When we draw a molecule on paper, its bonds usually appear as fixed lines joining atoms in fixed positions. A real molecule is very different. Its atoms are continually moving, and chemical bonds can be pictured, approximately, as tiny molecular springs.
Some of these movements repeatedly lengthen and shorten bonds, while others change the angles between bonds. These molecular vibrations provide an important link between molecular structure and infrared spectroscopy: a molecule can absorb IR radiation when the radiation can excite an allowed vibrational transition and the vibration produces a change in molecular dipole moment.
Try these five questions before reading the chapter. Focus on what actually changes as a molecule vibrates: bond length, bond angle, energy and dipole moment.
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Vibrational energy is quantised
A molecule can possess translational, rotational, vibrational and electronic energy. For molecular vibrations, however, the molecule cannot simply possess any arbitrary amount of vibrational energy. Its allowed vibrational energies occur as discrete, or quantised, levels.
Suppose a molecule initially occupies a lower vibrational energy level. To move to a higher allowed level, it must absorb a photon whose energy corresponds to the energy difference between the two levels involved in the transition.
A vibrational transition can occur when the energy of the absorbed photon corresponds to the separation between appropriate allowed vibrational energy levels.
Here, ΔE is the energy difference between the vibrational levels, h is the Planck constant and f is the frequency of the radiation. Vibrational energy separations commonly correspond to frequencies in the infrared region of the electromagnetic spectrum.
Why IR radiation is associated with molecular vibration
Different regions of the electromagnetic spectrum correspond to photons with different energies. The energy separations associated with many molecular vibrational transitions lie in the infrared region. Consequently, absorption of suitable IR radiation can increase the vibrational energy of a molecule.
If two allowed vibrational levels are separated by ΔE, radiation with the appropriate frequency can supply a photon for which ΔE = hf. The molecule can then undergo the corresponding vibrational transition.
Stretching and bending are the two fundamental types of vibration
A useful first model is to imagine a chemical bond as a spring joining two atoms. The atoms are not stationary: they oscillate about their equilibrium positions. Two broad types of molecular motion are particularly important — stretching and bending.
Stretching vibration: the bond length changes as bonded atoms move towards and away from one another approximately along the bond axis.
Bending vibration: the relative directions of bonds change, producing a change in bond angle.
Watch the difference between stretching and bending
The animations below exaggerate the atomic displacement slightly so that the type of motion is easy to see. The molecule continually oscillates through its equilibrium geometry; the atoms are not moving permanently towards either extreme.
| Symmetric stretching | Asymmetric stretching | Bending |
|---|---|---|
| Equivalent bonds lengthen together and shorten together. | One C=O bond becomes longer while the other becomes shorter. | The defining change is the O–C–O bond angle. |
Stretching vibrations change bond length
During a stretching vibration, the distance between bonded atoms repeatedly increases and decreases. The important feature is therefore a change in bond length.
In molecules containing two or more related bonds, stretching can often be described as either symmetric or asymmetric.
Symmetric stretching: equivalent bonds lengthen together and shorten together.
Asymmetric stretching: the bond-length changes are not in phase. In a simple linear triatomic molecule such as CO₂, one C=O bond lengthens while the other shortens during a particular part of the vibration.
Bending vibrations change bond angle
In a bending vibration, atoms move so that the angle between bonds changes. Bond stretching is therefore not the defining feature. Instead, the molecular geometry is repeatedly distorted as the bond angle becomes larger and smaller.
Bending → change in bond angle
This distinction is one of the most useful ways to recognise a vibration from a diagram. Ask which geometrical quantity is changing. If atoms move approximately along a bond axis so that the bond length changes, the motion is stretching. If the angle between bonds changes, the motion is bending.
Stretching vibrations generally require more energy than bending vibrations
It generally requires more energy to stretch a chemical bond significantly away from its equilibrium length than to distort the angle between bonds. For vibrations involving the same part of a molecule, stretching vibrations therefore commonly occur at higher frequencies and higher wavenumbers than bending vibrations.
Since photon energy increases with frequency, a higher-frequency vibrational transition corresponds to a larger photon energy.
