Electronegativity and Bonding in Solids

The other class I teach on a regular basis is Chemistry 121 (the first quarter of freshman chemistry). Today we are going to go back to some of the bonding concepts introduced in that course and examine them in greater detail.

One of the things that we teach the freshman is that bonding interactions can be characterized into one of the following categories:

Of course we don’t spend too much time to mention that most bonding interactions do not fall neatly into the above categories, rather they involve mixtures of the various types of bonding.

We have seen that the Coulombic interactions, from which ionic bonding is derived, are optimized by the following combination of atomic and structural characteristics:

In contrast, covalent bonding is dependent upon the degree of spatial and energetic overlap between atomic orbitals on neighboring atoms. It is favored by the following atomic and structural characteristics:

Metallic bonding goes hand in hand with the following atomic and structural characteristics:

In our last lecture we saw how the bonding interactions in the group IVA (14) solids change from covalent to metallic as we move the down the periodic table. This results from a decrease in the orbital overlap as the principle quantum number increases, and leads to a dramatic change in physical properties (color, electrical conductivity, hardness, etc.) as we go from diamond to lead.

Today we are going to examine the progression from purely covalent bonding to largely ionic bonding. Mixed ionic covalent character is present in any bond between two atoms of different types. The parameter which is used to quantify the degree of ionic character in a bond is called electronegativity (c). This quantity is defined as:

Electronegativity (c) The power of an atom in a molecule to attract electrons to itself.

Our use of electronegativity as a tool for quantifying the ionic and covalent contributions to a bond follows directly from its definition. As the electronegativity difference between two atoms increases the bonding electrons are increasingly drawn toward the more electronegative atom. When the electronegativity difference becomes extreme the electrons are really no longer shared but can be thought of being transferred from the cation to the anion (ionic bonding). In Chem 121 we use the following arbitrary cutoffs to differentiate covalent and ionic bonding:

Dc > 2 Ionic Bonding

0.5 < Dc < 2 Polar Covalent Bonding

Dc < 0.5 Covalent Bonding

Although these rules give beginners a feel for the scale (the Pauling scale) and use of electronegativity, one should realize that there is no sharp cutoff between ionic and covalent bonding. Rather it is a smooth transition between the two.

The importance of electronegativity in solid state chemistry is illustrated by its use as a parameter in structure sorting maps. For example, as we discussed in the last lecture the work of Philips and Van Vechten which showed that for binary AX compounds the structure type evolves from:

Sphalerite Wurtzite Rock Salt

as we increase the ionic character of the bonding. Another way to state this would be to say that this structural progression (Sphalerite to Rock Salt) takes place as the electronegativity difference increases.

A somewhat simpler route to the same conclusion is the structure sorting approach of Mooser and Pearson. In the map below the difference in electronegativity is plotted on the x axis and the average principle quantum number of the valence shell on the y axis. Once again we see that as the ionic character of the bonds increases (greater Dc and larger n) the observed structure type evolves from Sphalerite to Wurtzite to Rock Salt to CsCl.

[Insert Mooser-Pearson plot of AB compounds]

In a similar manner we can understand the structures adopted by AX2 compounds.

Fluorite structure

Cation coordination number = 8 (cubic)
Anion coordination number = 4 (tetrahedral)
Madelung constant = 5.04

Rutile structure

Cation coordination number = 6 (octahedral)
Anion coordination number = 3 (trigonal planar)
Madelung constant = 4.82

CdCl2 and CdI2 structures

These differ from rutile and fluorite in that anion layers are stacked on top of each other with cations present only between alternating layers of anions. The presence of neighboring anion layers (with no cations in between) is extremely unfavorable from a Coulombic point of view. Even though both structures are rather unfavorable from an ionic standpoint, the CdCl2 is slightly better due to the fact that the Cd ion positions are staggered from one layer to the next, which results in longer Cd-Cd distances.

From the above arguments we would expect that as the ionic component of the bonding interaction increases we should see the following structural evolution:

CdI2 CdCl2 Rutile Fluorite

Examining several series of MX2 compounds we see the following:

Compound

Dc

Structure

Compound

Dc

Structure

ZnI2

1.01

CdI2/CdCl2

MgI2

1.35

CdI2

ZnBr2

1.31

CdCl2

MgBr2

1.65

CdI2

ZnCl2

1.51

CdCl2

MgCl2

1.85

CdCl2

ZnF2

2.33

Rutile

MgF2

2.67

Rutile

           

CdI2

0.97

CdI2

CaI2

1.66

CdI2

CdBr2

1.27

CdCl2

CaBr2

1.96

Rutile

CdCl2

1.47

CdCl2

CaCl2

2.16

Rutile

CdF2

2.29

Fluorite

CaF2

2.98

Fluorite

Differences in electronegativity dictate not only structure type, but physical properties as well. It has been shown that the band gap of binary AX compounds increases as the electronegativity difference increases. In this way we can use electronegativity to predict whether a compound will be an insulator or a semiconductor.

