Table 5.
Comparison of exothermicity and barrier height from SCC-DFTB and high-level ab initio calculations for 37 elementary steps in the hydrolysis of MMP and DMPa
| Processb | ab initio | SCC-DFTB Single point |
SCC-DFTBPR Optimizationi |
MP2//SCC- DFTBPRj |
|---|---|---|---|---|
| com1→ts1 (MMP,B) | 31.0c/−1.7d | −0.9e/−3.0f/0.4g/3.1h | 1.1 | −0.9 |
| com1→int1 (MMP,E) | 30.6/−1.4 | −2.1/−2.2/0.7/2.1 | 1.4 | −0.8 |
| com1→ts1_2 (MMP,B) | 41.5/−2.1 | 1.2/−0.3/2.4/5.3 | −3.4 | −1.6 |
| com1→int1_2 (MMP,E) | 31.0/−1.1 | −4.4/−0.6/1.6/3.1 | 1.9 | −0.1 |
| int1_2→ts2_1 (MMP,B) | 11.9/−2.0 | −2.5/−2.1/−3.3/−2.3 | ---k | |
| int1_2→ts2_2 (MMP,B) | 3.6/0.1 | −5.4/−5.0/−5.2/−5.0 | 0.3 | 6.1 |
| int1_2→com2 (MMP,E) | −28.8/−0.9 | 2.5/0.6/0.2/0.4 | −0.4 | −0.8 |
| com1→diss_tsa (MMP,B) | 36.8/−4.2 | 4.7/4.0/2.4/4.8 | 2.6 | 0.2 |
| com1→diss_int (MMP,E) | 19.6/−6.4 | −7.1/−6.0/−3.5/−2.8 | −2.9 | −1.0 |
| com1_w2→ts1_2_w2 (MMP,B) | 39.9/−2.1 | −8.2/−9.4/−6.1/−3.7 | −5.4 | −2.5 |
| com1_w2→int1_2a_w2 (MMP,E) | 28.0/0.8 | −5.4/−2.5/−1.2/0.8 | 0.2 | −1.1 |
| int1_2a_w2→int1_2_w2 (MMP,E) | 0.4/−1.7 | 0.4/0.7/1.2/1.0 | 1.7 | 1.5 |
| int1_2_w2→ts2_0_w2 (MMP,B) | 11.4/−0.5 | −3.7/−7.3/−5.2/−3.8 | −7.3 | −1.1 |
| com1_da→ts1_da (MMP,B) | 55.0/−8.4 | −22.5/−12.3/−9.2/−10.1 | −8.9 | 0.0 |
| com1_da→int_da (MMP,E) | 4.5/−2.0 | −2.9/−0.7/−1.8/−0.4 | −12.1 | −1.5 |
| com1→ts1 (DMP,B) | 38.6/−1.4 | −0.9/−4.1/−0.8/3.1 | −1.6 | 0.8 |
| com1→int1 (DMP,E)j | 35.4/−0.2 | −5.6/−3.1/−0.5/0.2 | −0.5 | 0.6 |
| int1→int1_2 (DMP,E) | 1.3/−0.7 | −3.0/−0.9/−0.9/0.1 | −4.0 | 2.0 |
| int1_2→ts2 (DMP,B) | 0.6/−0.5 | 0.5/−0.1/−0.6/−0.6 | −0.5 | −1.6 |
| int1_2→com2 (DMP,E) | −35.2/−0.7 | 7.1/4.6/4.9/4.2 | 7.0 | −1.3 |
| n_com1→n_ts3 (DMP,B) | 33.6/−1.4 | 4.9/4.3/1.0/3.5 | 1.2 | −0.4 |
| n_com1→n_int1 (DMP,E) | 13.2/0.4 | −3.7/−0.8/0.4/1.1 | 0.1 | 0.1 |
| n_int1→n_ts4 (DMP,B) | 22.9/−1.6 | 6.4/4.9/2.0/4.2 | 0.9 | 1.0 |
| n_int1→n_com2 (DMP,E) | −15.8/−1.9 | 2.6/0.5/0.9/0.6 | 0.0 | 0.0 |
| DMP_P→diss_ts (DMP,B) | 40.9/−2.9 | 11.8/9.4/5.5/7.2 | 6.1 | −0.8 |
| DMP_P→diss_prod (DMP,E) | 28.2/−3.8 | 0.6/−2.1/−2.7/−2.9 | −2.6 | −1.2 |
| diss_prod2→diss_ts2 (DMP,B) | 13.5/0.7 | 13.4/13.0/7.5/11.7 | 8.4 | −0.5 |
| diss_prod2→MMP_P (DMP,E) | −29.8/3.6 | 0.8/2.8/2.6/3.6 | 2.8 | 0.2 |
| diss_w_reac→diss_w_ts (DMP,B) | 20.9/−2.3 | 5.9/3.4/−0.2/2.0 | −0.1 | −0.4 |
| diss_w_reac→diss_w_prod (DMP,E) | 18.4/−2.6 | 4.8/1.2/−2.5/−1.3 | −2.0 | −0.3 |
| diss_w_prod2→diss_w_ts2 (DMP,B) | 1.9/0.2 | 2.5/2.7/1.1/3.7 | 1.8 | −0.8 |
| diss_w_prod2→diss_w_reac2 (DMP,E) | −21.0/2.7 | −2.9/−0.5/0.9/1.5 | 0.4 | 0.3 |
| n_w_com1→n_w_ts3 (DMP,B) | 28.2/−1.8 | −3.0/−2.3/−4.8/−2.0 | --- | --- |
