Describiendo la materia a escala

microscópica con simulaciones cuánticas

... (o cómo pasar 25 años haciendo la Siesta)

Pablo Ordejón

ICN2 – Barcelona (Spain)

SIMUNE Atomistics – San Sebastian (Spain)

Cortesía del Prof. Helmut Dosch

Max Planck Institute for Metal Research

Stuttgart (Alemania)

From Nicola Marzari, PACS 2017

Computational Materials Science

R. Mata and M. A. Suhm, Angew. Chem. Int. Ed. 2017, 56, 11011 – 11018

,

Computational Materials Science

From Giulia Galli, PACS 2015

Quantum Mechanics: Approximations and

Computational schemes

The Approximations:

• Hartree Fock and beyond – Quantum Chemistry

• Density Functional Theory

o Local Density Approximation and beyond

• Stochastic approaches: Quantum Monte Carlo

~1965

~1985 – 1990 – 2010

> 1985

The ability to compute

In the 1990s, DFT and QC are massively used in

physics and chemistry, as the results of key

algorithmic and computational developments

Quantum Monte Carlo is applied to “real materials”

From Giulia Galli, PACS 2015

Quantum Mechanics: Approximations and

Computational schemes

The Approximations:

• Hartree Fock and beyond – Quantum Chemistry

• Density Functional Theory

o Local Density Approximation and beyond

• Stochastic approaches: Quantum Monte Carlo

~1985 – 1990 – 2010

> 1985

From Giulia Galli, PACS 2015

The ability to compute

• Pseudopotentials and all electron methods

• Ab-initio Molecular Dynamics (Car-Parrinello...)

• Linear sclaing methods within DFT and QMC

• Software development for HPC architectures

Molecular Dynamics with

forces from DFT

ab initio MD

Dynamical and

thermodynamic

properties from first

principles

~1965

3. Approximation: the effective XC potential - Local, Quasilocal, ...

)]([)( rVrV XCXC

)](),([)( rrVrV XCXC

LDA

GGA

)(})({ rr i

1. (Hohenberg-Kohn Theorems)particle density

DFT in a nutshell..

2. Interacting electrons: As if non-interacting electrons in an effective

potential (Kohn-Sham Ansatz)

)()(ˆ rrh nnn

))(()()(2

1ˆ 2 rVrVrVh XCHext ∇

W. Kohn, Nobel 1998

1. Choose a basis set

Plane Waves - APWs - LMTOs - Grids

Gaussians - Slaters

(Numerical) Atomic Orbitals

DFT in practice

2. Solve the self-consistent one electron problem:

Building Hamiltonian matrix and solving an eigenvalue problem

))(()()(2

1ˆ 2 rVrVrVh XCHext ∇

SCF nnn csch ˆˆ O(N3)

Plane Waves

NPW ∝ resolution 1/𝛿 (1/𝛿3 in 3D)

L

Plane Waves

2L

Plane Waves

NPW ∝ resolution 1/𝛿3

NPW ∝ Length (Volume in 3D)

• Systematic

• Not biased

• DFT Equations easy to implement

Atomic orbital basis (I)

LCAO:

Atomic-like orbitals

(Arbitrarily complete)

),()()( lmYrr

s p d f

Spherical harmonics

3s orbital of

Mg

),()()( lmYrr

Atomic orbital basis (II)

Radial Functions:

• Obtained in the free atom (with a given

pseudopotential)

• Finite radius is imposed (using a

confining potential)

Strictly Localized,

Numerical Pseudo-Atomic Orbitals

Arbitrarily complete bases

The Numerical Atomic Orbitals Basis Sets

• DZP Basis

• Eshift = 50 meV

• rc of TM increased to obtain

converged EB (variationally)

Arbitrarily complete bases

NPW ∝ resolution 1/𝛿3

NPW ∝ Volume in 3D

• Systematic

• Not biased

• DFT Equations easy to implement

NAO ∝ resolution (quality)

NAO ∝ Number of atoms

• Non Systematic

• Biased

• DFT Equations harder to implement

The SIESTA Method and Code

νμμν φhφh ˆ=ˆ

Strictly Localized Orbitals

Sparse Matrices

1 23

4

5

• Calculation and storage of Hamiltonian scales linearly with system size

• Natural local language to exploit WF or DM localization: linear scaling H solvers

Key to O(N): locality

‘Nearsightedness Properties’

W. Kohn, Phys. Rev. Lett. 76, 3168 (1996)

The properties at point r are not sensitive to changes of the potential at r’ at distant regions (larger than l, which defines the ‘locality’ of a given system).

