Origin story

• Q: Can we freezing electrons off-atom?
• A: Hum.. We'll probably need:
  • Electron donating elements
  • A way to stabilize them

Molecular crystal of Cs⁺(18-crown-6)₂e⁻

Ref: James L. Dye et al., Synthesis of cesium 18-crown-6: the first single-crystal electride?, J. Am. Chem. Soc. 1982, 104, 13, 3781–3782

Crown ethers

Cs

Prof.  James L. Dye

(1927-2021)

Origin story

• But we don't like organic stuff, inorganic crystals? Pretty please? 🥺

Mayenite-Ca₁₂Al₁₄O₃₃

Ref: W. Buessem and A. Eitel,Z. Kristallogr., Kristallgeom.,Kristallphys., Kristallchem., 1936,95, 175–188.

Ref: Hideo Hosono, et al. ,High-Density Electron Anions in a Nanoporous Single Crystal: [Ca24Al28O64]4+(4e-),Science, 2003,301,626–629.

• Mayenite have a framework of pores occupied by O²⁻ ions

​

• Once we coaxed them out as oxygen, we are left with electrons @ site.

Calcium

Oxygen

Aluminum

Origin story

more?

Yttrium

• Interstitial sites lie in a 2D plane between Yttrium atoms.

Y₂C

Ref: Zhang Xiao, et.al. Chem.Mater.2014, 26, 6638−6643

Carbon___

Okay, can we have

2D electron gas like behavior

Origin story

Strontium

Bismuth

Sr₅Bi₃

• Interstitial sites lie in a 1D cavity surrounded by strontium atoms.

Ref: Lee A. Burton, et.al. Chem.Mater.2018, 30, 7521−7526

More! !

Origin story

• Interstitial sites lie in a 0D cavity surrounded by Sodium atoms.

Na-hp4

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

More! ! !

High pressure (~200Gpa)

Elemental system

Origin story

• Electron emitters: R. H. Huang and J. L. Dye,Chem. Phys. Lett., 1990,166,133–136
• ​Superconductors: Zenner S. Pereira, et al. J. Phys. Chem. C 2021, 125, 8899-8906
• ​Battery anodes: J. Hu, et al ,ACS Appl. Mater. Interfaces, 2015,7, 24016–24022
• ​Catalysts: Michikazu Hara, et al. ACS Catal. 2017, 7, 4, 2313–2324​

Applications (properties):

Ref: Xiaoha Z., Recent Advances and Applications of Inorganic Electrides, J.Phys. Chem. Lett. 2020, 11, 3841-3852

Ref: Hideo Hosono, Advances in Materials and Applications of Inorganic Electrides, Chem. Rev. 2021, 121, 3121-3185

Definition

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

• Electride materials is that they are:

Sodium - hp4

GoalS

• Based on the theory, find a descriptor to identify electrides from databases.

*no unifying theory has been proposed, to the best of our knowledge.

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): tells the degree of localization of electrons based on 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

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

sites with more than 2 atoms (of the same type) surrounding it \( \rightarrow \) potential electride site.

ELF maxima

Atoms

DESCRIPTOR-ELF

Criteria for systems to be identified as electride:

High value ELF maxima @ center of atomic cage.

High ELF Bader basin integrated charge number.

ResultS

High-throughput screening of electrides:

• 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

ResultS

Our prediction for more electride-like systems

metallic-bonding systems

ResultS

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

Our prediction for more electride-like systems

metallic-bonding systems

ResultS

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

Our prediction for more electride-like systems

metallic-bonding systems

Ref: Zhu Q., et al., Computational Discovery of Inorganic Electrides from an Automated Screening,Matter, 2019, 1293-1303, 1(5). 

ResultS

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

Our prediction for more electride-like systems

metallic-bonding systems

Ref: Zhu Q., et al., Computational Discovery of Inorganic Electrides from an Automated Screening,Matter, 2019, 1293-1303, 1(5). 

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

ResultS

ResultS

•  As an starting point, we suggest checking systems with:
  • ELF maxima value > 0.8
  • Occupation (per spin channel) > 1.0

ResultS

Ca₆Ge₂O-[mp-1019564]

Descriptors:

ELF:       0.9877

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..

S-orbitals

Ref: Zhu Q., et al., Computational Discovery of Inorganic Electrides from an Automated Screening,Matter, 2019, 1293-1303, 1(5). 

S-orbitals

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

Na

K

• How come we don't see many group I and II elemental systems being identified as electrides?

S-orbitals

• Q: How come we don't see any group I and II elemental systems being identified as electrides?

