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Vanadium NMR Chemical Shifts of (Imido)vanadium(V) Dichloride Complexes with Imidazolin-2-iminato and Imidazolidin-2-iminato Ligands: Cooperation with Quantum-Chemical Calculations and Multiple Linear Regression Analyses Jun Yi,† Wenhong Yang,‡ Wen-Hua Sun,‡ Kotohiro Nomura,† and Masahiko Hada*,† †

Department of Chemistry, Tokyo Metropolitan University, Minami-Osawa 1-1, Hachioji, Tokyo 192-0397, Japan Laboratory of Engineering Plastics and Beijing National Laboratory for Molecular Science, Institute of Chemistry Chinese Academy of Sciences, Beijing 100190, China

‡

S Supporting Information *

ABSTRACT: The NMR chemical shifts of vanadium (51V) in (imido)vanadium(V) dichloride complexes with imidazolin-2-iminato and imidazolidin-2-iminato ligands were calculated by the density functional theory (DFT) method with GIAO. The calculated 51V NMR chemical shifts were analyzed by the multiple linear regression (MLR) analysis (MLRA) method with a series of calculated molecular properties. Some of calculated NMR chemical shifts were incorrect using the optimized molecular geometries of the X-ray structures. After the global minimum geometries of all of the molecules were determined, the trend of the observed chemical shifts was well reproduced by the present DFT method. The MLRA method was performed to investigate the correlation between the 51V NMR chemical shift and the natural charge, band energy gap, and Wiberg bond index of the VN bond. The 51V NMR chemical shifts obtained with the present MLR model were well reproduced with a correlation coefficient of 0.97.

1. INTRODUCTION Vanadium catalysts have unique characteristics in olefin polymerization, as exemplified by practical production of EPDM (synthetic rubber, copolymer of ethylene/propylene/ diene) using classical Ziegler catalysts, and study of synthesis of vanadium complex catalysts and thus they attracted considerable attention.1−6 (Imido)vanadium(V) complexes containing anionic ancillary donor ligands has been known as one of the promising candidates not only for olefin coordination insertion polymerization4 but also for ring-opening metathesis polymerization of cyclic olefins.5,6 For instance, (imido)vanadium(V) complexes with imidazolin-2-iminato,7−9 imidazolidin-2-iminato,7,10 and aryloxo11−15 ligands exhibit high catalytic activity for ethylene polymerization,7 ethylene/ norbornene copolymerization,7,11−13 and metathesis polymerization of cyclic olefins.10,14,15 Moreover, the (imido)vanadium(V) complexes containing (2-anilidomethyl)pyridine ligands show notable catalytic activity and high selectivity in ethylene dimerization.16 In recent studies, Nomura and co-workers found a good relationship between the catalytic activity and the vanadium NMR chemical shift for (imido)vanadium complexes,7,13 and they deduced that the high catalytic reactivity originates from stabilization of the active site by electrondonating substituents. The NMR chemical shift is sensitively affected by the electronic states in the vicinity of the resonant nucleus, and therefore the above deduction seems to be reasonable. Using the above relationship between the NMR © XXXX American Chemical Society

chemical shift and the catalytic activity, the catalytic activity can be quantitatively predicted by an appropriate quantumchemical method. However, accurate calculation of metal NMR chemical shifts is difficult. Therefore, an accurate alternative method is required to estimate metal NMR chemical shifts, for example, statistical estimation from simple molecular properties. By combining quantum-chemical calculations and statistical methods, it may be possible to combine these simple molecular properties and the catalytic activity from a NMR viewpoint. NMR chemical shifts are widely used in analytical chemistry, and they contain a lot of information about the electronic structures of molecules. In most quantum-chemical methods, the NMR chemical shift of compound M is defined as the deviation of the nuclear magnetic shielding constant σ from that of the reference molecule: δ = ΔσM = σ(ref) − σ(M)

(1)

σ can be divided into a diamagnetic term (σdia) and a paramagnetic term (σpara):

σ = σ dia + σ para

(2)

Received: August 21, 2017 Revised: November 7, 2017 Published: November 8, 2017 A

DOI: 10.1021/acs.jpca.7b08328 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

