LCAO Method

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According to LCAO method, the orbitals are formed by the linear combination (addition or subtraction) of atomic orbitals of the atoms, which form the molecule. This theory is applicable to hydrogen molecule as follows. Consider that hydrogen molecule consists of two atoms A and B. Each of these atoms has 1s-orbital of lowest energy. The atomic orbitals of these atoms may be represented by the wave functions y_A and y_B for hydrogen atoms A and B respectively. Now, when these atomic orbitals are brought closer, they combine to form molecular orbitals. According to LCAO method, the linear combination of atomic orbitals can take place by addition and by subtraction of wave functions of atomic orbitals. These two types of combinations give rise to two molecular orbitals as described below:

(i) Molecular orbital obtained by addition of wave functions of atoms may be represented as y(MO) = y_A + y_B. This molecular orbital is called bonding molecular orbital.

(ii) Molecular orbital obtained by subtraction of wave functions of atoms may be represented as y(MO) = y_A - y_B. The molecular orbital is called antibonding molecular orbital.

The physical picture of bonding and antibonding molecular orbitals can be obtained by considering the atomic orbitals. To illustrate this, we may take the combination of 1s-orbital of one hydrogen atom with 1s-orbital of second hydrogen atom to form two molecular orbitals in hydrogen molecule. As discussed above, there are two ways of combining atomic orbitals. The molecular orbital formed by the addition of overlapping of two1s-orbitals is shown in below figure.

fig 1.8 - Formation of bonding molecular orbital

It is clear from the figure that the region between the two nuclei where the two 1s-atomic orbitals overlap has high electron density. Such a molecular orbital is called bonding molecular orbital. It is designated as s1s (called sigma 1s) orbital. The sigma (s) signifies that the orbital is symmetrical about the molecular axis and the script '1s' indicates that it is formed by the combination of 1s-atomic orbitals.

The molecular orbital formed by the subtraction of overlapping of two 1s-orbitals is shown in the figure.

fig 1.9 - Formation of anti-bonding molecular orbital

It is clear from the figure that the electron density in between the two nuclei is practically zero and is concentrated in regions away from each nucleus. In this case, the electron probability densities of two atomic orbitals get cancelled in the centre (by subtraction) so that there is no probability of finding the electron in the region of overlap or between the nuclei. This situation does not favor the bond formation. Such an orbital is called antibonding molecular orbital. It is designated as s*1s (called sigma star 1s). The asterisk '*' is used to represent antibonding molecular orbital.

Thus, the bonding molecular orbital is designated as s 1s (called sigma bonding) and antibonding molecular orbital is designated as s*1s (called sigma antibonding).