water partition coefficients (Kow) of all PCB congeners by density functional theory

Journal of Molecular Structure: THEOCHEM 755 (2005) 137–145 www.elsevier.com/locate/theochem

Estimation of n-octanol/water partition coefficients (Kow) of all PCB congeners by density functional theory Wen Zhou a, Zhicai Zhai b,*, Zunyao Wang a,b, Liansheng Wang a a

State Key Laboratory of Pollution Control and Resources Reuse, School of the Environment, Nanjing University, Nanjing 210093, People’s Republic of China b School of Biological and Chemical Engineering, Jiaxing University, Zhejiang Jiaxing 314001, People’s Republic of China Received 22 April 2005; revised 11 August 2005; accepted 16 August 2005 Available online 14 October 2005

Abstract Optimized calculation of 209 PCBs was carried out at B3LYP/6-31G* level in GAUSSIAN98 program. Based on the theoretical linear solvation energy relationship (TLSER) model, the obtained structural parameters were taken as theoretical descriptors to establish the novel QSPR model for predicting n-octanol/water partition coefficients (lg Kow) of PCBs. The new model achieved in this work contains three variables, polarizability a, ELUMO and EHOMO, of which r2Z0.9484, SDZ0.18, with larger t values. In addition, the variation inflation factors (VIF) of variables in the present model are all less than 5.0, suggesting high accuracy of the lg Kow predicting model. And the results of cross-validation test (q2Z0.9455) and method validation also showed the model of this study exhibited optimum stability and better predictive power than semiempirical method. q 2005 Elsevier B.V. All rights reserved. Keywords: Polychlorinated biphenyls (PCBs); n-Octanol/water partition coefficients (Kow); Persistent organic pollutants (POPs); Quantitative structure–property relationship (QSPR); Density functional theory (DFT)

1. Introduction Polychlorinated biphenyls (PCBs), together with PCDDs and PCDFs play an important role as environmental contaminants, which have been included in many blacklists such as ‘persistent organic pollutants (POPs)’ and suspected ‘environmental endocrine disruptors (EEDs)’. PCBs are industrial chemicals which have been utilized for various commercial applications, e.g. as heat transfer fluids, organic diluents, plasticizers, paint additives, etc. Scientists estimate that hundreds of million pounds of PCBs have been released into the environment as a result of improper disposal practices and accidental releases. This is a significant environmental problem because PCBs are chemically and thermally stable and complex PCB mixtures generally are resistant to biodegradation. As widely known, they are toxic, lipophilic and tend to be bioaccumulated. As generally considered, there are 209 theoretically possible PCB congeners with various degrees of chlorination and substitution patterns at

* Corresponding author. Tel./fax: C86 573 3641881. E-mail address: [email protected] (Z. Zhai).

0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2005.08.020

available sites, of which approximately 150 PCB congeners are found in the environment [1]. Up to the present, a large number of calculation methods have been developed for estimation of the partition coefficient and aqueous solubility with varying success and applicability. According to the molecular descriptors scientists used, these methods can be classified into two groups: empirical method and theoretical method. Some papers using empirical molecular descriptors, such as gas chromatography retention index (GC-RI) [2], solubility parameters for fate analysis (SOFA) model descriptors [3–5], and mobile order thermodynamics model descriptors (MOD) [6,7]. However, the accurate determination of empirical molecular descriptors may be difficult and expensive in terms of cost and time, or even impossible for some PCBs, PCDDs and PCDFs, which might not have synthesized or purified. Also the experimental errors may be introduced, especially for those congeners difficult to be separated and identified by chromatography. Furthermore, the empirical molecular descriptors often reflect complex and multiple physical interactions. Hence, the interpretation of the respective property could be difficult and ambiguous. Because of the lack of experimentally determined data for the physicochemical properties of PCBs, there is an incentive and a growing need for non-experimental, quantitative structure–activity relationship (QSAR) methods for estimating

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W. Zhou et al. / Journal of Molecular Structure: THEOCHEM 755 (2005) 137–145

the physicochemical properties of PCBs. Many attempts have been made to model the physicochemical properties and bioactivities of PCBs by utilizing QSAR and quantitative structure–property relationship (QSPR) techniques [8–15]. For instances, Patil reported the correlation of aqueous solubility (KlgSw) and n-octanol/water partition coefficient (lg Kow) of PCBs based on molecular structure [16]. Wang et al. introduced a hologram derived QSPR model for predicting physicochemical properties of PCBs [17], while Yoshihiro explored a possible way to make a coplanar PCB stable at coplanar conformation by ab initio MO calculation [18]. In addition, Huang et al. reported the application of TLSER method obtained from semiempirical AM1 method in predicting the aqueous solubility and lg Kow of PCBs, PCDDs and PCDFs [19]. However, modern theoretical method in quantum chemistry such as DFT with high calculation precision should have its advantages in estimating properties of environmental toxics. Up to the present, relevant QSPR models for POPs by ab initio calculation have not been reported. The aim of the present study is to explore QSPR model relating to lg Kow of all PCBs by density functional theory, in an attempt to pave a new way for QSPR approaches. To do this, the calculated structural parameters were taken as theoretical descriptors and the theoretical linear solvation energy relationship (TLSER) methodology developed by Famini and Wilson et al. was also applied in the model of this work [20,21]. 2. Computational method All 209 theoretically possible PCB congeners were calculated at B3LYP/6-31G* level in GAUSSIAN98 program [22], resulting in useful structural parameters of these compounds. In calculation, molecular volume defined as the one inside a contour with charge density of 0.001 e/bohr3 was employed. In addition, the keyword ‘Tight’ was chosen so as to increase the calculation precision. All these computations, however, were performed on a Pentium IV 2.66G PC. Parameter setting of full descriptors discussed in this work are presented and interpreted in Table 1. Usually TLSER method uses a single set of descriptors and each of them describes a single, independent molecular event or characteristics [21,23]. In the present work, however, the QSPR equation was obtained by forward stepwise multiple Table 1 Parameter setting of full descriptors discussed in this work No.