Key to O(N): locality

‘Divide and conquer’ W. Yang, Phys. Rev. Lett. 66, 1438 (1992)

Large system

Locality of Wave Functions

Ψ1

Ψ21 = 1/2 (Ψ1+Ψ2)

2 = 1/2 (Ψ1-Ψ2)

occoccψUχ

Wannier functions (crystals)

Localized Molecular Orbitals (molecules)

Locality of Wave Functions(Wannier Functions)

Insulators:

Metals:

Carbon (diamond)

Aluminium

Goedecker & Teter, PRB 51, 9455 (1995)

Locality of Wave Functions(Wannier Functions)

Exponential localization (insulators):

610-21

7.6

Wannier function in Carbon (diamond)

Stephan and Drabold, PRB 57, 6391 (98)

Linear Scaling

i

iRc

rc

Ordejón et al, PRB 48, 14646 (1993)

Error decreases exponentially with Rc

Application to DNA

Dry DNA Poly(C)-Poly(G)

(A-DNA form)

Model: Periodic (11 pairs, 715 atoms each helix turn)

Previous study: H-bonds in 27 base-pairsBinding energy accurcy ~ 1 Kcal/mol (compared to MP2 results)Artacho et al, Mol. Sim.

de Pablo et al., PRL 85, 4992 (2000)

Technical details

• Initial coordinates: X-ray diffraction data of DNA fibers (Landolt-Bornstein)

Not enough (atomic) resolution refinement with

empirical forces

models

• DFT Functional: GGA (Perdew-Burke-Ernzerhof)

(good description of H-bonds)

• Basis: DZ, with short radii

DZP, with larger radii on H-bonds atoms

• Wannier Functions: Rc = 4 Ang. (errors in total energy around 1 meV/atom;

errors in forces around 0.04 eV/Ang)

• Relaxation: 1 Gb memory 30 - 50 min/step (DEC-Alpha 550)

After 400 steps: largest force 0.1 eV/Ang

(2 weeks) average force 0.01 eV/Ang

Experiment SIESTA

N2(H) --- O2 2.86 2.86

N2 – H 1.00 1.03

N1(H) --- N3 2.85 2.83

N1 – H 1.00 1.04

O6 --- (H) N4 2.86 2.73

H – N4 1.00 1.05

H-bond geometries (Ang):

Electrostatic Potentialblue: positivered: negative

de Pablo et al., PRL 85, 4992 (2000)

de Pablo et al., PRL 85, 4992 (2000)

Disorder ---- Localization

Irregular sequence (Swapped)

Regular sequence

HOMO LUMO

In collaboration with D. Scherlis and D. Estrin (U. Buenos Aires)

Reactive subsystem: QM

Environment: MM Additive scheme:

MM Force Field:

AMBER

QM / MM Methodologies

(Biosynthesis of aromatic aa in bacteria, fungi and plants)

Application: Chorismate Mutase Enzime

(Biosynthesis of aromatic aa in bacteria, fungi and plants)

• The catalitic effect is reproduced: barrier reduced.

• The choice of the QM subsystem is not very

important (in this particular case).

• No entropic effects considered here (constrained

optimizations).

• See Crespo et al., JACS (2005) for Free Energy

calculations! (Multiple Steered Molecular Dynamics)

Aqueous solution

Enzyme (QM-1)

Enzyme (QM-2)

Application: Chorismate Mutase Enzime

Challenge: Charge Transport at the Nanoscale

• Basic understanding of transport

phenomena in nanoscale

materials and devices

• Atomic detail

• “Ab-initio” (from first principles)

εTεfεfdεh

2eI RL

2

Atomistic; first-principles:

DFT + NEGF’s -- TranSIESTABrandbyge, Mozos, Ordejón, Taylor, Stokbro,

PRB 65, 165401 (2002)

Electronic Transport from Scattering Theory (Buttiker-Landauer)

IeV

0bands

2

bandsGN

h

2eN

V

IG

Nanopore DNA sequencing

Ionic Current Blockade unpon DNA

translocation

Combining QM/MM with Electronic Transport

Combining classical MD (LAMMPS)

for MD with SIESTA for analysis of

the electronic structure

Nanopore DNA sequencing Measuring the current across DNA

Combining QM/MM with Electronic Transport

Nanopore DNA sequencing

Combining QM/MM with Electronic Transport

Measuring the current across DNA

Nanopore DNA sequencing

Nanopore DNA sequencing

Understanding DNA sequencing (transverse current)

devices from Atomistic Simulations

• Very large systems (> 104 atoms)

• Very long time scales (0.01 - 1μs per nucleotide)

• Non equilibrium (electric fields, currents)

• Quantum effects are essential

Nanopore DNA sequencing

Ab-initio (DFT) Calculations

(QM/MM)

Simulation Protocol:

1. Equilibration: 300 ps MD with

Classical Potentials

2. Production runs: 2 ns MD with

Classical Potentials (sampling

the configurations of the

nucleotide while it passes the NP)

3. For 90 snapshots: Transport

calculation using QM/MM (with

different partitions)

Nanopore DNA sequencing

Conductance: Nucleotide selectivity?

• Measurable (but small) differences

between nucleotides

• Purines (A, G) and Pyrimidines (C, T)

give distinct signals

Nanopore DNA sequencing

• Differences in conductance correlate

with the charge in the nucleotide

while passing the pore

• A detalied analysis shows that the

changes in the conductance are due

to capacitive effects (electrostatic

potantial created on graphene by

the passing nucleotide)

• Water and Counterions play a key

role!

