The limits of reductionism

@nicgaston 1 April 2016 Nicola Gaston The MacDiarmid Institute for
Advanced Materials and Nanotechnology The University of Auckland The limits of reductionism (and why we should think about this in the computational sciences) OK http://xkcd.com/

@nicgaston My research: From clusters to materials… K.G. Steenbergen, NG,
PCCP 15, 15325 (2013) K.G. Steenbergen, NG, JCP, 140, 064102 (2014) K. G. Steenbergen, NG Chem – A Eur. J. 21, 2862–2869, (2015) R. Tonner,NG, PCCP (2014) K. G. Steenbergen, NG Nano Letters, (2016)

@nicgaston The computer – your Virgil in the world of
atoms “Chemists used to create models of molecules using plastic balls and sticks. Today, the modelling is carried out in computers. In the 1970s, Martin Karplus, Michael Levitt and Arieh Warshel laid the foundation for the powerful programs that are used to understand and predict chemical processes. Computer models mirroring real life have become crucial for Nobel Prize in Chemistry, 2013

@nicgaston Source: Nobelprize.org Divide and Conquer: Classical and Quantum

@nicgaston Divide and Conquer A natural strategy for highly parallel
processing Size (# atoms) Time (temperature) Physics (Quantum vs Classical)

@nicgaston A little history... 1600s 1700s Schrödinger 1926 1928 Lavoisier
Newton “approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation." now -P. A. M. Dirac

@nicgaston Explaining anomalous melting temperatures of nanoparticles Tm = 212
10 K for bulk gallium DFT-PAW-PW91 (90 K lower than expt) K. G. Steenbergen, NG Nano Letters, 16, 21-26, (2016)

@nicgaston How do nanoscale materials melt? Nuclei: relatively heavy compared
to electrons: we treat them classically Electronic interactions must be treated quantum mechanically

@nicgaston Born-Oppenheimer approximation: nuclear and electronic motion separated in time
(step by step)

@nicgaston “Multiscale methods” = QM/MM The quantum and classical regimes
are spatially separated Multi-copper-oxidase embedded in water e.g. bond formation and breaking No bond breaking – rotational and vibrational motion etc.

@nicgaston The limits of nanoscale simulation H ψ ∧ complexity:
size solution substrate relativity environment ... so what is “too much computation”? bigger systems: lower quality approximations Hψ= Eψ

@nicgaston Divide and conquer H(amiltonian): Coulomb interactions (charged particles) Kinetic
energy (masses) Hψ= Eψ Quantum vs Classical: Spatial separation Separation in time 3N-dimensional many-body problem

@nicgaston Divide and conquer Hψ= Eψ Size: Hi ψi =
Ei ψi H(amiltonian): now need to include Coulomb interactions (!! with averaging over other positions as their wavefunctions change) Kinetic energy (masses)

@nicgaston

@nicgaston “High energy configurations”

@nicgaston The problem of scale melting catalysis We are often
interested in what happens in the regime of 100s to 1000s of atoms: the potential of the nanoscale This makes it hard to use a full quantum mechanical treatment of the system metallicity

@nicgaston Calculations that do more than reproduce - they predict
and explain

@nicgaston A 2D liquid? 6 8 10 Average Axis Lengths
6 8 10 6 8 10 Axis Length (Å) 6 8 10 200 400 600 800 1000 Temperature (K) 6 8 10 Ga 32 + Ga 33 + Ga 34 + Ga 35 + Ga 36 + Distortion into flattened (2D) structures lowers the kinetic and configurational densities of states Ga36 + at 960K Reduced entropy of the liquid state

@nicgaston The many-body problem Pressure Temperature gas liquid solid How
do we get from individual characteristics to collective properties?

@nicgaston H He Li Be B C N O F
Ne Na Mg Al Si P S Cl Ar K Ca Sc Ti V Cr Mn Cu Fe Co Ni Zn Ga Ge As Se Br Kr In Sn Sb Te I Xe Tl Pb Bi Po At Rn Uut Fl Uup Lv Uus Uuo Y Zr Nb Mo Tc Ag Ru Rh Pd Cd La Hf Ta W Re Au Os Ir Pt Hg Ac Rf Db Sg Bh Rg Hs Mt Ds Cn Rb Sr Cs Ba Fr Ra Yb Lu Nd Pm Sm Eu Gd Er Tb Dy Ho Tm Ce Pr No Lr U Np Pu Am Cm Fm Bk Cf Es Md Th Pa Before 18th c 18th c 19th c 20th c 21st c By date of discovery

@nicgaston The end of the periodic table

@nicgaston Shell models Both potentials are centrosymmetric, but attraction vs
confinement leads to some differences (ordering of energy levels) Atoms Nuclei

@nicgaston Superatoms

@nicgaston Replace one GaR unit by 2 electrons Gallium superatoms!
D. Schebarchov and NG , PCCP 14, 9912-9922 (2012)

@nicgaston From clusters to materials, with ‘superatoms’? Greater dispersion of
the states near the Fermi energy – indication of the effect of crystal environment on electronic properties

@nicgaston Superatoms: collections of atoms (100-1000) that share electrons, to
mimic the behaviour of a single (nanosized) atom

@nicgaston From clusters to materials, with ‘superatoms’ New materials, new
properties: designed based on the ‘superatomic’ electronic states multiscale methods for prediction of properties An anti-reductionist view: reducing these nanoatoms to collections of ‘real’ atoms weakens our understanding rather than improving it

@nicgaston Emergence “More is Different” -Philip Anderson

@nicgaston Emergence

@nicgaston

@nicgaston A 2D liquid? Ga36 + at 150-260K

@nicgaston Emergence “More is Different” -Philip Anderson

@nicgaston Reductionism Do we learn more by being willing to
look at the world in a variety of ways?

@nicgaston Casablanca

@nicgaston Claude Rains

@nicgaston “Science is People.” - Alan MacDiarmid

@nicgaston Science is People Problems that are infrastructural, or that
deal with collective action …are problems of culture change. Sir Paul Callaghan, Wool to Weta

@nicgaston “In this world, the optimists have it, not because
they are always right, but because they are positive. Even when wrong, they are positive, and that is the way of achievement, correction, improvement, success. Educated, eyes-open optimism pays; pessimism can only after the consolation of being right. The one lesson that emerges is the need to keep trying. No miracles, no perfection, no millennium, no apocalypse. We must cultivate a sceptical faith, avoid dogma, listen and watch well, try to clarify and define ends, the better to choose means” - David Landes, The Wealth and Poverty of Nations

@nicgaston Code is language

@nicgaston “The limits of my language means the limits of
my world.” ― Ludwig Wittgenstein

@nicgaston Reductionism vs Emergence Skepticism Rationalism Objectivity Optimism Unpredictability Choice
of lens

@nicgaston Culture change is hard: optimism is necessary Can we
change the way we think, and talk, about science?

@nicgaston Current group members § Julia Schacht (PhD student) §
Dani Metin (PhD student) § James Gilmour (PhD student) § Adam Thickett (MSc student) § Dr Lukas Hammerschmidt (Postdoctoral Fellow) § Dr Tamsyn Hilder (Visiting Research Fellow) Previous group members § Dr Krista G. Steenbergen § Dr Dmitri Schebarchov § Dr Doreen Mollenhauer § Dr Udbhav Ojha § Amanda J. Parker Thanks

The limits of reductionism

The limits of reductionism

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