Chart 1. Structures of (Imido)vanadium(V) Dichloride Complexes with Imidazolin-2-iminato (1a−1c, 1e, 3c, and 4c) and Imidazolidin-2-iminato (2a−2d and 5c) Ligands

where σdia and σpara are the first-order and second-order terms in the second-order perturbation theory.17,18 Plenty of efforts have been made during the past decades in the calculation of NMR chemical shifts.19−22 Nakatsuji et al. have comprehensively investigated the electronic mechanisms of the multinuclear NMR chemical shifts of transition metal complexes.23−28 They found that the paramagnetic term is generally dominant in the NMR chemical shift and they proposed the dhole and p-electron mechanisms.23,24 In these mechanisms, the d-hole paramagnetic term is generated by back-donation of electrons from the metal d-orbitals to the ligand. Thus, the chemical shift increases with stronger electron-withdrawing ability of the ligands. The p-electron mechanism is because of donation of electrons from the ligand to the metal outer p orbitals, so the chemical shift increases as the electron-donating ability of the ligand increases. Malkin et al. introduced the sumover-states density functional perturbation theory (SOS-DFPT method) to calculate the 51V NMR chemical shifts.29 The calculated 51V chemical shifts are in good agreement with experimental data. Moreover, Bühl reported a linear relationship between the 51V chemical shifts and ethylene insertion barriers in imidovanadium(V) catalyst system.30 In the present study, we calculated the vanadium (51V) chemical shifts of (imido)vanadium(V) dichloride complexes with imidazolin-2-iminato and imidazolidin-2-iminato ligands (Chart 1). These vanadium complexes were synthesized by Nomura and co-workers.7 To be consistent with their experimental report, the symbols of the complexes in Chart 1 exactly agree with those in their paper. Density functional theory (DFT) was used to obtain the molecular geometries and several molecular properties, including the vanadium NMR chemical shifts. Multiple linear regression (MLR) analysis (MLRA) was performed to understand the relationships between the vanadium NMR chemical shift and the natural charge of the vanadium atom, highest occupied molecular orbital−lowest unoccupied molecular orbital (HOMO− LUMO) energy gap, and Wiberg bond index of the VN bond.

optimization, we compared two combinations of functionals and basis sets: CAM-B3LYP32/Gen and LC-BLYP33/Gen. In the Gen basis set, we used the mixed basis set of cc-pVTZ34 for the V atom, cc-pVDZ35 for the Cl, N, and C atoms, and D95 V36 for the H atoms. We optimized the molecular geometries of all compounds using the X-ray molecular structures as the initial structures. To check the accuracy of the calculations, some selected geometrical parameters of complex 1c are shown in Table 1. The root-mean-square errors φ (RMSE) of the bond length obtained by CAM-B3LYP/Gen and LC-BLYP/ Gen are similar, the values are 0.037 and 0.036 Å, respectively. The calculated bond length using CAM-B3LYP/Gen and LCBLYP/Gen are shorter than the experimental values. For the bond angles and dihedral angles, the φ values using CAMTable 1. Comparison of the Experimental and Calculated Geometrical Parameters of Complex 1c Bond Length (Å)

2. COMPUTATIONAL DETAILS All of the quantum-chemical calculations were performed with the Gaussian 09 software package.31 For molecular geometry B

complex 1c

expt

V−Cl1 V−Cl2 V−N1 V−N2 N1−C1 N2−C9 φ

2.231 2.225 1.668 1.731 1.382 1.319

LC-BLYP/Gen

2.196 2.202 1.597 1.706 1.383 1.301 0.036 Bond and Dihedral Angles (deg)

complex 1c

expt

Cl1−V−Cl2 Cl1−V−N1 Cl1−V−N2 Cl2−V−N1 Cl2−V−N2 N1−V−N2 V−N1−C1 V−N2−C9 V−N1−C1−C2 (A1) C9−N3−C10−C11 (A2) C9−N4−C24−C25 (A3) φ

