Co) Complexes

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Catalytic Activities of Bis(pentamethylene)pyridyl(Fe/Co) Complexes Analogue in Ethylene Polymerization by Modeling Method Sadia Ahmed, Wenhong Yang, Zhifeng Ma, and Wen-Hua Sun J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b09121 • Publication Date (Web): 29 Nov 2018 Downloaded from http://pubs.acs.org on November 30, 2018

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The Journal of Physical Chemistry

Catalytic Activities of Bis(pentamethylene)pyridyl(Fe/Co) Complexes Analogue in Ethylene Polymerization by Modeling Method Sadia Ahmed, ab Wenhong Yang, ab* Zhifeng Ma,ac and Wen-Hua Sunab* aKey

laboratory of Engineering Plastics and Beijing National Laboratory for Molecular Science, Institute of Chemistry, Chinese Academy of Sciences, No.2 North 1st Street, Zhongguancun, Beijing 100190, China bUniversity

of Chinese Academy of Sciences, Beijing 100049, China

cDepartment

of Chemistry, Tokyo Metropolitan University, Minami-Osawa 1-1, Hachioji, Tokyo 192-0397, Japan E-mail addresses: [email protected]; [email protected]; [email protected]; [email protected]

*Corresponding

to: Wenhong Yang (E-mail: [email protected]), Wen-Hua Sun (E-mail: [email protected])

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract: The catalytic activities of α,α’–bisimino–2,3:5,6–bis(pentamethylene)pyridyl(Fe/Co) chlorides analogue complexes are quantitatively investigated by the multiple linear regression analysis (MLRA) method. From the point of view of the electronic and steric effects, seven structural descriptors are selected and calculated, including Hammett constant (F), effective net charge (Qeff), energy difference (E), HOMOLUMO energy gap (Δ1, Δ2), open cone angle (θ) and bite angle (β). In order to get better model, the fitting analysis are carried out by using the combinations of four, three, two and single descriptor. The calculation results show quiet good correlation results. By using two descriptors (Qeff, β), the catalytic activities for both the Fe and Co complexes individually and also the variation between Fe and Co (FeCo) analogue system can be well predicted with the correlation coefficient values over 0.934. It is found that the effective net charge (Qeff) plays the dominant role in determining the catalytic activities for Fe and Co complexes. Furthermore, the lower values of catalytic activities in Co complexes are mainly attributed to the decreasing values of Qeff.

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1. Introduction Industrial and academic research has been extensively inspired by the ever growing demand of the high performance polyethylene due to their important roles in substantial technical interests of detergents, plastics, lubricants, oil additives and a variety of fine chemicals. The potential applications of polyethylene are determined by its physical and mechanical properties, which depend on the polymer composition and construction.1–4 Late transition metal complex catalysts, which can make the ethylene polymerization reaction feasible, have been one of the key techniques to produce polyethylene with various structures and properties.5–8 Among the various catalytic performances, the catalytic activity is one of the important target. Undoubtedly, there are many experimental reports focusing on increasing the catalytic activity by the modification of the framework of ligand and the substituents as well as the design of new structure of ligand,9–13 but the potential principle for higher catalytic activity is still not very clear at the molecular level. Essentially, the catalytic activity of the late transition metal complex is determined by the structure itself, including the electronic effect and steric effect.14–18 In previous studies, the electronic effect is investigated using DFTQEq method. Several descriptors are found to show good quantitative correlation with catalytic activity for Fe, Co and Ni complex systems,19–22 such as the effective net charge on the central metal atom (Qeff),19–21 HOMOLUMO energy gaps (Δε) between complex and ethylene,22 and energy difference between two spin states (ΔE).22 To consider the influence of steric effect, the open cone angle (θ) is proposed based on the previous report23 to describe the space within complex to accommodate the monomer of ethylene. Meanwhile, bite angle (β) which describes the coordination angle between metal and heteroatom is also considered.24–27 Then combined with the electronic effect, the catalytic activity is quantitatively predicted by the multiple linear regression analysis (MLRA) method. By choosing 3



four descriptors from electronic effect (Qeff and Hammett constant) and steric effect (θ, β), the calculated activities show good agreement with the experimental values for several 2–azacyclyl– 6–aryliminopyridylmetal (Fe, Co, and Cr) analogue complexes.28 Furthermore, the variation of activity between different 2–imino–1,10–phenanthrolinylmetal (Fe, Co and Ni) systems are studied by the modified MLRA method, which uses the difference of descriptors as independent variables and the difference of the activity as dependent variable.29 The calculated results show very good correlation for the analogues with different substitutes. However, the moderate results are observed for analogues with same ligand but different metal center.

