Neutron Scattering

Each new model of coupled motion requires the diagonalisation of a new hamiltonian matrix
which is always much more complex than the SPM . This is hard and sometimes impossible
work . The single particle model is such attractive because it involves only properties of the
rotating group and can be applied in any environment .
17.4 Calculation of potentials 'ab-initio'
The result of an analysis of tunnelling spectra, librational (E ol ) and activation (Ea ) energies is
the rotational potential up to some order of its Fourier components . The exponential dependence
of the tunnel splitting on the barrier height makes this probe especially important .
The determination of rotational potentials is a value in itself. However, a deeper understanding
requires its deduction from more fundamental quantities . A step towards this goal is
a parametrisation of interactions in a solid by atom-atom potentials
b ij qzqj
VU = az jex p(- (i zj r) - r6
+r (17 .45)
The first term represents the repulsive, the second the attractive van-der-Waals interactions . In
addition electrostatic terms may be added . The total potential energy is given as the sum over
all pair potentials . One important postulate/property of atom-atom potentials is their tranferability
- at least within certain classes of chemically related compounds . Thus the dynamic
properties of an unknown material should be calculable on the basis of the structure using
established pair potentials . This technique is used in studying reaction pathes in chemistry or
functionalities in biology and pharmacy.
With the more and more increasing power of computers it is possible to do energy calculations
really 'ab initio' . Quantum chemistry programs like GAUSSIAN98 minimize the energy
of the elctronic wave functions of a system of atoms . The aim is the same like with the pair potential
: e .g . to probe paths of a synthesis and thus avoid expensive practical tests in preparative
chemistry.