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

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

Sep 07, 2023 130 likes •721 views

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

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

Atoms and computers

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  • P. A. M. Dirac
  • Proc. Roy. Soc.
  • Ser. A,123, 714 (1929)

The fundamental laws necessary 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 equations that are too complex to be solved. A grim outlook

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Moore’s law

CC BY-SA 4.0, h-ps://en.wikipedia.org/w/index.php?curid=56315709

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Computer evolution during my career

CDC CYBER 170 Trieste 1984/85 Nokia N900 2010 Prof. N. Marzari, EPFL

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The genius of Fermi

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The triangle of science

Experiment Theory Simulation

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Galileo Galilei and Computational Physics

A hand wri-en slide from Ken Wilson Physics Nobel Prize, 1982

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Becoming respectable

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

  • f the experimental structure.
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What is molecular dynamics?

Molecular dynamics is a set of numerical techniques that allows the behaviour of complex assemblies

  • f 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.
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The fundamental equation

Mass time Acceleration= Force

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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. 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
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Sound track G. Piccini

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Drug design

Courtesy F. Gervasio

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Carbon capture

From our recent paper Glezakou et al. in Green Chemistry 2016, 18, 6004

Courtesy V. Glezakou and R. Rousseau

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New, cheaper photovoltaic cells

Silicon Perovskite Crystals Controlling the quality

  • f the perovskite crystals

is essential for efficiency and durability.

Collaboration with Paramvir Ahlawat, Pablo Piaggi, and Ursula Röthlisberger

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The challenges

Complexity A c c u r a c y Time Understanding

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The challenges

Complexity Time Understanding A c c u r a c y

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How do the forces look like

angle bending torsions bond stretching VdW + Electrostatic interactions

E = Kr

bonds

∑

r − req

( )

2

+ Kθ

angles

∑

θ −θeq

( )

2

+ Et

dihedrals

∑

+ Aij Rij

12 −

Bij Rij

6 +

qiq j εRij % & ' ' ( ) * *

i< j

∑

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The dance of the atoms

Making benzene molecules dance

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Chemical bonds

H H H H

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Quantum equations

Schöredinger equation Density functional theory

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The marriage of two worlds

Electronic structure theory provides the ability to describe the formation and breaking of chemical bonds.

Molecular dynamics can describe the complex and dynamic environment of real life chemistry.

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Silicon crystallisation

Non local chemistry

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Proton diffusion

Non local chemistry Courtesy Ali Hassanali

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The challenges

Complexity A c c u r a c y Time Understanding

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A complex system

hν 2H2O → 2H2 +O2

Absorb light Transport electrons and holes from the solid absorber to the liquid Harvest charges for chemical reaction Courtesy G. Galli

Photo-cataly\c water spli]ng

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The time challenge

seconds 10-5 − 10-15 − 10-10 − 1 − 105 − ms Nuclea'on, diffusion Drug unbinding, annealing
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Energy Barriers and Rare Events

KBT

  • Large barriers imply long time scales
  • Thermal excitation not sufficient in MD

Example: △G = 150 kJ/mol T = 300 K k = 4.78 10-14 s-1 t1/2 = 459824 s = 5.3 days The Higher the barrier the less frequent the transition

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A complex problem

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Back to the classics for inspiration

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.

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The research program

Switzerland Tuscany

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Learning from crystallisation

Free energy cost Fluctuations form clusters of the new phase. Use the cluster size n as

  • rder parameter
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Describe the system in a low dimensional space

The collective variables The free energy surface The probability distribution

s(R) = (s1(R), . . . , sM(R)) P(s) = ∫ dRδ(s − s(R))P(R) F(s) = − 1 βlogP(s)

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A dimensional reduction

From a high dimensional and rugged Potential Energy Surface To a low dimensional and smooth Free Energy Surface

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A dimensional reduction

local density local order

+

Collective Variables Fully atomistic description CV description

CV

Crystal-like Liquid-like

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Sampling methods

We have developed two collective-coordinates-based enhanced sampling methods

  • Metadynamics
  • Variationally enhanced sampling
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Barducci, Bussi and Parrinello PRL (2008) The bias potential is built iteratively by adding a local repulsive potential that discourages revisiting regions already explored. Laio and Parrinello PNAS (2002)

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Metadynamics

Standard dynamics Metadynamics

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Can’t help showing this too

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A rigorous result

The procedure amounts at solving the ordinary differential equation

* Dama, Parrinello and Voth PRL 2014

dV(s, t) dt = ∫ ds′G(s − s′)e− V(s′, t)

γ − 1 PV(s′,t)

and at enhancing the fluctuations in a controlled way using the parameter 𝛿. P(s) → P(s)

1 γ

PV(s, t) F(s) + V(s, t)

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Simple collective coordinates for chemistry

Let us start from the simple SN2 reaction

CH3F + Cl− → CH3Cl + F −

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The free energy surface

1 2 3 4 5 6 1 2 3 4 5 6 d2 d1

The standard approach one looks for the minimum free energy path and/or the transition state.

