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

Abstract

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

Diagnosis of the performance of the state‐specific multireference coupled‐cluster method with different truncation schemes

“…Another intriguing aspect of ${\rm Be}_2$ that was recognized in earlier studies is the presence of a true chemical bond between the two Be atoms at short distances (with a dissociation energy of $2.658 \pm 0.006\,{\rm kcal}/{\rm mol}$ 105) despite the closed shell character of the Be atom. This feature of the PEC has also been confirmed recently at the most rigorous levels of theory 100–104. For $X^1\Sigma^+ {\rm Be}_2$ , calculations that do not incorporate the effects of triple and quadruple excitations from the RHF wave function generally fail to locate the minimum on the PES 99, 100, 103.…”

“…‐1To benchmark the accuracy of SS‐MRCCSDT‐n, we computed the ground state PES of the Beryllium (${\rm Be}_2$ ) molecule. Despite the tremendous methodological developments, computational strategies capable of reliable calculation of the ground state energy surfaces of the Be‐dimer still remains an active research area in the realm of quantum chemistry 98–104…”

“…The use of the SS‐MRCCSD/CAS(2,2) with RHF orbitals still results in a repulsive potential as that of the RHF and full‐valence‐space multiconfiguration self consistent field (MCSCF) calculations 102. Thus, the binding in $X^1\Sigma^+ {\rm Be}_2$ is contingent on the effects of nondynamic and higher order dynamic electron correlation effects and of Nicolaides104 in his recent work stated that the unusual ${\rm Be}_2$ bond is produced predominantly by nondynamic correlations, whose characteristics originate from a participation in the bonding of a few low‐lying states of Be and not just of the $(a1s^2 2s^2 + b1s^2 2p^2)$ S Be ground state. In contrast, Schmidt et al102 suggested that the bond of $X^1\Sigma^+ {\rm Be}_2$ should be attributed exclusively to dynamical correlations.…”

State‐specific multireference perturbation theory with improved virtual orbitals: Taming the ground state of F2, Be2, and N2

“…The characterization of complete energy surfaces of the “deceptively” simple molecules such as F 2, Be 2, and N 2 [14,16,29,35,40,44,45,72–79] are widely used excellent testing grounds to illustrate the efficacy of new electronic structure method(s). It is worth stressing that their estimates agree very nicely.…”

“…Let us now proceed to the next example which is the description of the interaction potential of the ground‐state beryllium dimer, Be 2 . The primary difficulty in computing PES of Be 2 system emerges from the quite different character of the wave function in the equilibrium area and asymptotically dissociation region . This is due to the small radius of the core and the strong quasidegeneracy of 2s and 2p energy levels of the beryllium atom.…”