What is it?

Electride materials are:

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

Electron (density) in an octahedral interstitial site

Some confirmed electrides:

        Sodium-hP4 [high pressure]

       Na-TriPip222 [organic]

       Y₂C [inorganic]

       

Applications:

​        Electron emitters

​       Superconductors

​       Battery anodes

​       Catalysts

​

Ref: Liu C, Electride: a review, J. Matter. Chem. C, 2020, 8, 10551.

CLASSIFICATION

• Organic electride
• Inorganic electride
  • Elemental electride
  • 2D electride
• Intermetallic electride

• Activated electride
• High-pressure electride
• Magnetic electride
• Topological electride

Based on properties

Based on compositions

Ref: Liu C, Electride: a review, J. Matter. Chem. C, 2020, 8, 10551.

Problems

• An empty anionic site that's surrounded by positive charged ionic cores? How come this thing is stable?

 

• It's really hard to use this definition to construct a usable descriptor that covers all know electrides.

 

• Can metals be idneitifed as electrides as they some times also have local accumulation of charge?

This definition is not (easily) applicable and does not tell us the whole story🤔!

ATTEMPTS were made

1. Procrystal density: looking for void space.

2. Non Nuclear Maximum (NNM): looking for local max in charge density.

3. Magnetic moments: looking for magnetic electrides

4. Electron localization function (ELF): looking for the localization information.

5. nonlinear optical (NLO): looking for electride with nonliearn optical properties.

Ref: Stephen G. Dale, Theoretical Descriptors of Electride, J. Phys. Chem. A 2018, 122, 9371−9391

ATTEMPTS were made

• There are several papers use ELF complemented by other descriptors to search for electride materials. However, they either fail in including some known electrodes or 
• The most accurate attempt was tried by xxx et al. Where only ELF is used and an arbitrary cut-off parameter of 0.75 is used.
• All of this failed to describe 

Attemps were made

Ref [1]: Miao M., High-Pressure Electrides: The Chemical Nature of Interstitial Quasiatoms, J. Am. Chem, Soc. 2015, 137,3613-3637

Ref [2]: Miao M., High-pressure electrides: A predictive chemical and physical theory, Acc. Chem. Res., 2014, 47(4), 1311-1317

Ref[3]: Zhu Q. et al. Computational Discovery of Inorganic Electrides from an Automated Screening, Matter, 2019, 1, 1293-1303.

Ref[4]: Yunwei Zhang, et al. Computer-Assisted Inverse Design of Inorganic Electrides, Phys. Rev. X, 2017, 7, 011017

Theory was proposed but only focused on High-pressure electrides¹ ².

 

Various attempts of using a combined descriptor like electron localization function (ELF), partial charge density etc. were made³ ⁴. None of which tried to explain the origin of these behavior.

theory

Theory: Interstitial orbitals are (electron-deficient) multicentered bonding between orbitals on surrounding atoms.

• Have Electron localization function (ELF) maxima @ interstitial region (with a high value).
• Small \( \nabla^2 \) ELF @ interstitial site.
• High ELF basin integrated charge number 

Descriptor:

Theory

• An empty anionic site that's surrounded by positive charged ionic cores? How come this thing is stable?
  • Lower kinetic energy by forming a bonding orbital.
• Metals also have electrons localized at interstitial sites.
  • Weak  vs strong multicentered orbital
• It's really hard to use this definition to construct a usable descriptor that covers all know electrides.
  • Use ELF value + topological analysis.

Descriptor-ELF

In laymen's term:

ELF tells the degree of Pauli exclusion force of a test electron feel at a specific point in space. Hence, it describes the degree localization: More localized -> larger repulsion force (Fermi Hole)

DESCRIPTOR-ELF

• Have ELF maxima @ interstitial region (with a high value).

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

• High ELF basin integrated charge number.

DESCRIPTOR-ELF

• There are reports that they can be used to identify multicentered bonding .

 

• It is a local property that's based on pure quantum properties of electrons (Fermi hole) and can be calculated easily.

 

• It's explanation is intuitive: ELF = 0.5 -> free electron, ELF =1 -> perfect localization.

Topological analysis?

ELF alone only describes local information of electron localization.  

• ELF maxima at the center of the interstitial region.
• ELF maxima to be high (so that electron are actually localized)
• ELF pockets that surrounding the interstitial sites to have a high occupation so that enough electrons are localized inside the pocket.

To use it to identify interstitial multicenter bonding state, we need:

electron deficient?

Multicentered bonding can have different types. Usually The strongest bonding orbital has the lowest energy and as the degree of bonding decrease, the energy increases.

Systems with electrons only occupying the lowest bonding orbital is preferred for electrides.

COBI

• Crystal Orbital Bond Index (COBI) is a way to measure the bonding strength (number of bonds) between atoms.
•  
• For multicentered bonding, the magnitude of COBI represents the degree of occupation bonding, non-bonding, anti-bonding orbitals:
  • ICOBI > 0 : electron deficient
  • ICOBI < 0 : electron rich

Method

1. Apply Bader's AIM analysis on ELF to find local maxima points.
2. For all local maxima points, find the ones that are equidistant more than two surrounding atoms of the same type. (similar to the so-called "synaptic order")
3. Analysis the topology of the ELF around the maxima points by calculating the second derivative of ELF and integrated charge number under the ELF Bader basin.

DOES IT WORK?

ELF

Identified sites

Y₂C

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. Among them:
  • Elemental systems: 295
  • Binary systems: 5822
  • Ternary system: 4178

ResultS

ResultS

• There seems to be a direct correlation between systems that are more "electride-like" and the ELF amplitude at the identified site.

ResultS

All predicted structure

Structures w/ CHG max

More "electride-like":

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

Most Electrid-like

Ca6Ge2O

Ca₆Ge₂O-mp-1019564

ELF:       0.9877

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

Occ.:      1.7344

COBI [Ca₆Ge₂O]

COBI [Ca₆Ge₂O]

MAKING ELECTRIDES

BCC-Sodium

Equipped with the knowledge of where these bonding originates, we can force a system with metallic bonding into an electide.

ELF:       0.5505

\(\nabla^2 \)ELF: -0.0993

Occ.:      0.1604

MAKING ELECTRIDES

ELF

Tetragonal-Sodium

ELF:       0.7266

\(\nabla^2 \)ELF: -0.0992

Occ.:      0.7470

Making electrides

Previously, we used stain to control the transition from metallic bonding to electride bonding. This time, we use doping to bring out electride nature inside an typical ionic material

NaCl-Doped [4e]

ELF:       0.7525

\(\nabla^2 \)ELF: -0.5243

Occ.:      0.4094

The 🔗LINK

The 🔗LINK

*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

Let me show you some solid examples of s-orbital electrides.

INOrganic electrides

Electron localization function (ELF)

Yttrium

Carbon

Y₂C

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

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

high-pressure electrides

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

Electron localization function (ELF)

Sodium - hP4

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

Ref: James L. Dye, Acc. Chem. Res. 2009, 42, 10, 1564–1572

HOMO

LUMO-1

LUMO-2

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

Building block:

Na-Tripip222

ORGANIC ELECTRIDES

thank you 🤟

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