• A: Most elemental group I and II systems don't meet the distance criteria and the multicentere bonds are "weak".

edge cases

• But in some edge cases, we do have electride-like elemental metal systems!

Should they be identified as electrides?

ELF max:0.7

Occ.: 1.51

ELF max: 0.7

Occ.:       1.92

Intermetallics

• The question ‘‘Are Intermetallic Phases Electrides?’’ wasalready posed decades ago*.

* R. Nesper,Angew. Chem., Int. Ed. Engl., 1991,30, 789–817

Intermetallics

• The question ‘‘Are Intermetallic Phases Electrides?’’ wasalready posed decades ago*.

* R. Nesper,Angew. Chem., Int. Ed. Engl., 1991,30, 789–817

Intermetallics

• Intermetallic systems can have way more atomic arrangements comparing to elemental systems.

• At the same time, because metallic-like bonding is not easy to differentiate from electride-like bonding.

• The question ‘‘Are Intermetallic Phases Electrides?’’ wasalready posed decades ago*.

* R. Nesper,Angew. Chem., Int. Ed. Engl., 1991,30, 789–817

Our answer:

d-orbitals?

• d-orbital electrides do exist!
• They exist in smaller cages than s-orbital electrides
• They are less likely to have high polarizability but other features.

2D-LaBr

⭐️Unifying theory

• Inorganic electrides (atomic orbital)
• High pressured electrides (atomic orbitals)
• Organic electrides

⭐️Unifying theory

• Inorganic electrides (atomic orbital)
• High pressured electrides (atomic orbitals)
• Organic electrides

HOMO

LUMO-1

LUMO-2

LUMO-3

• The HOMO and LUMOs act like atomic orbitals.
• HOMO is s-shaped.

More stories can be found on the origin of these orbitals. In our view they should be categorized as SAMOs (Super Atomic Molecular Orbitals). But other argue they are metal atoms' extended s-orbitals.

Na-Tripip222

Organic ones

Point Defects

Bounce round: F-center defects (atomic orbtial)

Ref: Ferenc Karsai, et al.,F-center in lithium fluoride revisited: Comparison of solid-state physicsand quantum-chemistry approaches, Phys. Rev. B, 2019, 89(12).

Ref: Janotti, Anderson, Hydrogen multicentre bonds, science, Nature Materials, (2007), 44-47, 6(1)

• Li:[He] 2s1
• F:[He] 2s2 2p5

• Li \(^{+} \): [He]
• F\(^{-} \):[He] 2s2 2p6

1 electron @ defect site

Electride: periodic arrangement of point defects?

Point Defects

Previously, hydrogen multicentered bonding was preposed.

Ref: Janotti, Anderson, Hydrogen multicentre bonds, science, Nature Materials, (2007), 44-47, 6(1)

Future plan

• Detailed analysis of specific cases using more sophisticated methods like Natural Bond Orbitals (NBO), Solid State Adaptive Natural Density Partitioning (SSAdNDP) and Crystal Orbital Bond Index (COBI). Detailed blog posts of these method, coming soon!

• Focus on three cases:
  1.  A system that is most electride-like.
  2.  A  prototypically  metallic system (for comparison)
  3.  A system that is previously identified  electride but not with our method.

Future plan

• Finish several old projects
  • LaBr flat band, alpha T3 model
  • Multiferroicity of LaBr hydride (La2HBr2)

• Analysis of (inter)metallic systems that behave "almost" like electride and bond analysis of Mg for Binxing

ResultS

• Experimentally, charge maxima are more easily measured.

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

Interstitial charge maxima

ResultS

Ref:  Zhu et al., Computational Discovery of InorganicElectrides from an Automated Screening Matter, (2019) 1, 1293–1303

Our prediction for more electride-like systems

Our prediction for more electride-like systems

metallic-bonding systems

MAKING ELECTRIDES

We need two criterias to be satisfied:

• Occupation criteria

• Distance criteria

Doping!

Strain!

MAKING ELECTRIDES

BCC-Sodium

We can force a system with metallic bonding into an electide by tensile strain.

ELF max: 0.5505

Occ.:        0.1604

MAKING ELECTRIDES

Tetragonal-Sodium

We can force a system with metallic bonding into an electide by tensile strain.

ELF max: 0.7266

Occ.:        0.7470

Making electrides

This time, we use doping to bring out electride nature inside an typical ionic material

NaCl-Doped [4e]

ELF max:   0.7525

Occ.:          0.4094

Results

COBI [Ca₆Ge₂O]

COBI [Ca₆Ge₂O]