Using the molecular orbital model, write electron configurations for the following diatomic species and calculate the bond orders. Which ones are paramagnetic? a. \(\mathrm{Li}_{2}\) b. \(C_{2}\) c. \(S_{2}\)

Understanding electron configurations in molecules is often a challenging point for students, especially when approaching it through the molecular orbital (MO) model. However, it is a central concept in grasping how atoms bond in diatomic species. To simplify this, imagine that atoms combine their orbitals like two people would merge their individual belongings into a single household. In an MO diagram, lower energy 'rooms' or orbitals are filled first according to the Aufbau principle. Electrons also have a 'no sharing' rule for their personal spaces, as per the Pauli exclusion principle, which asserts that each orbital can hold a maximum of two electrons with opposite spins.
Hund's rule suggests that electrons would rather have their own space (orbital) before sharing, much like humans preferring their own rooms before having a roommate. When atoms form a molecule, they follow these principles to 'decorate' their communal molecular home. For example, the diatomic molecule \(\mathrm{Li}_{2}\) combines the electrons from each lithium atom, resulting in a shared electron configuration of \(\sigma_{1s}^2 \sigma_{1s*}^2 \sigma_{2s}^2\). This configuration illustrates the bonding interactions within the molecule—some orbitals encourage bonding (\sigma_{1s}, \sigma_{2s}), while others (\(\sigma_{1s*}\)) discourage it.
By visualizing the MO diagram and practicing the filling of orbitals according to these rules, you will not only be able to determine the electron configurations but also better understand the stability and properties of the molecule.

The bond order is essentially the strength of the bonding relationship, just like a measure of the strength of a friendship. A higher bond order typically means a stronger, more stable bond. It is calculated using a simple formula that takes into account the occupants of the molecular 'house':
Bond order = (number of electrons in bonding orbitals - number of electrons in antibonding orbitals) / 2
In this arithmetic, think of bonding electrons as positive interactions that create a strong friendship, while antibonding electrons are negative interactions that oppose that friendship. For example, if we have \(\mathrm{Li}_{2}\), with four electrons contributing positively and two negatively, the bond order is calculated as \(\frac{4 - 2}{2} = 1\), indicative of a single bond.
Understanding and calculating bond orders not only helps predict the strength of the bonds but also provides insight into the reactivity and potential chemical behavior of the species.

Paramagnetic species are like social butterflies—they have at least one unpaired electron that makes them magnetic and responsive to external magnetic fields. This can be tricky for students to identify, but it's all about finding that one electron without a 'dance partner.' In our MO diagram exercise, a species with unpaired electrons is paramagnetic because these lone electrons create a magnetic field.
To determine if a diatomic molecule is paramagnetic, you must look for unpaired electrons in the electron configuration. Recall our friend \(S_{2}\) from the exercise; it has one unpaired electron in each of the antibonding \(\pi_{2p_x*}\) and \(\pi_{2p_y*}\) orbitals, which makes it eager to interact with magnetic fields. In contrast, the all-paired-up electrons in \(\mathrm{Li}_{2}\) and \(C_{2}\) tell us they are diamagnetic and, like wallflowers, largely non-responsive to magnets. By identifying paramagnetic species, scientists can further understand the physical properties and potential applications (such as in magnetic resonance imaging) of the molecule.