Ionic and Covalent Binding - Classification of Chemical Bonds (2024)

Classification of Chemical Bonds

To make a quantitative assessment of the type of binding present ina particular molecule it is necessary to have a measue of the extent ofcharge transfer present in the molecule relative to the charge distributionsof the separated atoms. This information is contained in the density differenceor bond density distribution, the distribution obtained by subtractingthe atomic densities from the molecular charge distribution. Such a distributionprovides a detailed measure of the net reorganization of the charge densitiesof the separated atoms accompanying the formation of the molecule.

The density distribution resulting from the overlap ofthe undistorted atomic densities (the distribution which is subtractedfrom the molecular distribution) does not place sufficient charge densityin the binding region to balance the nuclear forces of repulsion.The regions of charge increase in a bond density map are, therefore, theregions to which charge is transferred relative to the separated atomsto obtain a state of electrostatic equilibrium and hence a chemical bond.Thus we may use the location of this charge increase relative to the positionsof the nuclei to characterize the bond and to obtain an explanation forits electrostatic stability.

In covalent binding we shall find that the forces bindingthe nuclei are exerted by an increase in the charge density which is sharedmutually between them. In ionic binding both nuclei are bound by a chargeincrease which is localized in the region of a single nucleus.

Covalent Binding

The bond density map of the nitrogen molecule (Fig.7-2) is illustrative of the characteristics of covalent binding.

Fig. 7-2. Bond density (or density difference)maps and their profiles along the internuclear axis for N₂ andLiF. The solid and dashed lines represent an increase and a decrease respectivelyin the molecular charge density relative to the overlapped atomic distributions.These maps contrast the two possible extremes of the manner in which theoriginal atomic charge densities may be redistributed to obtain a chemicalbond. Click herefor contour values.

The principal feature of this map is a large accumulation of chargedensity in the binding region, corresponding in this case to a total increaseof one quarter of an electronic charge. As noted in the study of the totalcharge distribution, charge density is also
transferred to the antibinding regions of the nuclei but the amounttransferred to either region, 0.13 e^-, is less than isaccumulated in the binding region. The charge density of the original atomsis decreased in regions perpendicular to the bond at the positions of thenuclei. In three dimensions, the regions of charge deficit correspond totwo continuous rings or roughly doughnut-shaped regions encircling thebond axis.

The increase in charge density in the antibinding regionsand the removal of charge density from the immediate regions of the nucleiresult in an increase in the forces of repulsion exerted on the nuclei,forces resulting from the close approach of the two atoms and from thepartial overlap of their density distributions. The repulsive forces areobviously balanced by the forces exerted on the nuclei by the sharedincrease in charge density located in the binding region.

A bond is classified as covalent when the bond densitydistribution indicates that the charge increase responsible for the bindingof the nuclei is shared by both nuclei. It is not necessary for covalentbinding that the density increase in the binding region be shared equallyas in the completely symmetrical case of N₂.We shall encounter heteronuclear molecules (molecules with different nuclei)in which the net force binding the nuclei is exerted by a density increasewhich, while shared, is not shared equally between the two nuclei.

The pattern of charge rearrangement in the bond densitymap for N₂ is, aside from the accumulationof charge density in the binding region, quite distinct from that foundfor H₂ (Fig.6-10), another but simpler example of covalent binding. The patternobserved for nitrogen, a charge increase concentrated along the bond axisin both the binding and antibinding regions and a removal of charge densityfrom a region perpendicular to the axis, is characteristic of atoms whichin the orbital model of bonding employ p atomic orbitals in formingthe bond. Since a p orbital concentrates charge density on oppositesides of a nucleus, the large buildup of charge density in the antibindingregions is to be expected.

In the orbital theory of the hydrogen molecule, thebond is the result of the overlap of s orbitals. The bond densitymap in this case is characterized by a simple transfer of charge from theantibinding to the binding region since s orbitals do not possessthe strong directional or nodal properties of p orbitals. Furtherexamples of both types of charge rearrangements or polarizations will beillustrated below.

Ionic Binding

We shall preface our discussion of the bond density map for ionic bindingwith a calculation of the change in energy associated with the formationof the bond in LiF. While the calculation will be relatively crude andbased on a very simple model, it will illustrate that the complete transferof valence charge density from one atom to another in forming a moleculeis in certain cases energetically possible.

Lithium possesses the electronic configuration1s²2s¹and is from group IA of the periodic table. It possesses a very low ionizationpotential and an electron affinity which is zero for all practical purposes.Fluorine is from group VIIA and has a configuration 1s²2s²2p⁵.It possesses a high ionization potential and a high electron affinity.The following calculation will illustrate that the 2s electron ofLi could conceivably be transferred completely to the 2p shell oforbitals on F in which there is a single vacancy. This would result inthe formation of a molecule best described as Li⁺F^-,and in the electron configurations 1s² forLi⁺ and 1s²2s²2p⁶for F^-.

