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In this paper, we used CALYPSO program which is conjuncted with DFT to investigate Li doped small-sized neutral Bn clusters. From ground-state and low energy structures, the properties and geometric significance of Li-doped boron clusters are greatly affected. Except for LiB9, which adds a B atom on preceding LiB8 boron wheel, the ground-state clusters of LiBn are formed by replacing the terminal boron atom of the Bn+1 clusters in the same size with a Li atom or by adding a Li atom to the Bn clusters. The transition point from 2 to 3D configuration of LiBn clusters appears at n = 5. The stability of LiBn clusters was analyzed by calculating the average binding energy, Gibbs free energy, first-order differential energy, second-order differential energy, HOMO–LUMO gap (the energy gap between the highest occupied and lowest unoccupied molecular orbital) and charge transfer. The results show that the LiB11 cluster with excellent symmetry and planar structure is the relative most stable structure. Molecular orbital and chemical bonding analysis indicated that the main reason for the stability of the LiB11 cluster is mainly due to the strong s-p bonding of B–B. [ABSTRACT FROM AUTHOR]

To understand the effects of Cs on pure boron clusters, the growth mode, electronic properties, and bonding characteristics of CsB n 0/− (n = 2–12) clusters were discussed by CALYPSO combined with DFT method. Photoelectron spectra of the ground-state structures are reliable and efficient based on the accurate structure search method, which can provide theoretical information for future related studies. Through the study of the three valid criteria, we conclude that the CsB 8 and CsB 8 − with point group symmetry C 7V have outstanding stability and electronic properties. The orbital composition analysis indicates that the molecular orbitals of these two clusters are mainly composed of B-2 s and B-2 p atomic orbitals (AOs), and there is a strong interaction between these two AOs. Furthermore, we also found that the high stability of CsB 8 and CsB 8 − clusters mainly originates from the s - p bonding, σ and π bonds of B–B, especially the CsB 8 − cluster has (σ+π) double aromaticity. • The evolution of the structures for CsB n (n = 2-12) clusters has be elucidated. • The corresponding ground state structures are determined. • It is found that the most stable isomer is a double pyramid structure with double aromaticity. • The molecular orbitals and bonding characteristics of the most stable structure are discussed by various methods. [ABSTRACT FROM AUTHOR]

• The evolution of the structures for Ba n Mg m 0/– (n = 1,2; m = 10–15) clusters has be elucidated. • The corresponding ground state structures are determined. • Two local stable ground state structures are found. • The properties of electrons and bonds of the most stable isomers are discussed. Projects about alkaline-earth metals doped magnesium are hot issues constantly in cluster science, while research in terms of Mid-Sized Ba atoms doped magnesium cluster was unreported. We adopted the CALYPSO method coupled with DFT calculation to simplify the process of structure searching at the range of Ba n Mg m 0/– (n = 1,2; m = 10–15) cluster. We found the doped Ba atoms tend to occupy convex capped sites in each structure. Meanwhile, the six-atom triangular prism as a major structure constructed the great mass of isomers. Based on the result of the relative stability survey, we selected BaMg 13 – and Ba 2 Mg 13 – to conduct further investigations, according to a different numbers of doped Ba atoms. Analysis of the bonding character manifests that the Mg- p orbital takes up the highest proportion for both BaMg 13 – and Ba 2 Mg 13 – cluster at HOMO, LUMO position as well as the existence of strong covalent bonds between Mg-Mg atoms and Ba-Mg atoms. [Display omitted] [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]

[Display omitted] • The evolution of the structures for Ba 2 Mg n (n = 1–10) clusters has be elucidated. • The corresponding ground state structures are determined. • A pagoda-like most-stable structure are found. • The properties of electrons and bonds of the most stable isomers are discussed. This paper reports systematic studies of small sized magnesium clusters doped with two barium atoms in both neutral and anionic species. The search, geometric optimization, and energy correction of stable and low-energy structures were completed using CALYPSO software package and DFT calculations. The structural evolution of Ba 2 Mg n 0/– clusters (n = 1–10) with increasing size were elucidated, and we found that most of the ground-state isomers of them inherit that of the corresponding pure Mg clusters well in terms of structure. After verifying the NBO (natural bond orbital) charge of the low-lying Ba 2 Mg n 0/– clusters (n = 1–10), a new fact was exposed: that all the doped Ba atoms in the structures are positively charged except in Ba 2 Mg–. A pagoda-like most-stable cluster Ba 2 Mg 8 with a HOMO-LUMO gap of 1.59 eV was found by relative stability analysis within the scope of our study. Further analyses of the molecular orbitals and bonding of Ba 2 Mg 8 clusters also revealed a strong interaction between Ba-6 s and Mg-3 p AOs, which may be the main reason for the high stability of Ba 2 Mg 8. We hope our studies will provide guidance for the synthesis and application of doped Mg-based nanomaterials in the future. [ABSTRACT FROM AUTHOR]