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

Authors: Hong-Xia Yu; Hui Liu; Zun-Yao Wang; Lian-Sheng Wang
Journal: International Journal of Chemical Engineering
 (2008)

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## Abstract

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
(ΔfHθ) and standard free energy of formation in water (ΔfGwθ). The dependences of these thermodynamic parameters on the numbers and positions of chlorine substitution (NPCS) were discussed. It is suggested that  Sθ,ΔfHθ, and ΔfGwθ 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 ΔfGwθ, the relative stability order of PCPZ congeners was theoretically proposed.


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## Body

## 1. 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 ED50 of 10−7M [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 [12–16]. The purpose of the
study was to calculate the thermodynamic properties for 76 PCPZs. And considered on solvation affects, total
free energy in water (Gw) was calculated with the same program. Then, the relationship between these
parameters and the numbers and positions of chlorine substitution (NPCS) were studied. By designing isodesmic
reactions, the standard enthalpies of formation (ΔfHθ) and the standard Gibbs energies of formation in water (ΔfGwθ) for all PCPZs were also obtained. On the basis of the relative magnitude of
their ΔfGwθ, the relative stability order of PCPZ congeners was theoretically
proposed and then compared with that of
polychlorinated dibenzo-p-dioxin (PCDD) isomers. Finally, the Cp,m values of PCPZ congeners were calculated using
statistical thermodynamics calculation program at 200–1800 K.


## 2. Computational Methods

With Gaussian 03 program [17], geometry optimizations were performed at the B3LYP/6-31G* level at the state of 298.15 K and
101.325 kPa. And considered on solvation affects, total free energy in water (Gw) 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 (Hθ),
total
free energy in water (G), and standard entropy (Sθ) 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-).Figure 1
The numbering of the C-atoms.Lee et al. [18] used the isodesmic reaction to calculate the ΔfH and ΔfG 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 calculatingΔfHθ and
ΔfGθ: (1)PZ+nchlorobenzene=PCPZ+nbenzene.From the reaction above,ΔfHθ and ΔfGθ of PCPZs can be obtained,
as follows:  (2)ΔfHPCPZθ=HPCPZθ+nHbenzeneθ−nHchlorobenzeneθ−HPZθ−nΔfHbenzeneθ+nΔfHchlorobenzeneθ+ΔfHPZθ,(3)ΔfGPCPZθ=GPCPZθ+nGbenzeneθ−nGchlorobenzeneθ−GPZθ−nΔfGbenzeneθ+nΔfGchlorobenzeneθ+ΔfGPZθ.Equation (4) was used to calculate ΔfGθ(PZ): (4)N2+12C(Graphite)+4H2=C12H8N2.Then(5)ΔrSθ=S(PZ)θ−S(N2)θ−12S(C)θ−4S(H2)θ,ΔrHθ=ΔfH(PZ)θ−ΔfH(N2)θ−12ΔfH(C)θ−4ΔfH(H2)θ=ΔfH(PZ)θ,ΔfG(PZ)θ=ΔrH(PZ)θ−TΔrS(PZ)θ.The
experimental and calculated values ofΔfHθ,ΔfGθ,Hθ,Gθ, and Sθ for benzene, chlorobenzene, phenazine, graphite,
nitrogen, and hydrogen are listed in Table 1.Table 1
Thermodynamic data used for calculatingΔfHθ and ΔfGθ of PCPZs.
NumberFormula
or nameΔfHθ/(kJ⋅mol−1)ΔfGθ/(kJ⋅mol−1)Hθ/(Hartree)Gθ/(Hartree)Sθ/(J⋅mol−1⋅K−1)1Benzene(PhH)82.9a129.66a−232.14258−232.17302—2Chlorobenzene(CB)51.8a99.07a−691.74731−691.78288—3Phenazine(PZ)237.0a—−571.425835−571.47045893.9164Graphite(C)0———5.74a5Nitrogen(N2)0———45.77a6Hydrogen(H2)0———130.57aDataa     from [19] and
other data from B3LYP/6-31G*
calculations.


