# Review on Mechanisms and Kinetics for Supercritical Water Oxidation Processes
## 4 Developments of Computational Chemistry
### Quantum Chemistry  
Quantum chemistry uses the methods and principles of quantum mechanics to study problems in chemistry. It includes three chemical bonding theories: valence bond theory, molecular orbit theory, and coordination field theory. Quantum chemistry calculations can obtain information on the optimal conformation and transition-state intermediates of reactants and their energy and charge transfer, which are difficult to measure in the laboratory. Thus, they can more accurately explain the mechanism  
Figure 16: Major reaction pathways for CH\({}_{3}\)NH\({}_{2}\) oxidation in SCW [148]. of chemical reactions, analyze the phenomena from a higher theoretical point of view, and provide a description of the molecular or atomic level. With the rapid development of quantum chemistry in the SCWO process, it has been used to predict reactive sites, analyze structural properties of matter, construct reaction path energies and kinetic modeling, and make qualitative/quantitative description of degradation properties and structural properties of organics. The calculations of cracking energy and the predictions of reaction sites by quantum chemistry well explained the degradation orders of different groups in SCWO processes. [PERSON] et al. [151] calculated the cracking energy for 2,4,6-trinitrotoluene (TNT) SCWO using the Dmol\({}^{3}\) by Materials Studio [152] software. The DFT calculations demonstrated that C-N bonds had the weakest cracking energy (69.6 and 75.6 kcal/mol) than other kinds of bonds (\(>\)95 kcal/mol), which explained that most of the initial reactions are relevant to the -NO\({}_{2}\) group. As an important concept in the conceptual density functional theory (DFT) framework, Fukui functions were defined by [PERSON] and [PERSON] in 1984 and have been widely used to predict reaction sites since then [153; 154; 155]. It is generally believed that the larger the Fukui indices value, the greater the reactivity of the corresponding site [156]. [PERSON] et al. [37; 43] found that the N atom in the -NH\({}_{2}\) group was more vulnerable than that in the -NO\({}_{2}\) group by calculating Fukui indices for the radical attack, indicating the -NH\({}_{2}\) group may be attacked first by hydroxyl radical rather than the -NO\({}_{2}\) group. The degradation pathway of BPA was also investigated by calculating the Fukui indices, indicating the hydroxyl groups on the benzene rings were replaced at first, and then the C-C bond between the two aromatic rings was attacked [157]. [PERSON] et al. [158] studied the temperature sensitivity of aromatic compound destruction in the SCWO process by analyzing the correlation coefficients between the highest slope of the temperature-effect curve (\(i_{\text{max}}\)) and various molecular descriptors calculated by using quantum chemical method. The correlation coefficients revealed that the effect of temperature on organics composition in SCWO was more related to dipole moment (\(\mu\)), heat of formation (HOF) and most positive partial charge of a hydrogen atom connected to a carbon atom (\(q_{\text{C-H+}}\)) than other molecular descriptors. Furthermore, [PERSON] et al. [37] explored the relationship between TN removal and molecular structural characteristics of 14 N-containing compounds using the DFT method to calculate molecular descriptors. The most negative partial charge on a carbon atom (\(q_{\text{C-}}\)), the most positive partial charge of a hydrogen atom connected to a carbon atom (\(q_{\text{C-H+}}\)), and the maximum values of Fukui indices of OH\(\bullet\) radical attack (F(0)\({}_{\text{x}}\)) had great impacts on temperature behavior of TN removal. For the catalytic supercritical water oxidation (CSCWO) process, bond order (BO\({}_{\text{n}}\)), and the most positive partial charge on a hydrogen atom (q(H)\({}_{\text{x}}\)) largely affected the TOC degradation behaviors [157]. Based on the qualitative analysis of material structures and degradation characteristics, [PERSON] et al.