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A heuristic CV

40 80 120 160

  • 3
  • 2
  • 1

1 2 3 5 10 15 Energy (kJ mol−1) Energy/RT d1 − d2 (Å) F(s) CH3F + Cl− CH3Cl + F −

s = d1 − d2

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Surfaces of constant collective variable value

1 2 3 4 5 6 1 2 3 4 5 6 d2 d1

s = d1 − d2

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Consider a two state system µA µB ΣB ΣA

The two states are identified with a set of descriptors Each metastable states has its own expectation value and covariance matrix. Can we get a good one dimensional collective variable from this information alone? d(R) d1(R) → d2(R) →

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d1 d2

Linear discriminant analysis

Search for the one dimensional projection that best separates the two different set of data.

z = wd

The number of descriptors can be very large!

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Harmonic Linear Discriminant Analysis

For the purpose of studying chemical reactions we introduce a variant that we call Harmonic Linear Discriminant Analisis that leads to:

s(R) = (µA − µB)T ✓ 1 ΣA + 1 ΣB ◆ d(R).

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No information on the transition state or reaction path is needed! It is all encrypted in the fluctuations!

d1 d2

ΣA μB ΣB μA

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Ideal for chemistry!

Lets study the classical Diels Alder reaction

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A multistep process

We want to simulate the reaction: We run two independent simulations in the initial and final state and compute the fluctuation of 14 permutation invariant descriptors, to find the HLDA reaction coordinate. 2H2 + 2(NO) → N2 + 2(H2O)

In collabora\on with Emilia Sicilia

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The main hurdle

2NO +2H2 TS2 N2O+H2O +H2 TS1 ONNO +2H2 400 200 TS3 N2+2H2O 100.7
  • 538.2
HONNHO +H2
  • 200
  • 400
  • 600
  • 1.7
280.1 137.3
  • 240.9
6.3
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First intermediate

2NO +2H2 TS2 N2O+H2O +H2 TS1 ONNO +2H2 400 200 TS3 N2+2H2O 100.7
  • 538.2
HONNHO +H2
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  • 400
  • 600
  • 1.7
280.1 137.3
  • 240.9
6.3
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Second intermediate

2NO +2H2 TS2 N2O+H2O +H2 TS1 ONNO +2H2 400 200 TS3 N2+2H2O 100.7
  • 538.2
HONNHO +H2
  • 200
  • 400
  • 600
  • 1.7
280.1 137.3
  • 240.9
6.3
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The final product

2NO +2H2 TS2 N2O+H2O +H2 TS1 ONNO +2H2 400 200 TS3 N2+2H2O 100.7
  • 538.2
HONNHO +H2
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  • 400
  • 600
  • 1.7
280.1 137.3
  • 240.9
6.3
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A variational alternative

The bias is constructed by minimising the convex functional Valsson and Parrinello, PRL (2014) Valsson and Parrinello, PRL (2014) At the minimum:

V(s) = − F(s) − 1 βlogp(s)

PV(s) = p(s)

i.e.

Ω(V(s)) = 1 β log ∫ dse−β(F(s)+V(s)) ∫ dse−βF(s) + ∫ dsp(s)V(s)

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In the practice

Valsson and Parrinello, PRL (2014) Valsson and Parrinello, PRL (2014)

Ω(α) rΩ(α)

V(s; α) = ∑

i

αi fi(s) Ω(V) → Ω(α)

The convex function

Ω(α)

is minimised using a stochastic steepest descent

  • algorithm. (Bach and Moulines)
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A deep bias

Valsson and Parrinello, PRL (2014) Represent the bias V(s) as a neural network.

Input= collective variables Output= bias potential

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The structure of a node

Valsson and Parrinello, PRL (2014)

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It does work

Valsson and Parrinello, PRL (2014)

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The group

Movies by Jean Favre and Valerio Rizzi

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Fine