Select The Vibrations That Should Be Infrared Active

Infrared (IR) spectroscopy is a powerful technique used to identify and study molecules based on their vibrational modes. Not all vibrations are created equal when it comes to IR activity; some are "silent," while others give rise to strong absorption bands. Understanding the criteria that determine whether a vibration is IR active is crucial for interpreting IR spectra and gleaning valuable information about molecular structure and dynamics.

Understanding Molecular Vibrations

At the heart of IR spectroscopy lies the concept of molecular vibrations. Molecules are not static entities; their atoms are constantly in motion, oscillating around their equilibrium positions. These vibrations can be categorized into several types, including:

• Stretching: A change in the bond length between two atoms.
• Bending: A change in the angle between two bonds.
• Symmetric: All similar bonds stretch or bend in phase.
• Asymmetric: Similar bonds stretch or bend out of phase.

Each of these vibrational modes has a specific frequency, corresponding to the energy required to excite that vibration. When a molecule is irradiated with infrared light, it can absorb photons whose energy matches the energy of a particular vibrational mode. This absorption leads to a decrease in the intensity of the transmitted light at that specific frequency, resulting in a dip in the IR spectrum.

The Selection Rule for IR Activity: A Change in Dipole Moment

Here's the crucial concept: Not all molecular vibrations can absorb infrared light. The key to IR activity lies in the change in the molecule's dipole moment during the vibration.

A dipole moment is a measure of the polarity of a molecule. It arises when there is an uneven distribution of electron density, resulting in a separation of positive and negative charges. For a vibration to be IR active, it must cause a change in this dipole moment.

Why the Dipole Moment Change Matters:

Infrared radiation is electromagnetic radiation, consisting of oscillating electric and magnetic fields. The oscillating electric field can interact with the molecule's oscillating dipole moment. If the frequency of the IR radiation matches the frequency of the vibrational mode, and the vibration causes a change in the dipole moment, then energy can be transferred from the IR radiation to the molecule, exciting the vibration.

In simpler terms: Think of the electric field of the IR radiation as "pushing" or "pulling" on the molecule's charges. If the vibration causes the charges to move in a way that interacts with this pushing and pulling, then the vibration can absorb the IR light. If the vibration doesn't change the charge distribution (no change in dipole moment), there's nothing for the IR light to interact with, and the vibration is IR inactive.

Determining IR Activity: A Step-by-Step Approach

To determine which vibrations of a molecule are IR active, follow these steps:

1. Determine the Molecular Geometry: The shape of the molecule is crucial. Use VSEPR theory or other methods to determine the three-dimensional structure.
2. Identify the Vibrational Modes: For a non-linear molecule with N atoms, there are 3N - 6 vibrational modes. For a linear molecule, there are 3N - 5 vibrational modes.
3. Visualize Each Vibrational Mode: Imagine the atoms moving in each mode. Sketching the vibrational modes can be helpful.
4. Assess the Change in Dipole Moment: For each vibrational mode, determine whether the vibration causes a change in the molecule's dipole moment. This is the most critical step.
5. Identify IR Active Vibrations: Vibrations that result in a change in the dipole moment are IR active. Vibrations that do not result in a change in the dipole moment are IR inactive.

Examples of IR Active and Inactive Vibrations

Let's illustrate these concepts with some examples:

1. Carbon Dioxide (CO2):

CO2 is a linear molecule with the structure O=C=O. It has 33 - 5 = 4 vibrational modes:

• Symmetric Stretch: Both C=O bonds stretch and contract in phase. In this mode, the dipole moment remains zero because the stretching is symmetrical, and the charges are equally distributed. IR Inactive.
• Asymmetric Stretch: One C=O bond stretches while the other contracts. This mode does create a change in the dipole moment. As one bond becomes more polar, the molecule develops a net dipole moment. IR Active.
• Bending (two degenerate modes): The molecule bends out of its linear shape. This also causes a change in the dipole moment. IR Active.

Therefore, CO2 exhibits two strong absorption bands in the IR spectrum corresponding to the asymmetric stretch and the bending modes. The symmetric stretch is IR silent.

2. Water (H2O):

Water is a bent molecule with the structure H-O-H. It has 33 - 6 = 3 vibrational modes:

• Symmetric Stretch: Both O-H bonds stretch and contract in phase. This vibration does change the dipole moment because the overall polarity of the molecule changes as the bonds lengthen and shorten. IR Active.
• Asymmetric Stretch: One O-H bond stretches while the other contracts. This also changes the dipole moment. IR Active.
• Bending: The H-O-H angle changes. This also changes the dipole moment. IR Active.

All three vibrational modes of water are IR active, resulting in three distinct absorption bands in the IR spectrum. This is why water is a strong absorber of infrared radiation.

3. Methane (CH4):

Methane is a tetrahedral molecule. It has a more complex vibrational structure, but we can analyze a few key modes:

• Symmetric Stretch: All four C-H bonds stretch and contract in phase. While the bond lengths change, the overall symmetry of the molecule is maintained, and there is no change in the dipole moment. IR Inactive.
• Asymmetric Stretch: The stretches are not in phase and can create a change in the dipole moment. IR Active.
• Bending Modes: Some bending modes will be IR active, while others will be inactive depending on whether they break the symmetry and create a dipole moment.