111.45 107.21 110.17 105.46 109.62 112.88 171.18 163.92 90.59 92.79 109.34

CAM-B3LYP/Gen 2.196 2.196 1.595 1.705 1.380 1.303 0.037

LC-BLYP/ Gen

CAM-B3LYP/ Gen

112.86 108.45 109.46 107.10 108.95 109.97 173.11 163.23 94.52 83.29 108.83 3.382

113.54 107.24 109.19 107.78 109.97 109.02 173.85 158.24 58.14 74.03 99.43 11.940


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3. RESULTS AND DISCUSSION 3.1. Geometries and Chemical Shifts. Figure 1 shows the correlation between the calculated and observed 51V NMR

B3LYP/Gen are much larger than that using LC-BLYP/Gen, especially for the dihedral angle. Because these angles significantly affect the overall molecular shapes, we adopted the molecular geometries calculated by LC-BLYP/Gen to evaluate the molecular properties of the vanadium complexes. The electron distributions were obtained by natural bond n

∑i (Xci − Xei)2

orbital analysis.φ =

n

, where Xci is the calculated

value for each bond length or bond angle and Xei is the experimental value for each bond length or bond angle. The subscripts c and e represent calculated and experimental, respectively, and i is the serial number of each bond length or bond angle. The 51V NMR chemical shifts of the vanadium complexes were calculated using LC-BLYP/Gen and CAM-B3LYP/Gen combined with the gauge-including atomic orbital (GIAO) method. The solvent effect was considered using LC-BLYP and CAM-B3LYP with the SMD model37 and the optimized geometries obtained without the solvent effect. Chloroform was used as the solvent. Complex 2a was selected as the reference to calculate the 51V NMR chemical shifts by eq 1. The relativistic terms were not considered, because their effect on the V-NMR chemical shift must be quite small in the present series of molecules due to the cancellation between the vanadium complexes. The HOMO−LUMO energy gap (Δε), natural charge of the vanadium atom (Q), and Wiberg bond index of the VN bond (ω) were simultaneously calculated by using LC-BLYP/Gen based on the optimized structures. We assumed that these parameters were related to the vanadium chemical shift by Δδ NMR = m0 + m1Δε + m2Q + m3ω

Figure 1. Correlation between calculated and experimental 51V NMR chemical shifts;the effect of rotation of the dihedral angles. Compound 2a is chosen as the reference. The black squares are the vanadium chemical shifts calculated with the optimized geometries from the Xray structure,and the red circles are the chemical shifts reoptimized geometries.

chemical shifts of all of compounds shown in Chart 1. There is reasonably good agreement, except for complexes 2c and 2d. We confirmed that the RMSE values are small (see Table S1 in the Supporting Information), which means that the optimized geometrical structures are close to the X-ray structures. Initially, we performed a simple assessment of the accuracy of the DFT functionals and considered the solvent effect. We found that the large deviations between the observed and calculated values for 2c and 2d are not improved by changing the DFT functional or including the solvent effect (Tables S2 and S3 and Figures S1 and S2). Fortunately, this problem was solved by changing the molecular conformation, namely, changing the dihedral angles of the substituents. The dihedral angles were rotated to make the dimethylbenzene group parallel to the R substituents. The vanadium chemical shifts of complexes 2c and 2d improved from −81 to +30 and −62 to −8 ppm, respectively. Thus, the vanadium chemical shifts of complexes 1b, 1c, 2b, 3c, and 5c were recalculated using the same process. After geometry reoptimization, all of the vanadium chemical shifts (Δδ) are increased more than 10 ppm except for those of complexes 1c and 3c. The reason is the dihedral angles of complexes 1c and 3c returned to their original values. For complexes 2c and 2d, the Δδ values are increased 111 and 54 ppm, respectively, and their dihedral angles A1 and A2 are significantly changed. The results indicate that Δδ mainly depends on A1 and A2, especially A1. The detailed values of ΔA and Δδ were provided in Table S4. In this part of work, there is a better correlation between the chemical shifts calculated with the reoptimized structures and the experimental vanadium chemical shifts than between the Xray structure optimized geometries and the experimental chemical shifts. Thus, geometry optimization using the geometry from the experimental crystal structure as an initial guess is not appropriate. This suggests that a conformation search is required before the NMR calculation. 3.2. Solvent Effect. Using the reoptimized molecular geometries, we investigated the solvent effect. The vanadium chemical shifts calculated considering the solvent effect or without the solvent effect are shown in Table 2. The vanadium

