Bond dissociation energies depend on both bond valence and bond character. For a given bond valence, bond energies can vary by hundreds of kJ/mol depending on whether the bond is ionic, covalent, or metallic in character. Covalent bonds less than 2 valence units are particularly affected by the lone pair bond weakening effect, where lone pair electron density on one atom repels bonding electron pairs, weakening the bond. The researchers analyzed bond dissociation energy data for many molecules and crystals, relating the energies to bond valence and character. Mathematical models relating these factors can help parameterize new valence-based force fields and rationalize crystal-chemical trends.

1. Bond Valence and Bond Energy
Dept. of Geological Sciences, Brigham Young University, Provo, UT 84602, USA. (*correspondence: barry_bickmore@byu.edu)
JOSHUA M. WHITMER, BARRY R. BICKMORE*, CHRIS A.SHURTLEFF,
DAVID W. YEATES, LINCOLN GEE, OWEN D. CRAVEN, AND MATTHEW C.F. WANDER
ABSTRACT
We are attempting to build a new kind of molecular mechanics
force field based on an expansion of the bond valence model. The
concept of bond valence (a method for estimating bond order
from bond length) has been used in many quantitative structure-
property models, including the Multisite Complexation (MUSIC)
model of Hiemstra and coworkers [1]. One assumption implicit in
these models is that bond valence is somehow proportional to the
bond energy. However, to date no one has demonstrated the form
of this relationship. Are other factors, such as bond character and
atomic size, important for determining bond energies?
We have categorized a large number of bonds in small
molecules and crystals according to bond valence, bond character
(estimated from electronegativity considerations) and bond
length, and used these quantities to roughly predict bond
dissociation energies.
A consistent, but complex picture emerges from the data. We
show that, even for the same bond valence, bond dissociation
energies can differ by hundreds of kJ/mol based on their ionic,
covalent, or metallic character. Furthermore, covalent bonds less
than 2 v.u. are strongly affected by the lone-pair bond-weakening
effect identified by Sanderson [2].Bond length plays a more minor
role. Mathematical models of this behaviour will help us
parameterize valence-based force fields, by providing initial
estimates of bond energies, and model forms. It should also be
useful for rationalizing crystal-chemical trends.
REFERENCES
[1] Hiemstra et al. (1996) J. Colloid & Interface Sci. 184,680-692. [2]
Sanderson (1983) Polar Covalence, New York, Academic Press. [3]
Bickmore et al. (2004) Bond-valence methods for pKa
prediction: critical
reanalysis and a new approach, Geochemica et Cosmochimica Acta[4]
Batsanov & Batsanov (2012) Introduction to Structural Chemistry, New
York, Springer. [5] Gillespie & Popelier (2001) Chemical Bonding and
Molecular Geometry: From Lewis to Electron Densities, Oxford University
Press.
Eqn. 3
METHODS
BDEs for a large number of molecules, as well as atomization energies of
crystals converted to individual BDEs, were taken from the literature [4][5].
Bond valences were inferred by applying the valence sum rule. Bond
character was described in terms of fraction ionic character (Ib
, based on the
difference in Pauling electronegativities between the bonded atoms), and the
average Pauling electronegativlty of the bonded atoms (ENavg
). Ib
denotes
how ionic vs. covalent/metallic a bond is, while ENavg
denotes how covalent
vs. metallic it is. We then optimized mathematical models to fit the data using
MATLAB.
Points represent actual molecular data, planes were fitted to the data
using MATLAB.
Fig. 1
RESULTS and CONCLUSION
Clearly, bond dissociation energy depends on bond valence, but it also
strongly depends on bond character. In fig.1 we see that for a given
valence, the bond energies vary, sometimes by hundreds of KJ/mol, so
models that assume bondenergy is proportional to bond valence will only
be applicable over a limited range of bond types. Covalent bonds (low Ib
and high ENavg
) are particularly affected by what Sanderson [2] called the
Lone Pair Bond Weakening Effect. As bonds become more covalent, the
lone pair electron density becomes more and more concentrated on one
side of high EN atoms, repelling the bonding pairs. When the bonded
atoms cannot move together any further, therepulsion between the lone
pairs and bonding pairs continues to grow, causing the bonds to actually
weaken, rather than the geometry continuing to be affected.
Eqn. 1 Eqn. 2
INTRODUCTION
The Bond Valence Model (BVM) has been widely used
for rationalizing combinations of bond lengths in crystal
structures. Essentially, it is a method for relating bond
order to bond length. Typically, Eqn. 1 is used to calculate
the valence of an individual bond (sij
) to the bond length (R).
Empirical parameters (R0
and B) specific to a particular atom
pair are calibrated on crystal (and sometimes molecular)
structures, while imposing the valence sum rule. The valence
sum rule (Eqn. 2) states that the valence of bonds incident to
an atom must equal the absolute value of the atomic
valence (Vi
).
A number of groups have also produced linear free energy
relationships (LFERs), which empirically relate reaction
energies to bond valence-related quantities. For example,
Hiemstra and coworkers formulated the popular
Multi-Site Complexation (MUSIC) model, which uses Eqn. 3
to relate a the valence of bonds incident to an oxygen atom
in an oxide surface functional group to the pKa
of that
functional group.
The formulation of Eqn. 3 implicitly assumes that only the
bond valence is important for estimating the reaction
energies. However, Bickmore and coworkers [3] showed that,
even for the solution monomers on which the MUSIC model
was calibrated, bond character (i.e., the degree of ionicity,
covalency, or metallicity of the bonds) is also important for
accurate pKa
estimates.
Here we show that bond energies are very strongly related
to both bond valence and bond character, by relating bond
dissociation energies (BDEs) to both factors.
ACKNOWLEDGEMENTS
This project was funded by the National Science Foundation,
Geobiology and Low-Temperature Geochemistry program.