R1

R2

N1 M N2 N3 Cl1 Cl2 R1 R1 M= Fe, Co

R1

R2

M1 M2 M3 M4 M5 R1 Me Et i-Pr Me Et R2 H H H Me Me

Scheme 1. The structure of α,α′–bis(arylimino)–2,3:5,6–bis(pentamethylene)pyridylmetal (Fe, Co) chlorides. In this study, we focus on the prediction of the catalytic activities for complex analogues with same ligand and substituents but different central metal atoms. The α,α’–bisimino–2,3:5,6– bis(pentamethylene)pyridyliron chlorides30 and its cobalt analogue31 are selected as the model complex systems with the structures shown in scheme 1. Compared with previous report which uses four fitting descriptors, herein we try to get good correlation results with less numbers of descriptors. The calculated results show that by using two descriptors, very good correlations can

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be obtained for each complex individually and also for the variations between two analogue systems. Accordingly, the contributions of each descriptor are analyzed.

2. Computational Details DFT calculations are performed to optimize the geometry of the complex using the DMol3 program.32–34 Electronic structure is described by the double numerical polarization (DNP)32–34 basis sets with effective core potential (ECP).35,36 To get better description of exchange and correlation, generalized gradient approximation(GGA) functional is used in conjunction with Becke–Perdew (BP).37,38 The convergence values for optimized energy, maximum force and displacement are 2.010-5 hartree, 4.010-3 hartree per bohr and 5.010-3 Å respectively. And the convergence criterion is 1.010-5 hartree for self–consistent field. After the optimization of the geometry, we calculate the value of descriptor for each complex. In this study, we consider five electronic descriptors, including effective net charge (Qeff), HOMOLUMO energy gaps (Δε1, Δε2), energy difference (ΔE) and Hammett constant (F), and two steric descriptors, including open cone angle (θ) and bite angle (β). Effective net charge (Qeff) is the difference between the net charge on central metal atom and averaged net charge on halogen atoms bonding with the metal in the complex molecule,19–21 calculating by equation S1. HOMO– LUMO energy gap is the energy gap between complex’s LUMO and ethylene’s HOMO orbitals (1) and the energy gap between ethylene’s LUMO and complex’s HOMO orbitals (2),22 as shown in equations S2 and S3 respectively. Energy difference (E) is the different optimized energy between two spin states.22 Hammett constant (F) is taken from reference.39 For steric effect, open cone angle () is calculated in the same manner as previous study28 by using equation S4.

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Bite angle () is the angle of N2–Fe(Co)–N3 in complex which can be measured from the optimized structure of precatalyst. To analyze the catalytic activities, we use the following multiple linear regression (MLR) equation (1) to correlate the calculated structural descriptors with the experimental catalytic activities, 𝑁

𝐴𝑐𝑡.(10 g ∙ mol a

―1

∙h

―1

)=

∑𝑚

o

+ 𝑚𝑖𝑋𝑖

(1)

𝑖=1

where N is the number of structural descriptors to correlate with catalytic activities, here we consider the cases for four, three and two different descriptors from the seven descriptors. Xi is the value for each selected structural descriptors. 𝑚o and 𝑚𝑖 represent coefficients which can be obtained after linear fitting using the LINEST function in Microsoft Excel.40 Regarding the variation of catalytic activities between Fe and Co analogue system, the variation values of descriptors (ΔX) between analogue system is calculated and correlated with the variation of experimental activities (ΔAct.) by using the modified MLRA29 shown in equation (2), 𝑁

