2.3 Electronic configurations and energy levels

Electronic Configuration Principles

Electronic configurations describe how electrons occupy orbitals in atoms and molecules. In photochemistry, these configurations matter because they determine which electronic transitions are possible when a molecule absorbs light, and that directly controls photochemical reactivity.

Electronic configurations of atoms and ions

Electrons fill orbitals according to three foundational rules:

• Aufbau principle: Electrons occupy the lowest-energy orbitals first. The filling order is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p. The reason 4s fills before 3d is that interelectron repulsion and shielding effects make 4s slightly lower in energy for neutral atoms of that row.
• Hund's rule: When filling orbitals of equal energy (degenerate orbitals), electrons occupy them singly with parallel spins before any pairing occurs. This maximizes total spin angular momentum and minimizes electron-electron repulsion.
• Pauli exclusion principle: No two electrons in an atom can share the same set of four quantum numbers ($n, l, m_l, m_s$). In practice, this means each orbital holds at most two electrons, and they must have opposite spins.

Notation shortcuts: Orbital diagrams use boxes with arrows (↑↓) to show individual electrons. Shorthand notation uses the noble gas core plus valence electrons. For example, sodium is written as [Ne]3s¹ rather than writing out 1s²2s²2p⁶3s¹.

Ground state vs excited state configurations

The ground state is the lowest-energy arrangement of electrons, following all three rules above. An excited state results when one or more electrons absorb energy and move to a higher-energy orbital, violating the Aufbau filling order.

Take beryllium as an example. Its ground state configuration is 1s²2s². If one of the 2s electrons absorbs a photon and jumps to the 2p orbital, the excited state becomes 1s²2s¹2p¹. This distinction between ground and excited states is central to photochemistry because photon absorption is what creates excited states, and excited-state molecules have fundamentally different reactivity than ground-state ones.

Valence electrons (those in the outermost shell) are the ones that participate in bonding and are most commonly involved in electronic transitions. Core electrons sit much closer to the nucleus and are tightly bound, so they rarely participate in photochemical processes.

In molecules, molecular orbital (MO) theory extends these ideas. Atomic orbitals on adjacent atoms combine to form bonding orbitals (lower energy, stabilizing) and antibonding orbitals (higher energy, destabilizing). In $H_2$, for instance, two 1s orbitals combine into one $\sigma$ bonding orbital and one $\sigma^*$ antibonding orbital. Photochemical excitation often promotes an electron from a bonding or nonbonding orbital into an antibonding orbital.

Energy levels and electronic transitions

Energy levels in atoms and molecules are quantized, meaning electrons can only exist in discrete energy states described by quantum numbers. Transitions between these levels involve absorbing or emitting photons whose energy matches the gap: $\Delta E = h\nu$.

Not all transitions are equally probable. Selection rules determine which transitions are "allowed" (strong absorption) versus "forbidden" (weak or absent):

• The orbital angular momentum quantum number must change by one: $\Delta l = \pm 1$
• The magnetic quantum number can change by: $\Delta m_l = 0, \pm 1$
• For multi-electron atoms, additional rules apply to total spin ($\Delta S = 0$ for spin-allowed transitions)

Spectroscopic term symbols like $^2S_{1/2}$ or $^2P_{3/2}$ compactly encode the total spin multiplicity, orbital angular momentum, and total angular momentum of an electronic state. The format is $^{2S+1}L_J$, where $S$ is total spin, $L$ is total orbital angular momentum (labeled S, P, D, F...), and $J$ is the total angular momentum quantum number.

The Franck-Condon principle is especially relevant in molecular photochemistry. It states that electronic transitions happen so fast that the nuclei don't move during the transition. The probability of a particular vibronic transition depends on the overlap between the vibrational wavefunctions of the initial and final electronic states. Transitions with greater wavefunction overlap produce stronger absorption bands.

Relative energies of electronic configurations

Several factors determine the energy ordering of electronic states:

• Principal quantum number ($n$) sets the main energy level. Higher $n$ means higher energy and greater average distance from the nucleus.
• Angular momentum quantum number ($l$) splits each shell into subshells. Within the same $n$, energy generally increases as $l$ increases (s < p < d < f) in multi-electron atoms due to differences in penetration and shielding.
• Effective nuclear charge ($Z_{eff}$): Inner electrons shield outer electrons from the full nuclear charge. Electrons in orbitals that penetrate closer to the nucleus (s orbitals, for example) experience higher $Z_{eff}$ and are more tightly bound.
• Electron-electron repulsion: Hund's rule reflects the fact that electrons in singly occupied orbitals with parallel spins have lower repulsion energy than paired electrons. This exchange energy stabilization is why half-filled and fully filled subshells are particularly stable.
• Spin-orbit coupling: The interaction between an electron's spin and its orbital angular momentum splits energy levels into fine structure components. The classic example is the sodium D line, where the $^2P$ state splits into $^2P_{1/2}$ and $^2P_{3/2}$, producing two closely spaced yellow emission lines.

For molecules, correlation diagrams track how atomic orbital energies evolve into molecular orbital energies as atoms approach each other. These diagrams are useful for predicting the electronic structure of diatomic molecules and understanding which MOs are occupied in ground and excited states. Hybridization models (like $sp^3$ in methane) offer a complementary, localized picture of bonding geometry, though MO theory provides the more complete framework for understanding photochemical transitions.