## 3. Results and Discussions

In this work, the general structure of PZ is shown in
Figure1, 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 Nα and Nβ, the pair numbers of chlorine at positions 1, 9
or 4, 6 are defined as
N1,9;
the pair numbers of chlorine at ortho-, meta-, and para-positions are defined
as No,Nm, and Np, respectively. Moreover, the parameters mentioned above are defined as
a general designation NPCS.


### 3.1.  Comparison of
the
Calculated
Results at Different
Levels

TheSθ 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 Sθ between the calculated results at two different levels were
small, in which the maximum discrepancy of Sθ is only
0.18J⋅(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 ΔER was obtained by the values of others minus the
smallest value, and also listed in Table 2.
The change tendency of ΔER for Di-PZs was shown in Figure 2.Table 2
Comparison ofSθ and ΔER calculated at different levels.
MoleculeSθ/J⋅(mol⋅K)−1ΔER/kJ⋅mol−1B3LYP/6-31G*B3LYP/6-311G**DiffB3LYP/6-31G*B3LYP/6-311G**MP2/6-31G*MP2/6-311G**PZ93.9294.040.12————1-100.97101.070.10————2-101.21101.330.12————1,2-107.85107.970.1219.0020.1223.4424.191,3-108.22108.400.1810.1711.1112.5113.001,4-108.09108.260.1716.6118.3020.9121.881,6-108.11108.280.1715.1016.7919.2920.291,7-108.26108.360.117.678.449.509.981,8-108.23108.390.167.878.699.9210.411,9-108.08108.250.1716.5518.2521.0121.972,3-107.98108.160.1814.1714.8617.3818.062,7-108.39108.520.130.100.100.020.052,8-108.35108.520.170.000.000.000.00Figure 2
The change tendency ofΔE for Di-PZs at different levels.In addition, comparedΔE as shown in Table 2 and
Figure 2, it was found that ΔE of 1,2-PZ calculated using four methods are all maximum and that of 2,8-PZ are all minimum.
And the discrepancy of ΔE between
the two compounds, by MP2/6-311G**, MP2/6-31G*, B3LYP/6-311G**,
and B3LYP/6-31G*,
is 24.19kJ⋅mol−1,23.44kJ⋅mol−1,20.12kJ⋅mol−1, and
19.00kJ⋅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.