Δ𝐴𝑐𝑡.(10 g ∙ mol a

―1

∙h

―1

)=

∑𝑤

o

+ 𝑤𝑖∆𝑋𝑖

(2)

𝑖=1

where N is the number of structural descriptors which ranges from 2 to 4, wo and wi are the linear fitting coefficient for the selected descriptors. In order to get the contribution of the each descriptor to the catalytic activity of the complex, descriptors and catalytic activities are standardized using ZScore method.41–43 Accordingly, the standardized values of coefficients can be obtained in the fitting equation. Then, the contribution values are calculated using the standardized values of coefficients and descriptors by the equation (3) 6


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𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 % =

|𝑤 ∙ ∆𝑋𝑗| 𝑀 ∑𝑗 = 1 𝑁 ∑𝑖 = 1|𝑤𝑖 ∙ ∆𝑋𝑖𝑗| 𝑀

× 100%

(3)

where 𝑤 and ∆𝑋 are the standardized values of fitting coefficients and variation of descriptors regarding one concerned descriptor, respectively. N represents the number of descriptors which is same as in equations (1) and (2), and M depicts the number of the complexes involved for each series of system.

3. Results and discussion 3.1 Predicted catalytic activity of Fe complexes Firstly, to validate the calculation parameters, the calculated geometry is compared with experimental observation of crystal structure for Fe-1 complex. As listed in Table 1, the standardized deviations for bond length and bond angle are 2.34 and 5.46 respectively at quintet, which are smaller than the results at other spin states. However, from the optimized energy, the structure at singlet has the lowest value of energy even the variation of energy is small. As the results of the selected electronic and steric descriptors are largely dependent on the optimized structure, therefore we choose the quintet state for Fe model complexes. After the geometry optimization for each complex, the five electronic descriptors and two steric descriptors are calculated accordingly. The detailed values of these seven structural descriptors for each complex are listed in Table 2 for Fe complexes.

Table 1. The comparisons of bond lengths and bond angles between calculated geometry and experimental values for complex Fe-1 along with the standard deviation (δ) and energy variation (ΔE) values at various spin states. 7



Fe-1 Fe1–N1 Fe1–N2 Fe1–N3 Fe1–Cl1 Fe1–Cl2 N2–C2 N3–C14

Exp.

Triplet

Quintet

2.13 2.27 2.26 2.30 2.30 1.28 1.27

Bond Lengths [Å] 1.84 2.06 1.99 2.25 2.22 1.31 1.32 7.09

1.87 2.04 2.00 2.29 2.22 1.32 1.32 7.14

2.11 2.25 2.24 2.29 2.28 1.29 1.29 2.34

72.38 72.65 141.10 140.8 99.98 96.39 110.04 102.53 105.00 109.12

Bond Angles [°] 80.13 81.77 159.86 139.48 93.32 94.69 91.34 93.78 95.40 129.11 11.86

78.97 79.54 147.78 162.86 96.53 96.96 94.19 102.70 102.55 102.93 8.68

74.17 74.07 142.69 145.5 98.49 96.67 96.11 100.94 101.42 118.28 5.46

0.29

2.52

 N1–Fe1–N2 N1–Fe1–N3 N2–Fe1–N3 N1–Fe1–Cl2 N2–Fe1–Cl2 N3–Fe1–Cl2 N1–Fe1–Cl1 N2–Fe1–Cl1 N3–Fe1–Cl1 Cl2–Fe1–Cl1



Singlet

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ΔE(kcal/mol)

0

In the Table 2, the values of Hammett constant (F) taken from the reference are only related to the type of substituent. Regarding the effective net charge (Qeff), the values show regular variation trend corresponding to the electronic property of R1 and R2 substituents. And there are clear correlations with the catalytic activities, that is, the activities present decreased trend with the increasing of Qeff which is agreement with previous report on Fe complexes.20 Open cone angle () obviously decreases from 126o to 87o as the substituents change from methyl to i-propyl which corresponds from Fe-1 to Fe-3 complexes. This is because that the steric hindrance around the central metal area increases with the increasing of substituent size, leading to the decreasing of the space to accommodate the ethylene monomer. For Fe-4 and Fe-5 complexes, with the introduction of the R2 substituent, the open cone angle decreases compared with Fe-1 and Fe-2, respectively.

