# Physics:Triatomic molecule

Carbon dioxide

Triatomic molecules are molecules composed of three atoms, of either the same or different chemical elements. Examples include H2O, CO2 (pictured), HCN and O3(ozone)

## 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
$\displaystyle{ \omega_a=\sqrt{\frac{k_1M}{m_Am_B}} }$
• Symmetric longitudinal vibrations with frequency
$\displaystyle{ \omega_{s1}=\sqrt{\frac{k_1}{m_A}} }$
• Symmetric transversal vibrations with frequency
$\displaystyle{ \omega_{s2}=\sqrt{\frac{2k_2M}{m_Am_B}} }$

In the previous formulas, M is the total mass of the molecule, mA and mB 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

### Homonuclear

Ozone, O3
Trihydrogen cation, H3+

Homonuclear triatomic molecules contain three of the same kind of atom. That molecule will be an allotrope of that element.

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. 4He3, the helium trimer is only weakly bound by van der Waals force and is in an Efimov state.[1] Trisulfur (S3) is analogous to ozone.

## Geometry

All triatomic molecules may be classified as possessing either a linear, bent, or cyclic geometry.Template:Expansion needed

### Linear

Linear triatomic molecules owe their geometry to their sp or sp3d hybridised central atoms. Well-known linear triatomic molecules include carbon dioxide (CO2) and hydrogen cyanide (HCN).

Xenon difluoride (XeF2) is one of the rare examples of a linear triatomic molecule possessing non-bonded pairs of electrons on the central atom.

## References

1. Kunitski, M.; Zeller, S.; Voigtsberger, J.; Kalinin, A.; Schmidt, L. P. H.; Schoffler, M.; Czasch, A.; Schollkopf, W. et al. (30 April 2015). "Observation of the Efimov state of the helium trimer". Science 348 (6234): 551–555. doi:10.1126/science.aaa5601. PMID 25931554. Bibcode2015Sci...348..551K.