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How big are atoms in crystals?

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Abstract

Atoms and bonds are central concepts in structural chemistry, but neither are concepts that arise naturally from the physics of condensed phases. It is ironic that the internuclear distances in crystals that are readily measured depend on the sizes of atoms, but since atoms in crystals can be defined in many different ways, all of them arbitrary and often incompatible, there is no natural way to express atomic size. I propose a simple coherent picture of Atoms-in-Crystals which combines properties selected from three different physically sound definitions of atoms and bonds. The charge density of the free atom that is used to construct the procrystal is represented by a sphere of constant charge density having the quantum theory of atoms in molecules (QTAIM) bonded radius. The sum of these radii is equal to the bond length that correlates with the bond flux (bond valence) in the flux theory of the bond. The use of this model is illustrated by answering the question: How big are atoms in crystals? The QTAIM bonded radii are shown to be simple functions of two properties, the number of quantum shells in the atomic core and the flux of the bond that links neighbouring atoms. Various radii can be defined. The univalent bonded radius measures the intrinsic size of the atom and is the same for all cations in a given row of the periodic table, but the observed bonded radius depends also on the bond flux that reflects the chemical environment.

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Glossary

V

Atomic valence

The amount of charge in valence units (electron units) an atom uses for bonding.

 

Bond critical point

The minimum in the charge density along a bond path.

s

Bond flux

A measure of the strength of a bond in valence units equal to the amount of charge contributed by each atom to form the bond, also known as the bond valence.

R MO

Bond length

The distance between a cation M and oxygen.

 

Bond path

The path of steepest descent in the charge density linking two neighbouring nuclei.

r

Bonded radius.

The distance between the atomic nucleus and the bond critical point.

S

Bonding strength.

The valence of a typical bond equal to the atomic valence divided by the typical coordination number (Eq. 5).

 

QTAIM

Quantum theory of atoms in molecules [1].

f

Fractional bonded radius

(Equations 18, 19).

n

Row number

In the periodic table, the rows are numbered with the H and He row as zero. The row number is equal to the number of quantum shells in the atom core.

N

Coordination number

The number of bonds formed by an atom

<N>

Typical coordination number

The average observed coordination number (Eq. 5).

S

Typical bond flux

See bonding strength.

R S

Typical bond length

The length of a bond with a flux equal to the cation bonding strength (Eq. 16).

r S

Typical bonded radius

The radius of an atom when forming a bond with a flux equal to its bonding strength (Eq. 21)

R n , R1

Univalent bond length

Length of the M-O bond with a bonding strength 1.0 vu where M is in the nth (or first) row of the periodic table (Eqs. 12, 15).

r 0

Univalent bonded radius

Typical bonded radius that an atom would have if its bonding strength were 1 vu.

vu

Valence unit

Unit of charge or flux, equal to one electron unit.

Author information

Authors and Affiliations

  1. Brockhouse Institute for Materials Research, McMaster University, Hamilton, ON, L8S 4M1, Canada

    I. David Brown

Authors
  1. I. David Brown
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Correspondence to I. David Brown.

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Conflict of interest

The author has no conflicts of interest.

Funding

This work was not supported by any funding.

Additional information

This paper is dedicated to Professor Lou Massa on the occasion of his Festschrift: A Path through Quantum Crystallography

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David Brown, I. How big are atoms in crystals?. Struct Chem 28, 1377–1387 (2017). https://doi.org/10.1007/s11224-017-0942-y

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  • DOI: https://doi.org/10.1007/s11224-017-0942-y

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