Table 4. Relative Energies Computed at pH = 7 for the Different Protonation States of the Oxidized State of the IspH Active Site Cluster, Using Eq 3 with Energies Obtained from (A) the DFT/COSMO Method; (B) the Total Free Energy Stemming from the Gas-Phase Energy Plus the Reaction Field (RF) Component of the DFT/SCRF Method (i.e., the sum of E0 and ERF from Table 5); (C) the Full DFT/SCRF Methoda,f.
| A. | |||||
|---|---|---|---|---|---|
| DFT/COSMO |
|||||
| state (charge) | ΔETot,COSMOb | nΔGref (H+)c | Σ(ZPE)id | nΔECorr,pH=7e | ΔETot,COSMO,pH=7E |
| RO–P–EH (−3) | 3.9 | 22.4 | –8.8 | –9.6 | 7.9 |
| RO–PHEH (−2) | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| ROHP–E– (−3) | 2.6 | 22.4 | –7.1 | –9.6 | 8.4 |
| ROHPHE– (−2) | 3.6 | 0.0 | 1.7 | 0.0 | 5.3 |
| ROHP–EH (−2) | 1.3 | 0.0 | 1.6 | 0.0 | 2.9 |
| ROHPHEH (−1) | 2.4 | –22.4 | 10.4 | 9.6 | 0.0 |
| B. | |||||
|---|---|---|---|---|---|
| DFT/SCRF
Reaction Field |
|||||
| state (charge) | ΔETot,RF | nΔGref (H+) | Σ(ZPE)i | nΔECorr,pH=7 | ΔETot,RF,pH=7 |
| RO–P–EH (−3) | 9.5 | 44.9 | –19.2 | –19.2 | 16.0 |
| RO–PHEH (−2) | –1.4 | 22.4 | –10.4 | –9.6 | 1.1 |
| ROHP–E– (−3) | 10.3 | 44.9 | –17.5 | –19.2 | 18.5 |
| ROHPHE– (−2) | 4.2 | 22.4 | –8.7 | –9.6 | 8.4 |
| ROHP–EH (−2) | 2.4 | 22.4 | –8.8 | –9.6 | 6.5 |
| ROHPHEH (−1) | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| C. | |||||
|---|---|---|---|---|---|
|
Full DFT/SCRF |
|||||
| state (charge) | ΔETot,SCRF | nΔGref (H+) | Σ(ZPE)i | nΔECorr,pH=7 | ΔETot,SCRF,pH=7 |
| RO–P–EH (−3) | 1.7 | 0.0 | –1.7 | 0.0 | 0.0 |
| RO–PHEH (−2) | 8.0 | –22.4 | 7.1 | 9.6 | 2.2 |
| ROHP–E– (−3) | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| ROHPHE– (−2) | 10.1 | –22.4 | 8.8 | 9.6 | 6.1 |
| ROHP–EH (−2) | 9.6 | –22.4 | 8.7 | 9.6 | 5.5 |
| ROHPHEH (−1) | 21.5 | –44.9 | 17.5 | 19.2 | 13.3 |
a
Decomposed terms used to compute relative energies with eq 3. See footnotes b–e.
b
The total energy of the protonation state considered, as obtained from (A) DFT/COSMO, (B) the RF component of the DFT/SCRF method, or (C) the full DFT/SCRF method.
c
The relative free energy of the titrating proton(s), taken from eq 2.
d
Energies correcting for differences in zero-point energy between protonation states.
e
Correction term applied to obtain relative energies at pH = 7.
f
All energies are given in kcal mol–1.