By D. ter Haar
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Additional resources for Theory and applications of the density matrix
In ice the protons are disordered, as we have seen, and this destroys the exact translational symmetry of the crystal structure. The result is that, instead of the elegant theory which has been developed for perfect crystals, we must use, at least in part, the sort of treatment which is at present being developed for liquid metals, glasses and other disordered systems. No such calculations have yet been made for ice, and indeed even the band-structure problem for liquid metals is still far from complete solution.
6. General form of the absorption spectrum of water vapour in the nearinfrared region (from data given by Hackforth, i960). In the lowest vibrational state of the molecule the values are slightly different: (O-H)0 = 0-957 x 10-8 cm; (H-O-H) 0 = 1050 3'. 14) In the far-infrared spectral region water vapour can absorb radiation by transition between different rotational levels without any vibrational or electronic changes. Such a pure rotational spectrum can only be exhibited by a molecule with a permanent dipole moment.
Distortion of the electron wave functions can only be achieved by adding in contributions THE WATER MOLECULE 21 from excited states. This requires energy but, since the excited states may increase the dipole moment parallel to the field, the total energy of the system can be lowered. The components of the polarizability tensor oc can be found by ordinary second-order perturbation theory and have the form a - where Wi is the energy of the excited state i/ri and Wo that of the ground state i/r0. To simplify this result it is often a good approximation to set Wi — Wo for all states i equal to the ionization energy / of the molecule, because the excited states in question are generally not far removed in energy from the beginning of the ionization continuum.