Stretching absorptions generally occur at higher frequency and wavenumber than bending absorptions involving the same group of atoms.
Not every molecular vibration absorbs infrared radiation
Having a possible vibrational transition is not enough for that transition to appear in an infrared spectrum. A second condition determines whether a particular vibrational mode can interact with IR radiation.
For a vibration to be IR active, the vibration must cause a change in the dipole moment of the molecule.
IR activity requires the molecular dipole moment to change during the vibration.
Why a change in dipole moment matters
Infrared radiation contains an oscillating electric field. A molecular vibration that produces an oscillating dipole can interact with this field, allowing energy to be transferred from the radiation to the vibrational motion.
If the molecular dipole moment does not change during a particular vibration, that vibration does not give the corresponding fundamental IR absorption. Such a vibration is described as IR inactive.
IR active vibration: the molecular dipole moment changes during the vibration.
IR inactive vibration: the molecular dipole moment does not change during the vibration.
A non-polar molecule can still have IR-active vibrations
A particularly important misconception is that a molecule must possess a permanent dipole moment before it can absorb IR radiation. That is not the criterion. What matters is whether the dipole moment changes while the molecule vibrates.
Carbon dioxide, CO₂, illustrates this clearly. Its equilibrium structure is linear and symmetrical:
The two C=O bond dipoles cancel at the equilibrium geometry, so CO₂ has no permanent molecular dipole moment. Nevertheless, some vibrations disturb this cancellation and produce a changing instantaneous molecular dipole. Those vibrations are IR active.
The four normal vibrational modes of carbon dioxide
CO₂ contains three atoms and is linear. It therefore has four normal vibrational modes: one symmetric stretch, one asymmetric stretch and two bending modes. The two bending motions occur in mutually perpendicular planes and are degenerate.
| Normal mode | Animated vibration | Dipole moment | IR activity |
|---|---|---|---|
| Symmetric stretch | The two C=O bond dipoles remain equal and opposite throughout the vibration, so the molecular dipole remains zero. | IR inactive | |
| Asymmetric stretch | The cancellation of the two C=O bond dipoles is disturbed, producing a molecular dipole that changes during the vibration. | IR active | |
| Bending mode 1 in plane | Bending disturbs the linear arrangement, so the C=O bond dipoles no longer cancel completely and the molecular dipole changes. | IR active | |
| Bending mode 2 perpendicular plane | This is the same type of bending motion in a plane perpendicular to the first. The molecular dipole again changes during the vibration. | IR active |
The two bending modes of CO₂ are degenerate. They are distinct vibrations occurring in mutually perpendicular planes, but they have the same vibrational energy and therefore the same fundamental vibrational frequency.
Why the symmetric stretch is IR inactive
During symmetric stretching, the two C=O bonds lengthen together and shorten together. The molecule remains symmetrical throughout the motion. The two bond dipoles therefore remain equal and opposite and continue to cancel.
Since the molecular dipole moment does not change during this mode, the symmetric stretching vibration of CO₂ is IR inactive.
Why the asymmetric stretch is IR active
During asymmetric stretching, one C=O bond becomes longer while the other becomes shorter during a particular phase of the vibration. The two bond dipoles therefore no longer cancel exactly at each instant.
The molecular dipole changes as the atoms vibrate, so the asymmetric stretching mode is IR active.
Why the bending modes are IR active
During a bending vibration, the molecule moves away from its linear geometry. The C=O bond dipoles are no longer arranged directly opposite one another, and the molecular dipole moment changes.
CO₂ can bend in either of two mutually perpendicular planes. These are separate normal modes, but because an isolated linear molecule is equivalent in every direction around its molecular axis, the two bending modes have the same energy. They are therefore degenerate.
How many vibrational modes does a molecule have?
A molecule containing N atoms requires three coordinates to describe the position of each atom in three-dimensional space. It therefore possesses a total of 3N degrees of freedom.
Not all of these correspond to vibration. Some describe translation of the whole molecule through space, while others describe rotation of the whole molecule.
Non-linear molecules
Every molecule has three translational degrees of freedom. A non-linear molecule also possesses three independent rotational degrees of freedom. The remaining degrees of freedom correspond to vibration.
