# Catalytic Performance of Cycloalkyl-Fused Aryliminopyridyl Nickel Complexes toward Ethylene Polymerization by QSPR Modeling

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

_{w}). Three-dimensional contour maps illustrate the predominant effect of a steric field on both catalytic properties; smaller sizes of cycloalkyl-fused rings are favorable to Act.y, whereas they are unfavorable to M

_{w}. This study may provide assistance in the design of a new nickel complex with high catalytic performance.

## 1. Introduction

**Fe**,

**Co**,

**Cr**) complexes on their catalytic performance [15]. The obtained results indicate the dominant role played by the conjugated degree in complexes on the catalytic activities.

## 2. Results and Discussions

#### 2.1. 2D-QSPR Modeling

^{2}), the root mean square error of the fitted data (RMSEF), the cross-validation coefficient (Q

^{2}), and the root mean squared error of cross-validation (RMSEV) are calculated and listed Table 1 to validate the stability and predictive power of the model. Additionally, the value of A means the number of components. As shown in Table 1, based on the VIP-PLS analysis, the number of descriptors gradually decreased from 63 to 22 and 12 to 5. An acceptable 2D-QSPR model should have higher R

^{2}and Q

^{2}values, as well as lower values of RMSEV/RMSEF under a smaller number of descriptors. Therefore, a set of 12 descriptors is selected as the optimum number of independent variables.

**Ni**complex.

^{2}) for the training set and test set are 0.892 and 0.814, respectively. The cross-validation coefficient (Q

^{2}) is 0.697, indicating the acceptable prediction and validation capabilities of the model. Comparatively, the R

^{2}values are not as high as in previous reports [9,10,15]. The reason might be the selection of model complexes, which not only vary in the sizes of the cycloalkyl-fused rings, but also vary in the presence of alkyl substituents on the fused ring, such as categories D and E in Scheme 1. The comparisons of experimental and predicted catalytic activities are plotted in Figure 2. The specific values of predicted catalytic activities for each complex are given in Table S3.

^{2}values of each descriptor in the fitting model, the contribution values to catalytic activities are also calculated and listed together. The descriptors were ranked from higher to lower according to their contribution values to catalytic activity. The explanations focus on the descriptors exhibiting higher contributions. It is clear that among all the selected descriptors, the minimum partial charges on a C atom (No.2), present the biggest contribution to the catalytic activities, with the value of 29.17%. This electrostatic descriptor describes the characteristics of the charge distribution of C atoms, showing that the minimum charge values on carbon atoms present largely positive correlations with catalytic activity.

_{D}is the solvent-accessible surface area of H-bonding donor H atoms, q

_{D}is the partial charge on H-bonding donor H atoms, and S

_{tot}is the total solvent-accessible molecular surface area. This descriptor shows the charge distribution on the H atoms and the interaction of hydrogen bonding. Different from the No.2 and No.3 descriptors, the No.9 descriptor has a negative correlation with catalytic activities, due to the generally positive charge of the H atoms.

#### 2.2. 3D-QSPR Modeling

^{2}) and test set (r

_{t}

^{2}) are 0.830 and 0.889, respectively, as shown in Figure 3a. Meanwhile, the cross-validation coefficient (q

^{2}) value is 0.692, indicating the good predictive and validated capabilities of the model. The contributions for steric and electrostatic fields are calculated with values of 87.3% and 12.7%, respectively, indicating the predominant role of steric fields on catalytic activity. As to the model of molecular weight, quantitative results are obtained as in Figure 3b. The correlation coefficients (r

^{2}, r

_{t}

^{2}) for the training and test sets are 0.950 and 0.893, respectively, and the q

^{2}value is 0.787. Comparatively, the predictive and validated powers are higher than that of the model for catalytic activity. The decisive effect on molecular weight comes from the steric field, with an overwhelming contribution of 89.1%.

