COMPUTATIONAL METHODS AND STRATEGIES
All calculations were performed with the Gaussian 16 program.28 Various types of functionals, such as GGA,meta -GGA, hybrid, and functionals with semi-empirical dispersion correction (D229, D330, and D3BJ31) were used for geometry optimizations. In these geometrical optimizations, the LANL2DZ basis set32together with effective core potential (ECP) was used for Pd and Br atoms and the 6-31G(d) basis set was used for C, H, O and N atoms. In order to verify the optimized stationary points and obtain the thermodynamic data at the actual reaction temperature, vibration frequency analyses were conducted at the same level of theory. Based on each optimized structure, single point calculation was performed with the corresponding DFT functional used for its geometrical optimization. In these single-point calculations, larger basis sets, viz., the SDD and associated effective core potential33 for Pd and Br atoms and the triple-zeta 6-311G(d,p) basis set for the remaining atoms, are applied, and the solvation effect of dichloromethane generally used in such copolymerization systems was considered by using SMD solvation model.34 The Gibbs free energy in solution, including gas-phase free energy correction, was used for discussion, unless otherwise specified. The functionals were screened by comparing the experimentally measured activation energy with the corresponding calculated value. For a comparison of the effect of solvation models, CPCM model34 was also considered for some calculations. Three model chemistries used for fitting the parameters of SMD solvation model by Truhlar et al. were selected in the solvation calculations, namely, M05-2X/6-31G(d), M05-2X/6-31+G(d,p), and M05-2X/cc-pVTZ.35 Similarly, in the CPCM solvation calculations, the two model chemistries of PBE0/6-31+G(d) and PBE0/6-31+G(d,p) were utilized, which was previously used for testing the accuracy of CPCM solvation model by Barone et al.34
The calculation strategy is shown in Figure 1. Based on the catalytic active species, the energy barrier for ethylene insertion is calculated and compared with the corresponding experimental value to screen the density functionals. Then, using the functionals with better performance, the insertion energy barrier of the two polar monomers were calculated, respectively. Compared with the corresponding experimental values, the functionals with better performance for the insertions of both ethylene and the polar monomer are considered to be suitable for the calculation of copolymerization system. According to the obtained results, single-point energy was further calculated at the specific theoretical levels together with the SMD and CPCM models, respectively, to evaluate the effect of solvation models. The density functional, which produces less than an energy barrier error of 1.0 kcal/mol compared with corresponding experimental values, is considered to be better for the calculations of such copolymerization systems.
Figure 1 . Flow chart of calculation strategy.