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The ADC( n) approximation scheme to the one-particle Green function is briefly outlined [ADC( n) stands for algebraic diagrammatic construction accurate to nth order of perturbation theory]. The solution of the equations can be done either by a pole search algorithm (PSA) or by the Davidson diagonalisation approach CDDA) whose problems and advantages are discussed. The results obtained for N 2 are compared. The methods are applied to interpret the ionisation spectra of p-quinodimethane, p-benzoquinone and to calculate the lowest ionisation energies of the transition metal diatomics CU2, Ag2, Cr2 and M02. The ADC(4) equations are computationally very demanding and additional approximations need to be introduced in order to apply this method to any but the smallest systems. Such a simplified model is presented and applied to N2 and CS2.

Recent Progress in a Green's Function Method for the Calculation of Ionisation Spectra