Descriptor

Interpretation

Unit

1 2 3

a m EHOMO

10K30 esu Debye EV

4

ELUMO

5

qK

6

qHC

7

Vm

Mean molecular polarizability Dipole moment of the molecules Energy of the highest occupied molecular orbital Energy of the lowest unoccupied molecular orbital Most negative atomic partial charge in molecule Most positive partial charge on a hydrogen atom Molecular volume

EV E E ˚3 A

regression technique following the multilinear form: XYZ Z XYZ0 C aa C bEHOMO C cqK C dELUMO C eqHC (1) where a, b, c, d, and e are regression coefficients. To determine the optimum number of components for the correlation models, the leave-one-out (LOO) cross-validation procedure was subjected to validate the derived QSPR models by using GQSARF20 program [24]. The quality of the models was evaluated in terms of the LOO cross-validation correlation coefficient q2, the squared conventional correlation coefficient r2, the standard deviation SD and t-score. 3. Results and discussion 3.1. QSPR model for predicting lg Kow of PCBs The structural parameters of the present 209 PCBs compounds resulted from computation at B3LYP/6-31G* level are presented in the Table 2, in which some experimental values of lg Kow for partial PCB congeners from the literature [16] are also listed. In order to work out QSPR model for predicting n-octanol/ water partition coefficients (lg Kow) of PCBs therefore, the linear regression analysis was performed on the experimental data of lg Kow and all structural parameters in Table 2, using GQSARF20 program [24]. The correlation model with three variables EHOMO, ELUMO and a is thus obtained as Eq. (2). lg Kow ZK3:073K18:704EHOMO K34:076ELUMO C 0:0168a (2) 2

2

r Z 0:9484; SD Z 0:18; q Z 0:9455 In contrast, if four variables are considered in the model, its squared correlation coefficient would be r2Z0.9487, and SDZ 0.17 and q2Z0.9454, suggesting that addition of descriptors would not significantly increase its r2 and reduce SD. Therefore, employment of three variables in the model herein is proper. Moreover, in the present study, multicollinearity between the descriptors of the Eq. (2) model was checked by calculating their variation inflation factors (VIF) to evaluate the correlation degree of each independent variable in the equation [20]. Here, VIFZ1/(1Kr2), in which r is the correlation coefficient of multiple regressions between one variable and the others in the equation. If VIFZ1.0, no intercorrelation exists for each variable; if VIF ranges from 1.0 to 5.0, the related equation is acceptable; and if VIF is larger than 10.0, the regression equation is unstable and recheck is necessary. Table 3 lists the intercorrelation coefficient of the independent variables in Eq. (2), VIF, standard regression coefficients (SR) and t-scores. It can be seen from the table, the max-VIF for Eq. (2) is only 4.031, and all the absolute t values are far larger than the standard one, suggesting Eq. (2) has obvious statistic significance. In addition, the maximum standard regression coefficient in Table 3 is 0.4634 found for a, while t-score indicates that

Table 2 Measured and predicted lg Kow of PCBs and corresponding structural descriptors by B3LYP/6-31G* Congener

Exp.

ELUMO

qHC

qK

a

Vm

m

Eq. (2)

Diff.

3.95

4.66 4.63 4.72 4.84 5.09 5.27 5.15 5.23 4.99 5.15

5.23

5.12 5.60 5.29 5.39 5.54 5.71 5.33 5.65 5.68 5.04

4.37 4.69 4.61 4.68 5.05 4.99 5.39 5.32 5.26 4.97 5.04 5.07 4.69 5.23 5.42

K0.2222

K0.0248

0.1321

K0.1736

120.4

191.8

0.000

K0.2322 K0.2313 K0.2264

K0.0275 K0.0354 K0.0348

0.1552 0.1568 0.1555

K0.1609 K0.1739 K0.1736

129.1 132.9 135.1

241.1 243.4 206.5

1.683 2.101 2.147

K0.2432 K0.2407 K0.2354 K0.2396 K0.2347 K0.2304 K0.2398 K0.2364 K0.2383 K0.2485 K0.2332 K0.2401

K0.0263 K0.0368 K0.0368 K0.0452 K0.0446 K0.0440 K0.0348 K0.0374 K0.0381 K0.0238 K0.0431 K0.0454

0.1565 0.1673 0.1579 0.1608 0.1589 0.1580 0.1611 0.1780 0.1665 0.1607 0.1633 0.1769

K0.1369 K0.1596 K0.1610 K0.1729 K0.1739 K0.1705 K0.1629 K0.1649 K0.1618 K0.1354 K0.1730 0.1723

137.5 141.3 143.4 145.4 147.9 150.4 141.2 143.8 142.4 137.3 147.3 146.0

270.8 262.0 250.4 267.6 220.7 291.1 266.3 248.9 289.4 298.2 221.8 212.2

2.009 3.232 2.965 3.049 1.832 0.000 2.803 2.169 0.728 0.995 3.203 2.428

0.16

K0.2495 K0.2477 K0.2419 K0.2467 K0.2445 K0.2393 K0.2463 K0.2455 K0.2415 K0.2472 K0.2479 K0.2418 K0.2409 K0.2365 K0.2484 K0.2479 K0.2426 K0.2416 K0.2458 K0.2493 K0.2416 K0.2530 K0.2398 K0.2473

K0.0306 K0.0435 K0.0435 K0.0363 K0.0457 K0.0458 K0.0334 K0.0467 K0.0464 K0.0270 K0.0328 K0.0441 K0.0522 K0.0517 K0.0463 K0.0544 K0.0537 K0.0427 K0.0447 K0.0340 K0.0453 K0.0357 K0.0507 K0.0298

0.1624 0.1681 0.1634 0.1792 0.1805 0.1801 0.1699 0.1688 0.1676 0.1621 0.1625 0.1739 0.1671 0.1648 0.1783 0.1792 0.1790 0.1669 0.1825 0.1694 0.1841 0.1822 0.1671 0.1630

