ABSTRACT
Vibrationally inelastic electron scattering calculations are much more dif“cult than those for elastic scattering. This applies particularly to polyatomic targets. In 2004, Itikawa characterizes the situation as that “a lot of problems are still to be solved” and “compared to the large number of theoretical studies of vibrational excitation of diatomic molecules, the number of theoretical works for polyatomic molecules is very limited” (Itikawa 2004). Whereas with very small molecules a sophisticated and rigorous approach can be employed (see, e.g., the application to the water molecule and CO2 (Haxton et al. 2004, Rescigno et al. 2002)), for larger molecules some approximations must be assumed. As in the theory of photon vibrational spectra, the only manageable approach to polyatomics seems to be that based on Born-Oppenheimer approximation and harmonic force “eld. Obviously such simpli“cations are open to uncertainties. Primarily it is the nonadiabaticity at low electron energies, for which rotations and electronic-vibrational coupling cannot be disregarded. Also the use of harmonic force “eld has its limitations. It disregards coupling between vibrational modes, its use is limited to 1 ← 0 transitions, not speaking about the effects of anharmonicity of potential curves along the vibrational coordinates. Still we considered it
8.1 Introduction .................................................................................................. 263 8.2 Basic Theory .................................................................................................264 8.3 Discrete Momentum Representation Method ...............................................264 8.4 Numerical Quadrature .................................................................................. 267 8.5 Evaluation of Coulomb Integrals ..................................................................268 8.6 Evaluation of Exchange Integrals ................................................................. 270 8.7 Polarization Effects....................................................................................... 272 8.8 Computational Details .................................................................................. 275 8.9 Application to Polyatomic Molecules ........................................................... 276
8.9.1 Methane ............................................................................................ 276 8.9.2 Cyclopropane .................................................................................... 278 8.9.3 Diacetylene ....................................................................................... 279
Acknowledgment ...................................................................................................280 References ..............................................................................................................280
