Why does covalent nature in ionic solids increase the lattice energy?

Question

I have observed in my textbooks that ionic solid that have a greater covalent character tend to have higher lattice energy. Can this be generalised as fact?

Answer 1

(First of all I have to note that I'm just a student, not a specialist in solid body physics or chemistry)

Let's consider chemical bond in general, starting with diatomic molecule (our findings for this case we will generalize to crystalline structure later):

When we say that chemical bond is formed, we mean that for electrons of each atom by atomic interaction (interaction of atomic orbitals of each atom to each other) become available to be situated on molecular orbitals(MO) (defining as superposition with different contributions of atomic orbitals(AO)). Now we must say that depending from atomic orbital energy and its symmetry, result of interaction with another AO may be different. If we have two interacting AOs with big (bigger than stated value) difference in energies it leads to formation of two MOs: one of them, bonding MO, must have energy closer to such AO that is lower by energy, another relatively must have energy closer to another AO (see picture). In this case we have low energy of stabilization (system weakly feel energy changing before and after interaction). If difference as big as whole system looks like we give both electrons to one of AOs it means that electron density of bond is shifted to one of atoms. In this case we say that we deal with IONIC bond. Now COVALENT bond: energies of interacting orbitals are close. This way we have big stabilization energy (see picture). Because of it we can say that covalent bond is stronger then ionic.

Simplifying: ionic bond is provided by Coulomb interactions (in approximation), but covalent bond is provided not only by them, and this is the reason why it's stronger.

Generalization to crystalline lattice: now we must consider group of interacting orbitals, but main findings remain the same: bond forming by AOs with same energy is stronger.

And, as lattice energy is energy of interacting particles forming lattice, it's clearly determined by MO's energy.

That's why I think yes, we may generalize your finding as a fact.

Answer 2

It depends on what is meant in the framing of the question—the lattice energy of a crystal is defined as the molar energy of sublimation for some ionic solid where it is sublimated into its constituent ions. For some ionic solid $A_mX_n$, the ionization is the change in internal energy $\Delta U_{lattice}$ of the following reaction:

$$ A_mX_n (s) \rightarrow m A^{n+} (g) + n X^{m-} (g) $$

You could approximate an ionic solid as only bound from Coulombic (i.e. charge/ionic) attraction and calculate what the change in energy would be of separating two ions by using Coulomb's law. If that's sufficient enough for you to understand, then you can skip this next math. If you would like to see the math, here's what that calculation would look like:

$$ N_{A} \int_{B_{l}}^{\infty}{\frac{-mnQ}{4\pi \epsilon _0r^2}}dr $$

where $N_{A}$ is Avogadro's number, $Q$ is the charge of the proton, $B_l$ is the bond length between the two ions, and $\epsilon _0$ is the vacuum permittivity.

When comparing this calculated energy (or an energy calculated from a similar ionic-only model), often the energy is greater than you would expect it to be. That's because there is some extra character that comes not just from Coulombic attraction but from covalent attraction.

Covalence is the stabilization of a bond through the quantum mechanical mixing of two atomic orbitals into a bonding orbital of low energy and an antibonding orbital of high energy. This covalent character further increases the stabilization of the lattice, and thus the energy required to break apart the ions will be greater.

The Coulombic attraction between two ions at the measured bond length distance doesn't change even if some of that bond length is determined by covalent character in the bond—if we measure the bond length and apply the ionic-only model, we underestimate the extra contribution of stabilization from the covalent character. However, covalent character won't completely determine trends in lattice energy; only with every other factor being equal could you compare two ionic solids and predict lattice energy from the covalent character.