K0.1366 K0.1581 K0.1603 K0.1383 K0.1595 K0.1618 K0.1366 K0.1606 K0.1616 K0.1374 K0.1351 K0.1599 K0.1729 K0.1728 K0.1595 K0.1724 K0.1688 K0.1522 K0.1623 K0.1347 K0.1636 K0.1365 K0.1721 K0.1353

149.2 153.5 155.8 151.8 156.3 158.7 150.2 154.9 156.9 147.4 149.9 155.2 160.0 163.0 154.4 158.7 161.3 155.2 154.9 150.4 156.5 151.8 159.7 150.8

254.7 263.0 263.8 302.2 217.0 310.3 307.5 270.8 226.5 258.0 302.8 260.5 261.8 244.4 326.7 259.0 320.6 270.8 308.3 276.3 259.7 293.5 275.1 286.1

3.112 3.673 2.878 2.734 2.597 1.429 1.955 1.550 1.383 1.623 2.720 4.091 3.197 1.564 3.140 1.951 0.337 3.253 2.057 1.131 2.262 0.988 3.545 3.079

5.67

5.51

5.71

5.71

5.68 5.44

0.19

K0.2540

K0.0329

0.1640

K0.1351

161.3

286.7 3.727 (continued on next page)

Diff.

3.95

K0.03 0.02 0.04 K0.21 0.10 K0.12 K0.17 K0.03 0.02 0.11

0.00

4.37 4.69 4.62 4.67 5.04 4.98 5.38 5.31 5.26 4.96 5.03 5.06 4.67 5.23 5.41

0.14

5.12 5.60 5.54 5.31 5.67 5.62 5.18 5.70 5.65 4.93 5.18 5.55 5.89 5.84 5.73 6.06 5.99 5.49 5.63 5.25 5.60 5.40 5.81 5.08

0.16

5.48

K0.02 K0.02 K0.26 0.06 K0.14 0.08 0.14 K0.06 0.02 0.10 0.15

K0.03

0.17 0.17

K0.03 0.01 0.05 K0.20 0.11 K0.11 K0.16 K0.03 0.03 0.12

0.00

0.00 0.00 K0.25 0.08 K0.13 0.09 0.15 K0.05 0.03 0.11 0.16

K0.02

0.19 0.19

139

5.24

5.14 5.62 5.55 5.33 5.68 5.63 5.19 5.71 5.66 4.94 5.20 5.56 5.90 5.85 5.74 6.08 6.00 5.51 5.65 5.27 5.62 5.42 5.82 5.10

Eq. (3)

W. Zhou et al. / Journal of Molecular Structure: THEOCHEM 755 (2005) 137–145

Biphenyl Mono2 3 4 Di2,2 0 2,3 0 2,4 0 3,3 0 3,4 0 4,4 0 2,3 2,4 2,5 2,6 3,4 3,5 Tri2,2 0 3 2,3,3 0 2,3,4 0 2,2 0 4 2,3 0 ,4 2,4,4 0 2,2 0 5 2,3 0 ,5 2,4 0 ,5 2,2 0 6 2,3 0 ,6 2,3 0 ,4 0 3,3 0 ,4 3,4,4 0 2,3 0 ,5 0 3,3 0 ,5 3,4 0 ,5 2,3,4 2,3,5 2,3,6 2,4,5 2,4,6 3,4,5 2,4 0 ,6 Tetra2,2 0 ,3,3 0

EHOMO

lg Kow

140

Table 2 (continued) Congener

EHOMO

ELUMO

qHC

qK

a

Vm

m

K0.0400 K0.0381 K0.0316 K0.0502 K0.0518 K0.0443 K0.0438 K0.0326 K0.0524 K0.0543 K0.0410 K0.0332 K0.0534 K0.0546 K0.0297 K0.0375 K0.0357 K0.0588 K0.0607 K0.0626 K0.0383 K0.0507 K0.0505 K0.0392 K0.0526 K0.0528 K0.0370 K0.0400 K0.0398 K0.0427 K0.0536 K0.0535 K0.0379 K0.0417 K0.0434 K0.0517 K0.0593 K0.0589 K0.0502 K0.0430 K0.0432

0.1808 0.1692 0.1638 0.1746 0.1799 0.1810 0.1814 0.1803 0.1820 0.1825 0.1701 0.1670 0.1753 0.1805 0.1631 0.1690 0.1792 0.1677 0.1807 0.1814 0.1686 0.1689 0.1690 0.1836 0.1846 0.1844 0.1706 0.1717 0.1715 0.0000 0.1864 0.1859 0.1834 0.1844 0.1842 0.1776 0.1707 0.1679 0.1758 0.1874 0.1881

K0.1380 K0.1425 K0.1355 K0.1548 K0.1575 K0.1381 K0.1380 K0.1387 K0.1588 K0.1597 K0.1432 K0.1357 K0.1612 K0.1591 K0.1363 K0.1351 K0.1351 K0.1717 K0.1709 K0.1667 K0.1365 K0.1585 K0.1602 K0.1409 K0.1573 K0.1596 K0.1371 K0.1332 K0.1327 K0.1008 K0.1616 K0.1628 K0.1372 K0.1363 K0.1362 K0.1594 K0.1724 K0.1690 K0.1620 K0.1349 K0.1340

163.8 162.5 159.6 167.6 166.7 166.4 164.9 161.4 170.8 169.6 163.6 160.6 169.0 167.7 158.0 163.0 162.5 175.3 173.5 171.9 162.7 167.8 170.3 162.7 167.3 169.7 160.5 162.9 164.1 164.1 169.4 171.8 161.8 164.4 166.2 167.8 172.7 175.8 168.2 164.3 163.8

273.3 266.1 306.8 275.6 287.9 295.9 325.6 301.7 322.9 319.4 373.9 308.8 295.4 273.5 303.5 352.0 296.2 260.0 258.7 286.1 335.7 270.5 247.4 235.6 290.6 305.2 296.5 245.1 351.7 267.8 382.0 263.8 273.0 333.1 293.2 269.0 301.0 332.9 291.2 264.3 283.6

2.830 2.524 3.092 3.932 2.934 1.691 1.699 2.874 2.604 1.505 0.236 1.634 2.396 1.643 0.000 3.977 3.240 2.521 1.381 0.000 3.709 3.418 2.168 2.856 2.205 0.939 1.985 2.238 2.237 3.062 1.785 0.195 2.089 1.615 1.096 4.124 2.726 1.444 3.000 1.841 1.137

K0.0407 K0.0458 K0.0380 K0.0566

0.1701 0.1821 0.1695 0.1751

K0.1339 K0.1379 K0.1356 K0.1546

175.0 177.6 173.1 182.4

284.4 310.1 343.0 335.4

3.697 2.489 3.870 3.021

Exp.