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This indicates that R2 substituent also has obvious influence on the open cone angle, and with the increasing of the substituent size, the value of open cone angle decreases. Table 2. The values of Hammett constant (F), effective net charge (Qeff), open cone angle (θ), bite angle (β), energy difference (E) and HOMOLUMO energy gap (Δ1, Δ2) along with experimental catalytic activities of complexes Fe-1Fe-5. Complex no.

Activity (106g·mol-1·h-1)

Descriptors θ [°] 126.76

β [°] 142.69

E [kcal/mol] 2.52

Δε1 [kcal/mol] 79.44


12.81

Fe-1

0.10

Q [e] 0.573

Fe-2

0.06

0.572

115.30

141.95

4.06

80.25

73.16

11.40

Fe-3

0.22

0.611

87.00

142.25

1.91

79.63

73.54

9.36

Fe-4

0.06

0.574

108.00

142.98

2.59

80.82

71.97

12.38

Fe-5

0.06

0.571

108.00

142.50

3.36

81.38

71.59

11.74

F

While the bite angle () has almost similar values for the whole series of Fe complexes as it represents the bond angle of N2–Fe–N3 which is less dependent on the change of R1 and R2 substituents. As to HOMO–LUMO energy gap, there are slightly increased values of Δ1 and decreased values of Δ2 observed in Fe-4 and Fe-5 complexes, compared with Fe-1 and Fe-2 complexes. This is mainly due to the higher value of HOMO/LUMO orbital energy of complex caused by the introduction of electron-donating R2 substituent. Meanwhile, energy difference (ΔE) shows similar variation trends with Δ1, indicating the same influence of substituent on the two electronic descriptors. In our previous study, we choose two electronic descriptors (F, Qeff) and two steric descriptors (θ, β) to correlate with catalytic activities using MLRA.8 Herein, firstly we try to use four descriptors to investigate the catalytic activities as well. Since we have seven descriptors as candidates, there are totally 35 different combination ways by taking 4 descriptors out of 7 9



descriptors. Before we perform the calculation for the all possible combinations, firstly we check the correlations between each pair of descriptors. As shown in Figure S1a in the Supporting Information, there are high correlation coefficient values between the descriptors of Hammett constant (F) and effective net charge (Qeff), and also between two HOMO–LUMO energy gap descriptors (Δ1 and Δ2). After removing the combinations containing dependent descriptors, there are 16 effective combinations. It is found that all the calculated values of R2 are very good which equal to 1. Selected results for some combinations are shown in the Table 3. To check the quality of each four-descriptor MLRA models, we calculate the weight factor and show the values in the Table S1 of the Supporting Information. It is clear that all these models give close values of weight factor, only slight higher values are observed for several combinations, such as the combination of “Q, 2, ,  ”, “F, 2, ,  ” and “F, , ,  ”. Since the number of complexes for Fe system is five, the very good correlation results may be due to the problem of over fitting. Usually, the number of descriptors should be less than half of the data set. In this sense, we further choose three and two descriptors to investigate the catalytic activities correspondingly. For the case of three descriptors, the number of all the effective combinations is 25. For most of the fitting results, the obtained correlation coefficient (R2) values are very good, as listed in Table 3. When the number of descriptors is two, the correlation results are decreased and ten combinations give R2 values over 0.9. Some selected high correlation results are listed in Table 3. To see the influence of each single descriptor on the catalytic activities, the correlation coefficients are also calculated for the fitting results using each descriptor individually and results are shown in Table 3 as well. Clearly, all the correlation results are not so good. The descriptors of effective net charge (Qeff) and open cone angle (θ) give the R2 values close to 0.9, indicating that the

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influence of the substituents on the variation of catalytic activities largely reflect on the effective net charge and open cone angle. Besides the results shown in Table 3, the results for all the other combinations of three, two and single descriptor are listed in the Table S2 of Supporting Information. Meanwhile, the obtained coefficient values (mi) for the fitting equation (2) by using two descriptors are listed in Table S3. Table 3. Selected correlation coefficient (R2) values of Fe complexes obtain by using the combinations of four, three, two and single descriptor. Four Descriptors E, F, ,  E, Q, , F 1, Q, E,  2, Q, , 

