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.

Recent high-resolution spectroscopic studies by Merritt, Bondybey, and Heaven (Science 2009, 324, 1548) have heightened the anticipation that small beryllium clusters will soon be observed in the laboratory. Beryllium clusters are important discrete models for the theoretical study of metals. The trigonal bipyramidal Be(5) molecule is studied using high-level coupled cluster methods. We obtain the optimized geometry, atomization and dissociation energies, and vibrational frequencies. The c~CCSDT(Q) method is employed to compute the atomization and dissociation energies. In this approach, complete basis set (CBS) extrapolations at the CCSD(T) level of theory are combined with an additive correction for the effect of iterative triple and perturbative quadruple excitations. Harmonic vibrational frequencies are obtained using analytic gradients computed at the CCSD(T) level of theory. We report an atomization energy of 129.6 kcal mol(-1) at the trigonal bipyramid global minimum geometry. The Be(5)→Be(4)+Be dissociation energy is predicted to be 39.5 kcal mol(-1). The analogous dissociation energies for the smaller beryllium clusters are 64.0 kcal mol(-1) (Be(4)→Be(3)+Be), 24.2 kcal mol(-1) (Be(3)→Be(2)+Be), and 2.7 kcal mol(-1) (Be(2)→Be+Be). The trigonal bipyramidal Be(5) structure has an equatorial-equatorial bond length of 2.000 Å and an axial-equatorial distance of 2.060 Å. Harmonic frequencies of 730, 611, 456, 583, 488, and 338 cm(-1) are obtained at the CCSD(T)/cc-pCVQZ level of theory. Quadruple excitations are found to make noticeable contributions to the energetics of the pentamer, which exhibits a significant level of static correlation.