Time-dependent density functional theory computational aspects

The description of the photoionization process by means of a method based on the Density Functional Theory (DFT) is reviewed. The present approach is based on a basis set expansion in B-spline functions, which are particularly suited to deal with the boundary conditions of the continuum states. Both Kohn-Sham (KS) and its extension to the Time Dependent (TD-DFT) formalism are considered. The computational aspects of the method are described the implementations for atoms, for molecules in One Centre Expansion (OCE) and for molecules with the Linear Combination of Atomic Orbital (LCAO) scheme. The applications of the method are discussed, from atoms to large fullerenes, with comparison with available experimental data. 

Matching the lubrication equation to thermodynamic theory requires some caution, since thermodynamic theory yielding an expression for pL should be applied to the entire system including dense (liquid) and dilute (vapor) phases in equilibrium, whereas only the dense phase may have a suitable aspect ratio. To make the approximation applicable, one has to assume that the interface dividing the dense and the dilute phase is only weakly inclined relative to the substrate and weakly curved, so that its position can be expressed by a function h x, t) with derivatives obeying the above lubrication scahng. Thermodynamic theory, either local or nonlocal, can be used to compute an equilibrium density profile across the interface (in the vertical direction), po z — h x, t)), which is weakly dependent on the horizontal 2D position and time only through its dependence on h, e.g. 

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