Be2 Molecules Research Articles

Photoelectron Velocity Map Imaging Spectroscopy of the Beryllium Trimer and Tetramer.

Computational studies of small beryllium clusters (BeN) predict dramatic, nonmonotonic changes in the bonding mechanisms and per-atom cohesion energies with increasing N. To date, experimental tests of these quantum chemistry models are lacking for all but the Be2 molecule. In the present study, we report spectroscopic data for Be3 and Be4 obtained via anion photodetachment spectroscopy. The trimer is predicted to have D3h symmetric equilibrium structures for both the neutral molecule and the anion. Photodetachment spectra reveal transitions that originate from the X2A2″ ground state and the 12A1' electronically excited state. The state symmetries were assigned on the basis of anisotropic photoelectron angular distributions. The neutral and anionic forms of Be4 are predicted to be tetrahedral. Franck-Condon diagonal photodetachment was observed with a photoelectron angular distribution consistent with the expected Be4-X2A1 → Be4X1A1 transition. The electron affinities of Be3 and Be4 were determined to be 11363 ± 60 and 13052 ± 50 cm-1, respectively.

Range-separated multideterminant density-functional theory with a short-range correlation functional of the on-top pair density.

We introduce an approximation to the short-range correlation energy functional with multideterminantal reference involved in a variant of range-separated density-functional theory. This approximation is a local functional of the density, the density gradient, and the on-top pair density, which locally interpolates between the standard Perdew-Burke-Ernzerhof correlation functional at a vanishing range-separation parameter and the known exact asymptotic expansion at a large range-separation parameter. When combined with (selected) configuration-interaction calculations for the long-range wave function, this approximation gives accurate dissociation energy curves of the H2, Li2, and Be2 molecules and thus appears as a promising way to accurately account for static correlation in range-separated density-functional theory.

Ultra-Weak Metal-Metal Bonding: Is There a Beryllium-Beryllium Triple Bond?

Metal-metal triple bonds featuring s-block element have not been reported until now. Only Be-Be double bonds between have been predicted theoretically based on the intuitive electron donation from four s1 type electron-donating ligands. Herein, we theoretically predicted a novel species featuring a Be-Be triple bond in the Li6 Be2 molecule. The molecule was found to be thermodynamically stable. The presence of the triple bond was confirmed by adaptive natural density partitioning (AdNDP), electron localization function (ELF), and atoms in molecules (AIM) analyses. Moreover, the mechanical strength of the Be-Be triple bond was analyzed by using compliance matrix, pointing towards its ultra-weak nature.

Computational study of Be2 using Piris natural orbital functionals

The third (PNOF3), fourth (PNOF4) and fifth (PNOF5) versions of the Piris natural orbital functional were used to characterize the beryllium dimer. The results obtained were compared to those gained afforded by CASSCF and CASPT2 as well as experimental data. The equilibrium distances (R e), dissociation energies (D e), effective bond orders (EBOs), and rovibrational levels were calculated. PNOF3, PNOF4, and CASPT2 predicted a bonded Be2 molecule, while PNOF5 and CASSCF did not, which demonstrates the importance of the dynamical electron correlation. We observed that PNOF3 yields the most accurate equilibrium distances, while PNOF4 most accurately calculates the rovibrational levels. However, both of these functionals overestimate dissociation energies. Both PNOF3 and PNOF4 predict EBOs that agree with that obtained using CASPT2.

The Beryllium tetramer: Profiling an elusive molecule

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.

Accurate calculations of dissociation energies of weakly bonded He2 and Be2 molecules by MRCI method

The He2 and Be2 ground state potential curves have been calculated by extrapolating to an infinite basis BSSE corrected MRCI total energies obtained with large Gaussian basis sets, large reference configuration spaces, and pseudo-natural molecular orbitals. The calculated De = 11.0031 K and Re = 5.607 a.u. of He2 are in an excellent agreement with De = 11.006 ± 0.004 K and Re = 5.608 ± 0.012 a.u. obtained recently by SAPT with SM energy correction. The obtained Be2 non-relativistic De = 822 cm−1 and relativistically corrected De = 818 cm−1 are in a good agreement with experimental De = 790 ± 30 cm−1 and the value of 829 ± 64 cm−1 obtained recently by a quantum Monte Carlo method.

