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.