Correlation Coefficient (R2) 1.00 1.00 1.00 1.00

Three Descriptors Q, ,  E, F,  1, Q,  E, Q, 2


Two Descriptors E, Q ,  Q,  2, 


Single Descriptor Q

 F




3.2 Predicted catalytic activity of Co complexes In the same manner, the catalytic activities of Co complexes analogue are investigated. From Table 4, it is clear that although the optimized energy of Co-1 complex is little higher at quartet, the geometry is more close to the experimental crystal structure with the lower standardized deviation values of bond lengths and bond angles. Therefore, we choose the quartet state for the calculations. Table 4. Comparisons of bond lengths and bond angles between the calculated geometry and experimental crystal data for complex Co-1 along with the standard deviation (δ) and energy variation (ΔE) values at various spin states. Co-1 Co1–N1 Co1–N2 Co1–N3 Co1–Cl1 Co1–Cl2

Exp. Doublet Bond Lengths [Å] 2.08 1.85 2.12 1.98 2.17 2.01 2.33 2.31 2.25 2.20 11


Quartet 2.07 2.20 2.24 2.28 2.24


N2–C2 N3–C14

1.28 1.27

1.31 1.32 5.43

 N1–Co1–N2 N1–Co1–N3 N2–Co1–N3 N1–Co1–Cl2 N2–Co1–Cl2 N3–Co1–Cl2 N1–Co1–Cl1 N2–Co1–Cl1 N3–Co1–Cl1 Cl2–Co1–Cl1



E(kcal/mol)

Bond Angles [°] 73.90 81.23 74.25 80.69 138.39 158.76 161.81 163.21 100.94 97.19 100.99 96.85 87.85 91.01 101.27 95.89 103.57 95.59 110.33 105.76 7.62 0

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1.29 1.29 2.20 74.21 73.72 140.22 151.14 98.86 97.93 89.52 101.36 101.27 119.32 3.85 7.54

After the optimization, in order to investigate the catalytic activities we calculate the structural descriptors and list the values in Table 5. For the values of Hammett constant (F), there is no change compared with Fe analogue because of the totally same framework of ligand and the substituents. Regarding the effective net charge (Qeff), the values of Qeff in complexes Co-1 to Co-3 are increased with the electron donating R1 substituent. And with the appearance of the R2 substituent, the Qeff values are deceased in complexes Co-4 and Co-5. These variation trends are well consistence with the catalytic activities, that is, the catalytic activities increase with the decreasing of effective net charge. Compared between Co and Fe analogues, we can see that the values of Qeff are much smaller in Co complexes than that in Fe complexes. The number of electron in the d orbital of Co complex is more than that in Fe complex, leading to the decrease of the effective net charge value on Co atom. Based on previous study,19,21 for late transition metal complex, the activities increase with the increasing of the effective net charge. Therefore, the lower charge value on Co atom is the main reason for the lower catalytic activities of Co complexes. As to the open cone angle (θ), the values of θ decrease from 129o to 91o when the R1 substituent changes from methyl to i-propyl groups. And with the appearance of R2 substituent, the values of θ decrease in Co-4 and Co-5 complexes. These variation trends are same as that in Fe analogue. 12


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Compared between these two analogues, little higher value of open cone angle is observed in Co complexes, indicating that the steric hindrance in Co system is slightly smaller. The values of bite angle for Co complexes are lower than that of Fe complexes, which is due to the smaller radius of Co atom (1.35 Å) compared with that of Fe atom (1.40 Å).44 From the previous reports, it shows that catalytic activity increases with the increasing of bite angle.45,46 Therefore the small bite angle may reduce the catalytic activities in Co complexes. The values of the HOMOLUMO energy gaps show similar variation as that in Fe analogue, namely, slightly higher values of Δ1 and lower value of Δ2 observed in Co-4 and Co-5 complexes. The values of energy difference (E) exhibit very small variations. To correlate the calculated structural descriptors and catalytic activities, linear fitting is performed by MLRA by using the combinations of four, three, two and one descriptor. From the correlation matrix for each pair of descriptors as shown in Figure S1b, there is high correlation between the descriptors of HOMO–LUMO energy gap (1) and bite angle (). After removing the combinations with these two dependent descriptors, the selected high correlation coefficient values are obtained and presented in Table 6.