The subtraction of 6 accounts for the three translational and three rotational degrees of freedom.
Linear molecules
A linear molecule also has three translational degrees of freedom, but only two independent rotational degrees of freedom.
The subtraction of 5 therefore accounts for three translational and two rotational degrees of freedom.
| Molecular geometry | Translational degrees | Rotational degrees | Vibrational modes |
|---|---|---|---|
| Linear | 3 | 2 | 3N − 5 |
| Non-linear | 3 | 3 | 3N − 6 |
Worked example: vibrational modes of carbon dioxide
Carbon dioxide contains three atoms and has a linear molecular geometry. Therefore:
= 4
CO₂ therefore has four normal vibrational modes.
The four modes are one symmetric stretching mode, one asymmetric stretching mode and two degenerate bending modes. Four normal modes do not therefore imply four separate fundamental IR absorption positions: the symmetric stretch is IR inactive, while the two bending modes are degenerate.
Number of normal modes: 4
Distinct fundamental IR-active vibration frequencies considered here: asymmetric stretching and bending.
Vibrational absorption helps explain the greenhouse effect
Molecular vibration is important far beyond the laboratory IR spectrum. The interaction between infrared radiation and molecular vibrations also helps explain why certain atmospheric gases contribute to the greenhouse effect.
Radiation from the Sun supplies energy to the Earth. The warmed Earth then emits electromagnetic radiation, much of it in the infrared region.
Absorption by greenhouse gases
If an atmospheric molecule possesses an IR-active vibrational transition at an appropriate frequency, it can absorb part of this outgoing infrared radiation.
The absorbed energy can subsequently be redistributed through molecular collisions, and IR radiation can also be emitted again in different directions. The overall effect is to reduce the rate at which thermal infrared energy escapes directly to space compared with an atmosphere that did not contain these IR-active gases.
A greenhouse gas can interact with terrestrial infrared radiation when it possesses suitable IR-active molecular transitions, including vibrational transitions that produce a changing molecular dipole.
Why CO₂ can absorb terrestrial IR radiation
Although CO₂ has no permanent molecular dipole, its asymmetric stretching and bending modes produce changing dipole moments. These modes can therefore absorb IR radiation at appropriate frequencies.
This is why the statement “CO₂ is non-polar, so it cannot absorb IR radiation” is incorrect. A permanent molecular dipole is not required. The relevant condition is a change in dipole moment during the vibration.
Why N₂ and O₂ behave differently
Nitrogen and oxygen are homonuclear diatomic molecules. Stretching the N–N or O–O bond does not produce a molecular dipole because the two atoms are identical.
Their fundamental stretching vibrations therefore do not involve a changing dipole moment and are IR inactive. Consequently, N₂ and O₂ do not absorb terrestrial infrared radiation through these fundamental vibrational transitions in the way that important greenhouse gases such as CO₂ do.
Bringing the ideas together
Molecular-vibration questions become much easier when three separate ideas are kept distinct.
| Question to ask | What to examine | Key idea |
|---|---|---|
| What type of vibration is occurring? | Bond length or bond angle | Stretching changes length; bending changes angle. |
| What photon frequency corresponds to the transition? | Vibrational energy separation | ΔE = hf for the relevant transition. |
| Can that vibration give an IR absorption? | Dipole moment during the vibration | The molecular dipole moment must change. |
Common Mistakes
| Common mistake | Why it is wrong | Better approach |
|---|---|---|
| Thinking stretching and bending both simply mean that a bond gets longer and shorter. | Bending is characterised by a change in bond angle rather than by a simple motion along the bond axis. | Ask whether the defining geometrical change is bond length or bond angle. |
| Assuming every normal vibrational mode produces an IR absorption. | A vibration is IR inactive if it does not cause the molecular dipole moment to change. | After identifying the vibration, check whether the molecular dipole changes during the motion. |
| Assuming a non-polar molecule cannot absorb IR radiation. | A molecule may have no permanent dipole but still develop a changing instantaneous dipole during particular vibrations. | Consider the dipole throughout the vibration, not only at the equilibrium geometry. |
| Using 3N − 6 for every molecule. | Linear molecules have only two independent rotational degrees of freedom and therefore possess 3N − 5 vibrational modes. | Determine whether the molecule is linear before choosing the expression. |
| Expecting four normal modes of CO₂ to give four separate fundamental IR absorption positions. | The symmetric stretch is IR inactive, while the two bending modes are degenerate. | Distinguish the number of normal modes from the number of distinct fundamental IR-active frequencies. |
What you should be able to do
Explain vibrational quantisation
Explain why molecular vibrational energies occur at discrete levels and relate a vibrational transition to ΔE = hf.
