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.