You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


Introduction {#Sec1}
============

Along with sustainable development of industry, a variety of organic pollutants are released into the environment through different ways, which is potentially noxious to human health and the environment \[[@CR1], [@CR2]\]. Due to the complexity of pollutants and the difficulty of destruction, conventional treatments could hardly remove organic compounds. Advanced oxidation processes (AOPs) have been proven particularly effective and fast for treating a wide variety of organic wastewater \[[@CR3]--[@CR6]\]. Supercritical water oxidation (SCWO), one of the AOPs, has been taken as an effective method to degrade substances for higher efficiency, faster reaction rate and less selectivity \[[@CR7], [@CR8]\].

Quantitative structure activity relationship (QSAR) models are rapid and cost-effective alternatives to predict theoretical data through building the relationship between molecular structure and physicochemical properties \[[@CR9], [@CR10]\]. Several researchers have applied QSAR models to evaluate the eco-toxicity of chemicals without experimental testing \[[@CR11]--[@CR13]\]. At present, numbers of studies have investigated the removal of organic pollutants in SCWO system, which mainly focused on two fields. One is the industrial application of the SCWO technology \[[@CR14], [@CR15]\]. Another is exploring relationship between reaction conditions and the degradation efficiency \[[@CR16], [@CR17]\]. Compared with factors like pressure and residence time, temperature has been deemed to play a controlling role as reported by Crain et al. \[[@CR18]\]. More importantly, the type of treated pollutant accounts for certain appropriate temperature, which is a key indicator when designing and running SCWO system. However, there are seldom researches about theoretical model to offer rapid predictions of systematic effective temperature, which overcome limitations in repeated experiments, like high operational cost and expensive materials \[[@CR8], [@CR19], [@CR20]\]. Therefore, in consideration of the rigorous requirements for reaction system, it is of great value and necessity to explore a convenient and efficient QSAR study. This model is significant in both industrial application and theoretical prediction.

It is our emphasis to figure out a common rule available for SCWO system. Also, the impact of Fukui indices and effective temperature on oxidation process were prioritized in QSAR analysis. Primarily, kinetic experiments of diverse compounds were explored. Later, temperature-dependent QSAR models were developed using multiple linear regression. Finally, validations were performed to testify that the optimal model can robustly make predictions.

Materials and methods {#Sec2}
=====================

Reaction system {#Sec3}
---------------

The experiments were conducted in a supercritical flow reactor (SFR) system that had been used for previous studies in our laboratory \[[@CR21]\]. The major parts consisted of high-pressure plunger pump, hydrogen peroxide tank, waste water tank, gas release valve, check valve, thermometer, pressure gage, heat exchanger, heater and reactor, temperature recording controller, condenser, back pressure regulator and effluent tank. The construction of the SFR was displayed in Fig. [1](#Fig1){ref-type="fig"}. It was designed to work under 773.15 K of operating temperature and 30 MPa of operating pressure.Fig. 1Supercritical flow reactor (SFR) system

With the aim to study the influence of temperature, compounds thermolysis and oxidation experiments were all performed under isoconcentration (1 g L^−1^) and isobaric (24 MPa) conditions. Meanwhile, reaction system was supplied with sufficient residence time (100--150 s) and oxygen (500% excess). The content of total organic carbon (TOC) in the samples was monitored using a TOC analyzer (TOC-V~CPN~, Shimadzu Corporation, Japan). Hydrogen peroxide (30 wt%) was used as the oxidant in the SCWO experiments and all reagents were analytical pure.