• Arbitrarily complete bases

“Quick &

Dirty”

State of the

Art

Speed

Accuracy

• s, p, d, ...

• Single-, multiple -

• Off-site orbitals

• Diffuse functions

• Band structures (k-point sampling)

• Population analysis

• Charge distributions

• Electrostatic Potentials

• Electric Polarization

• Density of States

• Spin, Magnetization

• Non-collinear spin states

• Electronic transport

• STM image simulation....

• Electronic structure information

• Relaxations

- Atomic coordinates

- Cell shape & size

• Phonons, elastic constants, ...

• Thermal transport

• Molecular Dynamics:

- E, V

- T, V (Nose Thermostat)

- P (Parrinello-Rahman)

- T, P

• Atomic forces and stress

SIESTA Features

• Massively parallel efficiency in Supercomputers

(with J.M.Cela, BSC)

• Hybrid QM/MM simulations

(with D. Estrin, UBA)

Theor. Chem. Acc 128, 825 (2011)

• Non-equilibrium transport -TranSIESTA

Phys. Rev. B 65, 165401 (2002)

• GW for electronic excitations

(with F. Giustino, Oxford)

Phys. Rev. B 85, 245125 (2012)

• Linear Response (Phonons)

Phys. Rev. 65, 075210 (2002)

(massive revamping ongoing)

• TD-DFT in real time

(D. Sanchez-Portal, San Sebastian)

Phys. Rev. B 66, 235416 (2002)

• Spin-Orbit coupling, including constrains

J. Phys. Cond Matt. 19 489001 (2007)

J. Phys.: Cond. Mat. 24 086005 (2012)

• Hybrid Functionals (upcoming)

J. Junquera, to be published

SIESTA Features

Current capabilities & developments:

> 16000 cites to date (to the 6 main methodological articles of SIESTA)

Citing articles by scientific discipline (according to WoK)

Citing articles by country (1996-2001)

Citing articles by country 1996-2005

Citing articles by country 1996-2019

Himanen et al. Advanced Science 6, Sept. 2019

Materials Discovery

High Performance Computing

(massively large calculations

Large systems / Long time scales)

High Throughput Computing

(massive number of runs)

Jack Deslippe, NERSC

Materials Discovery

N. Marzari, Nature Meterials 2016

Himanen et al. Advanced Science 6, Sept. 2019

Materials Discovery

Major efforts worldwide

MaX: European Centre of Excellence for materials design

Materials Cloud

• start from successful and widely

used open-source, community codes

in quantum materials simulations

• make them scalable and optimized

for current and future

architectures towards the

exascale, develop new capabilities

• leverage the convergence of HPC

with automated high throughput

computing and high-performance

data analytics

• hardware-software codesign in

practice

• widen access to codes, engage &

train users communities in industry

and academia

MaX: European Centre of Excellence for materials design

MaX coordination: CNR Modena, Italy www.max-centre.eu

MaX industrial pilot cases

102

103

104

MPI Processes

102

103

104

Tim

e fo

r firs

t S

CF

ste

p (

s)

DNA-25

C/BN

SIESTA Strong Scaling

102

103

104

MPI Processes

102

103

104

Tim

e fo

r firs

t S

CF

ste

p (

s)

400ppp

256ppp

144ppp

SIESTA Strong Scaling

102

103

104

MPI Processes

102

103

104

Tim

e fo

r firs

t S

CF

ste

p (

s)

100ppp

64ppp

SIESTA Strong Scaling

DNA-25 with PEXSI

C/BN with PEXSIC/BN with PEXSI

Diagonalization

180,000 orbs

170,000 orbs 2D, sp=0.91%

1D, sp=0.27%

PEXSI – Massive parallelism

Strong Scaling

Graphene / BN (Moire pattern) 12,770 atoms

DNA strand 17,875 atoms

materials modelling ecosystem

• Automation: run thousands of calculations daily

• Provenance: how data are produced, and what they are used for

• Reproducibility: go back to a simulation years later, and redo it with new parameters or codes

• Workflows: construct robust, complex “turnkey solutions” that calculate desired properties on demand

• Sharing: provide the distributed environment to disseminate workflows and data, and to provide services

Automation Data Environment Sharing

Automation Database Research environment

Social

Remote management Provenance Scientific workflows Sharing

High-throughput Storage Data analytics Standards

A factory A library A scholar A

community

N. Marzari’s group

http://www.aiida.net

(MIT BSD, allowing for industrial use)G. Pizzi et al., Comp. Mat. Sci. 111, 218 (2016)

N. Marzari’s group

• An evolving code, with increasing capabilities

• Widespread use in the academic community

(>16000 citations; ~1000 citations/year)

• Very efficient parallelization – towards exascale

• Ready for HPC/HTC

• Industrial use becoming wider....

Job Announcementhttps://jobs.icn2.cat

• Education

PhD in Physics, Materials Science, Chemistry, Computer Science, or related areas.

• Knowledge

DFT methods, coding in Fortran, Parallel computing (MPI, OpenMP, GPUs); python

• Professional Experience

Experience in computational science (ideally, with SIESTA), high-performance

computing, and high- throughput calculations.