CHENGCHENG XIAO

2021-07-16

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Chengcheng-Xiao

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

​

HOwever...

  • An empty anionic site that's surrounded by positive charged ionic cores? How come this thing is stable?
  • To make things worse, "simple metals" always have electrons (de)localized at interstitial sites.
  • This definition cannot be converted to descriptors (used to build electrides in a "bottom-up" way) as it's a based on a phenomena instead of the "root cause".

If you really think about it, this definition is not (easily) applicable and does not tell us the whole story🤔!

Now, can we do better?

BUT How?

Definition: [mass noun] The degree of distinctness in outline of an object, image, or sound.

 

To make a new definition, we need to figure out the distinctness of all known electride has that other materials doesn't. [categorization]

 

To make predictions, we need to understand the underlying principle that determines these behaviors. [analysis]

categorization

Organic electride:

 

Inorganic electride:

Organic-metal complexes act as corners that confine the interstitial electrons

metal-nonmetal systems in which metal atoms act as corners that confine the interstitial electrons.

Other categorisation based on the functionalities of electrides are also possible. One example: Electride: a review, Chang Liu, et. al.  J.Mater.Chem.C, 2020,8, 10551

 

Crown ethers

image/svg+xml
image/svg+xml

Molecular crystal of Cs⁺(15C5)₂e⁻

Sinlge unit of metal-organic compound

image/svg+xml

Cs

In organic electride, electron occupy interstitial sites surrounded by organic-metal complexes.

ORGANIC ELECTRIDES

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

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

Trend:

  • The building blocks - metal organic molecule complex have occupied super atomic s-orbitals.

ORGANIC 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

INOrganic electrides

Electron localization function (ELF)

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

INOrganic 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)

A janky theory: Mao-Sheng Miao, et.al. Accounts of Chemical Research, (2014), 1311-1317, 47(4)

INOrganic electrides

Trend:

  • Electron sites are all surrounded by alkaline metal atoms. All of these metal atoms have occupied s-orbitals.

OUR theory

Theory: Interstitial sites originate from overlapping occupied “s”-orbitals (including SAMOs and s-orbitals from metal atoms). i.e. multicentered bonding between "s"-orbitals.

Descriptor (definition) form this theory:

  • S orbitals have optimum overlap at the interstitial sites. [satisfies the overlap criteria]
  • Has a large enough electron/site ratio. [satisfies the occupation criteria]

S-orbtials you say?

Metal atoms' s-orbitals? But I thought those interstitial sites are at least 2 Å away from those metal atoms. Are those s-orbitals that extended?

Na

K

Yes, they are! And this is precisely why s-orbitals are important in electrides.

Let's test it

First thing comes to mind is NaCl, aka table salt 🧂where Na's s-orbital is fully unoccupied (just above the Fermi energy) while Cl's p orbitals are fully occupied. Now, let's n-dope it!

ELF

interstitial electrons!

\frac{\text{\#electrons}}{\text{\#sites}} = 1

Let's test it

Now, what about we keep the number of electrons in the system and play with the number of interstitial sites (that satisfies the overlap criteria)?

BCC

\frac{\text{\#electrons}}{\text{\#sites}} = \frac{1}{6}

Tetragonal

\frac{\text{\#electrons}}{\text{\#sites}} = 1

What can it do?

What this theory explains:

  • Organic electrides (super atomic molecular orbital)
  • High pressure electrides (metal's s orbital)
  • Intrinsic electrides (metal's s orbital)
  • F-center defects (metal's s orbtial)
  • Difference and similarities between metal and electride.
  • Explains the low work function these materials have (s electrons are typically more active)

Extention?

  • F-center defects (metal's s orbtial)

There are p orbitals  exist in F-cetner defect as well, since in my theory the interstitial orbitals are multicentered bonding orbitals, could there be multicentered anti-bonding orbitals?

Not convinced?

Although this theory (definition) is simple and very intuitive, it's not a mathematically distinct as there are parameters to be determined:

  • The optimum overlap criteria requires a  radius of the s orbitals.
  • the occupation criteria requires a parameters to tell if a system is metal or electride.

 

Also, we've only tested this theory on few know electrides, this doesn't mean it'll be applicable to all electrides.

HOW to?

So, how do we determine those parameters?

  • We can get an estimate of them using RDF of isolated atoms.
  • we can also test them with a filtering process on a database and tune them to find only typical electride materials.

 

How to make people believe us?

Use filtering process to filter out materials in a database that are unlikely to be electride and then do DFT on the remaining for validation.

Prediction process

  • First of all, we need to figure out which atom in our system are "metal" atoms and how many s electrons are going to be occupying the s-orbitals of them. [no idea how]
  • Then, do a filtering process using optimum overlap criteria to figure out the number of interstitial sites (as well as where those interstitial sites are)
  • Finally, calculate the #electron/#site ratio and give an estimate of a mterial is electride or not.
  • Validate the result using DFT.

FilterinG process

  • 1.Make a 3x3x3 supercell (so that the interstitial sites at the boundary can be captured)

  • 2.Generate a series of equally spaced test points inside the center unit cell.

  • 3.Delete all ”non-metal” atoms (based on ).

  • 4.Generate a neighbor list for each test points to the metal atoms. The distance between test points and their neighbor metal atoms should > nn_dist_min and < nn_dist_max. (a shell-like overlap criteria)

  • 5.Do an average of position for the remaining test points with the same neighbor list. Then the averaged position is used as the interstitial site of the polyhedron formed by those neighbors.

  • 6.Filter out interstitial sites that have distance to non-metal atoms less than a certain cutoff.

Does it work?

ELF

Predicted sites

Na-BCC

Na-tetragonal

Does it work?

ELF

Predicted sites

Y₂C

thank you 🤟

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