Full CI results for Be2 and (H2)2 in large basis sets

Dispersion, Rehybridization, and Pentacoordination: Keys to Understand Clustering of Boron and Aluminum Hydrides and Halides

The structure, stability, and bonding characteristics of dimers and trimers involving BX₃ and AlX₃ (X = H, F, Cl) in the gas phase, many of them explored for the first time, were investigated using different DFT (B3LYP, B3LYP/D3BJ, and M06-2X) and ab initio (MP2 and G4) methods together with different energy decomposition formalisms, namely, many-body interaction-energy and localized molecular orbital energy decomposition analysis. The electron density of the clusters investigated was analyzed with QTAIM, electron localization function, NCIPLOT, and adaptive natural density partitioning approaches. Our results for triel hydride dimers and Al₂X₆ (X = F, Cl) clusters are in good agreement with previous studies in the literature, but in contrast with the general accepted idea that B₂F₆ and B₂Cl₆ do not exist, we have found that they are predicted to be weakly bound systems if dispersion interactions are conveniently accounted for in the theoretical schemes used. Dispersion interactions are also dominant in both homo- and heterotrimers involving boron halide monomers. Surprisingly, B₃F₉ and B₃Cl₉ C_3v cyclic trimers, in spite of exhibiting rather strong B-X (X = F, Cl) interactions, were found to be unstable with respect to the isolated monomers due to the high energetic cost of the rehybridization of the B atom, which is larger than the two- and three-body stabilization contributions when the cyclic is formed. Another important feature is the enhanced stability of both homo- and heterotrimers in which Al is the central atom because Al is systematically pentacoordinated, whereas this is not the case when the central atom is B, which is only tri- or tetra-coordinated.

Beryllium bonding with noble gas atoms

Quantum chemical calculations were carried out to investigate the nature of the bonding between a neutral Be₃ ring and noble gas atom. Electronic structure calculation for these complexes was carried out at different computational levels in association with natural bond orbital, quantum theory of atoms in molecules, electron localization function, symmetry adapted perturbation theory, and molecular electrostatic potential surface analysis of Be₃ complexes. The Be atoms in the Be₃ moiety are chemically bonded to one another, with the BeBe bond dissociation energy being ~125 kJ mol^-1 . The Be₃ ring interacts with the noble gases through non-covalent interactions. The binding energies of the noble gas atoms with the Be₃ ring increases with increase in their atomic number. The non-covalent interaction index, density overlap region indicator and independent gradient model analyses reveal the presence of non-covalent inter-fragment interactions in the complexes. Energy decomposition analysis reveals that dispersion plays the major role towards stabilizing these systems.

Prediction of beryllium clusters (Ben; n = 3-25) from first principles

Evolutionary searches using the USPEX method (Universal Structure Predictor: Evolutionary Xtallography) combined with density functional theory (DFT) calculations were performed to obtain the global minimum structures of beryllium (Be_n, n = 3-25) clusters. The thermodynamic stability, optoelectronic and photocatalytic properties as well as the nature of bonding are considered for the most stable clusters. It is found that the cluster with n = 15 is the transition point at which the configurations change from 3D hollow cages to filled cage structures (with an interior atom appearing in the structure). All the ground state structures are energetically favorable with negative binding energies, suggesting good synthetic feasibility for these structures. The calculated relative stabilities and electronic structure show that the Be₄, Be₁₀ and, Be₁₇ clusters are the most stable structures and can be considered as superatoms. The electron configurations of Be₄, Be₁₀ and Be₁₇ clusters with 8, 20 and 34 electrons are identified as 1S² 1P⁶, 1S² 1P⁶ 1D¹⁰ 2S², 1S² 1P⁶ 1D¹⁰ 2S² 1F¹⁴, respectively. Theoretical simulations determined that all the ground state structures exhibit excellent thermal stability, where the upper-limit temperature that the structures can tolerate is 900 K. During AIMD simulation of O₂ adsorption onto the Be₁₇ cluster an interesting phenomenon was happening in which the pristine Be₁₇ cluster becomes a new stable Be₁₇O₁₆ cluster. Based on ELF (electron localization function) analysis, it can be concluded that the Be-Be bonds in the small clusters are primarily of van der Waals type, while for the larger clusters, the bonds are of metallic nature. The Be_n clusters show very strong absorption in the UV and visible regions with absorption coefficients larger than 10⁵ cm^-1, which suggests a wide range of potential advanced optoelectronics applications. The Be₁₇ cluster has a suitable band alignment in the visible-light excitation region which will produce enhanced photocatalytic activities (making it a promising material for water splitting).

Novel strategy to implement active-space coupled-cluster methods

A new approach is presented for the efficient implementation of coupled-cluster (CC) methods including higher excitations based on a molecular orbital space partitioned into active and inactive orbitals. In the new framework, the string representation of amplitudes and intermediates is used as long as it is beneficial, but the contractions are evaluated as matrix products. Using a new diagrammatic technique, the CC equations are represented in a compact form due to the string notations we introduced. As an application of these ideas, a new automated implementation of the single-reference-based multi-reference CC equations is presented for arbitrary excitation levels. The new program can be considered as an improvement over the previous implementations in many respects; e.g., diagram contributions are evaluated by efficient vectorized subroutines. Timings for test calculations for various complete active-space problems are presented. As an application of the new code, the weak interactions in the Be dimer were studied.