Arrhenius equation in SCWO system {#Sec4}
---------------------------------

Temperature is particularly vital in the supercritical reaction conditions. Some orthogonal experiment researches have confirmed the significance of temperature on destruction of the organic structures. The Arrhenius equation is a simple and remarkably accurate formula for the temperature dependence of the reaction rate constant, which can be expressed as follows.$$\documentclass[12pt]{minimal}
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                \begin{document}$$ k = Aexp^{{\frac{{ - E_{a} }}{RT}}} $$\end{document}$$

Based on Eq. ([1](#Equ1){ref-type=""}), an Arrhenius-type Eq. ([2](#Equ2){ref-type=""}) is presented as follows.$$\documentclass[12pt]{minimal}
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                \begin{document}$$ {\text{T}} = \frac{{E_{a} }}{R(lnA - lnk)} $$\end{document}$$where *A* is the pre-exponential factor and *R* is the gas constant. The units of *A* are identical to those of the rate constant *k* and will vary depending on the order of the reaction. It can be seen that either increasing the temperature T or decreasing the activation energy *E*~*a*~ (for example through the use of catalysts) will result in an increase in rate of reaction. When oxygen exceeds, the degradation process of SCWO system is in accordance with the pseudo-first-order kinetic reaction equation.$$\documentclass[12pt]{minimal}
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                \begin{document}$$ {\text{T}} = f\left( {\mu ,{\text{ q}}\left( {\text{CN}} \right),{\text{ BO}},{\text{ f}}\left( + \right) \ldots } \right) $$\end{document}$$

In short, the Arrhenius equation gives a reliable and applicable principle between ln*k* of oxidation reactions and T (in absolute temperature). Based on present researches focused on the relationship between ln*k* and quantum molecular parameters, function could be assumed as Eq. ([3](#Equ3){ref-type=""}) \[[@CR22], [@CR23]\]. It is reasonable to develop a temperatures-dependent QSAR in order to predict oxidation efficiency by theoretical descriptors.

Computation details {#Sec5}
-------------------

All the calculations were carried out by using chemical density functional theory (DFT) methods in Gaussian 09 (B3LYP/6-311G level) and Material Studio 7.0 (Dmol3/GGA-BLYP/DNP(3.5) basis) \[[@CR24]\]. Structure optimization and the total energy calculations of the optimized geometries were based on B3LYP method. During the calculation process, exchange and correlation terms were considered with a B3LYP function (6-311G basis set). Meanwhile, natural population analysis (NPA) of atomic charge was obtained by the same method. The localized double numerical basis sets with polarization functional (DNP) from the DMol3 software were adopted to expand the Kohn--Sham orbitals. The self-consistent field procedure was carried out with a convergence criterion of 10^−6^ a.u. on energy and electron density. Density mixing was set at 0.2 charge and 0.5 spin. The smearing of electronic occupations was set as 0.005 Ha. Molecular parameters of each organic compound are listed in Table [1](#Tab1){ref-type="table"}. They included energy of molecular orbital (E~LOMO~/E~HOMO~), bond order (BO), Fukui indices \[f(+), f(−) and f(0)\] and so on. In "[Optimization](#Sec7){ref-type="sec"}" section, they were introduced in detail.Table 1Molecular descriptors of 21 nitrogenous organic pollutantsMoleculeμqHq (CN)~n~q (CN)~x~E~LUMO~E~HOMO~BO~n~BO~x~f(+)~x~f(+)~n~f(−)~n~f(−)~x~f(0)~n~f(0)~x~(Debye)(e)(e)(e)(eV)(eV)----(e)(e)(e)(e)(e)(e)Methylene blue trihydrate12.0830.239− 0.3660.261− 0.127− 0.1731.0381.4180.0370.0090.0370.0100.0360.012Rhodamine B8.7880.482− 0.5810.442− 0.098− 0.1550.9241.5010.054− 0.0040.055− 0.0040.055− 0.004Eriochrome blue black R7.1100.497− 0.2710.451− 0.009− 0.2761.1871.5320.0460.0010.0390.0050.0460.007*o*-Nitroaniline4.7260.421− 0.2540.212− 0.087− 0.2301.1991.4620.0820.0230.1150.0480.0670.044Isatin4.6220.409− 0.2540.220− 0.105− 0.2490.8781.3920.1190.0260.0760.0170.0960.0253,4-Dichloroaniline5.0340.381− 0.7740.202− 0.027− 0.2151.1181.4240.1080.0370.1390.0390.0910.050*N*,*N*-dimethylbenzylamine0.6460.213− 0.503− 0.031− 0.009− 0.2200.9731.3970.1050.0020.244− 0.0160.1230.0262-Nitrophenol3.5790.492− 0.2510.370− 0.107− 0.2580.9831.4380.1150.0230.1250.0250.0890.037Nitrobenzene4.5410.238− 0.1910.060− 0.097− 0.2881.3231.3900.1230.0240.074− 0.0010.0870.025Aniline1.7150.362− 0.7830.1920.001− 0.1981.2881.4140.1230.0450.1640.0620.1050.057Methyl orange8.8010.217− 0.5470.252− 0.009− 0.2840.9751.5820.0940.0120.0320.0160.0860.016Crystal violet14.7630.271− 0.4240.260− 0.101− 0.1510.9281.4880.0530.0020.0510.0040.0520.007Phenol1.3440.460− 0.2910.342− 0.012− 0.2291.3201.3960.1240.0570.1360.0740.1040.0735-Chloro-2-methylbenzylamine3.8270.383− 0.7820.215− 0.010− 0.2081.0021.3780.1120.0260.1410.0210.0920.024*p*-Dimethylaminobenzaldehyde6.4270.218− 0.4200.414− 0.047− 0.2100.9561.4590.1410.0180.1000.0270.0980.022Indole2.2010.399− 0.5430.168− 0.208− 0.0151.0931.5630.1120.0290.1210.0300.1070.0371,10-Phenanthroline monohydrate3.1980.207− 0.4220.192− 0.061− 0.2381.1011.5700.0630.0250.1340.0180.0930.023Sulfanilic acid5.8690.487− 0.7600.215− 0.038− 0.2371.0871.4360.0840.0600.0870.0480.0730.0611-Methylimidazole4.1310.203− 0.4920.202− 0.2300.0190.9091.5970.1650.0420.1760.0260.1610.034Cyanuric acid3.0960.489− 0.7870.9540.141− 0.4211.1271.4250.1090.0970.2100.0600.1540.082Melamine0.0000.389− 0.7650.6420.023− 0.2321.1791.3760.0920.0740.1070.0440.0950.068

