The Beryllium tetramer: Profiling an elusive molecule

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.

Cumulants as the variables of density cumulant theory: A path to Hermitian triples

We study the combination of orbital-optimized density cumulant theory and a new parameterization of reduced density matrices in which the variables are the particle-hole cumulant elements. We call this combination OλDCT. We find that this new Ansatz solves problems identified in the previous unitary coupled cluster Ansatz for density cumulant theory: the theory is now free of near-zero denominators between occupied and virtual blocks, can correctly describe the dissociation of H₂, and is rigorously size-extensive. In addition, the new Ansatz has fewer terms than the previous unitary Ansatz, and the optimal orbitals delivered by the exact theory are the natural orbitals. Numerical studies on systems amenable to full configuration interaction show that the amplitudes from the previous ODC-12 method approximate the exact amplitudes predicted by this Ansatz. Studies on equilibrium properties of diatomic molecules show that even with the new Ansatz, it is necessary to include triples to improve the accuracy of the method compared to orbital-optimized linearized coupled cluster doubles. With a simple iterative triples correction, OλDCT outperforms other orbital-optimized methods truncated at comparable levels in the amplitudes, as well as coupled cluster single and doubles with perturbative triples [CCSD(T)]. By adding four more terms to the cumulant parameterization, OλDCT outperforms CCSDT while having the same O(V⁵O³) scaling.

Can density cumulant functional theory describe static correlation effects?

We evaluate the performance of density cumulant functional theory (DCT) for capturing static correlation effects. In particular, we examine systems with significant multideterminant character of the electronic wave function, such as the beryllium dimer, diatomic carbon, m-benzyne, 2,6-pyridyne, twisted ethylene, as well as the barrier for double-bond migration in cyclobutadiene. We compute molecular properties of these systems using the ODC-12 and DC-12 variants of DCT and compare these results to multireference configuration interaction and multireference coupled-cluster theories, as well as single-reference coupled-cluster theory with single, double (CCSD), and perturbative triple excitations [CCSD(T)]. For all systems the DCT methods show intermediate performance between that of CCSD and CCSD(T), with significant improvement over the former method. In particular, for the beryllium dimer, m-benzyne, and 2,6-pyridyne, the ODC-12 method along with CCSD(T) correctly predict the global minimum structures, while CCSD predictions fail qualitatively, underestimating the multireference effects. Our results suggest that the DC-12 and ODC-12 methods are capable of describing emerging static correlation effects but should be used cautiously when highly accurate results are required. Conveniently, the appearance of multireference effects in DCT can be diagnosed by analyzing the DCT natural orbital occupations, which are readily available at the end of the energy computation.

Density functional study of structural and electronic properties of small binary Be(n)Cu(m) (n + m = 2~7) clusters

The geometrical structures, electronic properties and relative stabilities of small bimetallic Be n Cu m (n + m = 2-7) clusters have been systematically investigated by using a density functional method at the B3PW91 level. In the most stable structures of Be n Cu m , the Be atoms tend to gather together and construct similar configurations to those of pure Be n clusters. Meanwhile, there is a tendency for Cu atoms to segregate toward the Be n cluster surface. The successive binding energies, cohesive energies, second difference of energies, the highest occupied-lowest unoccupied molecular orbital energy gaps and chemical hardness of Be n Cu m are also investigated. All of them demonstrate that the clusters with even number of copper atoms present relatively higher stabilities. The natural population analyses on the Be n Cu m clusters reveal that, the charge transfers from Be to Cu when the average coordination numbers (Nc) of Be atom is less than 3, whereas the charge-transferring direction reverses when Nc(Be) increases.

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

We have tested the linked version of a iterative (partial) triples correction for the Jeziorski-Monkhorst ansatz based state-specific multireference coupled cluster (SS-MRCC) approach with singles and doubles (SD) excitations [abbreviated as SS-MRCCSDT-1a and SS-MRCCSDT-1a+d]. The assessments of SS-MRCCSDT-1a and SS-MRCCSDT-1a+d schemes have been performed on the ground potential energy surface (PES) of P4, Li(2),Be(2) systems which demand the MR description, and on study of the excitation energy between the ground and first excited state for P4 system. Illustrations in the isomerization of cyclobutadiene also show the power of the schemes. One of the designed features of the SS-MRCCSDT-n methods introduced here is that they do not require storage of the triples amplitudes. In the entire range of geometries, we found a definite improvement provided by SS-MRCC with SDT-1a and SDT-1a+d schemes over the standard SD one. In the nondegenerate regions of PES, the closeness of the performance of the single-reference CC to the SS-MRCC methods increases after inclusion of even partial triple excitations. Generally, the performance of the SS-MRCCSDT-1a+d approach is closer to the corresponding full configuration interaction (FCI) one than to the SS-MRCCSDT-1a specially in the degenerate geometries (as is evident from nonparallelism error). The deviation from FCI for the first excited state of the P4 model using various SS-MRCC theories with different truncation schemes obtained by converging on the second root of the effective Hamiltonian has also been reported. We also compare our results with the current generation state-of-the-art single and multireference CC calculations to envisage the usefulness of the present approach. Initial implementation indicates that the SS-MRCCSDT-n formalism can provide not only reliable excitation energies and barrier height even when used in a relatively small model space, but also offers a considerable promise in generating the entire energy surface with low nonparallelity error.