Eq. (2)

Diff.

Eq. (3)

Diff.

5.72 5.73 4.84

K0.06 0.11 K0.54

0.09

5.76 5.60 5.36 6.07 6.25 5.89 5.85 5.46 6.15 6.31 5.72 5.36 6.18 6.29 5.27 5.62 5.61 6.39 6.54 6.72 5.67 6.11 6.06 5.69 6.23 6.19 5.55 5.71 5.71 5.81 6.23 6.18 5.63 5.81 5.86 6.12 6.45 6.40 6.06 5.92 5.85

K0.04 0.13 K0.52

5.96

5.78 5.62 5.38 6.09 6.27 5.91 5.87 5.49 6.17 6.33 5.74 5.38 6.20 6.31 5.29 5.64 5.64 6.40 6.55 6.75 5.69 6.13 6.07 5.71 6.25 6.21 5.57 5.73 5.73 5.83 6.24 6.20 5.65 5.84 5.88 6.14 6.47 6.42 6.08 5.94 5.87

0.11

K0.2536 K0.2496 K0.2512 K0.2481 K0.2556 K0.2502 K0.2502 K0.2534 K0.2454 K0.2517 K0.2499 K0.2474 K0.2469 K0.2518 K0.2515 K0.2511 K0.2549 K0.2423 K0.2484 K0.2567 K0.2529 K0.2492 K0.2440 K0.2520 K0.2524 K0.2476 K0.2504 K0.2518 K0.2510 K0.2507 K0.2485 K0.2440 K0.2523 K0.2528 K0.2503 K0.2477 K0.2471 K0.2423 K0.2468 K0.2561 K0.2526

6.18 5.60 6.79

6.07 6.26 5.96 6.59

K0.08 K0.36 0.20

6.04 6.24 5.93 6.57

K0.06 K0.33 0.22

K0.2575 K0.2563 K0.2582 K0.2499

5.94 5.87 5.51 5.98 5.79 5.55 6.22 5.24 5.76

5.79 6.10 6.24

6.10 4.84 5.76 5.69 6.32 6.10 5.75 6.03 6.03 5.98

0.03 0.00 0.02 K0.19 0.05 0.17 0.02 K0.05 0.12

0.10 K0.03 0.17

K0.11 K0.73 0.03 K0.14 0.08 K0.10 0.10 0.19 0.15 K0.16

0.05 0.02 0.05 K0.17 0.07 0.19 0.04 K0.03 0.14

0.12 K0.01 0.18

K0.09 K0.71 0.05 K0.12 0.09 K0.08 0.12 0.22 0.17 K0.14

W. Zhou et al. / Journal of Molecular Structure: THEOCHEM 755 (2005) 137–145

2,2 0 ,3,4 0 2,2 0 ,3,5 0 2,2 0 ,3,6 0 2,3,3 0 ,4 0 2,3,3 0 ,5 0 2,2 0 ,4,4 0 2,2 0 ,4,5 0 2,2 0 ,4,6 0 2,3 0 ,4,4 0 2,3 0 ,4,5 0 2,2 0 ,5,5 0 2,2 0 ,5,6 0 2,3 0 ,4 0 ,5 2,3 0 ,5,5 0 2,2 0 ,6,6 0 2,3 0 ,4 0 ,6 2,3 0 ,5 0 ,6 3,3 0 ,4,4 0 3,3 0 ,4,5 0 3,3 0 ,5,5 0 2,2 0 ,3,4 2,3,3 0 ,4 2,3,4,4 0 2,2 0 ,3,5 2,3,3 0 ,5 2,3,4 0 ,5 2,2 0 ,3,6 2,3,3 0 ,6 2,3,4 0 ,6 2,2 0 ,4,5 2,3 0 ,4,5 2,4,4 0 ,5 2,2 0 ,4,6 2,3 0 ,4,6 2,4,4 0 ,6 2 0 ,3,4,5 3,3 0 ,4,5 3,4,4 0 ,5 2,3,4,5 2,3,4,6 2,3,5,6 Penta2,2 0 ,3,3 0 ,4 2,2 0 ,3,4,4 0 2,2 0 ,3,4,6 0 2,3,3 0 ,4,4 0

lg Kow

6.32

5.87 5.92 6.20 6.41

6.57 6.30 6.23 6.11 6.40 6.42

6.38 6.92 6.50 6.44 6.06 6.41 6.39 5.60 6.32 6.30 6.45 6.71

7.30 6.20 6.72 6.32

6.75 6.11 6.29 6.17 5.95 6.84 6.08 5.99 6.22 6.40 6.26 6.72 6.72 6.85 6.07 6.19 6.07 6.00 6.28 6.35 6.64 6.72 5.95 6.96 6.24 6.67 6.17 6.32 6.33 6.15 6.33 6.33 6.40 5.98 6.12 5.84 6.24 5.99 6.63 6.72 6.09 7.11 6.64 6.60 6.42 7.12 6.71 6.44

0.03

K0.21 K0.07 K0.02 0.01

K0.15 K0.55 0.04 0.04 0.12 0.07

0.14 0.25 0.33 0.11 K0.09 0.08 0.06 K0.38 0.20 0.06 0.46 0.08

0.70 K0.22 0.01 K0.12

6.72 6.08 6.26 6.15 5.93 6.82 6.06 5.96 6.19 6.38 6.24 6.71 6.70 6.82 6.05 6.16 6.05 5.98 6.26 6.32 6.62 6.70 5.93 6.94 6.22 6.65 6.14 6.30 6.31 6.13 6.30 6.30 6.38 5.96 6.10 5.82 6.22 5.97 6.61 6.70 6.06 7.08 6.61 6.58 6.39 7.10 6.68 6.41