(3)

MLRA was performed with the LINEST function. The LINEST function performs linear regression for sample data using the least-square method.38 The m0, m1, m2, and m3 values are obtained by linear fitting. To compare the contributions of the HOMO−LUMO energy gap, natural charge of the vanadium atom, and Wiberg bond index of the VN bond to the vanadium chemical shift, the Δε, Q, and ω values were standardized by the Z-score method.39 The Z-score method is a fundamental normalization method in data analysis. The formula for the Z-score as eq 4:

Zi =

Xi − X̅ S

(4)

where X is the value of each descriptor, X̅ is the mean value, and S is the standard deviation. The percentage contributions of each parameter were calculated by standardizing the values: |m ·Δε |

11

Δε (%) =

∑i = 1 |m ·Δε | + |m1 ·Qi | + |m ·ω | i

1

∑i = 1 |m ·Δε | + |m2 ·Qi | + |m ·ω | 1

i

2

i

3

i

11

× 100

(5)

× 100

(6)

|m ·ω |

11

ω (%) =

i

3

i

|m ·Q |

11

Q (%) =

2

11

∑i = 1 |m ·Δε | + |m3 ·Qi | + |m ·ω | 1

i

2

i

3

i

11

× 100

(7)

where i runs over all of the complexes. C


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from the paramagnetic contributions. Large negative paramagnetic contributions are generated by strong electron donation from the ligand to the metal, and this trend corresponds to the electron population of the vanadium 3d orbitals. The supposition that the high catalytic reactivity originates from stabilization of the active site by electrondonating substituents can be confirmed by the NMR chemical shifts. The paramagnetic term can be decomposed into the contributions of the atomic orbitals (AO) in the same manner as Mulliken population analysis23,24 as shown in Table 4. The

Table 2. Vanadium Chemical Shifts Calculated Using LCBLYP, LC-BLYP with Solvent Effect, CAM-B3LYP, and CAM-B3LYP with the Solvent Effect (Chloroform) Δδ (ppm)

complex

LC-BLYP without solvent

LC-BLYP with solvent

CAM-B3LYP without solvent

CAMB3LYP with solvent

expt

1a 1b 1c 1e 3c 4c 2a 2b 2c 2d 5c

−1 45 64 42 149 102 0 51 30 −8 140

−6 52 72 51 157 106 0 61 40 −10 145

−2 49 60 39 148 101 0 54 29 −1 141

−9 56 68 43 157 106 0 65 40 −2 149

8 71 70 30 180 103 0 81 63 22 174

Table 4. AO Contributions of the Paramagnetic Term (ppm)

chemical shifts calculated using CAM-B3LYP are almost to the same as those calculated using LC-BLYP, it means that these functionals are almost equivalent for NMR calculation of the present compounds. When the values for LC-BLYP or CAMB3LYP without solvent are compared with those for LC-BLYP or CAM-B3LYP with the solvent effect, the calculated values are improved by including the solvent effect. All of the vanadium chemical shifts increase by more than 5 ppm, except for those of complexes 1a and 2d. And the largest increase in the vanadium chemical shift is over 10 ppm for complexes 2b and 2c. The results indicating the solvent effect play an important role in NMR chemical shifts calculation. 3.3. Decomposition of the Chemical Shift. The vanadium nuclear magnetic shielding constants are decomposed into the paramagnetic and diamagnetic terms in Table 3.

