Absorption and Fluorescence Spectroscopies Study Notes

Absorption and Fluorescence Spectroscopies

Learning Outcomes

• Understand different types of electronic transitions in organic molecules.

• Understand the mechanism of absorption of light.

• Understand different spectral shifts and be able to carry out calculations using the Beer-Lambert Law.

• Understand the relationship between absorption and fluorescence emission.

• Understand different photophysical processes in organic molecules.

• Understand different parameters used to characterize absorption and fluorescence emission processes.

Spectroscopy

• Definition: Spectroscopy is the study of interactions between radiation and matter.

• Different processes can be studied depending on the energy of radiation, providing insights into material properties.

• Interaction Overview:

  • Radiation → Matter → Information

Einstein-Planck Relationship

• Formula: The Einstein-Planck relationship expresses the relationship between energy (E), frequency (v), and wavelength (λ) of radiation:
  $E = h v = rac{h c}{ ext{λ}}$

• Key Constants:

  • Planck constant, $h = 6.626 imes 10^{-34} ext{ Js}$

  • Speed of light, $c = 2.99 imes 10^{8} ext{ m/s}$

• Energy and Frequency:

  • Energy is directly proportional to frequency (SI unit: $ext{s}^{-1}$ or Hertz).

  • Energy is inversely proportional to wavelength (normally in nanometers, nm).

• Conclusion: As energy/frequency increases, wavelength decreases.

Einstein-Planck Relationship – Class Exercises

1. Calculate Energy:

   • Given frequency of $5.78 imes 10^{14} ext{ Hz}:$
     $E = h v = 6.626 imes 10^{-34} ext{ Js} imes 5.78 imes 10^{14} ext{ s}^{-1} = 3.83 imes 10^{-19} ext{ J}$

2. Calculate Wavelength:

   • Given energy of $6.45 imes 10^{-19} ext{ J}:$
     $ext{λ} = rac{h c}{E} = rac{(6.626 imes 10^{-34} ext{ Js}) imes (2.99 imes 10^{8} ext{ m/s})}{6.45 imes 10^{-19} ext{ J}} = 3.07 imes 10^{-7} ext{ m} = 307 ext{ nm}$

Atomic and Molecular Orbitals

• Definition: Electrons in atoms organize in atomic orbitals, which are regions around the nucleus where an electron may be found.

• Orbital Types:

  • s orbitals: Spherical

  • p orbitals: Dumbbell-shaped

  • d orbitals: More complex shapes

  • f orbitals: Even more complex

• Electronic Configurations:

  • Example - Hydrogen (H): 1s¹

  • Example - Oxygen (O): 1s² 2s² 2p⁴

  • P orbitals consist of three degenerate orbitals, each accommodating two electrons.

Molecular Orbital Formation

• Atoms combine to form molecules with combined atomic orbitals creating molecular orbitals (MOs).

• Bonding Orbitals: Formed by the interaction of 's' atomic orbitals, labeled as sigma (σ) orbitals.

• Anti-bonding Orbitals: Destructive interactions lead to anti-bonding orbitals (σ*).

Electronic Transitions in Molecules

• Energy from light can excite electrons to higher orbitals, thus creating excited state configurations.

• Different electronic transitions in organic molecules are characterized by:

  • $ext{σ} <br>ightarrow ext{σ}^*$

  • $ext{π} <br>ightarrow ext{π}^*$

  • $n <br>ightarrow ext{π}^*$

• Importance of Energy Levels: Different energy levels correspond to these transitions in molecular orbitals.

Key Molecular Orbitals and Energy Gaps

• Properties of organic molecules depend on the energy of the Highest Occupied Molecular Orbital (HOMO) and Lowest Unoccupied Molecular Orbital (LUMO).

• HOMO-LUMO Transition: Typically $ext{π} <br>ightarrow ext{π}^*$ in conjugated systems.

• Energy Gap (ΔE):

  • $ext{ΔE}$ is inversely related to the degree of electronic delocalization; larger delocalization results in a smaller energy gap.

• Formula: $E = h v$ and $E = rac{h c}{ ext{λ}}$

Conjugation and Energy Gap

• Increased conjugation in molecules leads to a decrease in the HOMO-LUMO energy gap.

• Example: Order of energy gap by conjugation is:

  • Benzene > Naphthalene > Anthracene > Tetracene

• Implication: Tetracene has the lowest energy gap due to highest conjugation.

Interaction Between Light and Matter – Absorption

• When light interacts with matter, four processes can occur:

  • Absorption, where molecules are promoted to excited states.

  • Transmission of light.

  • Scattering of light (mostly in solids/concentrated solutions).

  • Reflection of light (also primarily in solids/concentrated solutions).

Instrumentation - Spectrophotometer

• Typically incorporates two lamps to excite the sample.

• Light passes through monochromator(s) and slit(s) for monochromatic radiation excitation.

