Introduction to computation material science. The presentation source can be downloaded here: http://www.attaccalite.com/wp-content/uploads/2022/11/CompMatScience.odp

1. Computational Material Science
Claudio Attaccalite

2. When quantum mechanics emerged in the early 20th century,
many believed it meant that nothing more than physics was now
needed to understand chemical phenomena.
As Paul Dirac put it:
‘The underlying physical laws necessary for the
mathematical theory of … the whole of chemistry (and
condensed matter physics) are thus completely known.’
Paul Dirac
We know all the equations...

3. In principle the microscopic equations known in principle
(classical and quantum mechanics)
But the complexity comes from the number of components
(molecules, atoms, electrons) and many phenomena cannot be
explained starting from the single constituents
More is different
Philip W. Anderson

4. Solving Schrodinger
Kinetic Energy Potential
Energy
One-body problem
Electronic levels

5. Solving Schrodinger: the next level
N-body problem
Now the Hamiltonian
is the sum of many
one-body Hamiltonians
Mean value
of e-e interaction Residual interaction
Mean-field approach
e-e repulsion

6. 1023
/cm3
N-body problem (e, N)
Quasi-particle
Electrons in solids….

7. Density Functional Theory 1/2
Kohn - Hohenberg - Sham
H=T+V ion+∑i< j
e2
|ri−r j|
2 H KS=∑i
Ti
+Vion
i
+V xc
i
(ρ)
From a N-body problem to
N one-body problems
1988
Hohenberg and Kohn , Phys. Rev. 136 (3B): B864–B871R (1964)
Kohn an Sham, Phys. Rev. 140 (4A): A1133–A1138 (1965)

11. Optimization of complex
structures 1/2
Sin
clusters on n-doped
graphene

12. Optimization of complex
structures 2/2
The formation energy plot of the intermediate
products during the calciation of Sn

13. Electronic structure and
density of states

14. Vibrational properties

15. Li diffusion
in an
electrode

16. Time Density Functional Theory
Runge – Gross Theorem
i ℏ
∂ Ψi(r ,t)
∂ t
=H KS Ψi(r ,t)
From a N-body time dependent
problem to N one-body time
dependent problems
Runge – Gross, Phys. Rev. Lett. 52 997 (1984)

17. Linear and non-linear spectroscopy

18. So there was light.

19. Computational Material Science
meets
High-throughput computing

25. From materials to properties...
Novel high-conductivity 2D semiconductors
N. Mounet et al. Nature Nanotech.,13, 246 (2018)
T. Sohier et al. 2D Materials, 8, 015025 (2021)

26. Computational Material Science
meets
Evolutionary algorithms

27. An evolutionary algorithm

28. An evolutionary algorithm at work

30. Computational Material Science
meets
Machine Learning

31. Machine learning for experiment analysis
Determining the chiral indices from
high-resolution transmission
electron microscopy analysis
G.D. Forster et al. Carbon 169, 465 (2020)

32. Machine Learning forces

33. Molecular dynamics
Liquid-solid
interface
Integrate
F=ma
for classical ions
where forces are
obtained
from DFT+ML

34. Nice reference
Thank you for your
attention