Fundamentals of Photophysics and Infrared Spectroscopy

Posted on Jun 20, 2026 in Chemistry

1. Principles of Infrared (IR) Spectroscopy

Infrared (IR) spectroscopy is an analytical technique used to determine the functional groups present within a molecule. When a molecule is exposed to infrared radiation, it absorbs specific frequencies that match its natural molecular vibrations, causing quantized transitions between vibrational energy levels.

The IR region of the electromagnetic spectrum useful for organic chemistry typically spans wavenumbers from 4000 cm⁻¹ to 400 cm⁻¹. Wavenumber (ν̄) is the reciprocal of wavelength and is directly proportional to energy (E) and frequency (ν).

2. Molecular Vibrations

The atoms within a molecule are not stationary; they behave like spheres connected by flexible springs. These movements are categorized into two primary types of vibrations:

A. Stretching Vibrations

A rhythmic movement along the bond axis that changes the interatomic distance.

• Symmetric Stretching: Atoms move in the same direction relative to the central atom simultaneously.
• Asymmetric Stretching: One atom moves toward the central atom while the other moves away. Asymmetric stretches generally require higher energy (occur at higher wavenumbers) than symmetric stretches.

B. Bending Vibrations (Deformations)

A movement that changes the bond angle between two bonds. Bending generally requires less energy than stretching, appearing below 1500 cm⁻¹.

• In-plane bending: Scissoring (moving toward each other) and Rocking (moving in the same direction in the plane).
• Out-of-plane bending: Wagging (moving up and down together out of the plane) and Twisting (one moves up, one moves down out of the plane).

3. Hooke’s Law

The frequency of a stretching vibration can be modeled classically using Hooke’s Law for a vibrating spring. For a diatomic system, the vibrational wavenumber (ν̄) is given by:

Where:

• c = Speed of light (cm/s)
• k = Force constant of the bond (g/s² or dyne/cm), which reflects bond strength.
• μ = Reduced mass of the system (g).

Key Insights from Hooke’s Law:

1. Bond Strength (k): Stronger bonds have higher force constants and vibrate at higher frequencies.
2. Atomic Mass (μ): Bonds involving lighter atoms vibrate at higher frequencies than bonds involving heavier atoms.

4. Selection Rules and Intensity

Not all molecular vibrations result in an IR absorption band.

• The Selection Rule: A molecular vibration is IR active only if it causes a net change in the dipole moment of the molecule during the vibration.
• Symmetric Molecules: Completely symmetrical bonds (like the homonuclear H₂, N₂, O₂ or the central triple bond in trans-2-butene) are IR inactive because their dipole moment remains zero throughout the vibration.
• Intensity of Bands: The intensity of an IR peak depends on the magnitude of the change in the dipole moment. Strongly polar bonds (like C=O) yield very intense peaks, while less polar bonds (like C=C) yield weaker peaks.

5. IR Spectrum Regions

An IR spectrum is conventionally split into two distinct zones:

• Functional Group Region (4000–1500 cm⁻¹): Diagnostic stretching.
• Fingerprint Region (1500–400 cm⁻¹): Contains a complex overlay of bending and molecular skeletal vibrations unique to every individual compound. Comparing this region against a reference database allows absolute identification of an unknown compound.

6. Characteristic Absorption of Functional Groups

Factors Affecting C=O Shifts

• Conjugation: Resonance decreases double-bond character, lowering the force constant and shifting absorption to a lower wavenumber.
• Ring Strain: Smaller rings increase s-character in the carbonyl bond, increasing the force constant and shifting the peak to higher wavenumbers.

7. Spectroscopic Parameters

Integrated Absorption Coefficient

A simple peak maximum (εmax) doesn’t capture the entire probability of a transition because electronic bands are broadened by vibrations. Instead, we use the integrated absorption coefficient, which is the area under the absorption curve.

Oscillator Strength (f)

Oscillator strength is a dimensionless quantity that compares the transition probability of a real molecule to a classical harmonically oscillating electron. It ranges from 0 (forbidden) to 1 (fully allowed).

8. Singlet and Triplet States

Molecular electronic states are classified by their spin multiplicity (2S + 1).

• Singlet State (S): All electron spins are paired (S = 0, Multiplicity = 1). S₀ is the ground state; S₁, S₂ are excited states.
• Triplet State (T): The promoted electron undergoes a spin flip (S = 1, Multiplicity = 3). According to Hund’s Rule, a triplet state (T₁) is lower in energy than its corresponding excited singlet state (S₁) due to reduced electron-electron repulsion.

9. The Jablonski Diagram

A Jablonski diagram maps the photophysical pathways of an electronically excited molecule.

Radiative Processes

1. Fluorescence (S₁ → S₀ + hν): Spin-allowed transition; happens rapidly (10⁻⁹ to 10⁻⁶ s).
2. Phosphorescence (T₁ → S₀ + hν): Spin-forbidden transition; highly improbable, leading to a slower emission rate (10⁻³ to 10² s).

Non-Radiative Processes

1. Vibrational Relaxation (VR): Rapid loss of excess vibrational energy.
2. Internal Conversion (IC): Isoenergetic transition between states of the same spin multiplicity.
3. Intersystem Crossing (ISC): Isoenergetic transition between states of different spin multiplicities.

10. Lifetime and Quantum Yield

The observed lifetime (τ) is the time required for the excited state population to decrease to 1/e of its initial value. The quantum yield (Φ) measures the efficiency of a process. Φ > 1 occurs in chain reactions, while Φ < 1 occurs due to non-radiative deactivation.

11. Photosensitized Reactions

A photosensitizer absorbs light and transfers excitation energy to a reactant that cannot absorb the light directly. A classic example is mercury vapor facilitating the reaction of H₂ or chlorophyll harvesting solar energy for photosynthesis.