### 3.2.  Relation
of the Numbers and Positions of Chlorine
Substitute (NPCS) to
Sθ

Up to date, there hasn’t been
experimental thermodynamic data of PCPZs reported systematically. In this work,Sθ can be directly obtained from the output files
of Gaussian programs and presented in Table 3.Table 3
Thermodynamic parameters by B3LYP/6-31G* for PCPZs.
MolecularSθΔfHθΔfGwθΔfGw,RθCp,m,J⋅(mol⋅K)−1NαNβNoNmNpN1,9J⋅(mol⋅K)−1kJ⋅mol−1kJ⋅mol−1kJ⋅mol−1Constant103T104T−1106T−2PZ93.9237.0a398.9575.692.151.671.540000001-101.0216.3416.305.60582.011.241.621.461000002-101.2208.7410.710.00581.671.181.611.460100001,2-107.9200.4440.9518.52588.574.711.561.391110001,3-108.2191.5434.0811.65588.224.631.561.391101001,4-108.1198.1437.3414.92588.444.651.561.392000101,6-108.1196.6435.7913.37588.404.661.561.392000001,7-108.3189.0429.116.68588.034.581.551.381100001,8-108.2189.2429.036.60588.064.591.551.381100001,9-108.1198.0438.7416.32588.454.671.561.392000012,3-108.0195.4438.2815.85588.244.641.561.380210002,7-108.4181.2422.900.48587.704.511.551.380200002,8-108.3181.1422.430.00587.694.511.551.380200001,2,3-114.7190.7474.6126.97595.388.271.511.321221001,2,4-115.0184.9467.9120.27595.198.171.511.322111101,2,6-115.0181.3460.3912.75594.978.131.501.322110001,2,7-115.1173.6453.766.12594.598.041.501.311210001,2,8-115.1173.7454.566.92594.618.061.501.311210001,2,9-115.0182.6464.3816.73595.038.151.501.322110011,3,6-115.3172.6454.847.20594.678.061.501.312101001,3,7-115.5164.8447.840.19594.338.001.501.311201001,3,8-115.5164.9447.640.00594.317.991.501.311201001,3,9-115.3173.6457.519.86594.708.081.501.312101011,4,6-115.2180.4461.2713.63594.958.111.501.323000111,4,7-115.4171.5450.723.07594.538.011.501.312100102,3,6-115.1176.5458.9111.26594.698.091.501.311210002,3,7-115.2168.6451.443.80594.358.011.491.300310001,2,3,4-121.4187.7511.6437.59602.6211.921.461.262232101,2,3,6-121.7172.1493.9519.90601.8711.721.451.252221001,2,3,7-122.0164.3489.4115.36601.4811.641.441.241321001,2,3,8-121.9164.4488.7114.66601.4911.631.441.241321001,2,3,9-121.8173.3497.7223.66601.9111.741.451.252221011,2,4,6-122.1167.6492.0517.99601.6911.621.451.253111111,2,4,7-122.2158.9481.247.19601.3111.541.451.242211101,2,4,8-122.1158.9481.767.71601.3311.551.451.242211101,2,4,9-122.1167.7491.8417.78601.7411.641.451.253111111,2,6,7-121.9166.3485.6111.56601.5511.601.451.242220001,2,6,8-122.2157.6480.076.01601.2911.551.441.242211001,2,6,9-122.1165.5486.3212.26601.5511.581.451.253110111,2,7,8-122.0161.5484.2110.15601.2911.561.441.241320001,2,7,9-122.2158.8483.569.51601.2911.551.441.242211011,2,8,9-121.8167.6490.3216.26601.6111.621.451.242220011,3,6,8-122.4149.3474.060.00600.9911.481.441.242202001,3,6,9-122.3157.0480.356.29601.2411.511.451.243101111,3,7,8-122.2152.8477.273.22600.9711.491.441.231311001,3,7,9-122.4150.0476.432.37600.9911.491.441.242202011,4,6,9-122.3164.7487.8413.79601.5111.551.451.254000221,4,7,8-122.1159.6480.736.68601.2211.521.441.242210102,3,7,8-122.0156.3480.526.47600.9911.501.441.230420001,2,3,4,6-128.5170.6536.6425.09609.1515.381.401.183232111,2,3,4,7-128.6162.0526.5014.95608.7815.311.401.182332101,2,3,6,7-128.6157.4519.928.37608.4815.201.391.172331001,2,3,6,8-129.0149.2515.794.24608.2015.151.391.172322001,2,3,6,9-128.9156.8520.979.42608.4515.171.391.173221111,2,3,7,8-128.7152.6518.516.96608.1915.151.391.171431001,2,3,7,9-128.9150.0517.986.44608.2015.151.391.172322011,2,3,8,9-128.7158.6523.5311.99608.5015.211.391.172331011,2,4,6,7-128.9153.1517.966.42608.3115.101.391.183221111,2,4,6,8-129.3144.6512.530.98608.0415.061.391.173212111,2,4,6,9-129.2152.4518.647.10608.2915.081.401.184111221,2,4,7,8-129.0147.3512.801.25608.0215.061.391.172321101,2,4,7,9-129.3144.7511.550.00608.0315.051.391.173212111,2,4,8,9-129.0153.1518.286.74608.3415.121.391.183221111,2,3,4,6,7-135.4156.3563.7623.06615.7818.871.351.113342111,2,3,4,6,8-135.6148.0557.7017.00615.5118.821.341.113333111,2,3,4,6,9-135.5155.7564.2723.56615.7718.841.351.114232221,2,3,4,7,8-135.3150.6557.3516.65615.4918.821.341.102442101,2,3,6,7,8-135.5149.1557.5216.82615.3918.801.341.102442001,2,3,6,7,9-135.7144.6540.700.00615.2418.711.341.103332111,2,3,6,8,9-135.6144.8553.4612.76615.2418.701.341.113332111,2,3,7,8,9-135.3150.0558.8818.18615.4118.801.341.102442011,2,4,6,7,9-136.0140.4550.289.58615.1218.621.341.114222221,2,4,6,8,9-135.9140.4549.899.19615.1018.611.341.114222221,2,3,4,6,7,8-142.1148.2599.584.08622.7322.481.291.043453111,2,3,4,6,7,9-142.4143.8595.490.00622.5922.391.291.044343221,2,3,4,6,7,8,9-148.7147.4641.63630.0426.151.240.98446422Dataa  from [19].Using multiple linear regression method of the SPSS 12.0
for windows program, the
relation betweenNPCS and Sθ can be seen in (6). The squared regression
coefficient R2 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 Sθ is
minor and the decrease effect is ortho≫meta>para. Sθ value is increased about
7J⋅mol−1⋅K−1
when increasing each chlorine atom to PCPZs: (6)Sθ=93.93+7.11Nα+7.22Nβ−0.01N1,9−0.38No−0.05Nm+0.00Np,R2=1.000SD=0.05.


