The nitrosyl ion, \(\mathrm{NO}^{+}\), is isoelectronic with \(\mathrm{N}_{2}\) and has two fewer electrons than \(\mathrm{O}_{2}\). The ion is stable and can be purchased as its hexafloorophosphate \(\left(\mathrm{PF}_{6}{ }^{-}\right)\)or tetrafluoroborate \(\left(\mathrm{BF}_{4}{ }^{-}\right.\)) salt. (a) Draw its molecular orbital diagram and compare it with those of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\). (b) \(\mathrm{NO}^{+}\)is diamagnetic. Can we tell which orbital, the \(\sigma_{2_{p}}\) or the \(\pi_{2_{p}}\), is higher in energy from this information?

The molecular orbital diagram is a powerful tool in the realm of chemistry that helps us to visualize and understand the bonding between atoms in a molecule. It represents how atomic orbitals combine to form molecular orbitals, which are the 'states' in which electrons exist within a molecule.

In constructing a molecular orbital diagram, electrons are distributed among the orbitals in order of increasing energy, abiding by the principles of the Aufbau principle, Hund's rule, and Pauli's exclusion principle. For diatomic molecules like NO+, N2, and O2, it is critical to note the change in the order of filling of the \(\pi\) and \(\sigma \ _{2p}\) orbitals. This switch occurs after 14 electrons, which can be seen when comparing the energy levels of N2 (less than or equal to 14 electrons) and O2 (more than 14 electrons).

If we take the nitrosyl ion (NO+), with 14 electrons, as an example, we can understand how this ion shares the same electronic structure as N2, based on their isoelectronic nature. The molecular orbital diagram for NO+, therefore, mirrors that of N2 with orbitals filled symmetrically and electrons paired, this symmetry translates into a diamagnetic property.

Diamagnetism is a magnetic phenomenon where a substance does not retain a net magnetic moment in the absence of an external magnetic field. This happens because all of the electrons are paired, so their individual magnetic moments—caused by their spin—cancel each other out.

Diamagnetic substances, such as the nitrosyl ion (NO+), are weakly repelled by a magnetic field. Analyzing the magnetic properties of a molecule can often tell us about the electronic configuration. For example, since NO+ is isoelectronic with N2, which has its electrons all paired and in lower energy orbitals, we can conclude that NO+ must also be diamagnetic. This conclusion is consistent with our molecular orbital diagram constructed previously, which shows all electrons in NO+ are paired. However, diamagnetic properties do not provide information on which specific orbital is higher in energy — for that, we must refer back to the molecular orbital theory and the established rules for electron filling.

Isoelectronic species are atoms, ions, or molecules that have the same total number of electrons. They can provide insightful comparisons when it comes to their chemical and physical properties because they often share similarities in their molecular structures and bonding characteristics.

The understanding of isoelectronic species is essential when comparing the molecular orbital diagrams of NO+, N2, and O2. For instance, NO+ and N2 each have 14 electrons making them isoelectronic. Conversely, with 16 electrons, O2 is not isoelectronic with the others but provides a helpful comparison as it illustrates the shift in energy of molecular orbitals with a different number of electrons. This lends insight into how differing electron counts can influence the order of filling of the \(\pi\) and \(\sigma \ _{2p}\) orbitals. Understanding these principles can lead to predictions about bonding, stability, and chemical reactivity of molecular species.