σpara

σtotal

complex

total

shift

total

shift

total

shift

1a 1b 1c 1e 3c 4c 2a 2b 2c 2d 5c

1727 1732 1734 1749 1734 1732 1728 1732 1732 1730 1734

−1 4 6 21 6 4 0 4 4 2 6

−3414 −3373 −3356 −3393 −3271 −3316 −3414 −3367 −3388 −3424 −3280

0 41 58 21 143 98 0 47 26 −10 134

−1687 −1641 −1622 −1644 −1537 −1584 −1683 −1634 −1655 −1691 −1547

−1 45 64 42 149 102 0 51 30 −8 140

complex

3d

other

N

Cl

other atoms

1a 1b 1c 1e 3c 4c 2a 2b 2c 2d 5c

−6 50 79 57 140 120 0 63 47 −8 133

6 −4 −15 −15 7 −19 0 −12 −18 1 4

−1 −1 0 −1 −1 0 0 0 0 −1 −1

0 0 0 0 0 0 0 0 0 0 0

1 −5 −6 −20 −3 −3 0 −4 −3 −2 −2

AO analysis was performed by self-written interface with Gaussian09 program, and the definition of the AO analysis of the paramagnetic part is described in ref 23. As expected, the contribution from the vanadium 3d orbitals mainly determines the total trend. The effects of the ligands and molecular conformation control the 51V NMR chemical shift through the 3d populations. The contributions from the N and Cl atoms that are directly attached to vanadium are 0 to −1 ppm. For complex 1e, the contribution from the other atoms is relatively large (−20 ppm), which may be because of the effect of the bulky ligands of 1e. 3.4. MLRA. As well as the dihedral angles and solvent interaction, the electron-withdrawing or electron-donating abilities of the ligands23,24 and the HOMO−LUMO energy25 influence the chemical shift. The VO bond length is the dominant geometrical parameter determining the vanadium chemical shifts of oxoperoxo vanadium complexes.40 Therefore, in this work, MLRA was used to investigate the influence of the Wiberg bond index of the VN bond, natural charge of the vanadium atom, and HOMO−LUMO energy gap on the vanadium chemical shifts. The three descriptors are linearly independent in the present V-NMR chemical shift as shown in Figure S3. The Q, Δε and ω values for the vanadium complexes are provided in the Supporting Information as Table S5. Note here that the change of the Δε is relatively small, and the HOMO−LUMO transitions are magnetically allowed in the present vanadium complexes. To compare the effect of each parameter on the vanadium chemical shift, the standardized values of Q, Δε, and ω were calculated by the Z-score method. On the basis of the Q, Δε, and ω values and the vanadium chemical shifts calculated using CAM-B3LYP with solvent effect in Table 2, the MLR equations were fitted by the LINEST function. According to the eq 3, the MLR model can be presented as following eqs 8 and 9:

Table 3. Decomposition of the 51V NMR Chemical Shifts (σtotal) into Diamagnetic (σdia) and Paramagnetic Terms (σpara) (ppm) σdia

atoms attached to the metal

metal

We chose 2a as the reference molecule for the chemical shifts. The chemical shift is the sum of diamagnetic and paramagnetic contributions. The diamagnetic contributions are less than 10 ppm for all compounds except 1e. The relatively large diamagnetic contribution of 1e (21 ppm) can be attributed to the large side chain of the phenyl group (2,6-(Ph2CH)2-4Me-C6H2). The paramagnetic contributions are significantly larger than the diamagnetic contributions, which means that the trend of the observed chemical shifts is essentially generated D


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the Wiberg bond index of the VN bond is influenced by the dihedral angles. Therefore, we suggest that the reason why the Wiberg bond index of the VN bond makes the greatest contribution to the vanadium chemical shift in the MLR model is that the Wiberg bond index of the VN bond is related to dihedral angles of the substituents. The detail values of the ΔA and Δω were provided in the Supporting Information as Table S7.

Δδ NMR = −1737.11 − 3109.41Δε − 2978.84Q (8)

+ 1466.95ω Δδ NMR (St) = −0.82Δε(St) − 0.65Q (St) + 1.19ω(St)

(9)

where the (St) is the data standardized by Z-Score method. The correlation coefficient R2 value of the eqs 8 and 9 is 0.97; it indicated the obtained MLR model has good fitting ability. In the MLR model, the vanadium chemical shift increases with decreasing natural charge of the vanadium atom, which means that the vanadium chemical shift will increase with stronger electron-donating ability of the ligand. For the orbital energy gap, the smaller HOMO−LUMO energy gap results in a higher vanadium chemical shift. This analysis may be valid only when the change of the Δε is relatively small. Moreover, the Wiberg bond index of the VN bond reflect the strength of the VN double bond. The vanadium chemical shift increases with increasing Wiberg bond index, indicating that a stronger VN double bond results in a higher vanadium chemical shift. The vanadium chemical shifts fitted by the MLR model are compared with the calculated data in Figure 2. The fitted

