CONCULUSION
The benchmark of DFT for α-diimine palladium catalyzed insertions of ethylene, methyl acrylate, and vinyl bromide has been studied, during which sixty-seven functional methods have been screened on the basis of experimental kinetic data.
For the ethylene/methyl acrylate copolymerization featuring the insertions of the both monomers, when the single-point calculation is performed at the level of M05-2X(SMD)/6-31G(d)∩SDD, 11 hybrid functionals (M06, BHandH, mPW1PW91, HSEh1PBE, mPW3PBE, LC-ωPBE, PBE0, M06-HF, M06-2X, mPW1PBE, M05-2X), 5 functionals with D3 dispersion correction (BPBE-D3, M062X-D3, PBE0-D3, PBEPBE-D3, LC-ωPBE-D3), and 3 functionals with D3BJ dispersion correction (B3PW91-D3BJ, PBE0-D3BJ, PBEPBE-D3BJ) used for geometrical optimization could give better results compared with other tested functionals. However, GGA and some meta -GGA functionals showed poor performance in the geometry optimization with respect to calculated free energy barrier in solution (SMD model). The hybrid functional B1B95 produced the worst result. When the CPCM model is applied at the level of PBE0(CPCM)/6-31+G(d)∩SDD, the aforementioned 11 hybrid functionals except M06-HF also showed good performance. At this single-point calculation level, the M06, M062X-D3, LC-ωPBE-D3, and PBE0-D3BJ geometries can also produce accurate free energy barrier in solution.
For the copolymerization ethylene and vinyl bromide, when the single-point calculation is carried out at the level of PBE0(CPCM)/6-31+G(d)∩SDD, the tested hybrid functionals except BHandH, TPSSh, and M06-2X perform well. However, the GGA and meta -GGA functionals have poor performance, like the case of ethylene/MA copolymerization. And, LC-ωPBE-D3 overestimated the energy barrier of vinyl bromide insertion, possibly due to the over-correction of dispersion force. At the level of M05-2X(SMD)/6-31G(d)∩SDD for single-point calculations, the GGA and meta -GGA still have poor performance. The dispersion correction augmented PBEPBE functional underestimated the barrier and showed worst performance among the tested functionals. The hybrid functionals except M06, TPSSh, and M06-HF perform well at this level.
It is noted that the performance of the common B3LYP functional with or without dispersion is not ideal in these systems. Compared with SMD solvation model, CPCM model slightly underestimated the energy barrier of ethylene insertion, but it is still within the acceptable error range.
ASSOCIATED CONTENT
Supporting Information
Additional table and figures showing the effect of dispersion corrections on the error of ethylene insertion energy barrier and monomer insertion energy barriers calculated at various levels together with SMD and CPCM solvation models as well as Cartesian coordinates of optimized stationary points. The Supporting Information is available free of charge on the ACS Publications website.
AUTHOR INFORMATION
Corresponding Author
* Y.L. (luoyi@dlut.edu.cn)
Notes The authors declare no competing financial interest.