Table 5. The values of Hammett constant (F), effective net charge (Qeff), open cone angle (θ), bite angle (β), energy difference (E) and HOMOLUMO energy gap (Δ1, Δ2) for complexes Co1Co-5 along with their experimental values of catalytic activities. Complex no.

Activity (106 g·mol-1·h-1)

Descriptors θ [°] 129.22

β [°] 140.22

E [kcal/mol] 7.54



3.42

Co-1

0.10

Q [e] 0.470

Co-2

0.06

0.477

123.99

141.40

7.36

75.74

84.58

2.88

Co-3

0.22

0.489

91.96

141.09

7.62

75.92

85.09

2.31

Co-4

0.06

0.469

112.61

140.05

7.65

78.87

82.07

3.69

F

13



Co-5

0.06

0.475

109.67

140.62

7.86

77.93

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81.95

2.91

Table 6. Correlation coefficient (R2) values of Co complexes for selected combinations of four, three, two and single descriptor. Four Descriptors F, Q, ,  E, Q, , F 1, Q, , E 2, Q, , 


Three Descriptors E, 1,  E, Q, 1 E, F,  E, 2, 


Two Descriptors E, 1 F, Q Q,  Q, 


Single Descriptor Q



1 F


Similar with the results in Fe complexes, the values of correlation coefficient (R2) for all the possible four combinations of descriptors are 1.00 which is also due to problem of overfitting. The weight factors for all the effective combinations of four descriptors are listed in Table S1, showing the slight different quality of each model. As to the results for combinations of three and two descriptors, almost 84% and 55% combinations give the R2 values over 0.9, respectively. The selected high values of correlation results are listed in Table 6. From the results by using two descriptors, most of the combinations giving good correlation coefficient values include the descriptor of effective net charge. Then we check the influence of each descriptor individually, and it shows that the correlation result by the effective net charge (Qeff) indeed gives the highest R2 value of 0.956 as in Table 6, clearly elucidating that catalytic activities of Co complexes are mainly determined by the effective net charge. All of the remaining R2 results are included in Table S4 of the supporting information. Meanwhile, the obtained coefficient values by using combinations of two descriptors are summarized in Table S5.

3.3 Comparisons between Fe and Co Complexes

14


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α,α’–bisimino–2,3:5,6–bis(pentamethylene)pyridyliron chlorides and its Co analogue have the totally same framework of ligand and substituents but only different central metal atoms. While, the catalytic activities of precatalysts present obvious difference, as the catalytic activities of Fe complexes are higher than that of Co complexes, clearly seen from Table 2 and Table 5 respectively. Comparisons of two analogue systems are carried out to illustrate the reason of variation in the catalytic activities. Two series of complexes are already modeled by MLRA method individually. In this section, we discuss the correlation between experimental and predicted catalytic activities for the variation of two analogue complexes. The differences of activities between Fe and Co complexes are used as dependent variables and the variations of seven descriptors between two analogues are taken as independent variables. Variations of the catalytic activities and the descriptors between Fe and Co analogues (FeCo) are calculated and shown in Table 7. As the framework of ligand and substituents are totally same in Fe and Co complexes, the variation of the Hammett constant (F) becomes null. Comparatively, the effective net charges (Qeff) show obvious variations with the value around 0.1, which is about 20% of the absolute value of Fe complexes. Meanwhile, the variations of open cone angle (θ) and bite angle (β) are relatively small with the values around 5° and 2° respectively. Therefore, we know the different central metal atom has more influence on the electronic effect than steric effect. There are also some variation values in the energy difference (E) and HOMOLUMO energy gaps (Δ1, Δ2). Table 7. The variation values of Hammett constant (F), effective net charge (Qeff), open cone angle (θ), bite angle (β), energy difference (E) and HOMOLUMO energy gap (Δ1, Δ2) between Fe and Co analogues along with the variation of catalytic activities (Act.). 15



Complex no.