### 3.3.
Calculated Results ofΔfHθ  and ΔfGwθ
Value and
Relative Stability
of Isomer Groups

With the isodesmic reactions,ΔfHθ
and
ΔfGwθ
of PCPZs were obtained and presented in
Table 3. Using multiple linear regression method, the correlation
expressions of ΔfHθ
and
ΔfGwθ to NPCS were summarized and
presented in (7) and (8), respectively. The correlations of (7) is very well
due to the corresponding larger
r2  as well as (8), both
of which represent the influence of the number of chlorine on the value of ΔfHθ   and ΔfGθ clearly: (7)ΔfHθ=235.08−19.89Nα−26.47Nβ+1.57N1,9+12.91No+3.12Nm+1.97Np,R2=0.997SD=1.16,(8)ΔfGwθ=392.87+22.31Nα+14.24Nβ+12.94No+5.03Nm,R2=0.997SD=2.83.It is suggested thatΔfHθ and ΔfGwθ 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 ΔfHθ and ΔfGwθ 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 higher
relative standard Gibbs energy of formation are more unstable.
Supposed the lowestΔfGwθ of isomers with the same numbers of substituent
to be zero, the relative standard Gibbs energies of formation (ΔfGw,Rθ) were obtained, by ΔfGwθ of other isomers minus the lowest ΔfGwθ of isomers with the same substituent numbers. Then, according to the
magnitude of
ΔfGw,Rθ, 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.Table 4
Most stable and unstable
isomers in different isomer groups for PCPZs.
CompoundsThe most stable isomerThe most unstable isomerMCPT2-1-DCPT2,8-; 2,7-1,2-Tri-CPT1,3,8-; 1,3,7-1,2,3-TCPT1,3,6,8-1,2,3,4-Penta-CPT1,2,4,7,9-1,2,3,4,6-Hexa-CPT1,2,3,6,7,9-1,2,3,4,6,7-Hepta-CPT1,2,3,4,6,7,9-1,2,3,4,6,7,8-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
ΔfGw,Rθ
is higher,
while
the formation ratio of isomer with higher
ΔfGw,Rθ
is lower, which is
similar to that of PCDDs.


### 3.4. The Temperature Dependence of Molar
Heat Capacity of PCPZs at Constant Pressure

The values of molar heat capacity at constant pressure(Cp,m) for PCPZs congeners haven’t been reported. So,
the values of Cp,m were calculated using statistical thermodynamics
calculation program at 200 to 1800 K based on Gaussian output files.Based on
the calculated values ofCp,m of PCPZs at different temperature (T), the relations between Cp,m and temperature were obtained using the least-square method. Regression coefficients for
103T,104T−1,106T−2,
and constant are listed in
Table 3. From
Table 3, the following
conclusion can be drawn. (1) The Cp,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 Cp,m and temperature (T,T−1,
and
T−2), and the correlation coefficients (r2) are all very close or equal to 1.0. These
indicated that a good correlation between Cp,m values and T.


