DFT Calculation on 76 Polychlorophenazines: Their Thermodynamic Function and Implication of Cl Substituted Position

Thermodynamic functions, including enthalpy (Hθ) and entropy (Sθ) for 76 polychlorophenazines (PCPZs) in the gas state at 298.15 K and 101.325 kPa, have been calculated using the B3LYP/6-31G∗ level with Gaussian 03 program, and considered on solvation affects. Total free energy in water (Gw) was calculated with the same program. Based on these data, the isodesmic reactions were designed to calculate the standard formation heat (Δ f Hθ) and standard free energy of formation in water (Δ f Gw). The dependences of these thermodynamic parameters on the numbers and positions of chlorine substitution (NPCS) were discussed. It is suggested that Sθ , Δ f Hθ , and Δ f Gw of PCPZs varied greatly with NPCS. Moreover, the values of molar heat capacity at constant pressure (Cp,m) from 200 to 1800 K for PCPZ congeners were calculated using a statistical thermodynamics calculation program based on Gaussian output files, and the temperature-dependence relation of Cp,m was obtained using the least-squares method. In addition, according to the relative magnitude of their Δ f Gw , the relative stability order of PCPZ congeners was theoretically proposed.


Introduction
Phenazine (PZ) shows properties of a wide range in significant applications [1,2].Natural and synthetic phenazines have attracted considerable attention because of their interesting biological activities [3], that is, antibiotic and anticancer agents [4,5].Halosubstituted phenazines are useful as herbicides [6].Because of there increasing dosage of chlorophenzines in recent years, their concentrations in the environment have also increased.Using the in vitro bioassay for dioxin-like activity showed that TBPZ has an ED 50 of 10 −7 M [7].It can draw the conclusion that polychlorophenzines also have dioxin-like activity.For studying their generation, degradation, and environmental risk, it is important to know the thermodynamic properties of PCPZs.In addition, solvation has huge effect on organic reactivity/stability, and these studies were reported previously.For example, Warshel [8] studied computer modeling of chemical reactions in enzymes and solutions; Bren et al. [9] studied the reaction between chloroethylene oxide and guanine; Kranjc and Mavri [10] reported the calculations of the activation free energy for a chemical reaction between ethylene oxide and guanine; Florián and Warshel [11] calculated chemical processes in aqueous solution using a new parameterization of the Langevin dipole (LD) model.
We have studied the thermodynamic properties for PCDFs, PCPTs, PBDF, PBNs and PCDTs [12][13][14][15][16].The purpose of the study was to calculate the thermodynamic properties for 76 PCPZs.And considered on solvation affects, total free energy in water (G w ) was calculated with the same program.Then, the relationship between these parameters and the numbers and positions of chlorine substitution (N PCS ) were studied.By designing isodesmic reactions, the standard enthalpies of formation (Δ f H θ ) and the standard Gibbs energies of formation in water (Δ f G θ w ) for all PCPZs were also obtained.On the basis of the relative magnitude of their Δ f G θ w , the relative stability order of PCPZ congeners was theoretically proposed and then compared with that of

Computational Methods
With Gaussian 03 program [17], geometry optimizations were performed at the B3LYP/6-31G * level at the state of 298.15K and 101.325 kPa.And considered on solvation affects, total free energy in water (G w ) was calculated with the same program.In terms of the numbers and different positions of constituted chlorine atoms, there are 76 possible structural patterns of PCPZs.Standard enthalpies (H θ ), total free energy in water (G), and standard entropy (S θ ) for 76 PCPZs were obtained from the Gaussian output files.As for the notation in this paper, PCPZ congeners with one to eight chlorine atoms are represented by MCPZ, DCPZ, Tri-CPZ, TCPZ, Penta-CPZ, Hexa-CPZ, Hepta-CPZ, and Octa-CPZ, respectively.Prefix numbers represent the positions (see Figure 1) of chlorine substitution (e.g., 2,3,7,8-TCPZ or simply 2,3,7,8-).Lee et al. [18] used the isodesmic reaction to calculate the Δ f H and Δ f G of PCDDs and obtained results consistent to experimental results.So it seems reasonable to expect that estimates of the thermodynamic properties of PCPZs, from DFT calculations based on isodesmic reactions, will be similarly accurate.
In this study, reaction 1 was designed for calculating Δ f H θ and Δ f G θ : PZ + n chlorobenzene = PCPZ + n benzene. ( From the reaction above, Δ f H θ and Δ f G θ of PCPZs can be obtained, as follows: Equation ( 4) was used to calculate Δ f G θ (PZ):  Then The experimental and calculated values of Δ f H θ , Δ f G θ , H θ , G θ , and S θ for benzene, chlorobenzene, phenazine, graphite, nitrogen, and hydrogen are listed in Table 1.

Results and Discussions
In this work, the general structure of PZ is shown in Figure 1, and the numbering of the C-atoms in the phenyl rings is indicated.The numbers of chlorine atoms at positions 1(4, 6, 9) and 2 (3,7,8) are defined as N α and N β , the pair numbers of chlorine at positions 1, 9 or 4, 6 are defined as N 1,9 ; the pair numbers of chlorine at ortho-, meta-, and para-positions are defined as N o , N m , and N p , respectively.Moreover, the parameters mentioned above are defined as a general designation N PCS .

Comparison of the Calculated Results at Different Levels
The S θ of PZ, Mono-PZs, and Di-PZs were also calculated at the B3LYP/6-311G * * level, and listed in Table 2. Seen from Table 2, the differences of S θ between the calculated results at two different levels were small, in which the maximum discrepancy of S θ is only 0.18 J•(mol•K) −1 .Moreover, the values of E for ten Di-PZs were calculated at levels of B3LYP and MP2.Defined the most smallest value of E at each level as zero, the ΔE R was obtained by the values of others minus the smallest value, and also listed in Table 2.The change tendency of ΔE R for Di-PZs was shown in Figure 2.