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Act. (106g·mol-1·h-1)

Descriptors θ [°] -2.46

β [°] 2.46

E [kcal/mol] -5.02


Δε2 [kcal/mol] -10.96

9.39

Fe-1Co-1

0

Q [e] 0.10

Fe-2Co-2

0

0.09

-8.69

0.54

-3.29

4.51

-11.42

8.52

Fe-3Co-3

0

0.12

-4.96

1.16

-5.71

3.71

-11.55

7.05

Fe-4Co-4

0

0.10

-4.61

2.93

-5.05

1.95

-10.10

8.69

Fe-5Co-5

0

0.09

-1.67

1.87

-4.50

3.45

-10.36

8.83

F

To quantitatively elucidate the change of catalytic activities caused by the structures, in the same manner, we perform the MLRA using four, three and two descriptors to investigate the catalytic activities by equation (2). Then the correlation between the calculated activities and experimental activities is calculated for the FeCo analogue system. As in the previous report, for analogue complexes with same ligand but different central metal, the correlation results are around 0.7 by using four descriptors.29 However, in the present study the correlation coefficient values are very good with the value of 1, as shown in Table 8. Not only the results using four descriptors, but also the correlation coefficient results for the combinations of three and two descriptors show very good correlations with the R2 values over 0.9. Here, some good results are illustrated in Table 8. Apparently, the correlation results are much better in this study. We think the lower correlation results are attributed to the abnormal higher experimental activities observed in 2–imino–1,10–phenanthrolinyl(Co/Ni) complexes compared with their Fe analogue in previous study.29 For the correlation of individual descriptors, the coefficient values obtained by Qeff is 0.782, which is slightly better than other descriptors. The R2 values for other combinations of three, two and single descriptor are illustrated in Table S6. Meanwhile, the obtained fitting coefficient values by using combination of two descriptors are listed in Table S7.

16


Page 17 of 27

Table 8. Correlation coefficient (R2) values of Fe–Co analogue system for selected combinations of four, three, two and one descriptor. Correlation Coefficient (R2) 1.00 1.00 1.00 1.00

Four Descriptors F, Q, ,  E, Q, , F 1, Q, , E 2, Q, , 

Three Descriptors 2, Q,  Q, 1, 2 E, 1,  1, Q, 


Two Descriptors 1, Q Q,  E, 1 E, Q


Single Descriptor Q 2



1


We observe that the combination of effective net charge (Qeff) and bite angle () shows correlation coefficient values over 0.9 for Fe and Co complexes as well as for Fe–Co analogue. The comparisons between the experimental and calculated catalytic activities for Fe complexes, Co complexes and Fe–Co analogue system by using the descriptors of Qeff and β are displayed in Figure 1a, 1b and 1c, respectively. To investigate the contributions of descriptors to the catalytic activities of each complex system, the calculated descriptors for Fe complexes, Co complexes and FeCo analogue system are standardized using Z–Score method. The obtained standardized values of effective net charge (Qeff), bite angle (β) and experimental catalytic activities are shown in Table 9.

-1 -1 6

11.9

(a) Fe-Complexes

Cal. Act. (106gmol-1h-1)

12.6

Cal. Act. (10 gmol h )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


R2= 0.964

11.2 10.5 9.8 9.1

3.6 3.3

(b) Co-Complexes 2

R = 0.971

3.0 2.7 2.4 2.1

9.1

9.8

10.5

11.2

11.9

12.6

2.1

Exp. Act. (106gmol-1h-1)

2.4

2.7

3.0

3.3

Exp. Act. (106gmol-1h-1)

17


3.6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Cal. Act. (106gmol-1h-1)


9.0

Page 18 of 27

(c)

FeCo analogue 8.5 R2= 0.934 8.0 7.5 7.0 7.0

7.5 8.0 8.5 9.0 9.5 Exp. Act. (106gmol-1h-1)

