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Practical Considerations in Determining Bond Valence Parameters

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Bond Valences

Part of the book series: Structure and Bonding ((STRUCTURE,volume 158))

Abstract

Based on an investigation of empirical links of the bond valence method to observable quantities, especially the electron density at the bond critical point as well as absolute electronic potential and hardness values in the frame of the hard and soft acids and bases concept, it is ascertained that bond valence can be understood as a functional of valence electron density. Therefrom a systematic approach for deriving bond valence parameters and related quantities such as coordination numbers and bond breaking energies is discussed that together allow for a conversion of the bond valence method to a simple effective atomistic forcefield.

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Notes

  1. 1.

    For this simple two-atom case the straight connecting line between the atoms is the bond path, i.e. the connecting line between the atoms for which each point on the line is a maximum of the electron density within the perpendicular plane. This does not necessarily remain true for multi-atom configurations or solids.

  2. 2.

    The simple expression \( {\rho_\mathrm{{BCP}}}=\exp \displaystyle\left[ {\frac{{\frac{2}{c} \ln \left( {2a} \right)-R}}{{\frac{2}{c}}}} \right]=\exp \left[ {\frac{{\frac{{ \ln \left( {2a} \right)}}{{\sqrt{2I }}}-R}}{{\frac{1}{{\sqrt{2I }}}}}} \right] \) would follow in the same way for the superposition of two identical atoms, but it may be questionable whether the electron density variation in such a perfectly covalent bond can still be thought of as a minor perturbation of the additive linear combination of the electron densities of the contributing atoms.

  3. 3.

    The electrostatic bond strength e.b.s. of an ionic bond is defined as the nominal charge (oxidation state) of the cation V id(M) divided by the coordination number N C(M) of the cation. For a cation Mm+ symmetrically coordinated by N C(M) anions Xz−, the numerical value of e.b.s.(M–X) is thus identical to the expectation value of the (conventional) bond valence s(M–X).

  4. 4.

    Note that Gibbs et al. refer to row numbers in the sense row number = n–1.

  5. 5.

    x = 1.14 (R 2 = 0.970) for the power law correlation, x = 1.0 (R 2 = 0.970) or x = 0.9 (R 2 = 0.982) for the exponential correlation when using e.b.s, or softBV parameters.

  6. 6.

    This correlation with the atomic row number n or (n − 1) is as mentioned hardly distinguishable from a correlation with atomic number or atomic mass and has been preferred here more in line with the existing proposal in the literature.

  7. 7.

    The quadratic dependence may also be derived from equating bond valence to bond fluxes in a point charge model. For details, see Brown [3].

  8. 8.

    For conventional bond valence values with fixed b = 0.37 Å the average G-value for the same set of reference structures was 0.184.

  9. 9.

    In order to eliminate the effect of the oxidation state of the central cation the bond valence values in Fig. 12 are scaled by the oxidation state V id(M).

  10. 10.

    Here we limit the comparison to O2−, S2−, F− due to the considerably lower number of data sets available for the other anions.

Abbreviations

b :

Bond valence parameter defining the compliance of a bond length R to external forces

b average :

Average b value for the interactions of all anions in a unit cell to a given cation M

b effective :

b value to be used in bond valence calculations for compounds containing several anion types (derived from partial b-averaging)

BVS:

Bond valence sum

BVSE:

Bond valence site energy

D 0 :

Bond dissociation energy

EA:

Electron affinity

E repulsion :

Energy penalty due to Coulomb repulsions among cations or among anions

G :

Global Instability Index

HSAB:

Hard and soft acids and bases

IE:

Ionization energy

k :

Force constant of a bond at the equilibrium distance

n :

Principal quantum number = period number in periodic table of the elements

N C :

Coordination number

N RCN :

Running coordination number

R 0 :

Bond valence parameter (distance corresponding to a bond valence value of 1 v.u.)

R 1 :

Radius of first coordination shell

R min :

Equilibrium distance M–X for a given coordination number

<R(M–X)>:

Expected M–X bond length

s min :

Bond valence corresponding to R = Rmin

V :

Bond valence sum

V id :

Oxidation state

α:

Bond stiffness parameter in the Morse interaction potential, here identified with 1/b

ΔE EVR :

Energy penalty for a deviation from the equal valence rule among bonds to the same central cation M

ρ(r):

Electron density as a function of distance r

ρ BCP :

Electron density at the bond critical point

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Acknowledgments

I am grateful to Dr. R. Prasada Rao for his contribution to the development of atomistic forcefields from bond valence parameters (Sect. 2.2), and to undergraduate students Wilson Low Kai Bin and Jenson Tham who contributed to the data collection for Sect. 3.4 in the frame of their Final Year Projects at NUS Singapore. Discussions with Jerry Gibbs (Virginia Tech) on the relationship between bond valence and electron density proved fruitful while elaborating Sect. 2.1. This research is supported by the National Research Foundation Singapore under its Competitive Research Programme (NRF-CRP 8-2011-4).

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Authors and Affiliations

  1. Department of Materials Science and Engineering, National University of Singapore, Singapore, 117576, Singapore

    Stefan Adams

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Correspondence to Stefan Adams .

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Editors and Affiliations

  1. McMaster University Brockhouse Institute for Materials Resea, Hamilton, Ontario, Canada

    I. David Brown

  2. Department of Chemistry, Northwestern University, Evanston, Illinois, USA

    Kenneth R. Poeppelmeier

1 Electronic Supplementary Material

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SoftBVParm (ZIP 9.23 kb)

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Adams, S. (2013). Practical Considerations in Determining Bond Valence Parameters. In: Brown, I., Poeppelmeier, K. (eds) Bond Valences. Structure and Bonding, vol 158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/430_2013_96

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