What is it?

Ref: Mikhail Y. Redko, et al., Design and Synthesis of a Thermally Stable Organic Electride, J. Am. Chem. Soc. 2005, 127, 35, 12416–12422.

"Ionic" compounds in which electrons are localized at interstitial sites and act as anions.

       Sodium-hP4 [high pressure]

       Na-TriPip222 [organic]

       Y₂C [inorganic]

• Electride materials are:

Sodium - hp4

Ref:Yanming Ma, et.al. Nature, (2009), 182-185, 458(7235)

• Some confirmed electrides:

Ref: Xiao Zhang, et al., Two-Dimensional Transition-Metal Electride Y2C, Chem. Mater. 2014, 26, 22, 6638–6643

GoalS

• We want a descriptor to identify electrides from database.

Electrides are materials with (electron-deficient, distance-optimized) multicentered bonding formed by orbitals of surrounding atoms*.

*Simlar idea were also proposed by Xiao Dong and Artem R. Oganov, (2017), Electrides and Their High-Pressure Chemistry, In G. G. N. Angilella, Antonino La Magna (editors) Correlations in Condensed Matter under Extreme Conditions, Springer Press, and by M. Hanfland et al. ,New high-pressure phases of lithium, Nature, (2000), 174-178, 408.

Theory

Descriptor-ELF

• Electron-localization function (ELF): Probe the localization information of a quantum state at a point in space using Pauli exclusion principle. 
  • ELF is a scalar field just like charge density
  • ELF = 0 \(\rightarrow\) delocalized;           ELF = 1 \(\rightarrow\) localized

Ref: Andreas Savin, et al., ELF: The Electron Localization Function, Angew. Chem. Int. Ed. Engl., 1997,36,1808-1832

Ref: A. D. Becke and K.E. Edgecombe, A simple measure of electron localization in atomic and molecular systems, J. Chem. Phys., 1990, 92, 5397.

To identify the multicentered bonding:

Charge density maxima @ interstitial site

ELF maxima @ interstitial site

ELF-isosurface

Known 2D electride: Y₂C

• ELF gives the location of the multicentered orbital.

• But how do translate this interpertation into an automated process?

Ref: Huaqing Huang, et al., Topological Electride Y2C, Nano Lett., 2018, 18(3), 1972-1977

DESCRIPTOR-ELF

High value ELF maxima @ center of atomic cage.

Small \( \nabla^2 \) ELF @ interstitial site.

High ELF Bader basin integrated charge number.

Topological analysis: Bader partition the space based on ELF zero-flux planes.

ResultS

First, some numbers:

• A total of ~55000 entries on the Materials Project data base is sampled.

• Around 10000 entries were found to possess interstitial ELF maxima (regardless of value). 

ResultS

Ref: Liu C. et al., Electrides: a review, J. Mater. Chem. C, 2020,  8, 10551.

Elemental Metals

Electrides

Metallic bonding also have this feature and the transition to electride bonding is smooth!

ResultS

More "electride-like":

high ELF value + lower \(\nabla^2\) ELF + high occupation

ResultS

• Cutting the graph at (arbitaraily):
  • ELF maxima value > 0.75
  • \( \nabla^2 \) ELF @ site > -0.5
  • Occupation per spin channel > 1.6

• We get: 300 electrides (mostly new)
  • 213 non-magnetic materials
  • 87 magnetic materials

http://chengcheng-xiao.github.io/electride-db/

ResultS

ResultS

Ca₆Ge₂O-[mp-1019564]

Descriptors:

ELF:       0.9877

\(\nabla^2 \)ELF: -0.0655

Occ.:      1.7344

Properties:

Insulator;

Has charge maxima @ interstitial site;

Ref: Jiacheng Gao, et al., Unconventional materials: the mismatch between electronic charge centers and atomic positions, Sci. Bull., In press..

ResultS

• Experiementally, charge maxims are more easily measured.

• Systems with charge maxima are also located at the upper right.

Interstitial charge maxima

Results

RESULTS

*Ref:Zhu et al., Matter, (2019) 1, 1293–1303 

S-orbtials

The s-orbitals of alkaline and alkaline earth metals are very dispersive + have no direction dependency.

That's why most discovered electrides are composed by them.

Na

K

COBI [Ca₆Ge₂O]

COBI [Ca₆Ge₂O]

ResultS

Ref: Liu C. et al., Electrides: a review, J. Mater. Chem. C, 2020,  8, 10551.

Elemental Metals

Electrides

Metallic bonding also have this feature and the transition to electride bonding is smooth!