== Valence bond theory == 

 Unit 1 
 Chemical Bonding 
 Module: 1.1 
 Valence Bond Theory 
 VBT was due to Heitler and London (1927). This was the first attempt to 
 explain H2 – molecule in terms of quantum mechanics. The theory was 
 improved by Pauling and Slater. 
 The valence bond theory (VB Theory) of bonding was the first quantum 
 mechanical theory of bonding to be developed. It is a way of expressing 
 Lewis concepts in terms of wave functions. In the VB Theory, the wave 
 function of an electron pair is formed by the interaction of the wave 
 functions for the separated parts or fragments of the molecule i.e. two e’s. 
 The potential energy curve shows the variation of the molecular energy 
 with internuclear distance. 
 In case of a H2 molecule, we consider the possibility of interchange of 
 electrons between the two H – atoms. Let us call the two hydrogen atoms 
 in a H2 molecule as HA and HB for convenience. When these two hydrogen 
 atoms are at infinite distance, no appreciable interactions (altercations or 
 repulsions) take place. Then there are two possible equivalent structure of 
 H2 molecule. They are written as structures (I) and (II). 
 This indicates that in structure (I), we have the nucleus HA with electron 1 
 and nucleus HB with electron 2. In structure (II) the electrons have been 
 exchanged. The wave functions for the two structures are written as 
                                                                    ψ 
 Respectively, then the true wave function, ψ, for the H2 – molecule is given 
 by 
 Where C1 and C2 are ψ known as the mixing coefficients. For hydrogen C1 
                                      1. Then two possible values of ≁ , the 
 =   C2 and C1 = 1: Hence C2 = 
 wave function of H2 molecule can be written as 
 When the two H atoms are close, it is not possible to know whether it is 
 electron 1 that is on HA or electron 2. An equally valid description is 
 therefore given by ≁II. 
 When two outcomes are equally probable, quantum mechanics describes 
 the true state of the system as superposition of the wave functions of the 
 two possibilities. Then a linear combination of the two possibilities is better. 
 This is what we represented in the combined wave functions. This function 
 is the VB wave function for a H – H bond. The formation of the bond can be 
 pictured as being due to the high probability of the two electrons to be 
 present between the two nuclei. Then the two atoms are bonded together. 
 It is easier to understand by saying that the two wave functions of the two H 
 – atoms (i.e. ≁I and ≁II ) interfere constructively and as a result. There is 
 an entrancement in the amplitude of the wave function in the region 
 between the two nuclei. Then the wave function describes only contributes 
 for bond formation. The electron distribution described by the wave function 
                – bond. We know that     – bond has a cylindrical symmetry 
 is called a 
 around the internuclear axis. The electrons in it have zero angular 
 momentum about the axis. 
 Potential energy curve: 
 The variation of the energy of a molecule (in the above example H2 
 molecule) with the internuclear distance, is calculated by changing the 
 internuclear separation and then evaluating the energy at that condition. 
 The figure given below shows the variation of energy with the 
 intermolecular separation. 
 From the figure it is noted that as 
 the two atoms are brought within 
 bonding distance, the potential 
 energy of the H – atoms in the 
 molecule falls below that of the two 
 separated atoms. And each 
 electron is free to migrate to the 
 other atom. The value of      s 
 remains unchanged by the 
 exchange of electronic combination. At the same time the columbic 
 repulsions between the two positively charged nuclei increase. This 
 increase in repulsions increases the potential energy and it becomes large 
 as the internuclear distance, R , becomes small. The two electrons then 
 have parallel spins, the energy continues to rise. No bond is formed. The 
 depth of the minimum of the curve is denoted by Do. The deeper the 
 minimum, the more strongly the atoms are bonded together. Also the 
 steepness of the potential energy well shows the rapid change in the 
 energy of the molecule as the bond is stretched or compressed. The 
 steepness of the curve is an indication of rigidity stiffness of the bond. This 
 reflects in the vibration frequency o the molecule (we shall refer to it in the 
 spectra of the molecules). 
 Curve ‘a’ is the result of the destructive interference of the wave functions. 
 This represents an anti-symmetric co