SMD model
All tested functionals having good performance (error of < 1.0
kcal/mol) for ethylene insertion are collected in Table 3. As shown in
this table, at the level of M05-2X(SMD)/6-31G(d)∩SDD, all functionals
except HCTH407, HCTH, and BPBE(D3BJ) performs well for ethylene
insertion using the SMD model. It is noted that double-zeta basis set is
sufficient to obtain accurate result and there is (usually) no need to
use the triple-zeta basis 6-311G(d,p) shown above. For copolymerization
of ethylene and MA, all the selected functionals give relatively
accurate insertion energy barriers. In addition, the M06 functional
shows good performance, which may be due to the fact that this
functional takes into account the weak interactions. This is also
reflected in both the functional with implicit weak interactions and
that with the correction of long-range interactions. For
copolymerization of ethylene and VB, the functional BPBE(D3) shows good
performance. All tested hybrid functionals gave good results except M06,
TPSSh, and M06-HF. The GGA and meta -GGA functional underestimate
the barrier and have relatively poor performance (error of
> 1.3 kcal/mol). It is also found that the error derived
from PBEPBE functional is still relatively large after adding D3 and
D3BJ dispersion correction (error of > 1.5 kcal/mol). For
the functionals with dispersion correction, viz. PBE0(D3), LC-ωPBE(D3),
B3PW91(D3BJ), and PBE0(D3BJ), perform well. Therefore, the M05-2X
functional together with double-zeta basis set 6-31G(d) (SDD for metal
atom) can be used for the solvation single-point calculation on the
geometries optimized by most functionals tested for such
copolymerization systems. To further confirm this, larger basis sets
(6-31+G(d,p) and cc-pVTZ) were also considered for the non-metal atoms,
respectively. The results are almost the same as that from
M05-2X/6-31G(d) level. (Figure S2-S7 in SI).