Vallico, july 2013

Correlated maximum probability domains in crystalsMauro Causa’ Andreas SavinUniversita’ di Napoli “Federico II”Universitè “Pierre et Marie Curie”, LCT-CNRS, Paris

C

O

Chemical “observable” Observable ρ (r)

In so far quantum mechanics is correct, chemical questions are

problems in “applied” mathematics (Eyring, Walter, Kimball, 1944)

Chemists like a local topology

Typical questions:

Atomic charges ?

Oxidation numbers ?

Bonds (order)?

Is more covalent or ionic?

ELF

Electron

Localization

Function

(Becke)

AIM

Atoms in

Molecule

(Bader)

MPD

Maximum

Probability

Domains

(Savin)

Atoms in Molecules R.Bader, 1960->

ρ(r) , number electronic density

Ω

Ω

N=drrρ

Bader, R. F. W. “Atoms in molecules: a quantum theory” Oxford

University Press: Oxford,1990

Analysis of the ρ(r) scalar field

Electron Localization Function (ELF)

1. (Local (Ek) cost for respecting Pauli principle)normalized

Elf region definition

Topological analysis and bifurcation

TiO2: ionic(0.6) and covalent(0.3) elf

Probability functions

p2(bond)=0.3-0.5

Pn(core)=0.7-1.0

Probability and number density

Ω

Ω

N=drrρ

Maximum Probability Domains (MPD)unique definition of a domain

molecules

MPD for solidsCrystalline solids only shows extreme and

peculiar chemical bonds

(ionic, metallic, covalent)

Based ol Localized Orbitals (for insulators)

For delocalized system->QMC

Ionic crystals

MC, AS JPC 115 2011 13139

Anions

Covalent crystals

Voronoi ELF MPD ELF-MPD

MC, AS ZAAC 637 2011 882

Semi-ionic crystals: α-SiO2

P(cov)=0.38;

p(O-)=0.37,p(O2-)=0.58

MPD-QMC(CASINO)

25 crystals in test

•Covalent

•Ionic

•Semi-ionic

•Metals

•Rare gases

•Easy work on configuration file for

VMC and DMC

•Configurations are distributed like

•|Ψvmc|2 |Ψdmc Ψvmc |

•Try to reducing numerical noise of

Shape Derivative

MPD-QMC preliminary results (VMC)

•For covalent and ionic crystal the shape of the domain

• doesn’t change (accuracy 0.1%)

•In covalent systems the core and bond probability increases:

•P2(bond,Si): 0.42 ---> 0.44

•P10(core,Si): 0.69 ---> 0.73

•In ionic crystals the Ionic probability seems unaffected by

electronic correlation

Next steps

Complete the data collection on all the 25 test

systems

Metals !!!!!! (QMC only)

DMC

Better accuracy (number of configurations)

Multiple domain probabilities (QMC only)