8 Molecular Fluorescence

A molecule is usually found in its ground electronic state (S₀) and its ground vibrational state (v₀), written in combination as S₀v₀. When a molecule gains energy, it transitions to an excited electronic state (S_n) and often an excited vibrational state (v_m), written in combination as S_nv_m. Molecules remain in their excited state for only a short period of time, relaxing back to their ground state by various mechanisms. One of these mechanisms is luminescence, which is the emission of a photon.

Fluorescence and phosphorescence are two specific mechanisms of photoluminescence. All of these terms refer to the emission of light from a molecule that reached its excited state through the absorption of a photon.

Excited-State Processes

Consider a molecule in an excited vibrational state of its first electronic excited state, an S₁v_m state. The excess vibrational energy is quickly transferred to the surrounding environment as heat through collisions during bond vibrations. This process is called vibrational relaxation and returns the molecule to the ground vibrational state of the excited electronic state, S₁v₀. From here, the molecule may follow one of the following pathways:

Fluorescence: A photon is emitted as the molecule transitions back to the ground electronic state, S₀v_m. When m ≠ 0, this photon emission is followed by vibrational relaxation to S₀v₀. Because fluorescence is usually preceded and followed by vibrational relaxation, most fluorescence is at a longer wavelength than absorption.

Internal conversion: The molecule transitions to S₀v_m without emission of a photon, where v_m is a highly-excited vibrational state of the ground electronic state (S₀). Rapid vibrational relaxation to S₀v₀ follows internal conversion and all of the original excitation energy is lost as heat. Internal conversion competes with fluorescence at S₁v₀ but dominates at S_nv₀ for n ≥ 2, leading to Kasha’s Rule that fluorescence occurs only from S₁v₀.

Intersystem crossing and phosphorescence: Intersystem crossing converts the excited state to a triplet state (T₁v_m) by flipping the spin of the excited-state electron. After rapid vibrational relaxation to T₁v₀, the molecule may phosphoresce, emitting a photon with a concurrent spin flip and transition to S₀v_m, or may internally convert with a concurrent spin flip to reach S₀v_m. Because the T₁ state is lower in energy than the S₁ state, phosphorescence occurs at longer wavelengths than fluorescence.

Molecules can also be excited to S₂v_m by photon absorption. In this case, vibrational relaxation occurs to S₂v0, followed by internal conversion to S₁v_m, and vibrational relaxation to S₁v₀.

Characteristics of Fluorescence

The quantum yield (Φ) of fluorescence for a molecule is the probability that fluorescence occurs in preference to internal conversion or intersystem crossing. Non-fluorescent molecules have Φ = 0, whereas molecules with Φ = 1 relax only via fluorescence. Molecules with non-zero quantum yields (i.e. 0 < Φ ≤ 1) are often called fluorophores.

The fluorescence emission spectrum of a molecule is generally the mirror image of its absorption spectrum. The reason is that an absorptive transition from S₀v₀ to S₁v_n and the converse fluorescence transition from S₁v₀ to S₀v_n have approximately equal probability. The aforementioned wavelength difference between the peaks of the absorption and fluorescence spectra is called the Stokes shift.

Fluorescence emission for most molecules occurs within a period of hundreds of picoseconds to tens of nanoseconds after excitation. A characteristic timescale for fluorescence emission from a given molecule is its fluorescence lifetime. Phosphorescence emission tends to occur within a period of microseconds to minutes. This difference in timescale arises from the low probability of intersystem crossing occurring in parallel with photon emission. The low probability also means that phosphorescence is often only observed at low temperatures or in solid matrices, whereas fluorescence is commonly observed at room temperature (and above) and in solution.

Connections

• What goes up, must come down: This chapter rounds out the story of what happens after a molecule absorbs a photon and becomes electronically excited (Ch. 6).
• The molar absorption coefficient (ε, Ch. 6) is a measure of the efficiency of light absorption; the fluorescence quantum yield (Φ) is a measure of the efficiency of light emission. The product of ε and Φ determines the brightness of a fluorophore. More absorbed photons lead to more emitted photons.
• The next chapter (Ch. 9) will address how fluorescence is measured.
• Fluorescence is a common source of interference in Raman spectroscopy (Ch. 15).

Post-Reading Questions

1. A population of fluorophores in a sample has a fluorescence quantum yield of Φ = 0.50. If 1000 fluorescence photons were emitted from the sample over a certain time period, calculate how many excitation photons were absorbed during the same time period.
2. The peak in the absorption spectrum of a fluorophore is at 598 nm. The Stokes shift for the fluorophore is 22 nm. Calculate the wavelength of the peak in its fluorescence emission spectrum.
3. Define Kasha’s rule. Is the fluorescence emission spectrum of a molecule the same regardless of excitation wavelength?
4. A time-resolved spectrometer measures the decay of a photoluminescence signal after a short pulse of excitation light. Within 4.1 ns, the signal decays to 37% of its initial intensity immediately after excitation. Predict whether fluorescence or phosphorescence is the likely mechanism of emission.

Topic Learning Objectives

The chapter is a primer for the following learning objectives, which will be covered in lecture and/or with additional assigned reading:

• Illustrate the processes of absorption, fluorescence, phosphorescence, vibrational relaxation, internal conversion, and intersystem crossing on an energy level diagram.
• Match excited state processes with typical timescales and/or rates.
• Describe and provide examples (where possible) of molecular and environmental factors that influence the quantum yield of fluorescence.
• Define quantum yield and fluorescence lifetime in terms of the rates of competitive excited-state processes.
• Discuss the differences between fluorescence and phosphorescence.
• Distinguish between photoluminescence and chemiluminescence.