Infrared Intensities

A Frequency Calculation not only determines the vibrational frequencies of a molecule but also predicts how strongly each vibration interacts with infrared (IR) radiation. This interaction is quantified by the infrared intensity of each normal mode.

Not every molecular vibration can absorb infrared light. A vibration is observed in an IR spectrum only if it changes the molecular dipole moment during the vibration.

Consequently, every normal mode has

• a vibrational frequency,
• an infrared intensity,
• and an associated pattern of atomic motion.

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Interaction with Infrared Radiation

Infrared radiation is electromagnetic radiation whose energy matches the energy differences between molecular vibrational states.

When the frequency of the incoming IR radiation matches a molecular vibration,

the molecule absorbs the radiation and begins to vibrate more strongly.

Infrared Light
       │
       ▼
Molecule
       │
       ▼
Molecular Vibration

Only vibrations that interact with the electric field of the infrared light produce absorption peaks.

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The Role of the Dipole Moment

The key requirement for infrared absorption is a change in the molecular dipole moment.

The dipole moment describes how electrical charge is distributed within a molecule.

δ+  ----------->  δ−

During a vibration,

the positions of the atoms change.

If this motion changes the dipole moment,

the vibration becomes infrared active.

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Infrared Active Vibrations

A vibration is IR active if the dipole moment changes during the motion.

Mathematically,

\[ \boxed{ \left( \frac{\partial \mu}{\partial Q} \right) \neq 0 } \]

where

• \( \mu \) is the molecular dipole moment,
• \( Q \) is the normal coordinate.

If this derivative is non-zero,

the vibration absorbs infrared radiation.

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Infrared Inactive Vibrations

If the dipole moment remains constant during the vibration,

\[ \boxed{ \left( \frac{\partial \mu}{\partial Q} \right) = 0 } \]

the vibration cannot interact with infrared radiation.

Such vibrations are called IR inactive.

Although these vibrations still exist physically,

they do not produce peaks in the infrared spectrum.

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Examples

Carbon Monoxide Stretch

C  ←────→  O

The stretching vibration changes the dipole moment.

Result:

• IR Active

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Nitrogen Molecule

N  ←────→  N

The molecule remains perfectly symmetric during stretching.

The dipole moment does not change.

Result:

• IR Inactive

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Water Molecule

      H
       \
        O
       /
      H

Both stretching and bending vibrations change the molecular dipole moment.

Result:

• Strong IR absorption bands.

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How Gaussian Calculates IR Intensities

After determining the normal modes,

Gaussian calculates how the molecular dipole moment changes along each normal coordinate.

Normal Mode
       │
       ▼
Change in Dipole Moment
       │
       ▼
Infrared Intensity

The larger the change in dipole moment,

the stronger the infrared absorption.

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Units of IR Intensity

Gaussian reports infrared intensities in

km/mol

This quantity measures how strongly a vibrational mode absorbs infrared radiation.

For example,

IR Inten --  0.5

corresponds to a weak absorption,

whereas

IR Inten -- 250.3

indicates a very strong infrared band.

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Relationship Between Frequency and Intensity

Every vibrational mode has both

• a frequency,
• an infrared intensity.

These two quantities describe different physical properties.

Quantity	Describes
Frequency	How fast the atoms vibrate
IR Intensity	How strongly the vibration absorbs infrared light

A high-frequency vibration is not necessarily highly intense.

Similarly,

a low-frequency vibration may produce a strong absorption if it causes a large change in the molecular dipole moment.

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Infrared Spectrum

The infrared spectrum is generated by plotting

• frequency along the horizontal axis,
• intensity along the vertical axis.

Intensity
 ^
 |
 |        │
 |    │   │
 |    │   │      │
 |____│___│______│_________

-------------------------------> Frequency (cm⁻¹)

Each peak corresponds to one infrared-active normal mode.

The position of the peak is determined by the vibrational frequency,

while its height depends on the infrared intensity.

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Interpretation of Gaussian Output

In the Gaussian output,

infrared intensities appear together with the vibrational frequencies.

Example

Frequencies --  1560.2  1755.6  3201.8

IR Inten    --    8.2    245.7    31.4

This indicates that

• the first vibration is weakly IR active,
• the second produces a strong absorption band,
• the third has moderate intensity.

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Applications

Infrared intensities are widely used in

• prediction of infrared spectra,
• identification of functional groups,
• comparison with experimental IR spectra,
• structural characterization,
• reaction monitoring,
• conformational analysis.

Because Gaussian calculates both frequencies and intensities simultaneously, theoretical spectra can be compared directly with experimental measurements.

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Summary

Infrared intensities describe how strongly each normal mode interacts with infrared radiation. A vibration is infrared active only if it changes the molecular dipole moment during the vibration. Gaussian determines the infrared intensity of each normal mode by evaluating the change in dipole moment along the corresponding vibrational coordinate. Together with the vibrational frequencies, these intensities allow the prediction of infrared spectra and provide valuable information for molecular identification and structural analysis.

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Next Section

The next chapter explains how Gaussian uses the calculated vibrational frequencies to evaluate thermodynamic properties, including Zero-Point Energy, thermal corrections, enthalpy, entropy, and Gibbs free energy.