Potential curves of the Be2 molecule in cylinder‐like cavities

AbstractSpatial confinement effects on the energy states of the beryllium atom and the electronic states of the beryllium dimer molecule are studied. Confinement effects are modeled by systems of point charges. Electronic structure calculations are carried out on the basis of the frozen core full configuration interaction method. Atomic states are treated within the even‐tempered basis set 17s13p9d consisting of 110 primitive Gaussians. The valence and the Rydberg states of the spherically confined Be atom exhibit different behavior under the compression. Inversions of the atomic terms are discussed. The potential energy curves of the cylindrically confined Be2 molecule are calculated within the cc‐pVTZ basis set. The employed cylindrical point charge environment model is shown to introduce significant end effects which are diminishing as the length of the cylinder increases. In very short tubes the above end effects may introduce additional changes into the molecular energy level picture. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Compact Molecule of Beryllium

The interaction potential for beryllium atoms is calculated using the Ritz variational method with molecular wave functions as trial functions. The results of calculations for Be2 molecules in the 1Σg+ state, which from the well–known data is considered ground, coincide with the results of previous studies. Similar calculations for the 3Σu+ state show that the minimum energy for this state is reached at horter internuclear distance and is lower than that for the 1Σg+ state.

Calculation of spectroscopic properties of the ground and excited states of Be2 according to the antisymmetrized geminal power (AGP) based excitation propagator

The ground and excited states of the beryllium dimer are calculated using the antisymmetrized geminal power-Tamm Dancoff approximation (AGP-TDA) that produces the excited states from a correlated reference ground state with excitation operators that diagonalize the excitation propagator, and the adjoints of which annihilate the reference state. The overall theoretical spectroscopy of the Be2 molecule is qualitatively in agreement with experiment.

Electron correlation in small metal clusters. Application of a theory of self-consistent electron pairs to the Be4 system

A knowledge of the properties of small metal particles is essential to the understanding of catalysis on a molecular level. In this regard, one particularly important property is the rate at which the dissociation energy of a small metal cluster approaches the bulk cohesive energy. The present research concerns the effect of electron correlation on the dissociation energy of a particularly stable beryllium cluster, the tetrahedral Be4 system. A contracted Gaussian basis set of size Be(9s 4p/5s 2p) was adopted in conjunction with the recently developed theory of self-consistent electron pairs (SCEP). Several new theoretical and computational wrinkles are discussed, including the incorporation of the SCEP/coupled electron pair approximation (SCEP/CEPA). The Be4 results provide strong evidence for the reliability of the Hartree–Fock approximation for alkaline earth cohesive energies. As suggested earlier the Be4 dissociation energy appears to be ∼40 kcal/mole. Analogous studies of the Be2 molecule are reported.

Optical spectra of Be atoms and Be2 molecules in rare gas matrices

Beryllium atoms, trapped at 4 °K in solid neon, argon, and krypton, showed a strong absorption near 235 nm which is assigned to the resonance transition 1P1 ← 1S0 appearing at 234.86 nm (42 565 cm−1) in the gas phase. Specifically, the absorption occurred at 232.0 nm (43 090 cm−1), 236.0 nm (42 360 cm−1), and 240.5 nm (41 567 cm−1) in Ne, Ar, and Kr, respectively. Excitation to the 1P1 state also led to long-lived emission in Ar and Kr matrices at 465.0 and 464.7 nm with lifetimes of 1.33(8) and 0.095(5) sec, respectively, and is assigned to the spin-forbidden 3P1 → 1S0 emission. In each case an adjoining emission band also appeared at longer wavelengths, which can most probably be attributed to coupling of the electronic transition to matrix phonons. In concentrated matrices, Be2 molecular absorption yielded a progression of bands with the (0,0) band at 350.15(5) nm (28 551 cm−1) in Ne and at 361.30(5) nm (27 670 cm−1) in Ar. In analogy with the similar van der Waals molecules Mg2 and Ca2, these bands are assigned to the A 1Σ+u ← X 1Σ+g transition. The vibrational frequency in the upper state is 489 cm−1 in Ne and 474 cm−1 in Ar matrices. No other molecular electronic transitions were detected out to 50 000 cm−1.

Theoretical Calculation of the Potential Curves of the Be2 Molecule

The low-lying electronic states of the Be2 molecule have been examined using MO SCF CI with a basis set of elliptical orbitals. The ground state of the molecule was found to be repulsive in the best calculation. The excited states all seem to be bound with potential curves similar to that predicted for Be2+. Two new techniques for improving the convergence of configuration interaction are introduced and applied to the ground-state calculation.