Definition

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

Electrides are:

Sodium - hp4

Application

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

Classification

Electride-like behavior has been identified in different types materials/systems with drastically different structural types and chemical compositions:

Organometallic crystals
High pressured elemental systems
Inorganic systems
Defected systems
Solvated electrons
Amorphous materials

Classification

For example, Cs-Crown ethers organic crystal is a prototypical organic electride material with an interstitial region of ~270Å³.

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

Classification

2D electride Y₂C, on the other hand only have a cage of around 11Å³.

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

Yttrium

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

Carbon___

GoalS

Understand the underlying mechanism that links all types of electrides together.

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

Electrides are materials with occupied interstitial localized multicentered bonds formed by orbitals of surrounding atoms*.

Theory

Atomic

Delocalized

\sigma_\mathrm{g}

\sigma_\mathrm{g}^*

\sigma_\mathrm{u}^*

s

Within the non-interacting LCAO approximation, the topology of the lowest energy bonding orbital is determined by the ratio of the cage size and orbital size.

Theory-model

Assuming regular cages composed by group-I and II elements, the existence of the interstitial maxima is determined by the gradient and Hessian eigenvalues at the cage center.

\begin{aligned} \nabla \psi(\vec r) |_{\vec r \to \vec r_c} &= 0 \\ \mathrm{Eig}[\mathbf{H_\psi}(\vec r)|_{\vec r \to \vec r_c}] &< 0. \end{aligned}

Analytically solving this gives us a set of critical cage size \(b_\mathrm{c}\) that can be used to predict the potential existance of interstitial localized multicentered bond in materials.

Theory-verify

For example, in hP4-Na, the cage size of Na is 1.9 Å, much larger than the calculated \(b_\mathrm{c}=2.8\) Å.

Descriptor-ELF

Electron localization function (ELF): tells the degree of localization of electrons, derived from DFT results.
- 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

Bug fix for VASP: https://github.com/Chengcheng-Xiao/VASP_LOL

The main drawbacks of our critical values are:

They only works with regular cages and s-orbitals
They cannot predict the occupation of the relevant state.

Thus, we proceed to build our electride descriptor using ELF as a surrogate.

ELF-isosurface

Known 2D electride: Y₂C

ELF gives the location of the multicentered orbital.

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

Workflow

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

WORKFLOW

ResultS

High-throughput screening of electrides:

A total of ~52,000 entries on the Materials Project data base is sampled.

Around 10,000 entries were found to possess interstitial ELF maxima that are surrounded by multiple atoms of the same type.

ResultS

Our prediction for more electride-like systems

Non-electrides

ResultS

There's no clear demarcation between non-electrides and electrides.

Our prediction for more electride-like systems

metallic-bonding systems

ResultS

There's no clear demarcation between non-electrides and electrides.

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

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

That leads to 629 (mostly new) electrides:
- 428 non-magnetic materials
- 201 magnetic materials

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..

⭐️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 ELECTRIDES

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.

ORGANIC ELECTRIDES

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

\Downarrow

1 electron @ defect site

Electride: periodic arrangement of point defects?

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)