Figure 3. The error bar of calculated energy barriers
(ΔG ≠, kcal/mol) for ethylene insertion in
comparison with the experimental value (17.2
kcal/mol).4 The functionals shown include available
semi-empirical dispersion corrections.
By using the 38 methods with better performance for ethylene insertion,
the insertion energy barriers of two polar monomers, MA and VB, have
been further calculated (Table 1, Figures 4 and 5). The reported kinetic
data for MA insertion are ΔH ≠ = 12.1±1.4
kcal/mol and ΔS ≠ = -14.1±7.0
cal/K⋅mol.27 Due to the large range of entropy change
(±7.0 cal/K⋅mol), the corresponding Gibbs free energy could vary
significantly from the central value and is unsuitable for functional
screen. Therefore, the enthalpy value for MA insertion was used instead.
The reported kinetic data for VB insertion are
ΔH ≠ = 11.9 ± 0.1 kcal/mol,
ΔS ≠ = -16.8 ± 0.1 cal/K⋅mol at 236.5 K, and the
corresponding ΔG ≠ is estimated to be 15.9 ± 0.1
kcal/mol.
The calculated energy barriers for MA insertion are shown in Figure 4.
It is found that 11 hybrid functionals, 5 functionals with D3 correction
and 4 functionals with D3BJ correction showed an error of less than 1.0
kcal/mol. That is, these methods behave better for the calculation of
α-diimine palladium catalyzed ethylene-MA copolymerization. All the GGA
and meta -GGA functionals produced an error of more than 1.0
kcal/mol. Among these functionals, B1B95 gives the worst result
(ΔH ≠ of 16.8 vs 12.1±1.4 kcal/mol). As a
result, GGA and meta -GGA functionals produced relatively large
errors for ethylene-MA copolymerization, and the inclusion of D3 or D3BJ
dispersion correction tend to reduce the energy barrier for MA insertion
compared with their original form without such corrections.
Unlike the case of ethylene/MA copolymerization, GGA and meta -GGA
functionals such as PBEPBE, PW91PW91, HCTH407, HCTH, TPSSTPSS and tHCTH
showed good performance in ethylene/VB copolymerization (Figure 5).
Moreover, several functionals with D3 and D3BJ correction and 10 hybrid
functionals have better performance. Functional TPSSTPSS-D2 gives the
worst result with the energy barrier value up to 18.1 kcal/mol
(experimental value of 15.9 ± 0.1 kcal/mol). In addition, the functional
such as BPBE with D3 or D3BJ dispersion correction generally
overestimated energy barrier compared with its original form (without
the dispersion correction).
Schreckenbach et al. found that the functionals, viz., BPBE, PBEPBE, and
B3LYP, augmented by D3BJ dispersion correction showed good performance
in the calculations of hydrocarbon isomerization and metal-free olefin
insertion model system.25 For the two copolymerization
systems in this study, BPBE(D3BJ) and PBEPBE(D3BJ) also performs well.
In a previously reported organocatalytic systems,75the M06-2X functional with implicit dispersion correction tended to give
high accuracy. This is also found in the current work. However, the
commonly used B3LYP functional showed relatively poor performance for
ethylene insertion regardless of the inclusion of dispersion correction
(with errors of 1.6 kcal/mol for B3LYP, 2.2 kcal/mol for B3LYP-D3BJ, and
4.0 kcal/mol for B3LYP-D2). The hybrid functionals M06-2X and PBE0 have
also good performance without dispersion correction. Besides, D2
dispersion correction significantly overestimated the insertion energy
barriers of these monomers (Figures 3-5). Therefore, D2 dispersion
correction could be unsuitable for such polymerization systems.