0.06

K0.19 K0.04 0.01 0.03

K0.13 K0.52 0.07 0.06 0.14 0.10

0.16 0.27 0.36 0.13 K0.07 0.11 0.09 K0.36 0.22 0.08 0.48 0.10

0.72 K0.19 0.04 K0.09

K0.0582 K0.0428 K0.0464 K0.0450 K0.0406 K0.0602 K0.0424 K0.0414 K0.0462 K0.0504 K0.0474 K0.0599 K0.0598 K0.0612 K0.0422 K0.0432 K0.0422 K0.0404 K0.0465 K0.0469 K0.0569 K0.0594 K0.0403 K0.0655 K0.0461 K0.0577 K0.0455 K0.0485 K0.0484 K0.0460 K0.0489 K0.0487 K0.0496 K0.0413 K0.0439 K0.0394 K0.0464 K0.0428 K0.0578 K0.0596 K0.0402 K0.0673

0.1812 0.1850 0.1853 0.1855 0.1844 0.1866 0.1817 0.1721 0.1732 0.1827 0.1873 0.1877 0.1877 0.1882 0.1849 0.1851 0.1848 0.1842 0.1858 0.1863 0.1781 0.1834 0.1862 0.1711 0.1785 0.1771 0.1884 0.1894 0.1892 0.1890 0.1900 0.1899 0.1416 0.1721 0.1713 0.1715 0.1866 0.1727 0.1767 0.1785 0.1725 0.1823

K0.1576 K0.1343 K0.1377 K0.1395 K0.1354 K0.1567 K0.1383 K0.1322 K0.1317 K0.1379 K0.1427 K0.1621 K0.1619 K0.1601 K0.1367 K0.1386 K0.1368 K0.1376 K0.1364 K0.1363 K0.1565 K0.1588 K0.1357 K0.1710 K0.1364 K0.1572 K0.1371 K0.1347 K0.1347 K0.1368 K0.1326 K0.1325 K0.1337 K0.1322 K0.1353 K0.1360 K0.1371 K0.1354 K0.1594 K0.1595 K0.1351 K0.1668

181.2 175.1 177.3 176.1 173.2 180.5 174.7 172.7 176.4 179.1 177.4 184.2 184.1 182.6 174.3 176.3 174.3 172.5 178.0 177.5 180.2 183.6 174.1 188.3 175.6 181.0 174.3 176.9 178.4 173.8 176.4 177.8 176.9 172.7 176.1 170.9 176.4 173.7 183.6 181.3 175.1 186.2

325.6 365.4 366.6 303.0 260.3 314.1 334.2 311.1 348.7 283.6 360.1 312.8 306.2 329.9 281.4 333.7 270.1 244.6 259.0 237.9 318.4 239.9 295.9 365.3 307.8 257.3 306.0 321.6 376.1 319.8 340.4 324.8 320.3 281.3 351.2 299.4 321.1 313.1 313.5 297.2 341.9 335.2

2.088 2.903 1.580 1.387 2.828 1.025 2.242 2.848 3.190 1.521 1.511 1.342 1.344 0.166 2.564 1.471 2.563 1.935 2.227 1.307 3.589 2.240 3.135 1.475 3.633 2.583 2.688 1.841 0.967 2.174 1.583 0.936 2.163 2.832 2.718 1.554 2.947 1.219 1.110 2.715 4.327 1.059

K0.2607 K0.2588 K0.2577 K0.2552 K0.2597 K0.2563

K0.0487 K0.0488 K0.0453 K0.0629 K0.0513 K0.0465

0.1716 0.1862 0.1735 0.1786 0.1867 0.1857

K0.1284 K0.1360 K0.1322 K0.1566 K0.1360 K0.1320

189.4 189.1 186.5 195.2 189.1 186.5

322.8 2.870 371.7 2.437 366.4 3.176 365.6 2.338 278.9 1.328 370.1 2.109 (continued on next page)

141

K0.2564 K0.2558 K0.2569 K0.2542 K0.2531 K0.2586 K0.2554 K0.2539 K0.2543 K0.2541 K0.2536 K0.2494 K0.2494 K0.2550 K0.2558 K0.2582 K0.2558 K0.2568 K0.2556 K0.2592 K0.2541 K0.2508 K0.2530 K0.2479 K0.2565 K0.2535 K0.2547 K0.2553 K0.2545 K0.2536 K0.2551 K0.2543 K0.2576 K0.2539 K0.2535 K0.2516 K0.2553 K0.2509 K0.2485 K0.2522 K0.2595 K0.2545