[Scan in figure 4.22 from Huhey]

Hopefully I have convinced you that electronegativity is a powerful concept, now let’s take a look at a variety of methods for estimating electronegativity (for it cannot be directly measured).

Pauling Electronegativity

Pauling was the first person to propose the concept of electronegativity and suggest a method for estimating its value. His derivation of electronegativity can be understood by considering the bonding in Cl2, F2 and ClF. The bond energies of these molecules are 2.51 eV, 1.59 eV and 2.64 eV respectively. He reasoned that the covalent bonding interaction in Cl-F should be the average of the Cl-Cl and F-F bond strengths, which would be (2.51 + 1.59)/2 = 2.05 eV. However, we see that the bond strength in Cl-F is much higher (2.64). Pauling postulated that the excess bond enthalpy can be attributed to the ionic interaction between the two atoms, which he called the ionic resonance energy. He then defined the difference in electronegativity between Cl and F to be equal to the square root of the ionic resonance energy:

c(F) - c(Cl) = sqrt (2.64 eV – 2.05 eV) = 0.77

One of the most important take home lessons from Pauling’s concept of electronegativity is that an interaction containing mixed ionic-covalent character can be stronger than either a pure covalent or a pure ionic bond. Chemists are sometimes guilty of assuming that the strength of a bond increases as the covalent character of the bond increases, which is not generally true.

Mulliken Electronegativity

The Mulliken electronegativity of an atom is probably the simplest, and can be easily calculated for most atoms. Mulliken proposed that the electronegativity should be an average of the ionization energy and electron affinity of an atom, c = [EA+IE]/2.

Sanderson Electronegativity

Sanderson’s electronegativity scale is based on the principle that the ability of an atom or ion to attract electrons to itself is dependent upon the effective nuclear charge felt by the outermost valence electrons. It is a well known fact that as the effective nuclear charge increases the size of the atom decreases. It becomes more compact. Sanderson reasoned that the electronegativity, S, should be proportional to the compactness of an atom. Specifically:

S = D/Da

where D is the electron density of an atom (its atomic number divided by its atomic volume (covalent radius cubed)) and Da is the expected electron density of an atom, calculated from extrapolation between the noble gas elements. Values of Sanderson electronegativities are given in Table 2.10 of West.

One of the most important contributions that Sanderson made to our understanding of electronegativity is his "principle of electronegativity equalization". This principle can be stated as follows:

Principle of Electronegativity Equalization When two or more atoms initially different in electronegativity combine chemically, they adjust to have the same intermediate electronegativity within the compound. This intermediate electronegativity is given by the geometric mean* of the individual electronegativities of the component atoms.

*The geometric mean of n numbers is obtained by multiplying all of the numbers together and taking the nth root of the product.

In other words the electron density will flow from the more electropositive atom to the more electronegative atom, creating a partial positive charge on the former and a partial negative charge on the latter. As the positive charge on the electropositive atom increases, its effective nuclear charge increases, hence its electronegativity increases. The same trend happens in the opposite direction for the more electronegative atom, until the two have the same electronegativity.

Example

Use Sanderson’s principle of electronegativity equalization to calculate the electronegativity of SnO2 and SrTiO3.

S(SnO2) = (SSn SO2)1/3 = (4.28 4.902)1/3 = 4.68

S(SrTiO3) = (SSr STi SO3)1/5 = (1.28 2.09 4.903)1/5 = 3.16

It should be noted that although the idea of electronegativity equalization was developed by Sanderson, it is valid to use it with other electronegativity scales.

Sanderson used his electronegativity scale and concept of electronegativity equalization to calculate partial charges and ionic radii of atoms in ionic-covalent compounds and molecules. The basic conclusion he reaches is that the partial ionic charge and ionic radius of an ion are not constants, but vary considerably depending upon the electronegativity of the surrounding atoms. Furthermore, Sanderson’s calculations suggest that the partial charge on an atom never exceeds +1 or –1. Once again reinforcing the idea that oxidation states do not reflect the true charge of an ion.

Details regarding the Sanderson system are given in chapter 2 of West or in more detail in Sanderson’s own writings (Chemical Periodicity (1961) and Chemical Bonds and Bond Energy (1976) by R.T. Sanderson).