🌈 Infrared Spectroscopy Simulator

In CO₂ the two oxygen atoms move outward and inward together while carbon stays still. Because CO₂ is perfectly symmetric, this motion never changes the molecule's dipole moment (it stays zero throughout), so no photon can be absorbed by it — the mode is IR-inactive. Only the asymmetric stretch and the bend, which do change the dipole moment, appear as peaks.

A stretch changes the distance between two bonded atoms along the bond axis. A bend changes the angle between two bonds sharing a common atom, without changing bond length. Stretches generally need more energy (higher wavenumber) than bends of the same atoms because bond length is stiffer than bond angle.

Wavenumber scales with √(k/μ). Hydrogen is the lightest atom, so the reduced mass μ of an O–H or C–H pair is small, which pushes the frequency high even though the bond itself isn't unusually stiff. That is why every X–H stretch (O–H, N–H, C–H) clusters in the same high-wavenumber region of the spectrum, well separated from heavier-atom stretches like C–O or C–C.

A double bond is roughly twice as stiff as the equivalent single bond, and force constant k sits inside a square root, so C=O (stiff, k large) lands around 1700 cm⁻¹ — well above a typical C–O single-bond stretch near 1050–1300 cm⁻¹ but below the light-atom X–H region.

Resonance is when the IR beam's frequency exactly matches a bond's natural vibrational frequency. Off-resonance, the beam passes through with almost no energy transfer (transmittance stays near 100%). On resonance, energy transfers efficiently into that specific vibration — its 3D amplitude grows sharply and the spectrum shows an absorption dip at that wavenumber.

A non-linear molecule with N atoms has 3N-6 vibrational modes. Water has 3 atoms, so 3(3)-6 = 3 modes: symmetric stretch, asymmetric stretch, and bend. All three change water's dipole moment, so all three are IR-active and all three appear in a real water IR spectrum.

A linear molecule with N atoms has 3N-5 vibrational modes (one more than a bent molecule of the same size, because it has one fewer possible rotation axis). CO₂ has 3 atoms, giving 3(3)-5 = 4 modes: symmetric stretch, asymmetric stretch, and a doubly-degenerate bend (two perpendicular bending motions at the same frequency).