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Correlated Maximum Probability Domains in Crystals

This research focuses on the use of Maximum Probability Domains (MPD) to analyze chemical questions in crystals. The study examines the correlation between localized orbitals and MPD in different types of crystals, such as covalent, ionic, semi-ionic, and metallic. Preliminary results from Quantum Monte Carlo (QMC) simulations show promising accuracy in determining core and bond probabilities in covalent and ionic crystals.

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Correlated Maximum Probability Domains in Crystals

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  1. Correlated maximum probability domains in crystals Mauro Causa’ Andreas Savin Universita’ di Napoli “Federico II” Universitè “Pierre et Marie Curie”, LCT-CNRS, Paris Vallico, july 2013

  2. In so far quantum mechanics is correct, chemical questions are problems in “applied” mathematics (Eyring, Walter, Kimball, 1944)‏ Chemical “observable” Observable ρ (r)

  3. Chemists like a local topology Typical questions: Atomic charges ? Oxidation numbers ? Bonds (order)? Is more covalent or ionic?

  4. AIM Atoms in Molecule (Bader) ELF Electron Localization Function (Becke) MPD Maximum Probability Domains (Savin)

  5. Atoms in Molecules R.Bader, 1960-> ρ(r) , number electronic density Bader, R. F. W. “Atoms in molecules: a quantum theory” Oxford University Press: Oxford,1990

  6. Analysis of the ρ(r) scalar field

  7. Electron Localization Function (ELF) 1. (Local (Ek) cost for respecting Pauli principle)normalized

  8. Elf region definition

  9. Topological analysis and bifurcation

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

  11. Probability functions p2(bond)=0.3-0.5 Pn(core)=0.7-1.0

  12. Probability and number density

  13. Maximum Probability Domains (MPD)‏ unique definition of a domain

  14. molecules

  15. MPD for solids Crystalline solids only shows extreme and peculiar chemical bonds (ionic, metallic, covalent)‏ Based ol Localized Orbitals (for insulators) For delocalized system->QMC‏

  16. Ionic crystals MC, AS JPC 115 2011 13139

  17. Anions

  18. Covalent crystals

  19. Voronoi ELF MPD ELF-MPD MC, AS ZAAC 637 2011 882

  20. Semi-ionic crystals: α-SiO2 P(cov)=0.38; p(O-)=0.37,p(O2-)=0.58

  21. MPD-QMC(CASINO) • 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 • 25 crystals in test • Covalent • Ionic • Semi-ionic • Metals • Rare gases

  22. 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

  23. 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)

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