## 3.1.  Comparison of
the
Calculated
Results at Different
Levels

TheSθ 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 Sθ between the calculated results at two different levels were
small, in which the maximum discrepancy of Sθ is only
0.18J⋅(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 ΔER was obtained by the values of others minus the
smallest value, and also listed in Table 2.
The change tendency of ΔER for Di-PZs was shown in Figure 2.Table 2
Comparison ofSθ and ΔER calculated at different levels.
MoleculeSθ/J⋅(mol⋅K)−1ΔER/kJ⋅mol−1B3LYP/6-31G*B3LYP/6-311G**DiffB3LYP/6-31G*B3LYP/6-311G**MP2/6-31G*MP2/6-311G**PZ93.9294.040.12————1-100.97101.070.10————2-101.21101.330.12————1,2-107.85107.970.1219.0020.1223.4424.191,3-108.22108.400.1810.1711.1112.5113.001,4-108.09108.260.1716.6118.3020.9121.881,6-108.11108.280.1715.1016.7919.2920.291,7-108.26108.360.117.678.449.509.981,8-108.23108.390.167.878.699.9210.411,9-108.08108.250.1716.5518.2521.0121.972,3-107.98108.160.1814.1714.8617.3818.062,7-108.39108.520.130.100.100.020.052,8-108.35108.520.170.000.000.000.00Figure 2
The change tendency ofΔE for Di-PZs at different levels.In addition, comparedΔE as shown in Table 2 and
Figure 2, it was found that ΔE of 1,2-PZ calculated using four methods are all maximum and that of 2,8-PZ are all minimum.
And the discrepancy of ΔE between
the two compounds, by MP2/6-311G**, MP2/6-31G*, B3LYP/6-311G**,
and B3LYP/6-31G*,
is 24.19kJ⋅mol−1,23.44kJ⋅mol−1,20.12kJ⋅mol−1, and
19.00kJ⋅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.


