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 Respectively then the true wave function for the H2 molecule is given by Where C1 and C2 are 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