W. Zhou et al. / Journal of Molecular Structure: THEOCHEM 755 (2005) 137–145

2,3,3 0 ,4,5 0 2,2 0 ,3,3 0 ,5 2,2 0 ,3,4 0 ,5 2,2 0 ,3,5,5 0 2,2 0 ,3,5,6 0 2,3,3 0 ,5,5 0 2,2 0 ,3,4 0 ,6 2,2 0 ,3,5 0 ,6 2,3,3 0 ,4 0 ,6 2,2 0 ,4,4 0 ,5 2,2 0 ,4,5,5 0 2,3,3 0 ,4 0 ,5 2,3 0 ,4,4 0 ,5 2,3 0 ,4,5,5 0 2,2 0 ,3 0 ,4,6 2,2 0 ,4,4 0 ,6 2,2 0 ,4,5 0 ,6 2,2 0 ,4,6,6 0 2,3 0 ,4,4 0 ,6 2,3 0 ,4,5 0 ,6 2,3,3 0 ,4 0 ,5 0 2 0 ,3,4,4 0 ,5 2,2 0 ,4,5,6 0 3,3 0 ,4,4 0 ,5 2,2 0 ,3,4,5 2,3,3 0 ,4,5 2,2 0 ,3,4,6 2,3,3 0 ,4,6 2,3,4,4 0 ,6 2,2 0 ,3,5,6 2,3,3 0 ,5,6 2,3,4 0 ,5,6 2,3,4,5,6 2,2 0 ,3,3 0 ,6 2,2 0 ,3,4,5 0 2,2 0 ,3,6,6 0 2,2 0 ,3 0 ,4,5 2,3,3 0 ,5 0 ,6 2,3,4,4 0 ,5 2,3 0 ,4 0 ,5,5 0 2,3 0 ,4 0 ,5 0 ,6 3,3 0 ,4,5,5 0 Hexa2,2 0 ,3,3 0 ,4,4 0 2,2 0 ,3,3 0 ,4,5 0 2,2 0 ,3,3 0 ,4,6 0 2,3,3 0 ,4,4 0 ,5 0 2,2 0 ,3,3 0 ,5,5 0 2,2 0 ,3,3 0 ,5,6 0

142

Table 2 (continued) Congener

Exp.

Eq. (2)

Diff.

Eq. (3)

Diff.

6.85

6.74 6.84 7.23 6.26 6.61 6.68 6.46 6.76 6.54 7.23 6.35 6.62 6.74 7.49 6.62 6.77 6.70 6.46 7.12 7.25 6.58 6.69 6.57 6.48 6.83 6.57 6.66 6.57 6.43 6.82 6.65 6.80 6.80 6.58 6.74 6.75

0.11

6.71 6.81 7.20 6.24 6.58 6.65 6.43 6.74 6.51 7.21 6.33 6.58 6.71 7.46 6.59 6.74 6.67 6.44 7.10 7.22 6.55 6.66 6.54 6.45 6.80 6.54 6.64 6.55 6.40 6.79 6.62 6.77 6.78 6.55 6.72 6.72

0.14

6.63 6.73 6.41 6.80 6.65 7.29 6.54 7.55 6.76 6.82 6.75 6.56 7.44 6.78 6.45

6.20 6.42 7.00

6.58 6.78 6.78 7.08 7.21 6.85 7.21 6.92 7.72 6.92 6.55

7.07 7.08 6.88 7.18 6.97 7.62 7.06 7.01 6.84

0.02 0.05 K0.05 0.04 0.11 0.06 K0.08 0.06 0.14 0.05 0.05 0.10 0.32 0.20 K0.12

K0.37 K0.15 0.18

0.00 0.04 0.03 0.01 0.13 K0.03 0.03 K0.05 0.10 K0.09 K0.29

7.04 7.05 6.85 7.15 6.94 7.59 7.03 6.98 6.81

0.05 0.08 K0.02 0.06 0.14 0.08 K0.04 0.09 0.17 0.08 0.08 0.12 0.34 0.23 K0.09

K0.34 K0.13 0.21

0.03 0.06 0.06 0.04 0.16 0.00 0.06 K0.02 0.13 K0.06 K0.26

EHOMO

ELUMO

qHC

qK

a

Vm

m

K0.2598 K0.2573 K0.2585 K0.2544 K0.2607 K0.2586 K0.2563 K0.2579 K0.2574 K0.2546 K0.2560 K0.2671 K0.2637 K0.2535 K0.2599 K0.2604 K0.2568 K0.2573 K0.2541 K0.2600 K0.2580 K0.2603 K0.2541 K0.2581 K0.2615 K0.2570 K0.2583 K0.2540 K0.2546 K0.2607 K0.2568 K0.2573 K0.2562 K0.2630 K0.2581 K0.2580

K0.0518 K0.0570 K0.0647 K0.0437 K0.0481 K0.0505 K0.0467 K0.0527 K0.0476 K0.0658 K0.0446 K0.0455 K0.0494 K0.0717 K0.0491 K0.0520 K0.0526 K0.0470 K0.0633 K0.0646 K0.0496 K0.0506 K0.0509 K0.0477 K0.0535 K0.0502 K0.0512 K0.0515 K0.0483 K0.0539 K0.0523 K0.0551 K0.0550 K0.0462 K0.0525 K0.0530

0.1885 0.1867 0.1874 0.1730 0.1747 0.1879 0.1875 0.1885 0.1878 0.1891 0.1856 0.1858 0.1872 0.1721 0.1788 0.1836 0.1800 0.1788 0.1777 0.1826 0.1899 0.1901 0.1903 0.1892 0.1912 0.1904 0.1907 0.1909 0.1897 0.1917 0.1620 0.1652 0.1630 0.1861 0.1907 0.1913

K0.1369 K0.1367 K0.1554 K0.1327 K0.1318 K0.1370 K0.1376 K0.1417 K0.1377 K0.1606 K0.1372 K0.1375 K0.1364 K0.1660 K0.1340 K0.1377 K0.1346 K0.1355 K0.1542 K0.1565 K0.1351 K0.1384 K0.1353 K0.1361 K0.1347 K0.1279 K0.1380 K0.1350 K0.1358 K0.1271 K0.1368 K0.1321 K0.0999 K0.1368 K0.1347 K0.1307

190.1 188.2 194.3 184.0 188.6 190.3 187.5 191.6 189.2 196.7 185.7 187.4 190.4 201.1 188.2 190.6 189.3 186.1 195.8 194.3 186.8 189.0 187.8 184.8 190.1 186.2 188.3 187.2 184.2 189.5 186.9 189.7 191.3 188.2 190.6 190.0

271.8 421.1 350.0 302.5 345.8 417.6 414.4 267.1 488.3 249.7 314.8 385.7 255.5 302.3 400.1 298.4 324.6 342.4 303.3 330.9 318.1 291.7 331.9 296.2 304.0 353.5 315.3 369.4 313.3 390.0 315.1 353.6 319.3 332.6 327.2 312.6

