hese results indicate that the energy barrier from the three functionals (BMK, B1B95 and wB97XD) are very close to that of DLPNO-CCSD(T) method within 3 kcal/mol.
For comparison of the reaction energy, shown in Figure 3b, according to Gibbs free energy, the functionals RAD compared with the results of DLPNO-CCSD(T) level, is divided into several groups in the following order:
(a) group 1 (RAD ϵ [0.40 kcal/mol, 2.23 kcal/mol]): HSE1PBE, HSEh1PBE, M06, mPW1PBE, mPW1PW91, wB97X, mPW1LYP, B1B95;
(b) group 2 (RAD ϵ [4.80 kcal/mol, 5.30 kcal/mol]): CAM-B3LYP, B971, B98;
(c) group 3 (RAD ϵ [7.31 kcal/mol, 8.44 kcal/mol]): wB97XD, B3PW91, B972, VSXC;
(d) group 4 (RMSE ϵ [9.36 kcal/mol, 30.28 kcal/mol]): B3LYP, BMK, tHCTHhyb, TPSSh, M06-L, O3LYP, HCTH147, HCTH(407), tHCTH, HCTH93.
These classifications indicate that the eight functionals (HSE1PBE, HSEh1PBE, M06, mPW1PBE, mPW1PW91, wB97X, mPW1LYP and B1B95) of group 1 have the more satisfactory results in comparison with that of DLPNO-CCSD(T) method within 3 kcal/mol.
So in the respect of thermochemical and activation parameters (including the energy barrier and reaction energy), the three functionals (B1B95, mPW1PBE and CAM-B3LYP) are consistent with the DLPNO-CCSD(T) result which the differences are within 5.06 kcal/mol. Then, the differences of HSE1PBE and HSEh1PBE functionals are within 6.45 kcal/mol followed.
Here, we summarize these results with the following remarks:
(i) In the process of search of transition states using various DFT methods for N–N bond cleave process, eighteen DFT methods (BP86, B97D, PBEPBE, BLYP, mPWPW91, PW91PW91, TPSSTPSS, B3P86, mPW3PBE, B1LYP, X3LYP, BHandH, BHandLYP, HSE2PBE, PBEh1PBE, M06HF, wB97, LC-WPBE) can’t locate successfully transition states. This shows that these are not suitable for N-N bond fracture system.
(ii) For the structure of diiron complexes, six HGGAs (B1B95, PBE1PBE, mPW1PBE, mPW1PW91, HSEh1PBE, HSE1PBE) can reproduce the geometries of MP2 method. And the B1B95 functional is best for structures.
(iii) For in the respect of the relative energy, the five functionals (B1B95, mPW1PBE, CAM-B3LYP, HSE1PBE and HSEh1PBE) are consistent with the DLPNO-CCSD(T) results which the differences are within 6.45 kcal/mol. And the B1B95 functionals has the smallest energy difference within 3 kcal/mol of the DLPNO-CCSD(T) data.