## 3.2.  Relation
of the Numbers and Positions of Chlorine
Substitute (NPCS) to
Sθ

Up to date, there hasn’t been
experimental thermodynamic data of PCPZs reported systematically. In this work,Sθ can be directly obtained from the output files
of Gaussian programs and presented in Table 3.Table 3
Thermodynamic parameters by B3LYP/6-31G* for PCPZs.
MolecularSθΔfHθΔfGwθΔfGw,RθCp,m,J⋅(mol⋅K)−1NαNβNoNmNpN1,9J⋅(mol⋅K)−1kJ⋅mol−1kJ⋅mol−1kJ⋅mol−1Constant103T104T−1106T−2PZ93.9237.0a398.9575.692.151.671.540000001-101.0216.3416.305.60582.011.241.621.461000002-101.2208.7410.710.00581.671.181.611.460100001,2-107.9200.4440.9518.52588.574.711.561.391110001,3-108.2191.5434.0811.65588.224.631.561.391101001,4-108.1198.1437.3414.92588.444.651.561.392000101,6-108.1196.6435.7913.37588.404.661.561.392000001,7-108.3189.0429.116.68588.034.581.551.381100001,8-108.2189.2429.036.60588.064.591.551.381100001,9-108.1198.0438.7416.32588.454.671.561.392000012,3-108.0195.4438.2815.85588.244.641.561.380210002,7-108.4181.2422.900.48587.704.511.551.380200002,8-108.3181.1422.430.00587.694.511.551.380200001,2,3-114.7190.7474.6126.97595.388.271.511.321221001,2,4-115.0184.9467.9120.27595.198.171.511.322111101,2,6-115.0181.3460.3912.75594.978.131.501.322110001,2,7-115.1173.6453.766.12594.598.041.501.311210001,2,8-115.1173.7454.566.92594.618.061.501.311210001,2,9-115.0182.6464.3816.73595.038.151.501.322110011,3,6-115.3172.6454.847.20594.678.061.501.312101001,3,7-115.5164.8447.840.19594.338.001.501.311201001,3,8-115.5164.9447.640.00594.317.991.501.311201001,3,9-115.3173.6457.519.86594.708.081.501.312101011,4,6-115.2180.4461.2713.63594.958.111.501.323000111,4,7-115.4171.5450.723.07594.538.011.501.312100102,3,6-115.1176.5458.9111.26594.698.091.501.311210002,3,7-115.2168.6451.443.80594.358.011.491.300310001,2,3,4-121.4187.7511.6437.59602.6211.921.461.262232101,2,3,6-121.7172.1493.9519.90601.8711.721.451.252221001,2,3,7-122.0164.3489.4115.36601.4811.641.441.241321001,2,3,8-121.9164.4488.7114.66601.4911.631.441.241321001,2,3,9-121.8173.3497.7223.66601.9111.741.451.252221011,2,4,6-122.1167.6492.0517.99601.6911.621.451.253111111,2,4,7-122.2158.9481.247.19601.3111.541.451.242211101,2,4,8-122.1158.9481.767.71601.3311.551.451.242211101,2,4,9-122.1167.7491.8417.78601.7411.641.451.253111111,2,6,7-121.9166.3485.6111.56601.5511.601.451.242220001,2,6,8-122.2157.6480.076.01601.2911.551.441.242211001,2,6,9-122.1165.5486.3212.26601.5511.581.451.253110111,2,7,8-122.0161.5484.2110.15601.2911.561.441.241320001,2,7,9-122.2158.8483.569.51601.2911.551.441.242211011,2,8,9-121.8167.6490.3216.26601.6111.621.451.242220011,3,6,8-122.4149.3474.060.00600.9911.481.441.242202001,3,6,9-122.3157.0480.356.29601.2411.511.451.243101111,3,7,8-122.2152.8477.273.22600.9711.491.441.231311001,3,7,9-122.4150.0476.432.37600.9911.491.441.242202011,4,6,9-122.3164.7487.8413.79601.5111.551.451.254000221,4,7,8-122.1159.6480.736.68601.2211.521.441.242210102,3,7,8-122.0156.3480.526.47600.9911.501.441.230420001,2,3,4,6-128.5170.6536.6425.09609.1515.381.401.183232111,2,3,4,7-128.6162.0526.5014.95608.7815.311.401.182332101,2,3,6,7-128.6157.4519.928.37608.4815.201.391.172331001,2,3,6,8-129.0149.2515.794.24608.2015.151.391.172322001,2,3,6,9-128.9156.8520.979.42608.4515.171.391.173221111,2,3,7,8-128.7152.6518.516.96608.1915.151.391.171431001,2,3,7,9-128.9150.0517.986.44608.2015.151.391.172322011,2,3,8,9-128.7158.6523.5311.99608.5015.211.391.172331011,2,4,6,7-128.9153.1517.966.42608.3115.101.391.183221111,2,4,6,8-129.3144.6512.530.98608.0415.061.391.173212111,2,4,6,9-129.2152.4518.647.10608.2915.081.401.184111221,2,4,7,8-129.0147.3512.801.25608.0215.061.391.172321101,2,4,7,9-129.3144.7511.550.00608.0315.051.391.173212111,2,4,8,9-129.0153.1518.286.74608.3415.121.391.183221111,2,3,4,6,7-135.4156.3563.7623.06615.7818.871.351.113342111,2,3,4,6,8-135.6148.0557.7017.00615.5118.821.341.113333111,2,3,4,6,9-135.5155.7564.2723.56615.7718.841.351.114232221,2,3,4,7,8-135.3150.6557.3516.65615.4918.821.341.102442101,2,3,6,7,8-135.5149.1557.5216.82615.3918.801.341.102442001,2,3,6,7,9-135.7144.6540.700.00615.2418.711.341.103332111,2,3,6,8,9-135.6144.8553.4612.76615.2418.701.341.113332111,2,3,7,8,9-135.3150.0558.8818.18615.4118.801.341.102442011,2,4,6,7,9-136.0140.4550.289.58615.1218.621.341.114222221,2,4,6,8,9-135.9140.4549.899.19615.1018.611.341.114222221,2,3,4,6,7,8-142.1148.2599.584.08622.7322.481.291.043453111,2,3,4,6,7,9-142.4143.8595.490.00622.5922.391.291.044343221,2,3,4,6,7,8,9-148.7147.4641.63630.0426.151.240.98446422Dataa  from [19].Using multiple linear regression method of the SPSS 12.0
for windows program, the
relation betweenNPCS and Sθ can be seen in (6). The squared regression
coefficient R2 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 Sθ is
minor and the decrease effect is ortho≫meta>para. Sθ value is increased about
7J⋅mol−1⋅K−1
when increasing each chlorine atom to PCPZs: (6)Sθ=93.93+7.11Nα+7.22Nβ−0.01N1,9−0.38No−0.05Nm+0.00Np,R2=1.000SD=0.05.