In order to obtain optimum number of variables for the correlation model, stepwise regression procedure was used to build QSAR models by the SPSS 17.0 for windows program. The quality of derived QSAR was evaluated in accordance with the squared regression coefficient (R^2^), the standard error (SE) as well as *t* test and the Fisher test. The internal validation was performed by leave-one-out cross-validation (q^2^), and the external validation was also computed (Q~EXT~^2^). In both validation methods, a validation value greater than 0.5 indicates a robust and predictive model.

Results and discussion {#Sec6}
======================

The degradation process of 21 kinds of organic pollutants was investigated at 24 Mpa from the subcritical to supercritical temperature with 500% excess oxygen. Sampling occurred from 523.15 to 773.15 K. An important design consideration in the development of SCWO is the optimization of operating temperature. As shown in Fig. [2](#Fig2){ref-type="fig"}, TOC degradation efficiency of compounds tends to be higher with the increase of operating temperature. When the temperature reached 773.15 K, most organics could be totally oxidized into water and carbon dioxide. The compounds are considered to be completely removed while the degradation efficiency reaches 95%. Consequently, we propose the concept of T~R95~, which is defined as the temperature at removal ratio of 95%, as the key indicator to evaluate compounds' complete oxidation. T~R95~ values of the reaction system are distinguished, ranging from 540.65 K (of Methylene blue trihydrate) to 764.26 K (of melamine), which indicate that organic compounds in this study are different and complex. Thus, among diverse molecules, it is significant to set up a temperature-dependent QSAR which can predict SCWO thermodynamics and oxidization activities and conclude universal rules.Fig. 2TOC removal of 21 organic pollutants in SCWO system at different temperatures

