The gross selection rule for the observation of vibrational Raman transitions is that the polarisability of the molecule should change as the molecule vibrates. Both homonuclear and heteronuclear diatomics fulfill this requirement, so both molecules are vibrationally Raman active. If we approximate the potential energy curve of a vibrating bond as a parabola (i.e. assume that the vibration is harmonic) then the … Read more
The rotational constant of a vibrationally excited state of a diatomic molecule will be slightly smaller than that of the vibrational ground state, as the excited state will have a slightly longer bond than the ground state (due to the anharmonicity of the vibration). Consequently the moment of inertia of the excited state will be greater and its rotational constant … Read more
If the vibrational spectrum of a gas-phase heteronuclear diatomic molecule is obtained at high enough resolution, it is found that each line of the spectrum actually consists of a large number of closely spaced components. These components arise from the rotational transitions that accompany vibrational transitions – since the gaps between vibrational levels are so much … Read more
The approximation of the potential energy to a parabola cannot be correct at all extensions, as it does not permit dissociation of the bond. At high vibrational excitations (i.e. in states with high values of the quantum number ν), the parabolic approximation is particularly poor. The motion at such a position is described as anharmonic, as the restoring force is … Read more
The gross selection rule for vibrational transitions is that the electric dipole moment of the molecule must change in the course of the vibrational motion. e.g. homonuclear diatomics are infrared inactive – stretching of the bond does not alter the dipole moment of the molecule, it remains at zero. However, heteronuclear diatomics may be infrared active, as bond stretching increases … Read more
A typical potential energy curve for a diatomic molecule has the following form: REqm is the internuclear separation between the atoms at equilibrium – the equilibrium bond length. At smaller separations the potential energy rises rapidly as a result of repulsion between the outermost electrons. At larger separations, the potential rises more slowly until it eventually levels out. At this … Read more
There is another convention in the labeling of molecular orbitals that we need to be aware of. This concerns the parity of the orbital. The parity of an orbital is its behaviour under inversion. An orbital of even parity appears the same when inverted through its centre, while one of odd parity changes sign. In the diagrams, the lighter … Read more
The procedure for working out a molecular orbital of a general diatomic molecule is quite simple. We construct molecular orbitals using the available orbitals on the atoms. We then fill up the molecular orbitals, starting with the lowest in energy, until all the electrons in the species have been assigned to an orbital. The filling of the orbitals obeys … Read more
Molecular orbital theory does not consider the electrons in a bond to be localised between two nuclei. Rather it considers them to occupy a molecular orbital. This orbital, the region of space in which the electron is most likely to be found, covers the whole molecule, and the atoms that make up the molecule are bound together … Read more
The fundamental aspects of valence bond theory as outlined on the previous page are that superposition of wavefunctions leads to a low energy bonding wavefunction in which the probability of finding the electrons in the internuclear region has been substantially increased. This discussion centred on the H2 molecule, which contains a single σ bond. To discuss more complicated molecules it … Read more