## 3. Computational Methods

#### 3.1. Data Set

_{2}[19]. Regarding category B, the 9-(2-Cycloalkylphenylimino)-5,6,7,8-tetrahydrocycloheptapyridylnickel complexes are found from the condensation reactions of 5,6,7,8-tetrahydrocycloheptapyridine-9-one with various anilines [20,25]. As to category C, N-(2-substituted-5,6,7-trihydroquinolin-8-ylidene)-arylaminonickel(II) dichlorides (complex

**17**–

**26**, Scheme 1) are synthesized by the one-pot stoichiometric reaction of nickel dichloride, 2-chloro- or 2-phenylsubstituted 5,6,7-trihydroquinolin-8-one, and the corresponding anilines [21]. Subsequently, the 8-(2-cycloalkylphenylimino)-5,6,7-trihydroquinoline derivatives react with (DME)NiBr

_{2}or NiCl

_{2}to form the corresponding cycloalkyl-substituted 8-arylimino-5,6,7-trihydroquinolylnickel halides (complexes

**27**–

**32**, Scheme 1) [22]. Propyl substituted 4-arylimino-1,2,3-trihydroacridylnickel dihalide complexes (category D) are prepared by the metal-induced template reaction with NiCl

_{2}.6H

_{2}O or (DME)NiBr

_{2}[23]. As with category B, the category E complexes are synthesized from the condensation of 2-chloro-6,6-dimethyl-cyclopenta[b]pyridin-7-one with the corresponding aniline [24]. The observed catalytic activities and the molecular weight of the products are also listed in Scheme 1, which are taken under optimum conditions [15]. This is because the ethylene polymerization reaction actually takes place after the precatalyst is activated into the active species, and optimum conditions guarantee that all the precatalysts can be activated. The detailed optimum conditions are listed in Table S6 for each complex. By Hoteling’s T

^{2}method [26] in principle component analysis (PCA) [27], seven complexes (

**6**,

**7**,

**9**,

**10**,

**13**,

**18**, and

**19**) are identified as outliers and removed. Further analyses are conducted on the rest of the 39 complexes.

#### 3.2. QSPR Modeling

^{2}) are calculated and show lower values below 0.6 for the model of the molecular weight of the product. Therefore, the modeling is proceeded only for the properties of catalytic activity. The obtained descriptors are cross-validated for the optimum values of the cross-validation coefficient (Q

^{2}) and the root mean squared error of cross-validation (RMSEV) using the k-fold method [44]. Descriptors are then further reduced with a k-fold value of 5, by the variable importance of projection (VIP) [45,46] method incorporated in the partial least-squares (PLS) toolbox [47,48]. The average of the squared VIP scores equals 1, thus the “greater than one rule” is commonly used as a criterion for variable selection, meaning that only the descriptors with an importance value over 1 are selected. This pruning is repeated cyclically to gradually eliminate the descriptors.

^{2}) is the square correlation coefficient between the experimental and predicted values of the activity, and the root mean square error of the fitted data (RMSEF) illustrates the difference between the predicted and experimental activities, which are defined as Equations (3) and (4), respectively.

^{2}) in Equation (5), and the root mean squared error of cross-validation (RMSEV) is calculated by Equation (6):

^{2}and Q

^{2}values close to 1.0, as well as values of RMSEF/RMSEV close to 0. Later on, the data set is divided into a training set and a test set to build and validate the model, respectively.

^{3}type corresponding to atom C.3 in the Tripos force field, and complex structures are calculated at each 3D grid point. As to the electrostatic field, coulomb interactions are calculated with the charge values assigned by the MMFF94 force field. Lennard-Jones potentials are used to assess steric fields by the interaction of van der Waals. The calculated 3D descriptors are not independent variables, thus PLS analysis has been performed to extract the value of the principle components. In order to investigate the predictive power of the models and to obtain the optimal number of principal components, leave-one-out (LOO) cross-validation is carried out to provide the result of the cross-validation coefficient (q

^{2}). Afterwards, non-cross-validated analysis (without any validation) is performed to get the value of predictive correlation coefficient (r

^{2}). Herein, q

^{2}and r

^{2}are described in Equations (7) and (8), respectively.

^{2}over 0.5 and r

^{2}over 0.6.