Optimization {#Sec7}
------------

The structure optimization of organic matter and the calculation of the total energy for the optimized geometry are based on the B3LYP method in Gaussian 09 and Dmol3 code in Material Studio 7.0. All quantum descriptors are directly available from the output file of two software. Finally, as shown in Table [1](#Tab1){ref-type="table"}, we got the following 15 molecular descriptors of organics: dipole moment (μ), most positive partial charge on a hydrogen atom (qH), most negative or positive partial charge on a carbon or nitrogen atom (q(CN)~n~/q(CN)~x~), energy of the lowest unoccupied molecular orbital (E~LUMO~), energy of highest occupied molecular orbital (E~HOMO~), minimum or maximum of bond order values in the molecule (BO~n~/BO~x~), and maximum or minimum of Fukui indices \[f(+)~x~/f(+)~n~, f(−)~x~/f(−)~n~ and f(0)~x~/f(0)~n~\].

Main theoretical parameters {#Sec8}
---------------------------

All organic pollutants and their 14 respective molecular parameters are listed in Table [1](#Tab1){ref-type="table"}. These theoretical parameters are important to observe which sites are active to be attacked and which bonds are sensitive to be ruptured. Fukui indices, frontier molecular orbits, bond orders are key concepts to portray the decomposition sequence of organic structure in oxidation.

Fukui indices are defined as affinity for radical attack. They are significant for analysis of site reactive selectivity among the oxidation paths, as hydrogen substitution by oxidant radicals and addition of oxidant group to double bonds are the most events. In this study, f(+)~n~, f(−)~n~ and f(0)~n~ stand for the minimum values of nucleophilic attack, electrophilic attack and ^·^OH radical attack respectively. f(+)~x~, f(−)~x~ and f(0)~x~ do for their respective maximum values on main chain of both carbon and nitrogen atoms. The average level of f(+)~n~, f(−)~n~ and f(0)~n~ are 0.030e, 0.026e, and 0.035e respectively, while those of f(+)~x~, f(−)~x~ and f(0)~x~ are 0.098e, 0.113e and 0.091e, respectively. The variation of each Fukui indices was extremely huge. Moreover, it is noticeable that cyanuric acid and 1-methylimidazole always have high values of all Fukui indices.

As stated earlier, NPA has been developed to calculate atomic charges and orbital populations of molecular wave functions in general atomic orbital basis sets. NPA is an alternative to conventional Mulliken population analysis. It improves numerical stability and describes the charge distribution better. qH is considered as charge of hydrogen atoms in the molecular structure system. q(CN)~n~ and q(CN)~x~, refer to the minimum and maximum of most negative partial charge on a main-chain carbon or nitrogen atom in the molecule. In this study, qH, q(CN)~n~ and q(CN)~x~ have the average values of 0.355e, − 0.498e and 0.295e respectively. At the same time, the maximum of qH, q(CN)~n~ and q(CN)~x~ reach 0.497e, − 0.191e and 0.945e respectively, while the minimum of them are 0.203e, − 0.787e and − 0.032e respectively. It is also noticeable that the distinguish between the largest and the smallest value of q(CN)~x~ is 0.977e, which is a wide range for compounds, leading the challenges and values of our study.

