Functional screening for copolymerization systems
Firstly, functionals in Table 2 are used to calculate the energy barrier
for ethylene insertion into the Pd−Me bond of initial active species
(Table 1). The obtained results are compared with the experimental
kinetic data (free energy barrier of 17.2 kcal/mol at the temperature of
243.6 K). As shown in Figure 2, B97D functional has the largest positive
deviation of 3.8 kcal/mol and M05 has the largest negative deviation of
-2.3 kcal/mol. On the other hand, the functionals with semi-empirical
dispersion correction (D2, D3, or D3BJ) overestimate the ethylene
insertion barrier except for B3PW91-D3, PBE0-D3, and M05-D3 (Figure 3).
A similar situation was reported by Maron et al. that dispersion
correction could overestimate the energy barrier for propene insertion
into early transition metal complexes.26 To get an
image about the effect of dispersion correction on the calculated energy
barrier, the absolute error of the barrier for ethylene insertion
calculated by individual functional without and with available
additional dispersion correction to the functional has been compared
(Figure S1). It is found that the TPSSTPSS (meta -GGA) functional
produced an error of 0.9 kcal/mol. In the case of dispersion correction
to this functional, viz., TPSSTPSS-D2, TPSSTPSS-D3, and TPSSTPSS-D3BJ,
the errors are 3.0, 1.7, and 1.6 kcal/mol, respectively, suggesting an
overestimation of insertion energy barrier by the dispersion correction.
Although some dispersion correction augmented functionals produced an
error of less than 1.0 kca/mol, such an overestimation caused by
dispersion correction was also observed for BPBE, BP86, PBEPBE, BLYP,
and B3LYP functionals, compared with corresponding functionals without
dispersion correction. There are 38 methods with better performance
(energy barrier error of less than 1.0 kcal/mol) for the ethylene
insertion. These functionals includes 6 GGA, 2 meta -GGA, 20
hybrid types of functionals, PBEPBE (D2), 5 functionals with D3
dispersion correction and 4 functionals with D3BJ dispersion correction
(Figures 2 and 3).