• Types of spectrophotometers:

  • Single beam

  • Double beam (sample & reference cuvettes monitored simultaneously)

Absorption and Transmittance

• In diluted solutions, light can be absorbed or transmitted.

• The measurable signal is the transmitted light (It) relative to incident radiation (I0):

  • Transmittance (T):
    $T = rac{I_t}{I_0}$

  • Absorbance (A):
    $A = - ext{log}(T) = - ext{log} rac{I_t}{I_0}$

Absorption Spectrum and Spectral Shifts

• Absorbance (A) vs wavelength (λ) results in an absorption spectrum.

• Key parameters:

  • Absorption maximum (λmax, in nm)

  • Molar absorptivity (ε, in $M^{-1} cm^{-1}$)

• Common shifts:

  • Hyperchromic, bathochromic, hypsochromic.

Absorption Maximum and Conjugation

• The absorption maximum correlates with conjugation; greater conjugation results in a bathochromic shift (lower energy gap) and decreased conjugation results in a hypsochromic shift (increase in energy gap).

• Example λmax trend:

  • Benzene (λmax = 255 nm) > Naphthalene (λmax = 286 nm) > Anthracene (λmax = 375 nm) > Tetracene (λmax = 477 nm)

Absorption Spectral Shifts

• Bathochromic and hypsochromic shifts are often referred to as red and blue shifts, respectively.

Beer-Lambert Law

• Relates absorbance to concentration:
  $A = ext{ε} l c$

• Where:

  • A = absorbance

  • ε = molar absorptivity (M^{-1} cm^{-1})

  • l = optical pathlength (cm)

  • c = concentration (M)

• Higher values of ε suggest effective absorption at smaller concentrations.

Experimental Determination of Molar Absorptivities

• Linear relation analyzed by measuring absorbance for known concentrations helps to determine ε.

• Data plotted as absorbance (y) vs concentration (x) yields a line where the slope represents molar absorptivity.

Beer-Lambert Law – Class Exercise

• Example: Given ε = 3.67 x 10^4 M^{-1} cm^{-1} and absorbance of 0.78, calculate concentration:
  $c = rac{A}{ ext{ε} l} = rac{0.78}{3.67 imes 10^{4} imes 1 ext{ cm}} = 2.12 imes 10^{-5} M$

Jablonski Diagram

• Summarizes main photochemical transitions in organic conjugated compounds.

• Key components include:

  • Energy levels

  • Vibrational energy levels

  • Kasha's rule

  • Spin multiplicity

  • Internal conversion and intersystem crossing

  • Fluorescence vs phosphorescence

Jablonski Diagram Overview

• Depicts:

  • Ground state (S0)

  • Excited states (S1, S2)

  • Transitions (IC, ISC)

Kasha’s Rule

• Any photochemical processes start with a transition from a higher vibrational energy level in the singlet excited state to the lowest vibrational level of the first singlet excited state.

• Approximate time for this transition: $10^{-12} s$; occurs via internal conversion.

Spin Multiplicity

• Calculated as: $m_s = 2S + 1$

  • Where S is the electron spin involved in transitions.

• Types of states:

  • Singlet (s=0, ms=1)

  • Triplet (s=1, ms=3)

Internal Conversion and Intersystem Crossing

• Internal Conversion (IC): Transitions between energy levels of the same multiplicity.

• Intersystem Crossing (ISC): Transitions between states of different multiplicity (e.g., singlet to triplet).

Fluorescence and Phosphorescence

• Fluorescence: Radiative decay from the lowest vibrational energy level of the first singlet excited state to a vibrational level of the ground state, occurring within nanoseconds ($10^{-9} s$).

• Phosphorescence: Radiative decay from the lowest vibrational energy level of the first triplet excited state to a vibrational ground state level, occurring within milliseconds to seconds.

Instrumentation – Luminescence Spectrometer

• Utilizes a 90-degree angle between the excitation source and the emitted radiation.

• Light passes through monochromator(s) and slits to ensure monochromatic excitation.

Characterisation of Fluorophores

• Key parameters for characterizing fluorophores include:

  • Emission maximum (λmax em)

  • Lifetime (τ)

  • Fluorescence quantum yield (ϕf)

Emission Maximum and Stokes Shift

• Graphical representation of normalized intensity vs wavelength shows the relationship between emission and absorption.

  • Notable parameters include λem (emission) and λabs (absorption).

Fluorescence Lifetime and Quantum Yields

• Radiative decay rate constant (kr) relates to the rate of fluorescence.

• Non-radiative decay rate constant (knr) relates to radiationless decay processes.

• Fluorescence Lifetime (τ) is the duration a molecule remains in the excited state prior to photon emission:
  $τ = rac{1}{k_{r} + k_{nr}}$

• Fluorescence Quantum Yield (ϕ) quantifies efficiency:
  $ϕ = rac{k_{r}}{k_{r} + k_{nr}}$

• The better the efficiency, more emitted photons relative to absorbed photons are achieved.