1.038 1.181 1.811 1.541 3.380 2.172 2.293 0.028 1.200 1.213 1.366 0.000 2.388 0.000 3.357 1.938 2.260 3.802 1.759 0.888 2.802 1.580 1.249 2.691 1.073 2.545 1.391 0.477 2.081 1.141 2.984 1.824 0.073 2.490 1.942 2.081

K0.2628 K0.2620 K0.2601 K0.2617 K0.2615 K0.2592 K0.2641 K0.2595 K0.2582

K0.0538 K0.0544 K0.0511 K0.0570 K0.0520 K0.0688 K0.0534 K0.0545 K0.0517

0.1792 0.1876 0.1798 0.1893 0.1875 0.1802 0.1910 0.1916 0.1905

K0.1343 K0.1329 K0.1321 K0.1369 K0.1369 K0.1552 K0.1351 K0.1350 K0.1357

202.5 202.3 199.6 203.7 201.4 208.5 200.9 200.8 198.1

372.1 384.5 344.8 405.6 480.5 355.3 375.2 322.1 359.1

2.384 1.595 2.923 1.017 1.957 0.925 2.365 1.224 1.986

W. Zhou et al. / Journal of Molecular Structure: THEOCHEM 755 (2005) 137–145

2,2 0 ,3,4 0 ,5,5 0 2,2 0 ,3,4 0 ,5,6 0 2,3,3 0 ,4 0 ,5,5 0 2,2 0 ,3,3 0 ,6,6 0 2,3,3 0 ,4 0 ,5 0 ,6 2,2 0 ,3,4,4 0 ,5 0 2,2 0 ,3,4 0 ,5 0 ,6 2,2 0 ,4,4 0 ,5,5 0 2,2 0 ,4,4 0 ,5,6 0 2,3 0 ,4,4 0 ,5,5 0 2,2 0 ,3,4 0 ,6,6 0 2,2 0 ,4,4 0 ,6,6 0 2,3 0 ,4,4 0 ,5 0 ,6 3,3 0 ,4,4 0 ,5,5 0 2,2 0 ,3,3 0 ,4,5 2,2 0 ,3,4,4 0 ,5 2,2 0 ,3,4,5,5 0 2,2 0 ,3,4,5,6 0 2,3,3 0 ,4,4 0 ,5 2,3,3 0 ,4,5,5 0 2,2 0 ,3,3 0 ,4,6 2,2 0 ,3,4,4 0 ,6 2,2 0 ,3,4,5 0 ,6 2,2 0 ,3,4,6,6 0 2,3,3 0 ,4,5 0 ,6 2,2 0 ,3,3 0 ,5,6 2,2 0 ,3,4 0 ,5,6 2,2 0 ,3,5,5 0 ,6 2,2 0 ,3,5,6,6 0 2,3,3 0 ,5,5 0 ,6 2,2 0 ,3,4,5,6 2,3,3 0 ,4,5,6 2,3,4,4 0 ,5,6 2,2 0 ,3,4,4 0 ,6 0 2,3,3 0 ,4,4 0 ,6 2,3,3 0 ,4 0 ,5,6 Hepta2,2 0 ,3,3 0 ,4,4 0 ,5 2,2 0 ,3,3 0 ,4,5,5 0 2,2 0 ,3,3 0 ,4,5,6 0 2,2 0 ,3,4,4 0 ,5,5 0 2,2 0 ,3,4,4 0 ,5,6 0 2,3,3 0 ,4,4 0 ,5,5 0 2,2 0 ,3,3 0 ,4,4 0 ,6 2,2 0 ,3,3 0 ,4,5 0 ,6 2,2 0 ,3,3 0 ,4,6,6 0

lg Kow

7.04 7.21 6.73 6.85 6.41 6.78 7.21 7.13 6.99 7.08 7.21 7.35 7.49 7.48 7.62 7.62 7.43 7.21 7.30

7.04 6.98 7.24 7.00 7.01 6.84 7.04 6.92 7.18 7.06 7.16 7.04 6.95 7.21 7.30

0.00

7.52 7.31 7.50 7.44 7.68 7.48 7.54 7.39 7.39 7.32 7.27 7.24

K0.17

K0.03 K0.27 K0.16 K0.43 K0.14 0.03 K0.03 K0.05 K0.13 K0.09

K0.01 0.04 K0.06 0.08 0.04 K0.11 0.03

7.01 6.95 7.21 6.97 6.98 6.81 7.01 6.89 7.15 7.03 7.13 7.02 6.92 7.18 7.27

0.03

7.49 7.28 7.47 7.41 7.65 7.45 7.50 7.36 7.35 7.29 7.24 7.21

K0.14

0.00 K0.24 K0.13 K0.40 K0.11 0.06 0.00 K0.03 K0.10 K0.06

0.02 0.07 K0.03 0.12 0.07 K0.08 0.06

K0.2594 K0.2626 K0.2650 K0.2605 K0.2593 K0.2573 K0.2593 K0.2588 K0.2634 K0.2600 K0.2620 K0.2561 K0.2594 K0.2598 K0.2633

K0.0548 K0.0525 K0.0571 K0.0539 K0.0551 K0.0524 K0.0553 K0.0531 K0.0567 K0.0562 K0.0572 K0.0575 K0.0544 K0.0590 K0.0599

0.1915 0.1907 0.1921 0.1915 0.1920 0.1910 0.1920 0.1912 0.1926 0.1671 0.1838 0.1725 0.1671 0.1715 0.1826

K0.1375 K0.1374 K0.1346 K0.1286 K0.1217 K0.1324 K0.1373 K0.1370 K0.1246 K0.1280 K0.1381 K0.1351 K0.1359 K0.1308 K0.1269

202.0 199.9 203.4 200.2 200.1 197.5 201.2 199.2 202.5 199.6 201.8 200.5 197.4 203.6 203.0

337.5 317.4 420.6 340.2 332.6 331.6 374.4 350.5 348.5 409.4 310.3 393.5 339.7 334.6 344.0

1.003 1.038 1.940 2.378 1.070 1.455 1.031 0.163 2.210 2.862 1.450 1.449 3.074 1.445 0.159

