Bond valence method
The bond valence method (or bond valence sum) (not to be mistaken for the valence bond theory in quantum chemistry) is a popular method in coordination chemistry to estimate the oxidation states of atoms.
The basic idea is that the valence V of an atom is the sum of the individual bond valences vi surrounding the atom:
- <math> V = \sum(v_i) </math>
The individual bond valences in turn are calculated from the observed bond lengths.
- <math> v_i=\exp \left( \frac {R_0-R_i} {b} \right) </math>
Ri is the observed bond length, R0 is a tabulated [1] parameter expressing the (ideal) bond length when the element i has exactly valence 1, and b is an empirical constant, typically 0.37 Å.
Also, :<math> v_i= \left( \frac {R_i} {R_0}\right)^{-6} </math> see [2]
Contents
Theory
The bond valence model has been described theoretically in terms of classical electrostatic theory without resorting to quantum mechanics.[3] In brief:
- The bonding between cation and anion is described in terms of electrostatic lines of force
- The concentration of lines of force between cation and ion constitutes the electrostatic bond
- Electrostatic bonds are separated by surfaces of zero flux
- These electrostatic bonds can be treated as if they were capacitors
- The bonding of the crystal or molecule can viewed as a network of capacitors and standard equations of electrostatics e.g. Gauss's law, Kirchhoff's Law applied
The infinite network of a crystal can be represented topologically by a finite network for computational purposes.
History
The bond valence method is a development of Pauling's rules.
In 1930 Bragg [4] showed that Pauling's electrostatic valence rule could be represented by electrostatic lines of force emanating from cations in proportion to the cation charge and ending on anions. The lines of force are divided equally between the bonds to the corners of the coordination polyhedron.
Starting with Pauling in 1947[5]
a correlation between cation−anion bond length and bond strength was noted. It was then shown later[6] that if bond lengths were included in the calculation of bond strength, its accuracy was improved, and this revised method of calculation was termed the bond valence. These new insights were developed by later workers culminating in the set of rules termed the bond valence model.[3]
Actinide oxides
It is possible by bond valence calculations [7] to estimate how great a contribution a given oxygen atom is making to the assumed valence of uranium. Zachariasen [8] lists the parameters to allow such calculations to be done for many of the actinides. Bond valence calculations use parameters which are estimated after examining a large number of crystal structures of uranium oxides (and related uranium compounds); note that the oxidation states which this method provides are only a guide which assists in the understanding of a crystal structure.
For uranium binding to oxygen the constants Ro and B are tabulated in the table below. For each oxidation state use the parameters from the table shown below.
| Oxidation state | Ro | B |
|---|---|---|
| U(VI) | 2.08Å | 0.35 |
| U(V) | 2.10Å | 0.35 |
| U(IV) | 2.13Å | 0.35 |
What level of accuracy do we have?
Upon calculating the bond valence sum for PMo12O40V2<math>^{-5}</math> with symmetry P-1[9], the following table was obtained
| Atom | Mo(V) | Mo(IV) |
|---|---|---|
| Mo12 | 6.116 | 6.491 |
However, according to the bond valence method the molybdenum on this molecule would have valence 7, which is chemically impossible.
Doing the calculations
It is possible to do these calculations on paper or software. A program which does it can be obtained free of charge.[10][11]
References
- ↑ Index of /ccp/web-mirrors/i_d_brown/bond_valence_param
- ↑ ALTERMATT, D. & BROWN, I. D. (1985). Acta Cryst. (1985). B41, 244-247
- ↑ 3.0 3.1 I.D. Brown (2002)The chemical bond in inorganic chemistry : the bond valence model IUCr Monographs in Crystallography 12 Oxford Science Publications ISBN 0198508700
- ↑ Bragg W.L. (1930). "The structure of silicates". Zeit. Cristallogr. 74: 237–305.
- ↑ Linus Pauling (1947). "Atomic Radii and Interatomic Distances in Metals". Journal of the American Chemical Society. 69 (3): 542–553. doi:10.1021/ja01195a024.
- ↑ G Donnay, R Allmann (1970). "How to recognize 02−, OH−, and H2O in crystal structures determined by X-rays". Amer. Min. 55: 1003.
- ↑ kristall.uni-mki.gwdg.de/softbv/references
- ↑ Zachariasen, J. Less Common Met., 1978, 62, 1-7
- ↑ Hill, C., Chen, Q., Inorg. Chem. 1996, 35, 8, 2403-2405doi:10.1021/ic951231n
- ↑ www.ccp14.ac.uk/ccp/web-mirrors/i_d_brown
- ↑ www.ccp14.ac.uk/solution/bond_valence/
