Rotational–vibrational spectroscopy

When such transitions emit or absorb photons (electromagnetic radiation), the frequency is proportional to the difference in energy levels and can be detected by certain kinds of spectroscopy.

[1] In the simplest cases the part of the infrared spectrum involving vibrational transitions with the same rotational quantum number (ΔJ = 0) in ground and excited states is called the Q-branch.

Numerical analysis of ro-vibrational spectral data would appear to be complicated by the fact that the wavenumber for each transition depends on two rotational constants,

Diatomic molecules with the general formula AB have one normal mode of vibration involving stretching of the A-B bond.

The term values of the ro-vibrational states are found (in the Born–Oppenheimer approximation) by combining the expressions for vibration and rotation.

Coupling of the electron spin angular momentum with the molecular vibration causes lambda-doubling[note 5] with calculated harmonic frequencies of 1904.03 and 1903.68 cm−1.

Since the electric dipole moment of the homonuclear diatomics is zero, the fundamental vibrational transition is electric-dipole-forbidden and the molecules are infrared inactive.

, J = N + 1, N, and N - 1, each J state of this so-called p-type triplet arising from a different orientation of the spin with respect to the rotational motion of the molecule.

The 16O nucleus has zero nuclear spins angular momentum, so that symmetry considerations demand that N may only have odd values.

[17] For homonuclear diatomics, nuclear spin statistical weights lead to alternating line intensities between even-

Centrosymmetric linear molecules have a dipole moment of zero, so do not show a pure rotation spectrum in the infrared or microwave regions.

On the other hand, in certain vibrational excited states the molecules do have a dipole moment so that a ro-vibrational spectrum can be observed in the infrared.

When the vibration induces a dipole moment change pointing along the molecular axis the term parallel is applied, with the symbol

This makes for an intense, relatively broad, Q-branch consisting of overlapping lines due to each rotational state.

In carbon dioxide, the oxygen atoms of the predominant isotopic species 12C16O2 have spin zero and are bosons, so that the total wavefunction must be symmetric when the two 16O nuclei are exchanged.

[21][22] These molecules have equal moments of inertia about any axis, and belong to the point groups Td (tetrahedral AX4) and Oh (octahedral AX6).

Molecules with these symmetries have a dipole moment of zero, so do not have a pure rotation spectrum in the infrared or microwave regions.

[24] Tetrahedral molecules such as methane, CH4, have infrared-active stretching and bending vibrations, belonging to the T2 (sometimes written as F2) representation.

[note 7] These vibrations are triply degenerate and the rotational energy levels have three components separated by the Coriolis interaction.

A third category involves certain overtones and combination bands which share the properties of both parallel and perpendicular transitions.

represents the Q-branch of the sub-structure, whose position is given by The C-Cl stretching vibration of methyl chloride, CH3Cl, gives a parallel band since the dipole moment change is aligned with the 3-fold rotation axis.

The line spectrum shows the sub-structure of this band rather clearly;[6] in reality, very high resolution spectroscopy would be needed to resolve the fine structure fully.

Allen and Cross show parts of the spectrum of CH3D and give a detailed description of the numerical analysis of the experimental data.

[35] The vibrational ground state (v = 0) is also doubled although the energy difference is much smaller, and the transition between the two levels can be measured directly in the microwave region, at ca.

[46] The symmetric and asymmetric stretching vibrations are close to each other, so the rotational fine structures of these bands overlap.

For example, to achieve a resolution of 0.1 cm−1, the moving mirror must have a maximum displacement of 10 cm from its position at zero path difference.

The throughput advantage of FTIR is important for high-resolution spectroscopy as the monochromator in a dispersive instrument with the same resolution would have very narrow entrance and exit slits.

When measuring the spectra of gases it is relatively easy to obtain very long path-lengths by using a multiple reflection cell.

For the excited state This function can be fitted, using the method of least-squares to data for carbon monoxide, from Harris and Bertolucci.

However, when centrifugal distortion is included, using the formula the least-squares fit is improved markedly, with ms residual decreasing to 0.000086 cm−1.

Simulated vibration-rotation line spectrum of carbon monoxide , 12 C 16 O. The P-branch is to the left of the gap near 2140 cm −1 , the R-branch on the right. [ note 2 ]
Schematic ro-vibrational energy level diagram for a linear molecule
Spectrum of R-branch of nitric oxide , NO, simulated with Spectralcalc, [ 6 ] showing λ-doubling caused by the presence of an unpaired electron in the molecule
Spectrum of bending mode in 14 N 14 N 16 O simulated with Spectralcalc. [ 6 ] The weak superimposed spectrum is due to species containing 15 N at natural abundance of 0.3%
Spectrum of a perpendicular band from acetylene , C 2 H 2 , simulated with Spectralcalc [ 6 ] showing 1,3 intensity alternation in both P- and R- branches. See also Hollas p157
Spectrum of the asymmetric stretching (parallel) band of carbon dioxide , 12 C 16 O 2 simulated with Spectralcalc. [ 6 ] The weak superimposed spectrum is due to absorption of the first vibrationally excited level (0 1 1 0), which due to its low energy is populated at room temperature
Upper: low-resolution infrared spectrum of asymmetric stretching band of methane (CH 4 ); lower: PGOPHER [ 23 ] simulated line spectrum, ignoring Coriolis coupling
Spectrum of the C-Cl stretching band in CH 3 Cl (parallel band) simulated with Spectralcalc. [ 6 ]
Part of the spectrum of the asymmetric H-C-H bending vibration in CH 3 Cl (perpendicular band), simulated with Spectralcalc [ 6 ]
Spectrum of central region of the symmetric bending vibration in ammonia simulated with Spectralcalc, [ 6 ] illustrating inversion doubling.
Nitrogen inversion in ammonia
Absorption spectrum ( attenuation coefficient vs. wavelength) of liquid water (red) [ 39 ] atmospheric water vapor (green) [ 40 ] [ 41 ] and ice (blue line) [ 42 ] [ 43 ] between 667 nm and 200 μm. [ 44 ] The plot for vapor is a transformation of data Synthetic spectrum for gas mixture "Pure H 2 O" (296K, 1 atm) retrieved from Hitran on the Web Information System. [ 45 ]
Plot of the differences R(J)-P(J) as a function of 2J+1 taken from observed data for the fundamental vibration of carbon monoxide [ 51 ]