| n_w_com1→n_w_int1 (DMP,E) | 13.1/1.0 | −4.2/−1.3/0.0/0.7 | −3.1 | −0.5 |
| n_w_int1→n_w_int2 (DMP,E) | −0.5/0.5 | 0.3/0.5/0.7/1.1 | 0.4 | 0.3 |
| n_w_int2→n_w_ts4 (DMP,B) | 15.1/−2.3 | 1.8/−0.5/−4.0/−2.3 | --- | --- |
| n_w_int2→n_w_com2 (DMP,E) | −13.0/−2.0 | 1.2/−1.0/−0.4/−2.0 | −1.3 | 0.6 |
| Error Analysisl | ||||
| MAXE | −8.4 | −22.5/13.0/−9.2/11.7 | −12.1 | 6.1 |
| RMSE | 2.5 | 6.1/4.6/3.3/3.9 | 4.0 | 1.4 |
| MUE | 1.9 | 4.4/3.3/2.4/2.9 | 2.8 | 1.0 |
| MSE | −1.4 | −0.4/−0.4/−0.4/0.8 | −0.5 | −0.2 |
No zero-point corrections are included in either exothermicity or barrier heights. All quantities are given in kcal/mol.
The processes are labeled in the following manner: e.g., “com1→ts1 (MMP,B)” refers to the reaction from the reactant “com1” to the transition state “ts1”, “MMP” in the parenthesis refers to the mono-methyl mono-phosphate ester model system, “B” in the parenthesis stands for “Barrier”. Similarly, “com1→int1 (DMP,E)” refers to the reaction from the reactant “com1” to the intermediate “int1”, “DMP” refers to the dimethyl di-phosphate ester model system, “E” stands for “Exothermicity”. For the structures, see Fig. S1 in the Supporting Materials.
The number before the slash refers to the MP2/G3Large single point calculation based on the B3LYP/6-31+G** optimized structures. For more details about G3Large basis set, see http://chemistry.anl.gov/compmat/g3theory.htm.
The number after the slash refers to the energy difference between the B3LYP result and the MP2/G3Large single point calculation at the B3LYP structure.
The difference between the standard (second-order) SCC-DFTB and MP2/G3Large single point energies at the B3LYP/6-31+G(d,p) structures.
The difference between the default 3rd-order SCC-DFTB and MP2/G3Large single point energies at the B3LYP/6-31+G(d,p) structures..
The difference between SCC-DFTBPR and MP2/G3Large single point energies at the B3LYP/6-31+G(d,p) structures.
The difference between the “Mix-optimized 3rd-order” SCC-DFTB and MP2/G3Large single point energies at the B3LYP/6-31+G(d,p) structures.
The difference between fully geometry-optimized SCC-DFTBPR energies and MP2/G3Large single point energies at the B3LYP/6-31+G(d,p) structures.
The difference between MP2/G3Large single point energies at the SCC-DFTBPR structures and those at the B3LYP/6-31+G(d,p) structures.
As discussed in the main text and illustrated in Fig. 2, only one transition state is found at the SCC-DFTBPR level.
The errors are defined in the same manner as in Table 3. For the entry for “ab initio”, the errors are for the B3LYP/6-31+G(d,p) energies relative to the MP2/G3Large results.