Persistent homology is a powerful and novel tool for quantifying the inherent topological features of structure. In this work, we used the persistent homology for the first time to study the closo-carboranes C2Bn-2Hn(...Persistent homology is a powerful and novel tool for quantifying the inherent topological features of structure. In this work, we used the persistent homology for the first time to study the closo-carboranes C2Bn-2Hn(n = 5~20) and their parent structures closo-boranes dianions BnHn2-(n = 5~20), where multiple elements are present. All these structures are first investigated with the standard Vitoris-Rips complex. We interpret all barcodes representation and associate them with structural details. By means of average bar length, a linear regression model was established to construct the relationship between persistent homology features and molecular stability, which was expressed by the relative energies. For closo-boranes dianions, we only use B atom set since B and H atoms are in pairs. The average lengths of β0, β1 and β2 bars are used as the features for linear regression, and excellent correlation coefficient(0.977) between the values predicted by persistent homology and those by quantum calculations was achieved. For closo-carboranes, C–B atom set(ignore the differences in the atoms), B atom set and C atom set were considered to get the persistent homology features(since there were only two C atoms in C2Bn-2Hn, only β0 bars were considered), and seven average bar lengths were calculated, respectively. Pearson coefficient of 0.937 was obtained. We found that the stability of carboranes showed a high linear correlation with the characteristics generated from topological bars in H0, H1 and H2. The results show that the topological information generated by persistent homology can be extended and applied to multi-element systems.展开更多
基金supported by the National Key R&D Program of China (2016YFB0700600)Soft Science Research Project of Guangdong Province (2017B030301013)+2 种基金Shenzhen Science and Technology Research Grant (ZDSYS201707281026184)supported in partial by NSF Grants DMS1721024,DMS1761320,IIS1900473NIH grants GM126189 and GM129004 Bristol-Myers Squibband Pfizer。
文摘Persistent homology is a powerful and novel tool for quantifying the inherent topological features of structure. In this work, we used the persistent homology for the first time to study the closo-carboranes C2Bn-2Hn(n = 5~20) and their parent structures closo-boranes dianions BnHn2-(n = 5~20), where multiple elements are present. All these structures are first investigated with the standard Vitoris-Rips complex. We interpret all barcodes representation and associate them with structural details. By means of average bar length, a linear regression model was established to construct the relationship between persistent homology features and molecular stability, which was expressed by the relative energies. For closo-boranes dianions, we only use B atom set since B and H atoms are in pairs. The average lengths of β0, β1 and β2 bars are used as the features for linear regression, and excellent correlation coefficient(0.977) between the values predicted by persistent homology and those by quantum calculations was achieved. For closo-carboranes, C–B atom set(ignore the differences in the atoms), B atom set and C atom set were considered to get the persistent homology features(since there were only two C atoms in C2Bn-2Hn, only β0 bars were considered), and seven average bar lengths were calculated, respectively. Pearson coefficient of 0.937 was obtained. We found that the stability of carboranes showed a high linear correlation with the characteristics generated from topological bars in H0, H1 and H2. The results show that the topological information generated by persistent homology can be extended and applied to multi-element systems.
