Atoms and computers MICHELE PARRINELLO USI, Faculty of - PowerPoint PPT Presentation

Atoms and computers MICHELE PARRINELLO USI, Faculty of Informatics, Institute of Computational Sciences, Lugano ETH, Department of Chemistry and Biotechnologies, Zurich � 1

A grim outlook The fundamental laws necessary Testo for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to P. A. M. Dirac equations that are too complex to Proc. Roy. Soc. Ser. A,123, 714 (1929) be solved.

Moore’s law Testo CC BY-SA 4.0, h-ps://en.wikipedia.org/w/index.php?curid=56315709 � 3

Computer evolution during my career Testo Nokia N900 CDC CYBER 170 2010 Prof. N. Marzari, EPFL Trieste 1984/85 � 4

The genius of Fermi Testo � 5

The triangle of science Theory Experiment Testo Simulation

Galileo Galilei and Computational Physics Testo A hand wri-en slide from Ken Wilson Physics Nobel Prize, 1982

Becoming respectable Testo Acquaporine is a protein that regulates the flux of water across the cell membrane. For resolving this structure Peter Agre got the 2003 Nobel prize. The movie is downloaded from the Nobel Prize site.The simulation is by K. Shulten, and is presented as a supporting evidence of the correctness of the experimental structure.

What is molecular dynamics? Molecular dynamics is a set of numerical techniques that allows the behaviour of complex assemblies Testo of molecules such as liquids, solids, surfaces and so on to be simulated. These simulations: • Help explain experiments, • Replace experiments, • Predict new phenomena, • Provide invaluable insight, • Are a kind of virtual microscopy. � 9

The fundamental equation Testo Mass time Acceleration= Force � 10

Is molecular dynamics of any practical use? The world about us, and biology itself, can be described as resulting from a set of complex physico-chemical reactions. Testo Together with experiments, simulations are an indispensable tool to understand these phenomena. This understanding can be used to solve many of mankind’s problems. We shall present three representative examples that address, with the help of molecular dynamics, three areas contemporary societal concern. • Health • Energy • Environment � 11

Drug design Testo Courtesy F. Gervasio Sound track G. Piccini � 12

Carbon capture Testo Courtesy V. Glezakou and R. Rousseau From our recent paper Glezakou et al. in Green Chemistry 2016, 18, 6004 � 13

New, cheaper photovoltaic cells Testo Crystals Perovskite Silicon Controlling the quality of the perovskite crystals is essential for efficiency and durability. Collaboration with Paramvir Ahlawat, Pablo Piaggi, and Ursula Röthlisberger � 14

The challenges Testo y Understanding c a Time r u c c A Complexity � 15

The challenges Testo y Understanding c a Time r u c c A Complexity � 16

How do the forces look like A ij B ij q i q j % ( 2 2 ( ) ( ) E = K r r − r eq K θ E t ∑ ∑ ∑ ∑ ' * + θ − θ eq + + 12 − 6 + Testo ε R ij R ij R ij ' * bonds angles dihedrals i < j & ) bond stretching angle bending torsions VdW + Electrostatic interactions � 17

The dance of the atoms Making benzene molecules dance Testo � 18

Chemical bonds Testo H H H H � 19

Quantum equations Testo Schöredinger equation Density functional theory � 20

The marriage of two worlds Testo Molecular dynamics can describe the complex and dynamic environment of real life chemistry. Electronic structure theory provides the ability to describe the formation and breaking of chemical bonds. � 21

Silicon crystallisation Testo Non local chemistry � 22

Proton diffusion Testo Courtesy Ali Hassanali � 23 Non local chemistry

The challenges Testo y Understanding c a Time r u c c A Complexity � 24

A complex system Photo-cataly\c water spli]ng Testo h ν 2H 2 O → 2H 2 +O 2 Absorb light Transport electrons and holes from the solid absorber to the liquid Harvest charges for chemical reaction Courtesy G. Galli � 25

The time challenge Testo Drug unbinding, annealing 10 5 − Nuclea'on, diffusion 1 − ms 10 -5 − 10 -10 − 10 -15 − seconds � 26

Energy Barriers and Rare Events • Large barriers imply long time scales • Thermal excitation not su ffi cient in MD Example: △ G = 150 kJ/mol T = 300 K k = 4.78 10 -14 s -1 t 1/2 = 459824 s = 5.3 days The Higher the barrier the less frequent the transition K B T

A complex problem Testo � 28

Back to the classics for inspiration Testo Isaiah 40:4 Every valley shall be raised up, every mountain and hill made low; the rough ground shall become level, the rugged places a plain. � 29

The research program Testo Switzerland Tuscany � 30

Learning from crystallisation Testo Fluctuations form clusters of the new phase. Use the cluster size n as order parameter Free energy cost � 31

Describe the system in a low dimensional space Testo s ( R ) = ( s 1 ( R ), . . . , s M ( R ) ) The collective variables P ( s ) = ∫ d R δ ( s − s ( R ) ) P ( R ) The probability distribution F ( s ) = − 1 The free energy surface β logP ( s ) � 32

A dimensional reduction Testo From a high dimensional and rugged Potential Energy Surface To a low dimensional and smooth Free Energy Surface � 33

A dimensional reduction local density local order Testo + CV description CV Collective Crystal-like Variables Liquid-like Fully atomistic description � 34

Sampling methods Testo We have developed two collective-coordinates-based enhanced sampling methods • Metadynamics • Variationally enhanced sampling

Metadynamics The bias potential is built Testo Standard dynamics Metadynamics iteratively by adding a local repulsive potential that discourages revisiting regions already explored. Laio and Parrinello PNAS (2002) Barducci, Bussi and Parrinello PRL (2008) � 36

Can’t help showing this too Testo � 37

A rigorous result The procedure amounts at solving the ordinary differential equation Testo = ∫ ds ′ � G ( s − s ′ � ) e − V ( s ′ � , t ) dV ( s , t ) γ − 1 P V ( s ′ � , t ) dt and at enhancing the fluctuations in a controlled way using the parameter 𝛿 . P V ( s , t ) F ( s ) + V ( s , t ) 1 P ( s ) → P ( s ) γ � 38 * Dama, Parrinello and Voth PRL 2014

Simple collective coordinates for chemistry Let us start from the simple S N 2 reaction Testo CH 3 F + Cl − → CH 3 Cl + F − � 39

The free energy surface Testo 6 5 4 d 2 3 The standard approach one looks for the 2 minimum free energy path and/or the transition state. 1 1 2 3 4 5 6 d 1 � 40

A heuristic CV Testo CH 3 F + Cl − CH 3 Cl + F − 160 15 Energy (kJ mol − 1 ) 120 Energy/RT 10 80 s = d 1 − d 2 5 40 0 0 F ( s ) -3 -2 -1 0 1 2 3 � 41 d 1 − d 2 (Å)

Surfaces of constant collective variable value Testo 6 5 4 d 2 s = d 1 − d 2 3 2 1 1 2 3 4 5 6 d 1 � 42

Consider a two state system Testo The two states are identified with Σ A a set of descriptors d ( R ) Each metastable states has its own expectation value µ A and covariance matrix. d 2 ( R ) → Can we get a good one dimensional Σ B collective variable from this information alone? µ B d 1 ( R ) → � 43

Linear discriminant analysis Testo Search for the one dimensional projection that best separates the two different set of data. z = wd d 1 The number of descriptors can be very large! d 2 � 44