Diatomic Molecules with 1s Atomic Orbitals
If two hydrogen atoms are far enough apart (> 10 Angstroms) the electron clouds are not influenced by the other atom.
If they approach each other the electrons are drawn toward the nucleus of the other atom.
An optimum distance is reached at which there is a merging or overlapping of the 1s orbitals. There is a concentration of electron probability density between the two nuclei. They will be bonded together by this sharing of electrons. A shorter distance between the nuclei would result in an increase in repulsive force between the two positive nuclei.
The bonding orbital formed by the overlap of the two 1s orbitals lowers the energy of the system. An approximation of the electron density is achieved by combining the two 1s wave functions of hydrogen atoms a and b and squaring the sum (1sa + 1sb)2.
The resultant orbital is called a molecular orbital. In this case it is a sigma (s) orbital because it is symmetrical along the axis passing through the two nuclei. It is a bonding orbital as well. Thus it is called a sigma bonding molecular orbital (sb).
Below is a graphic representation of the combining of the two atomic orbitals to form the molecular orbital.
The sigma bonding orbital can contain two electrons. The H2 molecule has two electrons, one from each hydrogen atom so the bonding orbital is filled. In the case of a He2+ ion there are three electrons. The third electron occupies the sigma antibonding orbital which is described as the difference between the atomic orbitals (1sa - 1sb)2 . This orbital is higher in energy than the atomic orbitals. The electron density is zero in a plane perpendicular to the line connecting the two nuclei that lies midway between the two nuclei. This is called a nodal plane.
Electrons in this orbital add nothing to the bonding of the molecule. Thus the bond strength in He2+ should be far less than in H2. Addition of a forth electron (as would occur with two He nuclei) would result in two electrons in the antibonding orbital. There would be an increase in the positive nuclear charges on going from H to He thus increasing the repulsive force between the nuclei and little increase in the electron density between the two nuclei. These would cancel the bonding effect of the two electrons in the bonding orbital, thus you would expect that there is no stable He2 molecule.
The sigma antibonding molecular orbital is less stable than the atomic orbitals. The sigma bonding orbital is more stable than the atomic orbitals. The sigma anti bonding orbital is represented by the symbol sigma star (s*). The energy levels of the orbitals are shown in the diagram below.
The atomic orbitals of two atoms are shown at the sides. In the center are the molecular orbitals formed by the overlap of these atomic orbitals when the atoms are at the internuclear distance of minimum energy. When electrons are shown they are placed in the circles. Just as with atomic orbitals, molecular orbitals can only contain two electrons and these must be of opposite spin. You begin by putting electrons into the lowest energy levels. The number of electrons are the same as the total number in the atomic orbitals of the atoms forming the molecule.
The energy level diagram above can be used to construct the electronic structure of H2, He2+, H2+ and He2. Of these, H2 is the most stable with two bonding electrons and no antibonding electrons. The bond energy is 103 kcal mole-1. The bond length will be shorter for a stronger bond. The H2 bond length is 0.74 Angstroms.
An H2+ ion would have one electron in the sigma bonding molecular orbital. The bond energy is 61 kcal mole-1 and the bond length is 1.06 Angstroms. He2+ is similar to H2+ with a bond energy of 60 kcal mole-1 and a bond length of 1.08 Angstroms. H2+ has one bonding electron and no antibonding electrons. He2+ has two bonding electrons and one antibonding electron. Both have a net of one bonding electron. He2 has two bonding and two antibonding electrons with a net of zero bonding electrons. Thus there is no stable He molecule.