State‐ and property‐specific quantum chemistry: Basic characteristics, and sample applications to atomic, molecular, and metallic ground and excited states of beryllium

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, Ψ n , in the form a 0 Ψ   0 n+ Φ   corr n , where a 0 ≈ 1. Ψ   0 nis 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 Ψ   0 nis 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 Φ   corr ndepends 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 Σ   + gstate, which has attracted the interest of quantum chemists for decades. By asserting that the formation of the bond at about 2.5 A˚´ 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 {2 s ,2 p ,3 s ,3 p ,3 d } orbitals. The initially heuristic predictions are supported by calculations (using the MOLPRO code) of the lowest seven Be 2 1 Σ   + gstates, whose Ψ   0 nare obtained at the state‐averaged complete active space self‐consistent field level. These results are verified by the computation of a 0 Ψ   0 n+ Φ   corr nat the MRCISD level, where indeed a 0 ≈ 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 origin of the Be 2 bond is to be found in “nondynamical” – type correlations. This conclusion differs from that of Schmidt et al. [J Phys Chem A, 2010, 114, 8687], who argued that the formation of the Be 2 weak bond should be attributed exclusively to “dynamical” correlations that are defined with respect to the {2 s ,2 p } “active space” associated with the Be 1 S ground state. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem 111:3347–3361, 2011