6 UV-Visible Absorption

Absorption of Light by Molecules

A molecule at room temperature is found in its ground electronic state (S₀) and, most frequently, its ground vibrational state (v₀). This combination is written as S₀v₀. The most energetic (i.e. valence) electrons are found in the highest (energy) occupied molecular orbital (HOMO).

When a molecule absorbs a UV or visible photon, a transition occurs to an excited electronic state. Commonly, this new state corresponds to an electron in what is normally the lowest (energy) unoccupied molecular orbital (LUMO), with either a ground or excited vibrational state (v_m). Such a state is denoted as S₁v_m. The energy of the absorbed photon matches the energy difference between the S₀v₀ and S₁v_m states—a condition known as resonance. A transition to the second lowest unoccupied molecular orbital (SLUMO; S₀v₀ to S₂v_m) may occur upon absorption of a higher-energy visible or UV photon.

Molecules or parts of molecules that strongly absorb UV and visible light are called chromophores. Organic chromophores tend to have conjugated double bonds, and often heteroatoms, in their structures. For simple molecules, the HOMO-LUMO transition frequently corresponds to an electron moving from a π bonding or non-bonding orbital to a π anti-bonding orbital.

Charge transfer absorption is common with inorganic chromophores and also occurs with some organic chromophores. An electron moves from one part of a molecule to another part upon transition to the excited state. Transitions involving d or f electrons may also occur with inorganic chromophores (cf. the s and p electrons that form molecular orbitals in organic chromophores).

Beer-Lambert Law

Transmittance is the fraction of incident light absorbed by a sample of molecules. That is, the ratio of light intensity transmitted through the sample, P(λ), and the original light intensity, P₀(λ). The absorbance, A, is the negative logarithm of this fraction (Eqn. 6.1), where ε(λ) is the molar absorption coefficient of the molecule at a defined wavelength (λ), b is the path length of light through the sample, and c is the concentration of the molecule. Note that absorbance and the molar absorption coefficient are wavelength-specific values.

        (Eqn. 6.1)        [latex]A(λ) =  -log[P(λ)/P_{0}(λ)] = ε(λ)bc[/latex]

The molar absorption coefficient is a measure of the probability that a photon of wavelength λ is absorbed by a molecule. Typical peak values of ε(λ) are 10⁴–10⁵ M^–1 cm^–1 for strongly absorbing organic molecules. Absorption spectra measure and plot absorbance as a function of wavelength.

At sufficiently dilute concentrations, the linear relationship between absorbance and concentration in Eqn. 6.1 will be observed experimentally. UV-visible spectrophotometry measures the absorbance of samples. It is a simple and popular method of determining analyte concentrations when the molar absorption coefficient is known or can be determined by a calibration curve derived from standard solutions. When there are multiple absorbing molecules in the same solution, the observed absorbance is the sum of the absorbances from each type of absorbing molecule (i.e. a sum of terms analogous to Eqn. 6.1).

Connections

• Incident light is the stimulus and the transmitted light is the response for this analysis method (Ch. 1).
• The wavelengths of light absorbed determine the observed colour of a solution (Ch. 2)
• For a defined wavelength, the Beer-Lambert Law relates the amount of light absorbed to the concentration(s) of light-absorbing molecules. This relationship is the basis of spectrophotometric analyses (Ch. 7).
• The absorption of a photon is the first step in generating fluorescence (Ch. 8).
• Similar to how molecules absorb UV-visible light to transition between molecular orbitals, atoms can absorb light to transition between atomic orbitals (Ch. 10).

Post-Reading Questions

1. Does the HOMO-LUMO transition correspond to the S₀→S₁ transition?
2. Do the S₀→S₂ transitions occur at longer or shorter wavelengths than the S₀→S₁ transitions?
3. Without looking back at the text, write the Beer-Lambert Law and define all terms.
4. Absorbance is a unitless ratio. If the molar absorption coefficient has standard units of M^–1 cm^–1, what are the standard units for concentration and path length in the Beer-Lambert Law?
5. The signal from a photodetector for a blank was 7.2 µA (microamperes, a unit of electrical current). The signal for the analytical sample was 0.72 µA. Calculate the corresponding absorbance value.
6. The measured absorbance of a pure solution of a chromophore is 0.15 at 555 nm, the path length is 1 cm, and the molar absorption coefficient is known to be 150 000 M^–1 cm^–1 at the same wavelength. Calculate the concentration of the chromophore.

Suggestion: Questions 5 and 6 do not require a calculator. Use scientific notation and the calculations will be simple enough for mental math.

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:

• Identify molecular structures that are likely to be chromophores.
• Predict the order of energies of photon absorption for a series of different molecular structures.
• List the conditions required for a photon to be absorbed by a molecule.
• Draw an energy level diagram that relates photon absorption to electronic transitions.
• Use qualitative descriptions and energy level diagrams to explain the positions and shapes of absorbance spectra.
• Predict colour (under approximate white light) from an absorbance spectrum and vice versa.
• Apply the Beer-Lambert Law in calculations.
• Discuss the limitations of the Beer-Lambert Law.