A friend tells you that the 2s orbital for fluorine starts off at a much lower energy than the 2s orbital for lithium, so the resulting \(\sigma_{2 s}\) molecular orbital in \(\mathrm{F}_{2}\) is more stable than in \(\mathrm{Li}_{2}\). Do you agree?

Understanding atomic orbital energies is crucial for students delving into the field of chemistry. Atoms consist of a nucleus surrounded by electrons that are arranged in different energy levels or 'shells'. Each shell is further divided into subshells comprised of atomic orbitals where electrons are likely to be found. The energy of an atomic orbital is a fundamental concept that depends on the orbital’s distance from the nucleus and the charge of the nucleus itself.

The lower the energy of an atomic orbital, the more tightly an electron within that orbital is bound to the nucleus, making it less reactive. For instance, in comparing the atomic orbital energies between fluorine and lithium, we note a significant difference. Fluorine's 2s orbital has a much lower energy than lithium's 2s orbital. This variation can be attributed to an increase in both the atomic number and the effective nuclear charge—two important factors that determine the energy levels of atomic orbitals.

When teaching this concept, it’s helpful to visualize the atomic orbitals as concentric circles around the nucleus with energy levels increasing as you move away from the center. The higher the effective nuclear charge (the net positive charge experienced by electrons), the more strongly electrons are pulled towards the nucleus, resulting in lower energy orbitals.

The concept of effective nuclear charge (ENC) is pivotal to comprehending why atomic orbital energies differ across elements. Essentially, ENC is the net positive charge experienced by an electron in a multi-electron atom. The full positive charge of the nucleus is mitigated by the negative charges of the other electrons, especially those between the nucleus and the electron under consideration—a phenomenon known as electron shielding.

ENC can be estimated using Slater's rules, which take into account the shielding effects of electrons in different shells. This simplified model aids in predicting how tightly an electron is held by the nucleus.

The core principle to convey here is that as the ENC increases, electrons are drawn closer to the nucleus, leading to a decrease in the energy of the orbital in which they reside. For example, fluorine has a higher ENC than lithium, since it has more protons in its nucleus, and its electrons are more effectively shielded, resulting in its 2s electrons being held more securely and a consequent decrease in the energy level of the 2s orbital.

Delving into the nature of sigma (\f\(\f\)sigma\f\() molecular orbitals requires an understanding of molecular orbital theory, which describes how atomic orbitals combine to form molecular orbitals when atoms bond together. Sigma molecular orbitals are a specific type of bonding orbital that form along the axis connecting two atomic nuclei.

A noteworthy point in teaching this subject is that when two atomic orbitals overlap to create a \f\)\f\(sigma\f\) molecular orbital, the resultant orbital's stability is directly tied to the original atomic orbitals' energies. More stable (lower energy) atomic orbitals lead to more stable \f\(\f\)sigma\f\( molecular orbitals. The overlapping results in a region of increased electron density between the nuclei, hence strengthening the bond.

In application, when the 2s orbitals of two fluorine atoms combine, they create a \f\)\f\(sigma_{2s}\f\) molecular orbital that is highly stable due to the low energy starting point of the individual 2s orbitals. This stability is contrasted with the \f\(\f\)sigma_{2s}\f\( orbital in a lithium molecule (\f\)\f\(Li_2\f\)), which is derived from higher energy 2s atomic orbitals. Depicting diagrammatic representations aids students in visualizing the overlaps and reinforces the link between atomic orbital energies and molecular orbital stability.