| Περίληψη: | The basic argument of the state- and property-specific approach (SPSA) to quantum chemistry is that many problems in atomic and molecular physics can be understood conceptually and quantitatively without necessarily trying to obtain as accurately as possible the total energy and the corresponding wavefunction of the state(s) involved. Instead, their solution can be achieved economically by using symmetry-adapted, state-specific wavefunctions whose computation, following analysis and computational experience, is geared so as to account for at least those parts that 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 chapter discusses the SPSA assumptions and computational procedures and the related concept of the state-specific multiconfigurational (Fermi-sea) zero-order description of ground and excited states of the discrete and the continuous spectrum, Psi(0)(n). For each state, Psi(n), the Psi(0)(n) is used as reference for analysis and for further improvement of the overall calculation if necessary. Thus, the aim is to obtain Psi(n) in the form a(0)Psi(0)(n) + Phi(corr)(n), where a(0) approximate to 1, and the level of accuracy of Phi(corr)(n) depends on the property under investigation. In this context, certain aspects of the issue of the separation of electron correlation into nondynamical (ND) and dynamical (D) parts are commented. Optimally, the function spaces of the ND and the D correlations are different, and both depend on how the Fermi-sea orbitals for each problem are chosen and computed. The arguments are supported by a number of results on prototypical ground and excited states of atoms and molecules. Most of these are compared with results from conventional methods of quantum chemistry, where single basis sets, orbital- or Hylleraas-type, are used. One set of examples illustrates the computational capacity of the SPSA and concepts such as Fermi-sea or ND correlations, by presenting, or referring to, new and old results for certain properties of the ground and the excited states of the Be atom and its derivative species, Be(-), (Be)(n) cluster and Be metal, and Be(2). Special attention is given to the weak bond of the Be(2) X(1)Sigma(+)(g) state, which has attracted the interest of quantum chemists for decades. By asserting that the formation of the bond at about 2.5 angstrom is influenced by the interactions involving excited states, I point to the corresponding significance in zero order (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 Fermi-sea (active space) is represented by the Be set of {2s, 2p, 3s, 3p, 3d} orbitals. The initially heuristic predictions are supported by calculations (using the MOLPRO code) of the lowest 11 Be(2) (1)Sigma(+)(g) states, whose Psi(0)(n) are obtained at the CASSCF level. These results are verified by the computation of a(0)Psi(0)(n) + Phi(corr)(n) the lowest 7 states at the MRCISD level, where indeed a(0) approximate to 1 over the whole potential energy curve. This type of analysis and the corresponding results imply that by a properly justified choice of the zero-order orbital set, the Be(2) bond can be understood in terms of ND-type correlations, a conclusion which disagrees with that of Schmidt et al. J. Phys. Chem. A 114, 8687 (2010). |
