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Chemistry · Glossary

What is Spectroscopic dissociation energy?

Definition 6.11 University Chemistry — Year 3 · Chapter 6 — Rotational and Vibrational Spectroscopy

The spectroscopic dissociation energy of a molecule is the depth of its potential, DeD_e, measured from the minimum, or D0=De−G(0)D_0 = D_e - G(0), measured from the lowest level — per molecule at 0 K0\,\mathrm{K}, unlike the bond dissociation enthalpy of the Year 2 volume, a molar enthalpy at 298 K298\,\mathrm{K}.

Left: the Morse potential of HCl built from its spectroscopic constants (solid), the harmonic parabola with the same curvature (dashed), and every third vibrational level, drawn between its turning points; the levels close up towards D_e. Right: the Birge–Sponer plot of the gaps; the shaded area is D_0.
Left: the Morse potential of HCl\ce{HCl} built from its spectroscopic constants (solid), the harmonic parabola with the same curvature (dashed), and every third vibrational level, drawn between its turning points; the levels close up towards DeD_e. Right: the Birge–Sponer plot of the gaps; the shaded area is D0D_0.

Examples

Example 6.14 (Hydrogen chloride)

For HX35X2235Cl\ce{H^{35}Cl}, ω~e=2990.95 cm−1\tilde\omega_e = 2990.95\,\mathrm{cm}^{-1} and ω~exe=52.82 cm−1\tilde\omega_ex_e = 52.82\,\mathrm{cm}^{-1}: the fundamental is at ω~e−2ω~exe=2885.3 cm−1\tilde\omega_e - 2\tilde\omega_ex_e = 2885.3\,\mathrm{cm}^{-1} and the first overtone at 2ω~e−6ω~exe=5665.0 cm−12\tilde\omega_e - 6\tilde\omega_ex_e = 5665.0\,\mathrm{cm}^{-1}, slightly less than twice the fundamental. The Morse model predicts De=42 342 cm−1D_e = 42\,342\,\mathrm{cm}^{-1} and D0=40 860 cm−1D_0 = 40\,860\,\mathrm{cm}^{-1}; the true D0D_0, from the enthalpies of formation of H, Cl and HCl at 0 K0\,\mathrm{K}, is 35 760 cm−135\,760\,\mathrm{cm}^{-1} (4.43 eV4.43\,\mathrm{eV}). The real potential flattens out faster than a Morse curve fitted at the bottom: Birge–Sponer extrapolations from the lowest levels overestimate dissociation energies.

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