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In vibrational spectroscopy (assuming harmonicity is valid), we measure the bond strength from the corresponding vibrational frequency. During vibrations, the atomic positions move from its equilibrium positions. The deviation from equilibrium is called Mean Square Displacement (MSD) (Mean squared displacement - Wikipedia). Neutron scattering technique can be used to MSD. Alternatively, RMSD, Root-Mean-Squared-Displacement (2²)¹/2, better parameter to judge the behaviour of vibrations. RMSD gives information about the displacement with respect to the equilibrium bond lengths. Given the following information for few selected molecules in their most stable isotope, find the RMSD in v 0 state and estimate the bond length is a

For Dihydrogen molecule H₂:

Vibrational frequency: 4401 cm 1

equilibrium bond length: 74.1pm

Comment why the estimated bond length from RMSD differs from the equilibrium bond length​

Answer 1

Explanation:

In vibrational spectroscopy (assuming harmonicity is valid), we measure the bond strength from the corresponding vibrational frequency. During vibrations, the atomic positions move from its equilibrium positions. The deviation from equilibrium is called Mean Square Displacement (MSD) (Mean squared displacement - Wikipedia). Neutron scattering technique can be used to MSD. Alternatively, RMSD, Root-Mean-Squared-Displacement (2²)¹/2, better parameter to judge the behaviour of vibrations. RMSD gives information about the displacement with respect to the equilibrium bond lengths. Given the following information for few selected molecules in their most stable isotope, find the RMSD in v 0 state and estimate the bond length is a

For Dihydrogen molecule H₂:

Vibrational frequency: 4401 cm 1

equilibrium bond length: 74.1pm

Comment why the estimated bond length from RMSD differs from the equilibrium bond length