20.7: Valence Bond Theory

Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable energy. These orbitals accept electron pairs from filled ligand orbitals (Lewis bases) to form coordinate covalent metal-ligand bonds. The type of hybridization and the number of hybrid orbitals determine the geometry of the complex.

In a tetrahedral complex, three vacant p orbitals and one vacant s orbital on the metal hybridize to form four sp³ hybrid orbitals, which overlap with the filled ligand orbitals to form the covalent coordinate bond. Similarly, six hybrid orbitals are created for the octahedral complexes by mixing the vacant atomic orbitals on the central metal ion (d²sp³ or sp³d² hybridization). In the case of linear complexes, the one s and one p orbitals overlap, leading to the formation of two sp hybrid orbitals.

Inner and Outer Orbital Complexes

The strength of the approaching ligands influence the hybridization of the atomic orbitals on the central metal ion. Consider the example of an octahedral complex such as [Co(NH₃)₆]³⁺. The Co³⁺ ion contains six electrons in the 3d orbitals and has vacant 4s and 4p orbitals. The incoming NH₃ ligands, which are strong field ligands, force the unpaired 3d electrons to rearrange and pair up with the other 3d electrons. This creates two vacant 3d orbitals, which combine with one 4s and three 4p orbitals to form six equivalent d²sp³ hybrid orbitals. The six hybrid orbitals overlap with the filled atomic orbitals of the ammonia ligands to form the octahedral complex. Since the inner d (3d) orbitals on the metal participate in hybridization, [Co(NH₃)₆]³⁺ is an inner orbital complex. Due to the absence of unpaired electrons, the complex is diamagnetic, or called a low spin complex.

In another octahedral complex like [Co(F)₆]³⁺, since the fluoride ligand is a weak field ligand, the 3d⁶ electrons of the metal do not rearrange. To provide vacant orbitals for hybridization, two of the outermost empty 4d orbitals combine with the one 4s and three 4p orbitals to form six vacant hybrid orbitals. Since the outermost d orbitals are used, the hybridization is referred to as sp³d² hybridization, and the complex is called an outer orbital complex. The presence of unpaired electrons makes the complex paramagnetic, and hence these complexes are also known as high spin complexes.

High-spin or outer orbital complexes are more labile and less stable (due to the higher energies of sp³d² orbitals) compared to the low-spin or inner orbital complexes.

Coordination complexes exhibit different geometries like octahedral, tetrahedral, and square planar, depending on the metal orbitals participating in the coordinate covalent bonds.

Valence bond theory, or VBT, explains this based on the metal’s hybridization of s, p, and d orbitals. Hybridization provides vacant orbitals of equivalent energies that can coordinate to the filled ligand orbitals.

Consider an octahedral complex, hexafluorocobaltate(III). The Co³⁺ ion has  partially filled 3d⁶ orbitals and vacant 4s, 4p, and 4d orbitals. 

To form the complex, the metal's six empty orbitals, 4s, 4p, and two 4d, are hybridized to six sp³d² orbitals, which are pointing towards the corners of an octahedron. The hybrid orbitals accept lone pairs from the six fluoride groups to form the paramagnetic complex.

In the hexamminecobalt(III), the amino groups cause the 3d electrons of cobalt to rearrange, creating two vacant 3d orbitals. 

These combine with the 4s and 4p orbitals to generate six d²sp³ hybrid orbitals, which then coordinately bind to the six ammonia groups to form the diamagnetic complex. 

Now, consider a tetrahedral complex — tetrachloronickelate.  Nⁱ²+ ion has a 3d⁸ configuration. The empty 4s and 4p orbitals hybridize to give four sp³ orbitals that point towards the corners of a tetrahedron. 

Here, four pairs of electrons, one from each chloride group, occupy the hybrid orbitals to form the paramagnetic complex. 

Lastly, examine a square planar complex like tetrachloroplatinate. The Pt²⁺ ion has a d⁸ configuration.

The chloride groups force the metal’s 3d electrons to rearrange, creating a vacant orbital. The vacant orbital combines with the 4s and two 4p orbitals to give four dsp² hybrid orbitals directed towards the corners of a square.

Upon accepting the electron pairs from the chloride ligands, the diamagnetic complex is formed. 

Although the coordination complexes vary in their colors and magnetic behavior, VBT does not explain their electronic spectra and the variation in their magnetic behavior with temperature.