Distinguish stretching from bending
Recognise stretching from a change in bond length and bending from a change in bond angle.
Distinguish symmetric and asymmetric stretching
Describe whether related bonds change length together or out of phase.
Predict IR activity
Decide whether a vibration is IR active by determining whether the molecular dipole moment changes.
Count vibrational modes
Use 3N − 5 for linear molecules and 3N − 6 for non-linear molecules.
Connect vibrations to the greenhouse effect
Explain why molecules with suitable IR-active vibrations can absorb infrared radiation emitted by the Earth.
These ten questions test whether you can connect vibrational motion, quantised energy, dipole changes, normal modes and infrared absorption.
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Frequently asked questions
Questions students often ask about molecular vibrations
Once stretching, bending and IR activity are separated clearly, most of the apparent complications disappear. These questions connect the ideas that students most often mix together.
Does every molecular vibration produce a peak in an IR spectrum?
No. A normal vibrational mode is IR active only if the molecular dipole moment changes during that vibration. A vibration can exist even though it is IR inactive.
Why does stretching normally occur at a higher wavenumber than bending?
For vibrations involving the same molecular group, stretching a bond generally requires more energy than changing its bond angle. The corresponding stretching transition therefore usually has a larger energy separation, which means a higher frequency and wavenumber.
If CO₂ is non-polar, how can it absorb infrared radiation?
CO₂ has no permanent molecular dipole at its equilibrium geometry, but IR activity depends on whether the dipole moment changes during a vibration. Its asymmetric stretching and bending vibrations produce a changing instantaneous dipole and are therefore IR active.
Why is the symmetric stretch of CO₂ IR inactive?
During symmetric stretching, both C=O bonds lengthen or shorten together. Their bond dipoles remain equal and opposite throughout the vibration, so the molecular dipole remains zero and does not change.
Why do linear molecules use 3N − 5 instead of 3N − 6?
All molecules have three translational degrees of freedom. Non-linear molecules also have three independent rotational degrees of freedom, but a linear molecule has only two. Removing three translations and two rotations from 3N leaves 3N − 5 vibrational modes.
Does four vibrational modes mean four separate IR peaks for CO₂?
No. CO₂ has four normal vibrational modes, but its symmetric stretch is IR inactive. Its two bending modes are also degenerate, meaning that they have the same fundamental vibrational frequency. The number of normal modes is therefore not automatically the number of distinct fundamental IR absorption positions.
What does it mean when two vibrational modes are degenerate?
Degenerate modes are distinct normal modes with the same vibrational energy and therefore the same frequency. The two mutually perpendicular bending modes of linear CO₂ are a standard example.
Why are N₂ and O₂ not important infrared greenhouse absorbers?
Their fundamental stretching vibrations do not change the molecular dipole moment. Because N₂ and O₂ are homonuclear diatomic molecules, each remains without a dipole as its bond stretches, so the fundamental stretch is IR inactive.
What is the fastest way to analyse an unfamiliar molecular-vibration question?
First identify the motion: a change in bond length indicates stretching, while a change in bond angle indicates bending. Then determine whether the molecular dipole changes during that motion. If the question asks for the number of modes, decide whether the molecule is linear before choosing 3N − 5 or 3N − 6.
The central idea is that molecular vibrations connect molecular geometry to quantised energy and infrared spectroscopy. Stretching changes bond length, bending changes bond angle, and a vibration gives a fundamental IR absorption only when it produces the required change in molecular dipole moment. CO₂ brings all of these ideas together: its symmetric stretch is IR inactive, its asymmetric stretch is IR active, and its two perpendicular bending modes are IR-active and degenerate.