Electronic Excited States

Introduction

Light absorption changes a molecule's electronic state much faster than heavy nuclei usually change position. The initially excited molecule therefore retains approximately its ground-state geometry. It can then move, stretch and reorganize on a new potential-energy surface . This time ordering is the core of Franck–Condon reasoning and explains why an absorption energy need not equal the energy of a later fluorescence photon or chemical barrier.

Core explanation

An electronic state has energy that depends on molecular geometry. Imagine plotting energy vertically and one bond length horizontally. The ground state has a curve with a minimum at its preferred bond length. An excited state may have a different minimum because promotion of an electron changes bonding. A photon can move the molecule between curves nearly vertically: electronic identity changes while the initial nuclear coordinate remains almost fixed.

The Franck–Condon principle describes this rapid-transition approximation. It does not say nuclei are permanently frozen or that every transition has identical intensity. After absorption, the molecule may be at a geometry high on the excited-state curve, with excess vibrational energy. Vibrational relaxation and solvent reorganization can move it toward a lower-energy excited-state region. From there, it may emit, react, transfer energy or cross to another state.

The energy of a vertical absorption at the ground-state equilibrium geometry is usually different from the energy difference between relaxed minima. A vertical emission from the relaxed excited geometry can have lower energy than the absorbed photon. This contributes to a Stokes shift between absorption and fluorescence, though solvent effects, conformational changes and different emitting states can add further causes. An energy diagram should therefore mark the geometry for each arrow, not just the electronic-state labels.

Molecules have many nuclear coordinates, not one. Each bond length, angle and torsion contributes to a multidimensional potential-energy surface. A two-curve drawing along one coordinate is a teaching slice. The excited molecule may relax by twisting about a bond while another bond length changes. It may find an excited-state minimum different from the ground-state geometry or move toward a region where two electronic surfaces approach.

Vibrational states are quantized on each electronic surface. The probability of absorbing into a particular vibrational level is influenced by overlap of initial and final vibrational wavefunctions, called a Franck–Condon factor. If the excited-state minimum is displaced relative to the ground-state minimum, a progression of absorption bands can appear. Band intensity is not determined only by the vertical energy gap; the electronic transition dipole and vibrational overlap also matter.

Solvent molecules also respond on finite timescales. Immediately after excitation, their positions and orientations are close to those around the ground state. If the excited molecule has a different dipole, the solvent can reorganize and stabilize it differently. Emission from a solvent-relaxed state may therefore vary with solvent polarity. A color change between solvents need not mean the molecule has changed chemical formula.

Excited-state reactivity follows the new surface. A bond that is strong on the ground-state curve may be weakened after promotion of an electron into an antibonding orbital. But photon energy alone does not guarantee bond breaking. The system must move along a path, compete with relaxation and possibly cross to a product-forming surface. A photon with more energy may simply relax vibrationally before chemistry.

The vertical picture also helps distinguish absorption onset from an adiabatic electronic gap. An observed spectrum contains vibronic transitions and broadening; extracting a zero-zero transition or state-minimum difference needs careful analysis. A single peak maximum is not always the bare electronic energy difference between minima.

Step-by-step reasoning

Choose a relevant molecular coordinate and draw ground and excited potential curves with their minima. Place the molecule at the ground-state minimum before absorption. Draw the absorption arrow vertically to the excited curve. Follow relaxation along that curve to a lower-energy geometry, then draw possible emission or reaction pathways. Use the lengths of vertical arrows, not horizontal displacement, to compare photon energies.

Visual explanation

On an energy-versus-bond-length graph, draw two offset bowl-shaped curves. A vertical upward arrow begins at the ground-state minimum and ends above the excited-state minimum. A downhill curved arrow follows the excited surface toward its minimum. A shorter vertical downward arrow from that point ends on the ground curve at the new geometry. Label the difference in arrow lengths as part of the Stokes shift.

Real-world analogy

Imagine instantly moving a ball from one shaped track to another while keeping its horizontal position fixed. The ball then rolls toward a new low point. The instantaneous switch resembles electronic excitation; the later roll resembles nuclear relaxation. Real molecules have quantum vibrational states and many coordinates, so the ball picture is only a way to separate the fast electronic event from slower structural motion.

Real-world example

A fluorescent dye absorbs at a shorter wavelength than it emits. A plausible reason is that after vertical absorption, its geometry and solvent surroundings relax before emission. The researcher compares absorption and emission spectra in solvents of different polarity to test whether solvent reorganization contributes. A changed emission peak alone cannot identify which bond or solvent coordinate moved.

Why?

Photochemical selectivity depends on which excited geometry is populated and which pathways can be reached before decay. Franck–Condon reasoning prevents the common mistake of treating an absorbed photon's full energy as a permanent reservoir available for any reaction. The initial vertical state and the later relaxed state can have different energies and reactivities.

Common misconception

“Vertical transition” does not mean the molecule travels vertically in space or that nuclei never move. It means the electronic jump is represented at nearly fixed nuclear coordinates on an energy diagram. Another mistake is reading an absorption peak and fluorescence peak as two unrelated electronic states; relaxation on the same excited-state surface can produce a substantial separation.

Worked example

A dye absorbs most strongly at 450 nm and emits at 520 nm. Approximate photon energies are 1240/450 = 2.76 eV and 1240/520 = 2.38 eV. The emitted photon carries about 0.38 eV less energy. Excited-state vibrational and solvent relaxation can account for some of that difference, though the two peak maxima alone do not partition it among mechanisms or uniquely determine a state-minimum energy.

Quick check

1. What stays approximately fixed during a Franck–Condon vertical electronic transition? Answer: Nuclear positions or molecular geometry remain approximately fixed during the rapid electronic transition.

Exam focus

Draw two potential curves with correctly vertical absorption and emission arrows at different geometries. Explain relaxation between the arrows and link longer photon wavelength to lower energy. State that the one-coordinate drawing simplifies a multidimensional molecular surface.

Advanced insight

The Condon approximation treats the electronic transition dipole as nearly constant over relevant nuclear coordinates; vibronic intensities then depend strongly on vibrational overlap. Herzberg–Teller effects can make otherwise weak transitions appear when the dipole changes with nuclear motion. In complex molecules, conical intersections provide routes between surfaces that cannot be captured by two independent smooth parabolas.

Summary

Electronic excitation is fast relative to most nuclear motion, so absorption initially creates an excited state at nearly the ground-state geometry. The molecule then relaxes or reacts on a new energy surface. Potential curves and Franck–Condon factors explain vibronic spectra and why absorption and emission energies often differ. The vertical arrow marks an initial event, not the entire photochemical pathway.

Practice questions

1. Why is an absorption arrow drawn vertically on an energy-versus-bond-length diagram? Answer: The electronic transition occurs before the nuclei appreciably change position, so bond length is approximately fixed during the jump. 2. What happens after a molecule lands above the minimum of its excited-state curve? Answer: It can undergo vibrational and structural relaxation toward lower energy, while competing with emission or reaction. 3. Why can emission have a longer wavelength than absorption? Answer: Relaxation before emission can lower the excited-state energy, yielding a lower-energy, longer-wavelength photon. 4. Does a 450 nm absorption maximum directly equal an excited-state minimum-to-minimum energy difference? Answer: No; it is a vibronic spectral maximum associated with vertical transitions and broadening, not necessarily the adiabatic gap.

Sources: IUPAC Franck–Condon and vertical-transition definition; IUPAC photochemistry glossary; Primary study linking spectra to excited-state potential surfaces.