Many problems in Atomic and Molecular Physics can be understood conceptually and quantitatively by using symmetry-adapted, state-specific wavefunctions whose computation is geared so as to account for at least those parts which describe reliably the characteristics of closed-and open-(sub)shell electronic structures that contribute overwhelmingly to the property or phenomenon of interest. If additional terms in the wavefunction are required by the problem, this is feasible via methods of configuration-interaction or low-order perturbation theory. This is the main argument of the state-and property-specific approach (SPSA) to Quantum Chemistry. In this framework, the aim is to obtain the state wavefunction, C n , in the form a 0 C 0 n þ F corr n , where a 0 % 1. C 0 n is a state-specific zero-order description of ground and excited states of the discrete as well as of the continuous spectrum. In general, it is multiconfigurational and its construction follows from the ''Fermi-sea'' set of orbitals. The C 0 n is used as reference for analysis and/or for further improvement of the overall calculation, if necessary. The level of accuracy of the computation of the remaining F corr n depends on the property under investigation. The arguments are supported by characteristic examples on ground and excited states of atomic, molecular and metallic Beryllium. Some of these SPSA results are compared with results from more conventional methods of electronic structure. Special attention is given to the weak bond of the Be 2 X 1 R þ g state, which has attracted the interest of quantum chemists for decades. By asserting that the formation of the bond at about 2.5 Ǻ is influenced by the interactions involving excited states, I point to the corresponding significance in zeroorder (''Fermi-sea'') not only of p-waves but also of d-waves whose origin is in the valence-Rydberg state mixing of the lowest 1 D and 1 P o states of Be. Therefore, the