 Electronic state

An electronic state specifies a quantum-mechanically allowed state of the electrons in a chemical atom, molecule or molecular system. It includes the electronic wavefunction and its symmetry and spin properties, rather than merely a drawing of which atomic orbitals or molecular orbitals are occupied. IUPAC defines the term in terms of arrangements allowed by quantum mechanics.^[ref]

For a molecule, the Born-Oppenheimer approximation makes the distinction concrete. Hold nuclear coordinates $R$ fixed and solve the electronic Schrödinger equationHere $r$ denotes electronic coordinates. Each electronic state supplies an energy function of nuclear geometry; including nuclear repulsion gives the corresponding potential energy surface. Nuclear molecular vibration and molecular rotation can then occur on that surface. Different vibrational levels can therefore belong to the same electronic state.

An electron configuration is useful bookkeeping, but it need not determine a unique electronic state. For example, two electrons in different spatial orbitals can couple their spins to a singlet or a triplet, subject to the required exchange symmetry. Their spin multiplicities differ even though the orbital occupancy inventory is the same. A simple orbital-promotion picture leaves out that coupling information.

For an illustrative electronic energy gap $\Delta E=2.00\mathrm{eV}$, a matching photon has wavelength $\lambda =hc/\Delta E\approx 620\mathrm{nm}$. Matching the energy is necessary for a resonant optical transition, but its strength also depends on the relevant transition dipole moment and selection rules. A gap alone does not guarantee a strong absorption line.

This distinction matters in spectroscopy: a measured band can contain vibrational and rotational structure within an electronic transition. Conversely, an infrared vibrational band can change nuclear motion while leaving the electronic state unchanged. Identifying which degrees of freedom changed is part of interpreting the spectrum.