot charges on origin

Periodic conditions, box size = 10BohrPeriodic conditions, box size = 20BohrPeriodic conditions, box size = 30Bohr

Isolated conditions

the potentials are correct in the boundary regions ;

the 1r

behavior is valid whatever the supercell size.


E i till ff t d b b i




library

PSolverdescription

Interpolets


PSolver inABINIT

02poisson

Real space

Results

BigDFT in

ABINITOutlines

Structure

Results

Outlook

E total is still affected by box size

Total energy of a silane molecule

-6.23

-6.22

-6.21

-6.2

-6.19

-6.18

-6.17

-6.16

6 8 10 12 14 16 18 20

E n e r g y ( H a r t r e e )

Supercell size (size len th in Bohr)

Periodic (Ec=50Ht)Real space (Hartree and ionic) (Ec=50Ht)

Total energy is not significantly modified by accurate potential treatment.

the kinetic part of the energy is strongly dependent onthe periodicity of the super-cell ;

a full real-space is mandatory for isolated and/orinhomogeneous systems.


A i k i i t Bi DFT hi




library

PSolverdescription

Interpolets


PSolver inABINIT

02poisson

Real space

Results

BigDFT in

ABINITOutlines

Structure

Results

Outlook

A quick view into BigDFT machinery

Every steps of electronic calculations are treated in realspace on a systematic basis set.

Pseudo-potentials are described by separable functions(GTH and HGH) ;Wave-functions are expanded on a Daubechies’ waveletbasis set (i.e. a set of coefficients on a real spaceadaptative grid).

New tools have been developped to handle theSchrödinger’s equation.

A real space laplacian, using filters on wavelets ;Storage and matricial computation of wave-functions ona two-resolution grid ;

A real space preconditionner for wavelets.

The ground state is computed in a direct minimisationloop, using either the steepest descent algorithm or aDIIS scheme.


I t f b t Bi DFT d ABINIT




library

PSolverdescription

Interpolets


PSolver inABINIT

02poisson

Real space

Results

BigDFT in

ABINITOutlines

Structure

Results

Outlook

Interface between BigDFT and ABINIT

All informations have been gathered into Fortran types.

Data storage

wvl_wf_type - stores the decomposition of wave-functions ;

wvl_keyArrays_type - description of the two-resolution grid ;

wvl_projectors_type - stores the projector parts ofpseudo-potentials.

Most of the main routines have been branched and call theBigDFT library (using a module interface).

New interface routines

src/08seqpar/wvl_vtorho() - the main part within theminimisation loop (build the Hamiltonian, compute the gradient andcreate new wave-functions using steepest descent or DIIS) ;

src/05common/wvl_mkrho() - compute density fromwave-functions ;

src/04wvl_wfs - contains basic routines to create, free, manipulatewave-functions on a two-grid wavelet basis set ;


New input variables




library

PSolverdescription

Interpolets


PSolver inABINIT

02poisson

Real space

Results

BigDFT in

ABINITOutlines

Structure

Results

Outlook

New input variables

Main specific variables to control the basis set

wvl_hgrid the grid size

wvl_frmult the expansionaround atoms for fine grid

wvl_crmult the expansionaround atoms for coarsegrid

All wavelet specific input variable are prefixed by wvl_ .

Other relevant variablesusewvl to enable a wavelet computation ;

nwfshist for the DIIS history.


An accurate total energy




library

PSolverdescription

Interpolets


PSolver inABINIT

02poisson

Real space

Results

BigDFT in

ABINITOutlines

Structure

Results

Outlook

An accurate total energy

The main convergence parameter iswvl_hgrid and an usual value for organicmolecule is 0.35Bohr.

[Convergence of E total versus wvl_hgrid for a silane]

1e-06

1e-04

0.01

0.2 0.3 0.4 0.5 0.6 0.7

Total energy for a silane molecule

-6.24

-6.22

-6.2

-6.18

-6.16

-6.14

-6.12

6 8 10 12 14 16 18 20

E n e r g y ( H a r t r e e )

Supercell size (size length in Bohr)

Ec=10HtEc=15HtEc=25HtEc=35Ht

Wavelet computed value (hgrid = 0.5)

E wvltotal = E

pwtotal with a converged cut-off.


Summary and Outlook




library

PSolverdescription

Interpolets


PSolver inABINIT

02poisson

Real space

Results

BigDFT in

ABINITOutlines

Structure

Results

Outlook

Summary and Outlook

The standalone code created in the frame of the Europeanproject BigDFT, has been included in ABINIT for developper

usage. It is characterised by:a systematic real space basis set ;

an accurate ground state computation.

The next development will import the capability to

run on parallel with a split on bands (mature in BigDFT) ;

compute forces for geometry optimisation (mature inBigDFT) ;

use a scheme to improve accurancy without increasingthe basis-set (recently introduced in BigDFT).

A simple linear scaling approach is under development in theBigDFT project and schedule for inclusion in ABINIT in 5.4series.

Wavelet computations for end-users will be presented during

next autumn in a CECAM tutorial.EU Nest Adventure - BigDFT project www.abinit.org

Liege Caliste Bigdft

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