Question

10
Explain the concept of potential-energy curves for Bonding and Antibonding
molecular orbitals with examples.​

Answer 1

Explanation:

The two molecular orbitals of the H+H+ ion were created via the linear combinations of atomic orbitals (LCAOs) approximation were created from the sum and the difference of two atomic orbitals. Within this approximation, the jth molecular orbital can be expressed as a linear combination of many atomic orbitals {ϕiϕi}:

|ψJ⟩=∑iNcJ,i|ϕi⟩(9.5.1)(9.5.1)|ψJ⟩=∑iNcJ,i|ϕi⟩

A molecule will have as many molecular orbitals as there are atomic orbitals used in the basis set (NN in Equation 9.5.19.5.1). Adding two atomic orbitals corresponds to constructive interference between two waves, thus reinforcing their intensity; the internuclear electron probability density is increased. The molecular orbital corresponding to the sum of the two H 1s orbitals is called a σ1s combination (parts (a) and (b) of Figure 9.5.19.5.1).

Figure 9.5.19.5.1: Molecular Orbitals for the H2H2 Molecule. (a) This diagram shows the formation of a bonding σ1sσ1s molecular orbital for H2H2 as the sum of the wavefunctions (ΨΨ) of two H 1s atomic orbitals. (b) This plot of the square of the wavefunction (Ψ2Ψ2) for the bonding σ1s molecular orbital illustrates the increased electron probability density between the two hydrogen nuclei. (Recall that the probability density is proportional to the square of the wavefunction.) (c) This diagram shows the formation of an antibonding σ∗1sσ1s∗ molecular orbital for H2H2 as the difference of the atomic orbital wavefunctions (ΨΨ) of two H 1s atomic orbitals. (d) This plot of the square of the wavefunction (Ψ2) for the σ∗1sσ1s∗ antibonding molecular orbital illustrates the node corresponding to zero electron probability density between the two hydrogen nuclei. (CC BY-SA-NC; anonymous by request).

In the sigma (σσ) orbital, the electron density along the internuclear axis and between the nuclei has cylindrical symmetry; that is, all cross-sections perpendicular to the internuclear axis are circles. The subscript 1s denotes the atomic orbitals from which the molecular orbital was derived.

|σ1s⟩=12(1+S)−−−−−−−√(|1sA⟩+|1

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