Quantum Monte Carlo calculation of the binding energy of the beryllium dimer

The accurate calculation of the binding energy of the beryllium dimer is a challenging theoretical problem. In this study, the binding energy of Be2 is calculated using the diffusion Monte Carlo (DMC) method, using single Slater determinant and multiconfigurational trial functions. DMC calculations using single-determinant trial wave functions of orbitals obtained from density functional theory calculations overestimate the binding energy, while DMC calculations using Hartree-Fock or CAS(4,8), complete active space trial functions significantly underestimate the binding energy. In order to obtain an accurate value of the binding energy of Be2 from DMC calculations, it is necessary to employ trial functions that include excitations outside the valence space. Our best estimate DMC result for the binding energy of Be2, obtained by using configuration interaction trial functions and extrapolating in the threshold for the configurations retained in the trial function, is 908 cm(-1), only slightly below the 935 cm(-1) value derived from experiment.

Diagonalization of large matrices: a new parallel algorithm

On the basis of a dressed matrices formalism, a new algorithm has been devised for obtaining the lowest eigenvalue and the corresponding eigenvector of large real symmetric matrices. Given an N × N matrix, the proposed algorithm consists in the diagonalization of (N - 1)2 × 2 dressed matrices. Both sequential and parallel versions of the proposed algorithm have been implemented. Tests have been performed on a Hilbert matrix, and the results show that this algorithm is up 340 times faster than the corresponding LAPACK routine for N = 10(4) and about 10% faster than the Davidson method. The parallel MPI version has been tested using up to 512 nodes. The speed-up for a N = 10(6) matrix is fairly lineal until 64 cores. The time necessary to obtain the lowest eigenvalue and eigenvector is nearly 5.5 min with 512 cores. For an N = 10(7) matrix, the speed-up is nearly linear to 256 cores and the calculation time is 5.2 h with 512 nodes. Finally, in order to test the new algorithm on MRCI matrices, we have calculated the ground state and the π → π* excited state of the butadiene molecule, starting from both SCF and CASSCF wave functions. In all the cases considered, correlation energies and wave functions are the same as obtained with the Davidson algorithm.

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.

Beryllium dimer--caught in the act of bonding

The beryllium dimer is a deceptively simple molecule that, in spite of having only eight electrons, poses difficult challenges for ab initio quantum chemical methods. More than 100 theoretical investigations of the beryllium dimer have been published, reporting a wide range of bond lengths and dissociation energies. In contrast, there have been only a handful of experimental studies that provide data against which these models could be tested. Ultimately, the uncertain extrapolation behavior associated with the available data has prevented quantitative comparisons with theory. In our experiment, we resolve this issue by recording and analyzing spectra that sample all the bound vibrational levels of the beryllium dimer molecule's electronic ground state. After more than 70 years of research on this problem, the experimental data and theoretical models for the dimer are finally reconciled.

Structural and electronic properties of small beryllium clusters: A theoretical study

Geometric structures and electronic properties of small beryllium clusters (Be(n), 2< or = n< or =9) are investigated within the gradient-corrected density functional theory. The computations are performed with the Becke exchange and Perdew-Wang correlation functionals. Both low and high multiplicity states are considered. A predominance of higher multiplicity states among the low-energy isomers of the larger clusters is found. An analysis of the variations in the structural and electronic properties with cluster size is presented, and the results are compared with those of earlier studies.

Strongly bound doubly excited states of Be2

The triplet and singlet potential curves of Be2 generated by single and double excitations from 2σu into 3σg and (or) 1πu are studied with a multireference configuration interaction (MRD-CI) method. Relative to X1Σg+(2σg2 σu2) with Re = 4.72 bohr and ωe = 258 cm−1 (calculated here), these antibonding MO → bonding MO excitations lead to average decreases in bond distance (in bohr) of 0.55 (2σu → 3σg), 0.88 (2σu → 1πu), 0.93 (2σu2 → 3σg1πu), and 1.22 (2σu2 → 1πu2). The increase in vibrational frequencies ranges from 240 to 600 cm−1. The 3σg MO is found to be less bonding than 1πu, confirming predictions made by Bader et al. The experimental states A1Πu and B1Σu+ correspond to doubly excited 11Πu (2σu2 → 3σg1πu) and singly excited 11Σu+(2σu → 3σg), respectively. The 13Σg− and 11Δg states, both 2σu2 → 1πu2, preserve their doubly excited structure up to dissociation. Within the Franck–Condon region, 13Πu changes from bound (2σu2 → 3σg1πu) to repulsive (mixed 2σu → 1πg/2σg → 1πu), thereby creating the unusual situation of a strongly bound potential (short Re, high ωe) with an adiabatic dissociation energy near zero. The singlet counterpart 11Πu, however, behaves regularly as its doubly excited character is maintained up to large R(Be—Be). Key words: ab initio calculations, beryllium dimer, doubly excited states, electronic transitions, potential curves.