Construction of QSAR models {#Sec9}
---------------------------

Using the obtained molecular descriptors as variables, the correlation models of the predictable rate constants were developed by Multivariate linear regression (MLR) method. There are three out of 14 descriptors, f(+)~n~, qH, and BO~x~, correlated well with T~R95~ respectively. With the exclusion of parameters of the least importance, the relationship for degradation rate of organic pollutants was established using MLR analysis. Three effective models with their associated data indices are shown in Table [2](#Tab2){ref-type="table"}. All the predictable values of T~R95~ values (Pred.) by three QSAR models and the experimental values are listed in Table [3](#Tab3){ref-type="table"}.Table 2Regression models for calculating T~R95~ of organic pollutantsNoModelR^2^SEFq^2^Q~EXT~^2^1T~R95~ = 599.849 + 1492.671f(+)~n~0.50239.12719.1210.3800.3652T~R95~ = 654.775 + 1761.910f(+)~n~ − 77.211qH0.62035.08714.7020.5700.7413T~R95~ = 396.855 + 1874.189f(+)~n~ − 158.091qH + 169.801BO~x~0.66533.90511.2550.4680.884 Table 3Tested and three predicted T~R95~ values of 21 organic pollutantsNoMoleculeTested (K)Pred. (K)1231Methylene blue trihydrate540.653613.283628.263616.6332Rhodamine B562.093593.883562.323568.0533^a^Eriochrome blue black R575.303601.343568.463580.3134*o*-Nitroaniline587.053634.183620.653621.7135Isatin600.023638.663628.063617.20363,4-Dichloroaniline621.533655.083652.393647.6837*N*,*N*-dimethylbenzylamine622.873602.833620.553604.14382-Nitrophenol625.273634.183608.073606.3939Nitrobenzene627.043635.673654.843640.20310^a^Aniline635.453667.023669.833664.13311Methyl orange656.223617.763637.443653.65312Crystal violet658.803602.833610.273610.36313Phenol659.973684.933673.593667.993145-Chloro-2-methylbenzylamine664.803638.663632.673619.04315*p*-Dimethylaminobenzaldehyde667.433626.723647.833643.90316Indole669.283643.143635.113653.49317^a^1,10-Phenanthroline monohydrate682.103637.173662.103677.50318Sulfanilic acid695.473689.413674.093676.153191-Methylimidazole703.193662.543692.733714.68320Cyanuric acid715.433744.643738.863743.38321Melamine764.263710.313716.103707.663^a^ Samples in an external test set

It is widely reported that favorable models are generally determined by R^2^ and SE \[[@CR25], [@CR26]\]. According to the predictable performance shown in Fig. [3](#Fig3){ref-type="fig"} \[model (1), (2) and (3)\], R^2^ increase with the number of variables. To avoid the over-parameterization of model, the value of leave-one-out cross-validation q^2^ closer to corresponding R^2^ was chosen as the breakpoint criterion. Therefore, model (2) with two descriptors was considered as the best one, which also fits well with both ideal regression (R^2^ = 0.620 \> 0.600) and internal validation (q^2^ = 0.570 \> 0.500). These statistics guarantee that the model is very robust and predictive. Apart from that, it can be seen from Fig. [3](#Fig3){ref-type="fig"} that model (2) also had the best fitting curve between the predicted and experimental data. Tested T~R95~ values increase almost linearly with all organic pollutants except for methylene blue trihydrate and crystal violet. Most T~R95~ values predicted by optimum model are evenly distributed around regression line. The measured T~R95~ and those calculated with model (2) are in observed to be in good agreement. In this view, it is worthwhile and reasonable to predict degradation rules by model (2).Fig. 3Three QSAR models for degradation rules of organic pollutants

Model (2), the optimum model, contains two variables f(+)~n~ and qH. Each variable plays an important role in the supercritical water oxidation process, revealing the reaction rules. Firstly, f(+)~n~ is a measurement of the affinity for nucleophilic attack. When f(+)~n~ is larger, it is easier of main-chain atom (carbon or nitrogen) to be attacked. So, compounds with high f(+)~n~ values have weak endurance to oxidants and not so high appropriate temperature, such as isatin and 3,4-dichloroaniline. Secondly, qH shows the non-uniformity of electric charge on hydrogen, which indicates the ease or complexity of valence-bond breakage of organic molecules. Take Eriochrome blue black R for example, it is tested as high qH value (0.497e), leading to its low efficient degradation temperature (T~R95~ = 575.30 K).

