COVALENT BOND

The covalent bond 

Now let us consider the formation of a molecule. For convenience, we shall picture this as happening by the coming together of the individual atoms, although most molecules are not actually made this way. We make physical models of molecules out of wooden or plastic balls that represent the various atoms; the location of holes or snap fasteners tells us how to put them together. In the same way, we shall make mental models of molecules out of mental atoms; the location of atomic orbitals-some of them imaginary-will tell us how to put these together. 

For a covalent bond to form, two atoms must be located so that an orbital of one overlaps an orbital of the other; each orbital must contain a single electron. When this happens, the two atomic orbitals merge to form a single bond orbital which is occupied by both electrons. The two electrons that occupy a bond orbital must have opposite spins, that is, must be paired. Each electron has available to it the entire bond orbital and thus may be considered to "belong to" both atomic nuclei. 

This arrangement of electrons and nuclei contains fewer energy-that is, is more stable than the arrangement in the isolated atoms; as a result, the formation of a bond is accompanied by the evolution of energy. The amount of energy (per mole) that is given off when a bond is formed (or the amount that must be put in to break the bond) is called the bond dissociation energy. For a given pair of atoms, the greater the overlap of atomic orbitals, the stronger the bond. 

What gives the covalent bond its strength? It is the increase in electrostatic attraction. In the isolated atoms, each electron is attracted by and attracts one positive nucleus; in the molecule, each electron is attracted by two positive nuclei. 

It is the concept of"overlap" that provides the mental bridge between atomic orbitals and bond orbitals. Overlap of atomic orbitals means that the bond orbital occupies much of the same region in space that was occupied by both atomic orbitals. Consequently, an electron from one atom can, to a considerable extent, remain in its original, favorable location for its nucleus, and at the same time occupy a similarly favorable location concerning the second nucleus; the same holds, of course, for the other electron.

The principle of maximum overlap, first stated in 1931 by Linus Pauling (at California Institute of Technology), has been ranked only slightly below the exclusion principle in importance to understanding molecular structure. 

As our first example, let us consider the formation of the hydrogen molecule, H2, from two hydrogen atoms. Each hydrogen atom has one electron, which occupies the 1s orbital. As we have seen, this 1s orbital is a sphere with its center at the atomic nucleus. For a bond to form, the two nuclei must be brought close enough to overlap the atomic orbitals. The system is most stable for hydrogen when the distance between the nuclei is 0.74 V\A; this distance is called the bond length. At this distance, the stabilizing effect of overlap is exactly balanced by repulsion between the similarly charged nuclei. The resulting hydrogen molecule contains 104 kcal/mol less energy than the hydrogen atoms from which it was made. We say that the hydrogen-hydrogen bond has a length of 0.74 Ả and a strength of 104 kcal. 

This bond orbital has roughly the shape we would expect from the merging of two s orbitals. it is sausage-shaped, with its long axis lying along the line joining the nuclei. It is cylindrically symmetrical about this long axis; that is, a slice of the sausage is circular. Bond orbitals having this shape are called (sigma bond symbol) orbitals (sigma orbitals) and the bonds are called (sigma bond symbol) bonds. We may visualize the hydrogen molecule as two nuclei embedded in a single sausage-shaped electron cloud. This cloud is densest in the region between the two nuclei, where the negative a charge is attracted most strongly by the two positive charges. 

The size of the hydrogen molecule-as measured, say, by the volume inside the 95% probability surface-is considerably smaller than that of a single hydrogen atom. Although surprising at first, this shrinking of the electron cloud is actually what would be expected. It is the powerful attraction of the electrons by two nuclei that gives the molecule greater stability than the isolated hydrogen atoms; this must mean that the electrons are held tighter, closer, than in the atoms. 

Next, let us consider the formation of the fluorine molecule, F2, from two fluorine atoms. As we can see from our table of electronic configurations, a fluorine atom has two electrons in the 1s orbital, two electrons in the 2s orbital, and two electrons in each of two 2p orbitals. In the third 2p orbital there is a single electron that is unpaired and available for bond formation. Overlap of this p orbital with a similar p orbital of another fluorine atom permits electrons to pair and the bond to form. The electronic charge is concentrated between the two nuclei so that the back lobe of each of the overlapping orbitals shrinks to a comparatively small size. Although formed by the overlap of atomic orbitals of a different kind, the fluorine-fluorine bond has the same general shape as the hydrogen-hydrogen bond, being cylindrically symmetrical about a line joining the nuclei; it, too, is given the designation (sigma symbol) bond. The fluorine-fluorine bond has a length of 1.42 A and a strength of about 38 kcal. 

As the examples show, covalent bond results from the overlap of two atomic orbitals to form a bond orbital occupied by a pair of electrons. Each kind of covalent bond has a characteristic length and strength.