Figure 1. Comparisons between calculated and experimental activities of (a) Fe complexes, (b) Co complexes and (c) FeCo analogue system, using the descriptors of effective net charge (Qeff) and bite angle (β). The contributions from each descriptor are calculated using equation (3) and shown in Table 10. For both Fe and Co complexes, effective net charge (Qeff) shows dominant effect with the values of 64.50% and 67.17% respectively, which are agreement with the results of the high correlation coefficient by using the single descriptor of effective net charge in Tables 3 and 4. These results indicate that the effective net charge is the predominant factor in determining the catalytic activities of both Fe and Co complexes. Regarding the Fe–Co analogue system, the contribution values of effective net charge (Qeff) and bite angle (β) are very close. Table 9. Standardized values of effective net charge (Qeff), bite angle (β), along with values of experimental catalytic activities of Fe complexes, Co complexes and analogues Fe–Co system. Complex Systems

Standardized Parameters

Fe-1

Q [e] -0.41

β [°] 0.54

Activity (106g·mol-1·h-1) 0.95

Fe-2

-0.47

-1.32

-0.10

Fe-3

1.78

-0.55

-1.63

Fe-4

-0.35

1.27

0.63

Fe-5

-0.53

0.06

0.15

Co-1

-0.75

-0.79

0.07

Complex no.

Fe Complex

Co Complex

18


Page 19 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fe–Co system

Co-2

0.12

1.27

-0.03

Co-3

1.62

0.72

-0.13

Co-4

-0.87

-1.10

0.12

Co-5

-0.12

-0.10

-0.02

Fe-1Co-1

-0.11

0.69

1.025

Fe-2Co-2

-0.84

-1.29

0.027

Fe-3Co-3

1.64

-0.65

-1.658

Fe-4Co-4

0.07

1.17

0.222

Fe-5Co-5

-0.75

0.08

0.383

Table 10. Values of contribution of standardized effective net charge (Qeff) and bite angle (β) for Fe complexes, Co complexes and analogue Fe–Co system. Complex System

Q [e]

β [°]

Fe Complex

64.50

35.49

Co Complex

67.14

32.85

Fe–Co analogues

50.10

49.89

Overall, from the results, it can be found that effective net charge (Qeff) is dominant factor in Fe and Co complexes. Meanwhile the dramatic decrease of catalytic activities in Co complexes is mainly due to the decreasing of the effective net charge (Qeff).

4. Conclusion In

the

present

study,

the

catalytic

activities

of

α,α’–bisimino–2,3:5,6–

bis(pentamethylene)pyridyl(Fe/Co) chlorides analogue complexes are examined by using the MLRA approach. Seven structural descriptors are chosen based on previous studies, including five electronic descriptors and two steric descriptors. Regarding electronic descriptors, it comprises of Hammett constant (F), effective net charge (Qeff), energy difference (E) and HOMOLUMO energy gap (Δ1, Δ2). For steric descriptors, it includes open cone angle (θ) and bite angle (β). Multivariate approaches are performed on individual complexes using four, three, two and single 19



descriptor. Furthermore, the variation of catalytic activities between Fe and Co analogue system is investigated by the modified MLRA as well. From the calculation results, the combination of two descriptors (Qeff, β) give good correlation for Fe complexes, Co complexes and FeCo analogue system, with the coefficient values of 0.964, 0.971, 0.934 respectively. After the standardization, the contribution of each descriptor is calculated and shows that the effective net charge (Qeff) is the dominant role in determining the activities for both Fe and Co complexes. Additionally, from the results for Fe–Co analogue, it is indicated that the lower catalytic activities of Co complexes are due to the decreasing value of Qeff. This study explores the determining role of charge in catalytic activities for Fe and Co complexes, which may help to design new complex precatalyst with higher catalytic activity.

Acknowledgements This work was financially supported by National Science Foundation of China (Nos. 21204092 and U1362204) and “One-Three-Five” Strategic Planning of ICCAS.

Supporting Information The correlation coefficient values by using the combinations of three, two and single descriptor and the fitting coefficient values supplied as Supporting Information.

20


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TOC Graphic

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Co) Complexes

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