3. Results and discussion
3.1. Database establishment and selection of feature values The crystal structure of the single vacancy graphene adsorption single atom is shown in Fig. S1, where the gray atoms represent the C atoms and the blue atoms represent the adsorption atoms. We calculate the adsorption energy using the following equation [34]:
 �   =  total −    −  atom (1)
Where E   �  represents the total energy of the single vacancy graphene after adsorption of single atoms, E  represents the total energy of the single vacancy graphene, and E�    represents the energy of the adsorbed atoms. The adsorption distance and adsorption energy results are shown in Table S1.
Based on the adsorption energy and adsorption distance data ob- tained from DFT calculations for thirty-three elements on the single vacancy graphene surface, we collected sixteen characteristic quantities to evaluate the adsorption energy and adsorption distance of differ- ent atoms on the single vacancy graphene surface, including Atomic number, Atomic radius, Ionic radius, Covalent radius, Atomic vol- ume, Relative atomic mass, Period, Electron configuration(s), Electron configuration(p), Electron configuration(d), Electron configuration(f), Electron affinity, 1st ionization energy, 2nd ionization energy, 3rd ionization energy and Group.
Further, we make a selection of the descriptors. The descriptors of adsorption distance and adsorption energy were screened among the 16 characteristic quantities mentioned above, respectively. Pearson corre- lation coefficient is an indicator of the degree of correlation between the response variables. Pearson correlation coefficient is calculated to find out the factors that have the greatest influence on the adsorption distance and adsorption energy respectively, so as to determine the descriptors for each of them. The Pearson correlation coefficient is calculated as follows [35–37]:
  ,  =
∑( � −  ̄)( � −  ̄)
√∑( � −  ̄)2 ∑( � −  ̄)2 (2)
where     denotes the Pearson correlation coefficient, X� and Y� are the eigenvalues and target values,   and   are the average of X and Y, respectively, Its magnitude ranges from −1 to 1, where 0 indicates that the two variables are not correlated and the more the data converge to 1 or −1 indicates a stronger correlation.
As shown in Fig. 2, the ionic radius has the greatest effect on the adsorption energy and the adsorption distance with the Pearson correlation coefficients reaching 0.56 and 0.67, respectively. Consid- ering all kinds of factors, we identify the descriptors of the adsorption energy as atomic radius, ionic radius, atomic volume, 2nd ionization energy and 3rd ionization energy. The descriptors of the adsorption distance are identified as atomic number, ionic radius, period, electron configuration(p) and electron affinity.
Based on the above correlation analysis, we use the adsorption en- ergy and its descriptors, and the adsorption distance and its descriptors as the training data of the machine learning model, respectively, where the descriptors are used as the input data of the machine learning dataset, and the adsorption energy or the adsorption distance are used as the target data of the machine learning dataset. The adsorption performance database used for machine learning is shown in Table S2.
During training, to ensure that each variable is in the same range, both input and output variables are normalized in the range of 0 to 1 with the following equation [38]:
 ′
�
=
 � −  min  max −  min
(3)
Where X� represents the data individual, X �  is the maximum value in that class of data, and X �  is the minimum value.  翻译成中文