Nanoclusters and nanoalloys of group 13 elements (B, Al, and Ga): benchmarking of methods and analysis of their structures and energies.

We investigated the structural and energetic properties of nanoclusters and nanoalloys composed of group 13 elements (B, Al, and Ga) up to a cluster size of 12. We conducted a comprehensive benchmark analysis of density functional and post-Hartree-Fock methods to identify efficient and accurate approaches for studying these systems using our benchmark dataset (BAlGa16) consisting of sixteen dimers and trimers. We compared different density functionals and post-Hartree-Fock methods using bond length and binding energy as parameters. B2PLYP closely follows CCSD(T) for geometry optimization, while REVPBE, BPBE, and PBE show cost-accuracy balanced performances. MRACPF was used as the reference for benchmarking energies, with NEVPT2 being the most accurate method, followed by CCSD(T) and DLPNO-CCSD(T). M06 and range-separated hybrid functionals perform well. Based on a cost-accuracy analysis, we recommend M06/def2-SVP as the preferred method. Additionally, we explored the structural evolution of pure, binary, and ternary clusters of group 13 elements up to 12 atoms, uncovering global and local minima. Ga clusters exhibited more rectangular faces compared to the predominantly trigonal faces of B and Al clusters. Binary clusters showed B in center positions, while Ga preferred outer positions, confirming the higher cohesion of B. The most favorable size of binary clusters (12) exhibited similar compositions of Al and Ga atoms. Compositions with 16.67-40% B, 16.67-60% Al, and 20-50% Ga were estimated to have negative mixing energies, indicating their relative stability.

Performance of Density Functionals and Semiempirical 3c Methods for Small Gold-Thiolate Clusters.

In light of the recent surge in computational studies of gold thiolate clusters, we present a comparison of popular density functionals (DFAs) and three-part corrected methods (3c-methods) on their performance by taking a data set named as AuSR18 consisting of 18 isomers of Aun(SCH3)m (m ≤ n = 1-3). We have compared the efficiency and accuracy of the DFAs and 3c-methods in geometry optimization with RI-SCS-MP2 as the reference method. Similarly, the performance for accurate and efficient energy evaluation was compared with DLPNO-CCSD(T) as the reference method. The lowest energy structure among the isomers of the largest stoichiometry from our data set, AuSR18, i.e., Au3(SCH3)3, is considered to evaluate the computational time for SCF and gradient evaluations. Alongside this, the numbers of optimization steps to locate the most stable minima of Au3(SCH3)3 are compared to assess the efficiency of the methods. A comparison of relevant bond lengths with the reference geometries was made to estimate the accuracy in geometry optimization. Some methods, such as LC-BLYP, ωB97M-D3BJ, M06-2X, and PBEh-3c, could not locate many of the minima found by most of the other methods; thus, the versatility in locating various minima is also an important criterion in choosing a method for the given project. To determine the accuracy of the methods, we compared the relative energies of the isomers in each stoichiometry and the interaction energy of the gold core with the ligands. The dependence of basis set size and relativistic effects on energies are also compared. The following are some of the highlights. TPSS has shown accuracy, while mPWPW shows comparable speed and accuracy. For the relative energies of the clusters, the hybrid range-separated DFAs are the best option. CAM-B3LYP excels, whereas B3LYP performs poorly. Overall, LC-BLYP is a balanced performer considering both the geometry and relative stability of the structures, but it lacks diversity. The 3c-methods, although fast, are less impressive in relative stability.

CSinGe4-n2+ (n = 1-3): prospective systems containing planar tetracoordinate carbon (ptC).

Density functional theory (DFT) based calculations have been carried out to explore the potential energy surface (PES) of CSinGe4-n2+/+/0 (n = 1-3) systems. The global minimum structures in the di-cationic states (1a, 1b, and 1c) contain a planar tetracoordinate carbon (ptC). For the CSi2Ge22+ system, the second stable isomer (2b) also contains a ptC with 0.67 kcal mol-1 higher energy than that of the 1b ptC isomer. The global minima of the neutral and mono-cationic states of the designed systems are not planar. The 1a, 1b, and 1c structures follow the 18 valence electron rule. The relative energies of the low-lying isomers of CSiGe32+, CSi2Ge22+, and CSi3Ge2+ systems with respect to the global minima were calculated using the CCSD(T)/aug-cc-pVTZ method. Ab initio molecular dynamics simulations for 50 ps time indicate that all the global minimum structures (1a, 1b, and 1c) are kinetically stable at 300 K and 500 K temperatures. The natural bond orbital (NBO) analysis suggests strong σ-acceptance of the ptC from the four surrounding atoms and simultaneously π-donation occurs from the ptC center. The nucleus independent chemical shift (NICS) showed σ/π-dual aromaticity. We hope that the designed di-cationic systems may be viable in the gas phase.

A Global Optimizer for Nanoclusters.

We have developed an algorithm to automatically build the global minimum and other low-energy minima of nanoclusters. This method is implemented in PyAR (https://github.com/anooplab/pyar) program. The global optimization in PyAR involves two parts, generation of several trial geometries and gradient-based local optimization of the trial geometries. While generating the trial geometries, a Tabu list is used for storing the information of the already used trial geometries to avoid using the similar trial geometries. In this recursive algorithm, an n-sized cluster is built from the geometries of n-1 clusters. The overall procedure automatically generates many unique minimum energy geometries of clusters with size from 2 up to n using this evolutionary growth strategy. We have used our strategy on some of the well-studied clusters such as Pd, Pt, Au, and Al homometallic clusters, Ru-Pt and Au-Pt binary clusters, and Ag-Au-Pt ternary cluster. We have analyzed some of the popular parameters to characterize the clusters, such as relative energy, singlet-triplet energy difference, binding energy, second-order energy difference, and mixing energy, and compared with the reported properties.