Validation and performance {#Sec10}
--------------------------

To check the stability of optimum model, leave-one-out cross-validation, pairwise correlation coefficients, *t* test and Fisher test are employed using SPSS 17.0 for window program. The values of leave-one-out cross-validation q^2^ of three models are shown in Table [2](#Tab2){ref-type="table"}. As can be seen from that, q^2^ of model (2) is the best of three models and is larger than 0.500. Pairwise correlation coefficients of model (2) are shown in Table [4](#Tab4){ref-type="table"}. The correlation coefficients order between the tested values of T~R95~ and independent variables are as follows: f(+)~n~ \> qH \> BO~x~. The correlation coefficient is 0.346 between f(+)~n~ and qH, so model (2) is acceptable.Table 4Correlation coefficient(r) matrix for variables of model (2)T~R95~f(+)~n~qHBO~x~T~R95~1.000------f(+)~n~0.8681.000----qH− 0.0960.3461.000--BO~x~0.053− 0.301− 0.2591.000

The standard regression coefficients and t values of independent variables for model (2) are listed in Table [5](#Tab5){ref-type="table"}. And all the absolute t values are larger than the standard one, suggesting that four variables are able to accept. Furthermore, we could evaluate the correlation degree of each independent variable by calculating their variation inflation factors (VIF). VIF = 1/(1 − r^2^), in which r is the correlation coefficient of multiple regressions between one variable and the others. If VIF ranges from 1.000 to 5.000, the related equation is acceptable; and if VIF is larger than 10.000, the regression equation is unstable and recheck is necessary. It can be seen from Table [5](#Tab5){ref-type="table"}, most VIF values are slightly over 1.000 and the maximum is 5.226, indicating model (2) has obvious statistical significance. An external validation of suggested model has been performed for three compounds, which are not involved in the model-building process. A test set was randomly selected with interval of seven, including Eriochrome blue black R, aniline and 1,10-phenanthroline monohydrate. The Q~EXT~^2^ value (as shown in Table [2](#Tab2){ref-type="table"}) of 0.741 (\> 0.500) indicates that suggested models have good predictive potential.Table 5Checking statistical values for three modelsRegression coefficientstSig.VIFModel (1) Constant599.84924.5490.000-- f(+)~n~1492.671 ± 0.7084.3730.0004.055Model (2) Constant654.77514.6500.000-- f(+)~n~1760.252 ± 0.8355.3960.0005.226 qH− 177.214 ± 0.376− 2.3720.0291.010Model (3)Constant396.8550.7160.035-- f(+)~n~1874.189 ± 0.8895.7820.0004.067 qH− 158.091 ± 0.328− 2.1570.0461.009 BO~x~169.801 ± 0.2251.5090.1501.003

Conclusions {#Sec11}
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Appropriate reaction temperature is an important factor to design and operate the supercritical water oxidation (SCWO) system. In this paper, QSAR models for organic compounds were developed on the basis of Arrhenius equation between oxidation reaction rate and temperature in SCWO process. According to the calculations of molecular parameters by DFT methods in Gaussian 09 and Material Studio 7.0, f(+)~n~, qH and BO~x~ appeared in established QSAR models focusing on the impact of Fukui indices and effective temperature, which reveals they are significant in understanding degradation mechanism. The optimum model has ideal regression and internal validation (R^2^ = 0.620, SE = 35.1). The results of *t* test and Fisher test suggested that the model exhibited optimum stability. Both internal and external validations showed its robustness and predictive capacity. Coincidentally, the obtained determinant factors are included with degradation process including the affinity for attack, difficulty of electron loss as well as non-uniformity of valence bond. Together with them, the degradation mechanism could reasonably be illustrated from each perspective, providing a deeper insight of universal and propagable oxidation rules.

All authors read and approved the final manuscript.

Acknowledgements {#FPar1}
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This work was supported by the National Science Foundation of China (Project No. NSFC 21177083, NSFC key project 21537002), and National water pollution control key project 2014ZX07214-002.

Competing interests {#FPar2}
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The authors declare that they have no competing interests.

Availability of data and materials {#FPar3}
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Not applicable.

Ethics approval and consent to participate {#FPar4}
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Not applicable.

Funding {#FPar5}
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This work was supported by the National Science Foundation of China (Project No. NSFC 21177083, NSFC key project 21537002), and National water pollution control key project 2014ZX07214-002.

Publisher's Note {#FPar6}
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