Space-focus plane calculation

For the purposes of this review it is convenient to focus attention on that class of molecules in which the valence electrons are easily distinguished from the core electrons (e.g., -n electron systems) and which have a large number of vibrational degrees of freedom. There have been several studies of the photoionization of aromatic molecules.206-209 In the earliest calculations either a free electron model, or a molecule-centered expansion in plane waves, or coulomb functions, has been used. Only the recent calculation by Johnson and Rice210 explicitly considered the interference effects which must accompany any process in a system with interatomic spacings and electron wavelength of comparable magnitude. The importance of atomic interference effects in the representation of molecular continuum states has been emphasized by Cohen and Fano,211 but, as far as we know, only the Johnson-Rice calculation incorporates this phenomenon in a detailed analysis. 

The largest observable d-spacing of such a camera depends on the limits of diffuse scattering in the detector plane. This limit — L — can be approximately calculated from the size of the aperture slits (St), the distance of the detector plane from the guard slits (Lj) and the size of the focus (a) [4], In real space one can write ... 

When the depth of focus relates to a single plane in object space, it can be calculated... 

The present method focuses on solving Kohn Sham equations and calculating electronic states, total energy and material properties of non-crystalline, nonperiodic structures. Contrary to the variety of well established k-space methods that are based on Bloch s theorem and applicable to periodic structures, we don t assume periodicity in any respect. Precise ab-initio environment-reflecting pseudopotentials proven within the plane wave approach are connected with real space finite-element basis in the present approach. The main expected asset of the present approach is the combination of efficiency and high precision of ab-initio pseudopotentials with universal applicability, universal basis and excellent convergence control of finite-element method not restricted to periodic environment. 

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