The Beryllium tetramer: Profiling an elusive molecule

Abstract

The structure and energetics of Be(4) are investigated using state-of-the-art coupled-cluster methods. We compute the optimized bond length, dissociation energy, and anharmonic vibrational frequencies. A composite approach is employed, starting from coupled-cluster theory with single, double, and perturbative triple excitations extrapolated to the complete basis set (CBS) limit using Dunning's correlation consistent cc-pCVQZ and cc-pCV5Z basis sets. A correction for full triple and connected quadruple excitations in the smaller cc-pCVDZ basis set is then added, yielding an approximation to CCSDT(Q)/CBS denoted c∼CCSDT(Q). Corrections are included for relativistic and non-Born-Oppenheimer effects. We obtain D(e) = 89.7 kcal mol(-1), D(0) = 84.9 kcal mol(-1), and r(e) = 2.043 Å. Second-order vibrational perturbation theory (VPT2) is applied to a full quartic force field computed at the c∼CCSDT(Q) level of theory, yielding B(e) = 0.448 cm(-1) and fundamental frequencies of 666 (a(1)), 468 (e), and 571 (t(2)) cm(-1). Computations on the spectroscopically characterized Be(2) molecule are reported for the purpose of benchmarking our methods. Perturbative estimates of the effect of quadruple excitations are found to be essential to computing accurate parameters for Be(2); however, they seem to exert a much smaller influence on the structure and energetics of Be(4). Our extensive characterization of the Be(4) bonding potential energy surface should aid in the experimental identification of this thermodynamically viable but elusive molecule.

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

“…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. Schmidt et al102 also compared a number of ground state energy surfaces of the Be‐dimer generated via the current generation high‐level SRCC methods using a revised version of the aug‐cc‐pVQZ set (containing 5s,4p,3d,2f,1g contracted functions, which are augmented by a set of s,p,d,f,g functions with small exponents).…”

Ab initio study of many-body decomposition of the interaction energy in small beryllium clusters

“…Our aim is a deeper understanding of interaction forces leading to much higher stability of Be clusters in comparison with the smallest Be 2 species. In the recent paper on Be pentamers and tetramers from Schaefer's group [8,9], authors analysed the IE of these complexes in terms of sequential dissociation energies for Be 2À5 clusters. They found that the magnitude of the energy necessary for the dissociation of the tetramer to Be 3 + Be stands out from the trend.…”

The Beryllium Pentamer: Trailing an Uneven Sequence of Dissociation Energies

“…[10,11,[18][19][20][21][22][23][24][25][26][27] A number of fac-tors complicate the bonding in these molecules, including orbital hybridization, multiconfigurational effects, strong dynamical correlation, and the small 2s-2p energy gap in atomic beryllium. [7] Previous work on these clusters has been reviewed elsewhere; [1,7,9,17,28] we rehearse the highlights here. The dimer and the trimer both have a formal bond order of zero and neither is bound at the Hartree-Fock (HF) level of theory.…”

“…Theory predicts significant jumps in the atomization energy for the next two clusters, with D e = 17.2 kcal mol À1 for Be 3 [8] and D e = 89.7 kcal mol À1 for Be 4 . [9] The atomization energy of the Be 5 cluster is thought [10,11] to lie well above 100 kcal mol À1 . Beryllium clusters continue to provoke significant theoretical interest and serve as a proving ground for high-level theoretical methods.…”

“…The beryllium tetramer is the first cluster in the series to be bound at the HF level; an atomization energy of approximately 40 kcal mol À1 is predicted. [9] Correlation increases this value dramatically, and triple and quadruple excitations from the zeroth-order wavefunction provide noticeable contributions to the dissociation energy. [9,22] Single-reference theoretical methods are generally considered inappropriate for Be 2 and Be 3 due to the magnitude of static correlation effects in these clusters.…”