Interpretation and Analysis of Spectra using Molecular Modelling

In this chapter we discuss the theoretical modelling of inelastic neutron scattering (INS) spectra. We shall see that INS spectra can be calculated accurately, both their intensities and frequencies. The modelling enables us to assign the spectra, the prerequisite for chemical and structural interpretations. 

The calculation of molecular structures and dynamics has been an area of knowledge that has advanced dramatically in the last twenty years. With the advent of more powerful computers, and their increased affordability, it is now possible to perform calculations on small-to-medium size molecules on a personal computer using ab initio methods. Our ability to do this has changed the way we interpret and analyse INS spectra. In particular, we take advantage of the fact that the intensity of the spectral lines in INS spectra is not subject to the photon selection rules, unlike infrared and Raman spectroscopy. This particular characteristic gives an increased certainty to the spectral assignments when aided by theoretical calculations. 

Although, strictly speaking, the description ab initio implies the solution of the quantum mechanical problem without parameterization, quantum mechanics is generally employed only in the calculation of the energy hypersurface that the nuclei feel and move over. The minimization of structures and calculation of their vibrations is most often a classical mechanics problem. 

Embedded in the theoretical framework of the study of molecules and solids, there is an approximation, the Bom-Oppenheimer approximation, which is justified in most cases and allows us to use classical mechanics to calculate the stmcture and dynamics of molecules and solids. 

Since we shall use the Bom-Oppenheimer approximation [1] throughout this chapter it is worth describing in some detail. The adiabatic Bom-Oppenheimer approximation states that the mass difference between the electron and a nucleus is so big that the separation of the Schrddinger equation into terms describing the nuclear and electronic motion is allowed. During nuclear motion, the electrons move as if the nuclei are fixed in their instantaneous positions. The Hamiltonian is expanded in powers of a parameter k. For a molecule of A/atom atoms, labelled /, each of mass w/ 

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Interpretation and Analysis of Spectra using Molecular Modelling... 

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