4. Homonuclear Diatomic Molecules (e.g., H2, N2, O2, Cl2):

These molecules consist of two identical atoms bonded together. Because the electron density is equally distributed between the two atoms, these molecules have no permanent dipole moment. Furthermore, stretching the bond between the two atoms does not create a dipole moment. Therefore, homonuclear diatomic molecules are IR Inactive. They are transparent to infrared radiation. They are Raman active, which is a complementary vibrational spectroscopy technique.

Group Theory and IR Activity: A More Formal Approach

While visualizing the change in dipole moment is a good starting point, a more rigorous approach to determining IR activity involves group theory. Group theory uses the symmetry properties of molecules to predict which vibrational modes are IR active.

Here's a brief overview:

1. Determine the Point Group: Assign the molecule to its appropriate point group based on its symmetry elements (e.g., Cnv, Dnh, Td, Oh).
2. Find the Irreducible Representations: Determine the irreducible representations for the vibrational modes. This can be done using character tables for the molecule's point group.
3. Check for IR Activity: A vibrational mode is IR active if its irreducible representation transforms as x, y, or z (the Cartesian coordinates) in the character table. In other words, if the irreducible representation of the vibration matches the irreducible representation of a translation (movement along the x, y, or z axis), then the vibration is IR active.

Example: Water (H2O) and Group Theory

Water belongs to the C2v point group. The character table for C2v shows that the translations (x, y, z) transform as B1, B2, and A1, respectively. The three vibrational modes of water transform as 2A1 + B1. Since A1 and B1 match the transformations of z and x, respectively, all three vibrational modes are IR active.

Benefits of Using Group Theory:

• More Accurate Predictions: Group theory provides a more reliable and accurate way to predict IR activity, especially for complex molecules.
• Systematic Approach: It offers a systematic method for analyzing the symmetry properties of molecules.
• Understanding Selection Rules: Group theory helps to understand the selection rules that govern IR transitions.

Factors Affecting IR Absorption Intensity

While the selection rule (change in dipole moment) determines whether a vibration is IR active, the intensity of the absorption band depends on several factors:

• Magnitude of the Dipole Moment Change: A larger change in the dipole moment during the vibration leads to a stronger absorption band.
• Concentration of the Sample: Higher concentrations of the analyte will lead to stronger absorption bands. This follows Beer-Lambert Law.
• Path Length of the Beam: A longer path length of the IR beam through the sample will also increase the absorption. This also follows Beer-Lambert Law.
• Transition Dipole Moment: The intensity of the absorption is proportional to the square of the transition dipole moment, which is a quantum mechanical quantity that describes the probability of the transition.

Applications of IR Spectroscopy

Understanding IR activity is essential for a wide range of applications:

• Molecular Identification: IR spectroscopy can be used to identify unknown substances by comparing their IR spectra to known standards. Functional groups have characteristic absorption frequencies.
• Structural Determination: IR spectroscopy can provide information about the structure and bonding of molecules. The presence or absence of specific absorption bands can indicate the presence or absence of certain functional groups or structural features.
• Quantitative Analysis: The intensity of IR absorption bands can be used to determine the concentration of a substance in a sample.
• Monitoring Chemical Reactions: IR spectroscopy can be used to monitor the progress of chemical reactions by observing the changes in the IR spectra of the reactants and products.
• Materials Science: IR spectroscopy is used to characterize the vibrational properties of materials, such as polymers, semiconductors, and ceramics.
• Environmental Monitoring: IR spectroscopy is used to detect and quantify pollutants in air and water.
• Biochemistry: IR spectroscopy is used to study the structure and dynamics of proteins, lipids, and nucleic acids.

Common Pitfalls and Considerations

• Overtones and Combination Bands: In addition to the fundamental vibrational modes, IR spectra can also exhibit overtones (multiples of the fundamental frequencies) and combination bands (sums or differences of two or more fundamental frequencies). These bands are typically weaker than the fundamental bands but can still complicate the spectrum.
• Fermi Resonance: Fermi resonance occurs when two vibrational modes have similar energies and the same symmetry. This can lead to a splitting or shifting of the absorption bands.
• Hydrogen Bonding: Hydrogen bonding can significantly affect the frequencies and intensities of IR absorption bands, particularly for O-H and N-H stretching vibrations. Hydrogen bonding typically broadens the peaks and shifts them to lower frequencies.
• Sample Preparation: The way a sample is prepared can affect the IR spectrum. Solid samples are often prepared as KBr pellets or mulls. Liquid samples are typically analyzed in thin films or solutions. Gas samples require special gas cells.
• Spectral Resolution: The resolution of the IR spectrometer can affect the appearance of the spectrum. Higher resolution instruments can resolve closely spaced absorption bands.

Conclusion

The selection rule for IR activity, which states that a vibration must cause a change in the molecule's dipole moment to be IR active, is a fundamental concept in IR spectroscopy. By understanding this rule and applying it to specific molecules, we can predict which vibrations will be IR active and interpret IR spectra to gain valuable information about molecular structure, bonding, and dynamics. While visualizing the change in dipole moment is a helpful starting point, group theory provides a more rigorous and accurate approach for determining IR activity, especially for complex molecules. IR spectroscopy is a versatile and powerful technique with applications in a wide range of fields, from chemistry and materials science to environmental monitoring and biochemistry. Mastering the principles of IR activity is crucial for effectively utilizing this technique and unlocking the wealth of information it provides. Remember to consider factors such as the magnitude of the dipole moment change, concentration, and sample preparation when interpreting IR spectra. By carefully analyzing IR spectra, researchers can gain valuable insights into the molecular world.