## 4. Conclusions

## Supplementary Materials

^{2}, Q

^{2}, R

_{t}

^{2}, RMSEF, and RMSEV values for 39 complexes; Table S3: The values of the experimental and predicted catalytic activities for the training set of 29 complexes and the test set of 10 complexes from the 2D-QSAR analysis; Table S4: The values of the experimental and predicted catalytic activity for the training and test sets from the 3D-QSPR analysis; Table S5: The values of the experimental and predicted molecular weight for the training and test sets from the 3D-QSPR analysis; Table S6: Experimental values of catalytic activities, molecular weights, and melting temperatures of products under the optimum reaction conditions; Table S7: The calculated bond lengths and bond angles by DFT compared with experimental crystal structures for complex

**8**along with the values of the standard deviation (δ); and Table S8: The values of different self-defined descriptors for each Ni complex.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Scheme 1.**Structures of the initial data set for 46 nickel complex precatalysts along with their catalytic activities and molecular weight of produced polyethylene under the optimum conditions.

^{a}, 10

^{6}g·mol

^{−1}·h

^{−1},

^{b}, g·mol

^{−1}.

**Figure 2.**Experimental catalytic activities versus predicted values by the 2D-QSPR model for the training set and test set.

**Figure 3.**Experimental catalytic activities (

**a**) and molecular weight (

**b**) versus the predicted values by 3D-QSPR model for the training set and test set.

**Figure 4.**The 3D contour maps of the steric field for the model of (

**a**) catalytic activity, and (

**b**) molecular weight of product. The green and yellow regions indicate the positive and negative effects of the bulky group on catalytic performance, respectively.

**Table 1.**The values of the R

^{2}, Q

^{2}, RMSEF, and RMSEV for the 2D-QSAR model for catalytic activity at different numbers of descriptors.

No. | A | R^{2} | Q^{2} (k = 5) | RMSEF | RMSEV |
---|---|---|---|---|---|

63 | 6 | 0.9211 | 0.5810 | 0.6390 | 0.2772 |

22 | 5 | 0.8770 | 0.6892 | 0.5503 | 0.3461 |

12 | 5 | 0.8755 | 0.7328 | 0.5103 | 0.3483 |

5 | 2 | 0.7363 | 0.6731 | 0.5644 | 0.5069 |

**Table 2.**Regression coefficients and the contribution of each molecular descriptor in the final model.

No. | Molecular Descriptor | Coeff. | Contr.(%) |
---|---|---|---|

2 | Min partial charge for a C atom [Zefirov’s PC] | 0.7854 | 29.17 |

3 | WNSA-3 Weighted PNSA (PNSA3*TMSA/1000) [Zefirov’s PC] | 0.6168 | 17.38 |

9 | HA dependent HDCA-2/TMSA [Quantum-Chemical PC] | −0.3804 | 12.74 |

12 | Min valency of a H atom | −0.2534 | 9.21 |

11 | Avg valency of a N atom | 0.4056 | 9.15 |

10 | Max SIGMA-SIGMA bond order | 0.1834 | 5.47 |

8 | WNSA-3 Weighted PNSA (PNSA3*TMSA/1000)[Quantum-Chemical PC] | 0.1593 | 5.32 |

1 | Average Information content (order 2) | 0.1381 | 3.85 |

6 | Max 1-electron react. index for a C atom | 0.1501 | 3.59 |

5 | Max electroph. react. index for a C atom | 0.0899 | 3.29 |

7 | FNSA-2 Fractional PNSA(PNSA-2/TMSA)[Quantum-Chemical PC] | −0.0123 | 0.44 |

4 | HOMO–LUMO energy gap | −0.0141 | 0.40 |

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Meraz, M.M.; Malik, A.A.; Yang, W.; Sun, W.-H.
Catalytic Performance of Cycloalkyl-Fused Aryliminopyridyl Nickel Complexes toward Ethylene Polymerization by QSPR Modeling. *Catalysts* **2021**, *11*, 920.
https://doi.org/10.3390/catal11080920

**AMA Style**

Meraz MM, Malik AA, Yang W, Sun W-H.
Catalytic Performance of Cycloalkyl-Fused Aryliminopyridyl Nickel Complexes toward Ethylene Polymerization by QSPR Modeling. *Catalysts*. 2021; 11(8):920.
https://doi.org/10.3390/catal11080920

**Chicago/Turabian Style**

Meraz, Md Mostakim, Arfa Abrar Malik, Wenhong Yang, and Wen-Hua Sun.
2021. "Catalytic Performance of Cycloalkyl-Fused Aryliminopyridyl Nickel Complexes toward Ethylene Polymerization by QSPR Modeling" *Catalysts* 11, no. 8: 920.
https://doi.org/10.3390/catal11080920