Étale group scheme

Carbon dioxide

Triatomic molecules are molecules composed of three atoms, of either the same or different chemical elements. Examples include H₂O, CO₂ (pictured) and HCN.

Molecular vibrations

The vibrational modes of a triatomic molecule can be determined in specific cases.

Symmetric linear molecules

A symmetric linear molecule ABA can perform:

• Antisymmetric longitudinal vibrations with frequency

${\omega }_a=\sqrt{\frac{k_{1}M}{m_A{m}_B}}$

• Symmetric longitudinal vibrations with frequency

${\omega }_{s1}=\sqrt{\frac{k_1}{m_A}}$

• Symmetric transversal vibrations with frequency

${\omega }_{s2}=\sqrt{\frac{2k_{2}M}{m_A}}$ This formula is not correct, the units do not match.

In the previous formulas, M is the total mass of the molecule, m_A and m_B are the masses of the elements A and B, k₁ and k₂ are the spring constants of the molecule along its axis and perpendicular to it.

Types

Trihydrogen cation

Ozone

Ozone, O₃ is an example of a triatomic molecule with all atoms the same. Triatomic hydrogen, H₃, is unstable and breaks up spontaneously. H₃⁺, the trihydrogen cation is stable by itself and is symmetric.