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In this paper, the geometric structure and physicochemical properties of Li2Bn0/− (n = 1–12) clusters were investigated using CALYPSO structure prediction software in combination with density functional theory at B3LYP/6-311G level. The results suggest that the doping of Li atoms has a significant effect on the ground state geometry of the Bn clusters. The stability changes with the increase in the number of boron atoms. Then two stable ground state structures, Li2B8 and Li2B9−, are selected for further analyzing their molecular orbitals and bonding properties. It is demonstrated that the stability of the Li2Bn0/− (n = 1–12) clusters originates from the s–p hybridization between B–B and Li–B. It is expected that this work can provide some references for future research on boron-based nanomaterials. [ABSTRACT FROM AUTHOR]

In this study, the unbiased crystal structure analysis by particle swarm optimisation (CALYPSO) combined with the density functional theory (DFT) method were used to perform a structure search for neutral Cs2Bn (n = 1–12) clusters, as well as the corresponding global minimum of the potential energy surface were determined. The ground-state structures of the Cs2Bn (n = 1–12) clusters have four types of geometries: planar, arch bridge, double pyramid, and shield shape. Subsequently, the relative stability of the ground-state structures was systematically analysed based on three effective rules, which indicates that the C7V Cs2B8 with a double pyramid structure has unusual stability. The results of the molecular orbitals (MOs) and density of states analysis (DOS) show that the B-2s and 2p atomic orbitals of Cs2B8 are the main components of MOs. In addition, from the results of adaptive natural density partitioning (AdNDP) and localised orbital locator (LOL), it can be seen that the excellent stability of Cs2B8 originates from the delocalised large π bonds with aromaticity and the s–p bonding of B–B. Our results reveal the structural growth mode of Cs2Bn clusters and enrich the chemical bonding properties of boron-based clusters. [ABSTRACT FROM AUTHOR]

Divalent metal clusters, such as alkaline-earth metal clusters, have drawn extensive attention because of the appealing size-evoked nonmetal-to-metal transition and attractive characters related to the size, shape, and doping of clusters. Herein, the structural properties of small-size neutral and anionic Mgn+1 and BaMgn (n = 2–10) clusters are investigated thoroughly through a combination of the CALYPSO software package and DFT optimization. The final calculation results indicate that with the increase in Mg atom number, Ba atoms are inclined to substitute Mg atoms located at the skeleton convex cap. What is worth mentioning is that BaMg9 cluster which presents tower framework possesses excellent stability in specified size range on account of the detailed analysis of bond energy, second-order energy difference, and the charge transfer. In addition, the analysis of the bonding characteristics manifests that the strong s–p interaction between Ba and Mg atomic orbitals is conducive to the improvement in the stability of BaMg9. [ABSTRACT FROM AUTHOR]

• The evolution of the structures for Mg 2 Bn0/– (n = 1–12) clusters has be elucidated. • The corresponding ground state structures are determined. • The local stable ground state structure is found. • The properties of electrons and bonds of the most stable isomers are discussed. In this paper, a global search for the lowest energy structure of Mg 2 B n 0/- (n = 1–12) clusters is performed based on Density functional theory combined with the particle swarm optimization algorithm program CALYPSO. The geometry, stability, charge transfer, and bonding properties of the clusters were analyzed at the B3LYP/def2-tzvp level. Then Mg 2 B 8 with high symmetry D 4h was found to be the magic numbers cluster among them. The doped clusters Mg 2 B n 0/− were compared with the pure boron clusters B n+2 0/− (n = 1–12) at the same level. The following results are obtained: as the number of boron atoms increases, the boron clusters doped with Mg atoms change from a two-dimensional planar or quasi-plane structure to a three-dimensional structure. The doped magnesium atoms are always positively charged in the convex capped position. And the doping of Mg atoms drives the overall stabilization of the boron clusters and makes the clusters more compact. There is a large amount of charge transfer between the Mg atom and the B atom, and the main orbitals involved are the S and p orbitals. There are strong interactions between the two atoms of boron and magnesium. Through the analysis of the bonding properties, it was found that the s-p hybridization mode between Mg B is the main reason for the enhanced cluster stability. [Display omitted] [ABSTRACT FROM AUTHOR]

• The evolution of the structures for Ca 2 Mg n – (n=1-15) clusters has be elucidated. • The corresponding ground state structures are determined. • One of the most stable structural units are found. • The properties of electrons and bonds of the most stable isomers are discussed. In recent years, the structure and properties of alkaline earth metal-doped Mg clusters have attracted much attention. Here, we investigated the structural properties, stability analysis, chemical bonding properties and charge transfer properties of Ca 2 Mg n ˉ (n=1-15) nanoclusters by using the efficient CALYPSO structure search software and the DFT full domain search method based on B3PW91 level calculation. It is found that most of their ground state structures can inherit pure Mg n+2 ˉ (n=1-15) clusters with high symmetry. We further compare the experimental and theoretical PES spectral data using pure Mg n+2 ˉ (n=1-15) and find a high agreement, which also indicating the validity of my calculated all-domain most stable structure. We found the outstanding stability of the pentagonal Ca 2 Mg 7 ˉ by stability analysis. Charge transfer occurred in all Ca 2 Mg n ˉ clusters, and this transfer was from Ca to Mg. The chemical bonding properties and molecular orbital revealed that the contribution of Mg- s and Mg- p to the molecular orbitals led to the formation of strong Mg-Mg bonds in the Ca 2 Mg 7 ˉ cluster, the s-p hybridization between Ca and Mg atoms and between Mg and Mg atoms also led to more powerful Mg-Mg bonds and Ca-Mg bonds, which is strong evidence for the stability of the Ca 2 Mg 7 ˉ clusters. [ABSTRACT FROM AUTHOR]

