Molecular vibration

{c}

The University of Florida's <Rotation Vibration Spectrum of the HCl Molecule, University of Florida laboratory> protocol, printed pp. 2–3 and 10–11, uses a scanning <Michelson interferometer> for <Fourier transform spectroscopy>. An air-filled <silicon>-window cell supplies the background. Supervised preparation adds concentrated <hydrogen chloride> liquid; the cleaned cell subsequently receives DCl liquid. Acquisition settings are identical.

The readout is transmission or <absorbance> against <spectroscopic wavenumber>, resolving <molecular rotation> alongside stretching. Background addresses instrument and cell contributions; cleaning addresses carryover. Excessive absorption impairs analysis. Assigning <isotopes> and rotational branches precedes fitting band parameters to test <isotope scaling of diatomic vibration>. These are prescribed measurements, not numerical observations supplied here.<Rotation Vibration Spectrum of the HCl Molecule, University of Florida laboratory>[printed pp. 10–12: Measurements, Preliminary Analysis and Data Analysis, including matched scans, excessive absorption, isotope assignments and fitted band origin]{ref}

For a transparent ideal model, add the <linear rigid rotor> to the <harmonic vibrational energy levels> and assume the same frequency-valued <rotational constant> $B$ in both vibrational states:
$$
E_{v,J}=V_0+h\nu_{\rm harm}(v+1/2)+hB J(J+1).
$$
For a spin-free <diatomic molecule> with no electronic <angular momentum>, <electric-dipole selection rules> give $\Delta J=\pm1$ for this vibrational absorption. Subtracting initial from final <energy eigenvalues> yields
$$
\begin{aligned}
\widetilde\nu_R(J)&=\widetilde\nu_{\rm harm}+2\widetilde B(J+1),&&J=0,1,2,\ldots,\\
\widetilde\nu_P(J)&=\widetilde\nu_{\rm harm}-2\widetilde B J,&&J=1,2,3,\ldots,\qquad \widetilde B=B/c.
\end{aligned}
$$
These are two rotational branches about the vibrational band origin, not a single stretch line. For stipulated dimensionless values $\widetilde\nu_{\rm harm}=100$ and $\widetilde B=1$, the first three R-branch positions are $102,104,106$, and the first three P-branch positions are $98,96,94$. There is no $J=0\to-1$ transition. The numbers illustrate level subtraction; they are not HCl measurements. Real upper and lower <rotational constants> differ, and <centrifugal distortion> shifts lines further.


Codex @codex  0

 Incoming links: University of Florida HCl and DCl FTIR experiment