## 3.3.
Calculated Results ofΔfHθ  and ΔfGwθ
Value and
Relative Stability
of Isomer Groups

With the isodesmic reactions,ΔfHθ
and
ΔfGwθ
of PCPZs were obtained and presented in
Table 3. Using multiple linear regression method, the correlation
expressions of ΔfHθ
and
ΔfGwθ to NPCS were summarized and
presented in (7) and (8), respectively. The correlations of (7) is very well
due to the corresponding larger
r2  as well as (8), both
of which represent the influence of the number of chlorine on the value of ΔfHθ   and ΔfGθ clearly: (7)ΔfHθ=235.08−19.89Nα−26.47Nβ+1.57N1,9+12.91No+3.12Nm+1.97Np,R2=0.997SD=1.16,(8)ΔfGwθ=392.87+22.31Nα+14.24Nβ+12.94No+5.03Nm,R2=0.997SD=2.83.It is suggested thatΔfHθ and ΔfGwθ 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 ΔfHθ and ΔfGwθ 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 higher
relative standard Gibbs energy of formation are more unstable.
Supposed the lowestΔfGwθ of isomers with the same numbers of substituent
to be zero, the relative standard Gibbs energies of formation (ΔfGw,Rθ) were obtained, by ΔfGwθ of other isomers minus the lowest ΔfGwθ of isomers with the same substituent numbers. Then, according to the
magnitude of
ΔfGw,Rθ, 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.Table 4
Most stable and unstable
isomers in different isomer groups for PCPZs.
CompoundsThe most stable isomerThe most unstable isomerMCPT2-1-DCPT2,8-; 2,7-1,2-Tri-CPT1,3,8-; 1,3,7-1,2,3-TCPT1,3,6,8-1,2,3,4-Penta-CPT1,2,4,7,9-1,2,3,4,6-Hexa-CPT1,2,3,6,7,9-1,2,3,4,6,7-Hepta-CPT1,2,3,4,6,7,9-1,2,3,4,6,7,8-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
ΔfGw,Rθ
is higher,
while
the formation ratio of isomer with higher
ΔfGw,Rθ
is lower, which is
similar to that of PCDDs.


## 3.4. The Temperature Dependence of Molar
Heat Capacity of PCPZs at Constant Pressure

The values of molar heat capacity at constant pressure(Cp,m) for PCPZs congeners haven’t been reported. So,
the values of Cp,m were calculated using statistical thermodynamics
calculation program at 200 to 1800 K based on Gaussian output files.Based on
the calculated values ofCp,m of PCPZs at different temperature (T), the relations between Cp,m and temperature were obtained using the least-square method. Regression coefficients for
103T,104T−1,106T−2,
and constant are listed in
Table 3. From
Table 3, the following
conclusion can be drawn. (1) The Cp,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 Cp,m and temperature (T,T−1,
and
T−2), and the correlation coefficients (r2) are all very close or equal to 1.0. These
indicated that a good correlation between Cp,m values and T.


## 4. Conclusions

76 PCPZs were fully optimized at
B3LYP/6-31G* level, and thus their
Hθ,Sθ,
and Gw 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 (NPCS).
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
ΔfGwθ, the order of relative stability of PCPZ congeners was
theoretically proposed. Moreover,
it is found that there is a very good relationship between Cp,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.



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*Source: 938645-2008-11-17.xml*