We can calculate the energy change for the reaction

in stages. The energy which must be supplied to ionize the 1s electronon the Li atom is:

(1)

The energy released when an electron combines with an F atom is given bythe electron affinity of F:

(2)

The two ions are oppositely charged and will attract one another. The energyreleased when the two ions approach one another from infinity to form theLiF molecule is easily estimated. To a first approximation it is simply-e²/R where R is thefinal equilibrium distance between the two ions in the molecule:

(3)
	(large distance apart)	(at R)

The sum of these three reactions gives
and the overall change in energy is the sum of the three energy changes,or approximately -2 ev. The species Li⁺F^- possessesa lower energy than the separated Li and F atoms and should therefore bea stable molecule.

The transfer of charge density from lithium to fluorineis very evident in the bond density map for LiF (Fig.7-2). The charge density of the 2s electron on the lithium atomis a very diffuse distribution and consequently the negative contours inthe bond density map denoting its removal are of large spatial extent butsmall in magnitude. The principal charge increase is nearly symmetricallyarranged about the fluorine nucleus and is completely encompassed by asingle nodal surface. The total charge increase on fluorine amounts toapproximately one electronic charge. The charge increase in the antibindingregion of the lithium nucleus corresponds to only 0.01 electronic charges.(The great disparity in the magnitudes of the charge increases on lithiumand fluorine are most strikingly portrayed in the profile of the bond densitymap, also shown in Fig. 7-2) It is equally importantto realize that the charge increase on lithium occurs within the regionof the 1s inner shell or core density and not in the region of thevalence density. Thus the slight charge increase on lithium is primarilya result of a polarization of its core density and not of an accumulationof valence density.

The pattern of charge increase and charge removal in theregion of the fluorine, while similar to that for a nitrogen nucleus inN₂, is much more symmetrical, and the chargedensity corresponds very closely to the distribution obtained from a single2ps electron. Thus the simple orbitalmodel of the bond in LiF which describes the bond as a transfer of the2s electron on lithium to the single 2psvacancy on fluorine is a remarkably good one.

While the bond density map for LiF substantiates the conceptof charge transfer and the formation of Li⁺ and F^-ions it also indicates that the charge distributions of both ions are polarized.The charge increase in the binding region of fluorine exceeds slightlythat in its antibinding region (the F^- ion is polarized towardsthe Li⁺ ion) and the charge distribution of the Li⁺ion is polarized away from the fluorine. A consideration of the forcesexerted on the nuclei in this case will demonstrate that these polarizationsare a necessary requirement for the attainment of electrostatic equilibriumin the face of a complete charge transfer from lithium to fluorine.

Consider first the forces acting on the nuclei inthe simple model of the ionic bond, the model which ignores the polarizationsof the ions and pictures the molecule as two closed-shell spherical ionsin mutual contact. If the charge density of the Li⁺ ionis spherical it will exert no net force on the lithium nucleus. The F^-ion possesses ten electrons and, since the charge density on the F^-ion is also considered to be spherical, the attractive force this densityexerts on the Li nucleus is the same as that obtained for all ten electronsconcentrated at the fluorine nucleus. Nine of these electrons will screenthe nine positive nuclear charges on fluorine from the lithium nucleus.The net force on the lithium nucleus is, therefore, one of attraction becauseof the one excess negative charge on F.

For the molecule to be stable, the final force on the lithiumnucleus must be zero. This can be achieved by a distortion of the sphericalcharge distribution of the Li⁺ ion. If a small amount of the1s charge density on lithium is removed from the region adjacentto fluorine and placed on the side of the lithium nucleus away from thefluorine, i.e., the charge distribution is polarized away from the fluorine,it will exert a force on the lithium nucleus in a direction away from thefluorine. Thus the force on the lithium nucleus in an ionic bond can bezero only if the charge density of the Li⁺ ion is polarizedaway from the negative end of the molecule.

A similar consideration of the forces exerted on the fluorinenucleus demonstrates that the F^- ion density must also be polarized.The fluorine nucleus experiences a net force of repulsion because of thepresence of the lithium ion. The two negative charges centred on lithiumscreen only two of its three nuclear charges. Therefore, the charge densityof the F^- ion must be polarized towards the lithiumin order to exert an attractive force on the fluorine nucleus which willbalance the repulsive force arising from the presence of the Li⁺ion. Thus both nuclei in the LiF molecule are bound by the increase incharge density localized in the region of the fluorine.

The charge distribution of a molecule with an ionic bondwill necessarily be characterized not only by the transfer of electroniccharge from one atom to another, but also by a polarization of each ofthe resulting ions in a direction counter to the transfer of charge, asindicated in the bond density map for LiF.

The bond density maps for N₂and LiF are shown side by side to provide a contrast of the changes inthe atomic charge densities responsible for the two extremes of chemicalbinding. In a covalent bond the increase in charge density whichbinds both nuclei is shared between them. In an ionic bond both nucleiare bound by the forces exerted by the charge density localized on a singlenucleus. It must be stressed that there is no fundamental differencebetween the forces responsible for a covalent or an ionic bond. They areelectrostatic in each case.