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Molecular orbital theory informs us that electrons in a molecule are not confined to individual atoms but are distributed over the entire molecule in regions known as molecular orbitals. This theory helps us understand molecular structure and bonding by considering the wave-like properties of electrons. In the case of the hydrogen molecule ion, H2-, molecular orbitals are formed by the mathematical combination of the atomic orbitals of the two hydrogen atoms.

When two hydrogen atoms approach each other, their atomic orbitals overlap to form a lower-energy bonding molecular orbital (sigma) and a higher-energy antibonding molecular orbital (sigma*). The bonding orbital, which is symmetrical along the axis connecting the two nuclei, can host two electrons with opposite spins. The antibonding orbital, on the other hand, has a node between the nuclei and is less stable. Electrons in the antibonding orbitals work against bond formation, hence the name 'antibonding'.

The electron configuration of a molecule reveals how electrons are distributed among the available molecular orbitals. In our H2- ion, the electron configuration is represented as \(\sigma^2\sigma^{*1}\), where the sigma orbital is filled with two electrons and the sigma* orbital contains one electron. The superscripts designate the number of electrons in each orbital.

Understanding electron configuration is crucial because it determines the properties and behavior of the molecule. Counting the electrons in bonding and antibonding orbitals will not only allow us to predict molecular stability but also its magnetic properties and how it might interact with light or other molecules.

The bond order of a molecule gives us a simple measurement of its bond strength and stability. It is calculated by subtracting the number of electrons in antibonding orbitals from the number of electrons in bonding orbitals and then dividing by two. In mathematical terms for H2-, the bond order is given by the formula: \[Bond \, Order = \frac{1}{2}(2 - 1) = \frac{1}{2}\]. A larger bond order typically indicates a stronger and more stable bond. A bond order of zero signifies that a molecule will have no stability and therefore not likely exist under normal conditions. The fractional bond order of 0.5 for H2- suggests that this ion possesses a relatively weak and less stable bond compared to H2 with a bond order of 1.

The concept of excited-state stability is crucial when discussing how molecular systems interact with energy, for instance, light absorption. An excited-state occurs when electrons absorb energy and transition to a higher-energy orbital, typically to an antibonding orbital. For H2-, when light is absorbed, one electron from the bonding orbital (sigma) is excited to the antibonding orbital (sigma*), changing the electron configuration to \(\sigma^1\sigma^{*2}\).

This electron rearrangement leads to an excited-state with a bond order of zero \[Bond \, Order = \frac{1}{2}(1 - 2) = 0\], indicating that the excited-state H2- ion has no net bonding interactions between the two hydrogen nuclei, and therefore, is not stable. It highlights that provided enough energy, even a weakly bonding system can be broken apart. This instability has crucial implications in fields such as photochemistry and in understanding chemical reactions under the influence of light.