Consider the following molecular orbitals formed from the combination of two hydrogen 1s orbitals: a. Which is the bonding molecular orbital and which is the antibonding molecular orbital? Explain how you can tell by looking at their shapes. b. Which of the two molecular orbitals is lower in energy? Why is this true?

When two atomic orbitals combine, they form molecular orbitals. The combination of two hydrogen 1s orbitals produces two molecular orbitals: a sigma (σ) bonding molecular orbital and a sigma (σ*) antibonding molecular orbital. The bonding molecular orbital (σ) is formed when the electron wave functions of the two 1s orbitals have the same phase, which means they constructively interfere with each other, leading to increased electron density between the two nuclei. The increased electron density creates a stabilizing effect on the molecule. The shape of this orbital looks like a single elongated cloud of electrons connecting the two hydrogen nuclei. The antibonding molecular orbital (σ*) is formed when the electron wave functions of the two 1s orbitals have opposite phases, which means they destructively interfere with each other, leading to decreased electron density between the two nuclei. The decreased electron density creates a destabilizing effect on the molecule. The shape of this orbital looks like two separate clouds of electrons, one around each hydrogen nucleus and a node (a region with zero electron density) between them.

The bonding molecular orbital (σ) has lower energy than the antibonding molecular orbital (σ*). This is because the bonding molecular orbital has increased electron density between the two nuclei, which leads to a stabilizing effect on the molecule. This stabilizing effect results in the electrons in the bonding molecular orbital being attracted to both nuclei, thus lowering the energy. In contrast, the antibonding molecular orbital has decreased electron density between the two nuclei, creating a destabilizing effect on the molecule. This destabilizing effect means that the electrons in the antibonding molecular orbital are less strongly attracted to both nuclei and, as a result, have a higher energy. In summary: a. The bonding molecular orbital (σ) is the one with increased electron density between the two hydrogen nuclei, and the antibonding molecular orbital (σ*) is the one with decreased electron density and a node between the nuclei. b. The bonding molecular orbital (σ) is lower in energy due to its stabilizing effect on the molecule, while the antibonding molecular orbital (σ*) is higher in energy because of its destabilizing effect.