4. CONCLUSIONS We have performed GIAO-DFT calculations of the vanadium chemical shifts of (imido)vanadium(V) dichloride complexes. The vanadium chemical shifts calculated by the GIAO-DFT method agree well with the experimental 51V NMR chemical shifts. A conformation search is necessary before the NMR calculation. The paramagnetic contribution is the dominant contribution to the vanadium chemical shift. The dihedral angles of the substituents and the solvent significantly affect the vanadium chemical shift. Using MLRA, the natural charge of the vanadium atom, HOMO−LUMO energy gap, and Wiberg bond index of the VN bond were used to reproduce the vanadium chemical shifts. The correlation coefficient value is 0.97 and the fitted vanadium chemical shifts are very close to the experimental data, indicating that the vanadium chemical shifts can be quantitatively described by the MLR model. In the model, the vanadium chemical shift increases with higher Wiberg bond index of the VN bond, whereas the natural charge and HOMO−LUMO energy gap have negative correlations with the vanadium chemical shift. These results indicate that vanadium complexes with more stable VN double bonds, stronger electron-donating ligands, and lower HOMO−LUMO energy gaps will have higher vanadium NMR chemical shifts.

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ASSOCIATED CONTENT

S Supporting Information *

Figure 2. Correlation between the fitted V NMR chemical shifts and the chemical shifts calculated by the CAM-B3LYP with solvent effect. 51

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b08328. Structure comparison of the optimized geometries (Table S1), theoretical vanadium NMR chemical shifts calculated by CAM-B3LYP and CAM-B3LYP with the solvent effect (Tables S2 and S3), calculated vanadium chemical shifts compared with the experimental data (Figures S1 and S2) and between the three descriptors and vanadium chemical shifts (Figure S3), the value of ΔA (Tables S4 and S7), and the data related to fitted vanadium chemical shifts by the MLR model (Tables S5 and S6) (PDF)

chemical shifts are given in the Supporting Information as Table S6. It is clear that the fitted vanadium chemical shifts are in good agreement with the calculated data. The MLR model reproduces the calculated results very well, indicating that the model has the ability to predict the vanadium chemical shifts of these (imido)vanadium(V) dichloride complexes. To clarify the influence of the effect of each parameter on the vanadium chemical shift, the contribution of each parameter was calculated with eqs 5−7. The obtained contributions are 27% from the HOMO−LUMO energy gap, 31% from the natural charge, and 42% from the Wiberg bond index of the VN bond. These values indicate that the Wiberg bond index of the VN bond is the dominant parameter that determines the 51 V NMR chemical shifts of (imido)vanadium(V) dichloride complexes. Because the dihedral angle has an effect on the vanadium chemical shift, the differences of the natural charge of the vanadium atom, HOMO−LUMO energy gap, and Wiberg bond index of the VN bond were calculated with different dihedral angles. For complexes 2c, 2d, and 5c, the dihedral angles clearly change and the Wiberg bond indexes of the V N bond also significantly change. In particular, for complex 2d, when the dihedral angle A2 rotates 118°, the value of the Wiberg bond index changes by 0.057. These results show that

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AUTHOR INFORMATION

Corresponding Author

*Masahiko Hada. Tel: +81-42-677-2554. Fax: +81-42-6772525. E-mail: [email protected]. ORCID

Wen-Hua Sun: 0000-0002-6614-9284 Kotohiro Nomura: 0000-0003-3661-6328 Masahiko Hada: 0000-0003-2752-2442 Notes

The authors declare no competing financial interest. E


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ACKNOWLEDGMENTS This research is supported by the Core Research for Evolutional Science and Technology (CREST), the Japan Science and Technology (JST) Agency, “Creation of Innovative Functions of Intelligent Materials in the basis of the Element Strategy”. Part of this work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sport, Science and Technology, Japan. We also thank the Research Center for Computer Science/Institute for Molecular Science, Okazaki, Japan, for providing the computational resources used in this study.

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