The structures and electronic properties of copper and sulfur doped copper clusters have been systematically investigated by means of the CALYPSO structure searching method combined with density functional theory. According to optimized Cu n S geometries, the dominant growth pattern is described as one Cu atom being added on the Cu n −1 S clusters. The planar ( C 2 v ) Cu 2 S cluster is the most stable geometries of Cu n S clusters. From n = 3, the doped systems show the appearance of three-dimensional (3 D ) geometries. In addition, the calculated HOMO–LUMO gaps are in the energy range of 1.42–2.96 eV, which make Cu n S clusters suitable candidates for renewable energy sources. At last, the molecular orbital energy, density of states, electrostatic potential and electron density deformation are also respectively analyzed for realizing the doped microscopic mechanism and providing strong support for essential theoretical and experimental research. [ABSTRACT FROM AUTHOR]

The structures properties of Cu n+1 and Cu n Se clusters have been investigated using an unbiased CALYPSO structure searching method. Firstly, an unbiased search relying on several structurally different initial clusters have been undertaken. Subsequently, geometry optimization by means of density functional theory is carried out to determine the relative stability of various candidates for low lying clusters obtained from the unconstrained search. The results shown that the ground state Cu 9 cluster is found to prefer a unique and previously unrecognized structure, with the total energies much lower than all structures proposed in the literature so far. The Cu 2 Se cluster is the most stable geometries for Cu n Se clusters. Additionally, the calculated HOMO-LUMO gaps ranges from 1.27 to 2.85 eV, which make Cu n Se clusters suitable candidates in photocatalyst materials. Lastly, the molecular orbital energy and density of states; the adaptive natural density partitioning; the electron localization function, localized orbital locator and Mayer Bond order are also studied for the ground state to develop a deeper understanding on the electronic properties. [ABSTRACT FROM AUTHOR]

[Display omitted] • This study used sesquiterpenoids with 97 carbon skeletons for model construction. • The scheme based on the DFT method combined with triple correction can accurately calculate Δ c H of sesquiterpenoid HEDFs. • We developed the MLR equation with only 4 features for predicting Δ c H for sesquiterpenoid HEDFs. • The proposed DFT-QSPR scheme can effectively guide the design of novel sesquiterpenoid HDEFs. Sesquiterpenoids that are renewable and have high energy density and low freezing point are promising biomass high-energy–density fuels (HEDFs). The enthalpy of combustion (Δ c H) is the key characteristic to measure the heat energy content of HEDFs. Its accurate theoretical prediction and evaluation is essential for designing novel sesquiterpenoid HEDFs. Combining the screened and optimized density functional theory (DFT) method with triple computational correction, we presented a standardized calculation scheme for Δ c H with an average absolute error of only 2.6 % by 295 structurally diverse sesquiterpenoid HEDFs. Then, the extreme gradient boosting (XGBoost) algorithm was used to determine the correlation between the calculated Δ c H and 54 quantum chemical (QC) descriptors and the shapley additive explanation (SHAP) method to elucidate the key factors affecting Δ c H. Lastly, a quantitative structure–property relationship (QSPR) prediction model with only four QC features was constructed by using the SHAP results via the multiple linear regression (MLR) algorithms. Notably, the model has excellent prediction performance, decreased complexity, and improved applicability. The coefficient of determination (R 2) of the internal training set and external test set of the model are 0.957 and 0.956, while the root mean square error (RMSE) are 8.626 kcal/mol and 9.012 kcal/mol, respectively. The proposed DFT-QSPR (the ingenious combination of DFT and QSPR) scheme can effectively guide the design of Δ c H of novel sesquiterpenoid HDEFs. [ABSTRACT FROM AUTHOR]

Here we reported the structures, electronic, spectral and thermodynamic properties of MB n −(M = La, Ce, Pr; n = 8, 9) clusters using Crystal structure Analysis by Particle Swarm Optimization (CALYPSO) searching method and density functional theory (DFT). Results found that the lowest structures of MB n −(M = La, Ce, Pr; n = 8, 9) possess the half-sandwich structure with C s symmetry, respectively. Based on the lowest energy structures, the electronic properties are analyzed by calculating charge transfer, electron localization function and polarizability; the photoelectron spectra, infrared spectra, Raman spectra and UV-vis spectra are computationally simulated to facilitate their spectral characterizations. At last, thermodynamic properties are symmetrically investigated for doped systems. We believe that our research will provide useful motivation for further experimental and theoretical investigations of lanthanide-doped boron based nanomaterials. [ABSTRACT FROM AUTHOR]

[Display omitted] • The evolution of the structures for Sr 2 Mg n (n =1–12) clusters has be elucidated. • The corresponding ground state structures are determined. • Several stable structural units are found. • The properties of electrons and bonds of the most stable isomers are discussed. Alkali earth metal clusters have been the subject of intense interest due to the wide range of applications and unique characteristics of transition from nonmetallic to metallic bond. In this work, the structural evolution and electronic properties of neutral and anionic strontium-doped magnesium clusters have been studied by structural search code of CALYPSO and subsequent calculation of DFT at B3PW91 level. The results reveled that most of the Sr 2 Mg n 0/– clusters are viewed as the substituted structures of corresponding pure magnesium clusters, in which the Sr atoms prefer to occupy the convex capped sites. Analysis of the natural population show that the Sr atoms always play the role of electron donor in the charge transfer process except for Sr 2 Mg 1-3 –. In the range of studied size, the neutral Sr 2 Mg 8 cluster with a tower-like structure and outstanding stability is uncovered. The molecular orbital and chemical bonding analysis indicate that the stronger Sr-Mg interaction lead to s-p hybridization between Sr and Mg atoms can stabilize the Sr 2 Mg 8 cluster. [ABSTRACT FROM AUTHOR]