Number
Formula or name

Relation of the Numbers and Positions of Chlorine Substitute (N PCS ) to S θ
Up to date, there hasn't been experimental thermodynamic data of PCPZs reported systematically.In this work, S θ can be directly obtained from the output files of Gaussian programs and presented in Table 3.
Using multiple linear regression method of the SPSS 12.0 for windows program, the relation between N PCS and S θ can be seen in (6).The squared regression coefficient R 2 is 1000 and standard deviation SD is 0.05.From the equation, the number of chlorine substitute has obvious effect on entropy, but the spatial effect of chlorine on the parameter S θ is minor and the decrease effect is ortho meta > para.S θ value is increased about 7 J•mol −1 •K −1 when increasing each chlorine atom to PCPZs:

Calculated Results of Δ f H θ and Δ f G θ w Value and Relative Stability of Isomer Groups
With the isodesmic reactions, Δ f H θ and Δ f G θ w of PCPZs were obtained and presented in Table 3.Using multiple linear regression method, the correlation expressions of Δ f H θ and Δ f G θ w to N PCS were summarized and presented in ( 7) and (8), respectively.The correlations of ( 7) is very well due to the corresponding larger r 2 as well as (8), both of which represent the influence of the number of chlorine on the value of Δ f H θ and Δ f G θ clearly: It is suggested that Δ f H θ and Δ f G θ w of PCPZs varied greatly with the positions of chlorine substitution, with an order of decrement for these parameters being position β> position α.It was also found that Δ f H θ and Δ f G θ w increase with two chlorines at the same aromatic ring, and the increase effect order is ortho meta > para.Of the PCPZ compounds in each isomer group, the isomers with lower relative standard Gibbs energy of formation are relatively more stable, whereas those with the   a Data from [19].
higher relative standard Gibbs energy of formation are more unstable.Supposed the lowest Δ f G θ w of isomers with the same numbers of substituent to be zero, the relative standard Gibbs energies of formation (Δ f G θ w,R ) were obtained, by Δ f G θ w of other isomers minus the lowest Δ f G θ w of isomers with the same substituent numbers.Then, according to the magnitude of Δ f G θ w,R , the theoretic relative stability orders of the isomers were proposed, and the most stable isomer and the most unstable one are listed in Table 4.As can be observed from Table 4, the most unstable isomers in MCPTs, DCPTs, Tri-CPTs, TCPTs, Penta-CPTs, Hexa-CPTs, and Hepta-CPTs are all those with chlorines being attached at the same aromatic ring and close to each other.On the contrary, the most stable isomers are all those with bromines replaced at two aromatic rings as possible, so that the bromines can be apart from each other.
We have calculated the gas phase thermodynamic functions of polychlorinated dibenzo-p-dioxins (PCDDs) via DFT method and designed isodesmic reactions [20].The relative contents of isomers were found to correlate with the values of free energies, that is, the isomer with lower free energy has higher relative content.So it can be concluded that the formation ratio of isomer with lower Δ f G θ w,R is higher, while the formation ratio of isomer with higher Δ f G θ w,R is lower, which is similar to that of PCDDs.

The Temperature Dependence of Molar Heat Capacity of PCPZs at Constant Pressure
The values of molar heat capacity at constant pressure (C p,m ) for PCPZs congeners haven't been reported.So, the values of C p,m were calculated using statistical thermodynamics calculation program at 200 to 1800 K based on Gaussian output files.
Based on the calculated values of C p,m of PCPZs at different temperature (T), the relations between C p,m and temperature were obtained using the least-square method.Regression coefficients for 10 3 T, 10 4 T −1 , 10 6 T −2 , and constant are listed in Table 3. From Table 3, the following conclusion can be drawn.(1) The C p,m values of PCPZs are in direct ratio to temperature T, T −1 , and T −2 .(2) All PCPZ congeners have very good relationships between C p,m and temperature (T, T −1 , and T −2 ), and the correlation coefficients (r 2 ) are all very close or equal to 1.0.These indicated that a good correlation between C p,m values and T.

Conclusions
76 PCPZs were fully optimized at B3LYP/6-31G * level, and thus their H θ , S θ , and G w were consequently obtained.In addition, the standard formation heat and standard formation free energy of each PCPZ molecule were calculated by isodesmic reactions.The result showed that all these thermodynamic parameters have close relationship with the numbers and positions of chlorine substituents (N PCS ).So, the enthalpies and Gibbs free energies of formation for 76 PCPZ congeners should be valuable in further thermodynamic modeling studies.According to the relative magnitude of their Δ f G θ w , the order of relative stability of PCPZ congeners was theoretically proposed.Moreover, it is found that there is a very good relationship between C p,m and temperature for the PCPZ congeners.In a word, this work about thermodynamic properties is useful and significative for studying the generation, degradation, and potential environmental risk of PCPZs.

Figure 1 :
Figure 1: The numbering of the C-atoms.

Figure 2 :
Figure 2: The change tendency of ΔE for Di-PZs at different levels.

Table 1 :
Thermodynamic data used for calculating Δ f H θ and Δ f G θ of PCPZs.

Table 2 :
Comparison of S θ and ΔE R calculated at different levels.
kJ•mol −1 , 20.12 kJ•mol −1 , and 19.00 kJ•mol −1 , respectively.The values of ΔE calculated using four methods are different, but the order of the relative magnitude and the change tendency of ΔE are accordant.So the relative stability order of PCPZ congeners proposed at the B3LYP/6-31G * level was feasible theoretically.

Table 4 :
Most stable and unstable isomers in different isomer groups for PCPZs.