K0.2653 K0.2600 K0.2612 K0.2637 K0.2672 K0.2614 K0.2651 K0.2635 K0.2629 K0.2641 K0.2609 K0.2601

K0.0599 K0.0583 K0.0612 K0.0590 K0.0625 K0.0610 K0.0595 K0.0570 K0.0575 K0.0553 K0.0559 K0.0559

0.1732 0.1750 0.1894 0.1876 0.1750 0.1876 0.1806 0.1924 0.1928 0.1916 0.1921 0.1922

K0.1287 K0.1325 K0.1374 K0.1372 K0.1244 K0.1214 K0.1342 K0.1350 K0.1201 K0.1357 K0.1354 K0.1144

213.9 210.8 214.9 212.7 216.3 213.6 216.0 214.2 213.4 212.6 211.8 211.0

324.6 425.0 378.2 354.8 390.8 378.1 385.4 386.9 380.4 375.9 425.0 308.8

2.112 2.233 0.051 1.147 1.230 0.976 1.166 1.624 1.791 1.164 0.938 0.001

7.94 7.88

7.86 7.77 7.71

0.08 0.11

7.82 7.74 7.68

0.12 0.14

K0.2653 K0.2653 K0.2626

K0.0633 K0.0617 K0.0617

0.1811 0.1924 0.1928

K0.1198 K0.1355 K0.1141

227.2 225.4 224.5

441.5 437.2 457.4

1.011 0.970 0.971

8.20

8.09

0.11

8.05

0.15

K0.2667

K0.0638

0.1113

K0.0896

238.4

440.5

0.000

W. Zhou et al. / Journal of Molecular Structure: THEOCHEM 755 (2005) 137–145

2,2 0 ,3,4,4 0 ,5 0 ,6 2,2 0 ,3,4,4 0 ,6,6 0 2,3,3 0 ,4,4 0 ,5 0 ,6 2,2 0 ,3,3 0 ,4,5 0 ,6 0 2,2 0 ,3,3 0 ,5,5 0 ,6 2,2 0 ,3,3 0 ,5,6,6 0 2,2 0 ,3,4 0 ,5,5 0 ,6 2,2 0 ,3,4 0 ,5,6,6 0 2,3,3 0 ,4 0 ,5,5 0 ,6 2,2 0 ,3,3 0 ,4,5,6 2,2 0 ,3,4,4 0 ,5,6 2,2 0 ,3,4,5,5 0 ,6 2,2 0 ,3,4,5,6,6 0 2,3,3 0 ,4,4 0 ,5,6 2,3,3 0 ,4,5,5 0 ,6 Octa2,2 0 ,3,3 0 ,4,4 0 ,5,6 2,2 0 ,3,3 0 ,4,5,6,6 0 2,2 0 ,3,4,4 0 ,5,5 0 ,6 2,2 0 ,3,4,4 0 ,5,6,6 0 2,3,3 0 ,4,4 0 ,5,5 0 ,6 2,3,3 0 ,4,5,5 0 ,6 0 6 2,2 0 ,3,3 0 ,4,4 0 ,5,5 0 2,2 0 ,3,3 0 ,4,4 0 ,5,6 0 2,2 0 ,3,3 0 ,4,5,5 0 ,6 0 2,2 0 ,3,3 0 ,4,4 0 ,6,6 0 2,2 0 ,3,3 0 ,4,5 0 ,6,6 0 2,2 0 ,3,3 0 ,5,5 0 ,6,6 0 Nano2,2 0 ,3,3 0 ,4,4 0 ,5,5 0 ,6 2,2 0 ,3,3 0 ,4,4 0 ,5,6,6 0 2,2 0 ,3,3 0 ,4,5,5 0 ,6,6 0 Deca2,2 0 ,3,3 0 ,4,4 0 ,5,5 0 ,6,6 0

143

144

W. Zhou et al. / Journal of Molecular Structure: THEOCHEM 755 (2005) 137–145

Table 3 Intercorrelation coefficients of independent variables in Eq. (2), VIF, standard regression coefficients (SR) and t-scores for Eq. (2) Variable

r2

VIF

SR

t(ta/2Z1.645)

EHOMO a ELUMO

0.7204 0.2015 0.7519

3.576 1.252 4.031

K0.1951 0.4634 K0.3938

K3.833 6.080 K8.721

EHOMO actually has the most remarkable influence on lg Kow. Of the three variables in Eq. (2), EHOMO has the least t-score value of onlyK3.833, suggesting EHOMO exhibits the least effect on lg Kow. With this model, the predicted values of lg Kow of all PCBs and their corresponding differences in respect of the experimental values, are listed in Table 2, in which the maximum discrepancyK0.73 is found for 2,2 0 ,3,6tetra-CB. Observation of Eq. (2) may lead to the following significant interpretations: (1) The value of lg Kow is in inverse ratio to EHOMO and ELUMO, i.e. large value of EHOMO and ELUMO would result in small value of lg Kow for PCBs. This is because EHOMO represents the proton acceptance ability in forming hydrogen bond, while ELUMO represents the proton donation ability in formation of hydrogen bond. Therefore, the compounds with large value of EHOMO and ELUMO tend to donate or accept protons easily. In this case, hydrogen bond can be easily formed between PCBs and H2O molecules, and PCBs is able to enter water phase, resulting in low lg Kow value. (2) The greater the a is, the larger the lg Kow is, implying that a PCB molecular with large a possesses great dispersion force and can easily enter n-octanol phase. This is because PCB compounds with great a tend to have good lipophilic property.

3.2. Validation of method In order to check the reliability of the lg Kow prediction model developed in the present study, all the 135 PCB congeners with experimental data of lg Kow in Table 2 were divided into two groups: group one containing 60 PCB congeners in the front and 35 ones at the bottom of the table; and group two are the left 40 PCB congeners in the middle. Using the same regression method as for Eq. (2), the validation model fitting the lg Kow values with the structural parameters of the 95 compounds in group one was created as shown in Eq. (3). lg Kow ZK2:885K17:920EHOMO K34:167ELUMO C 0:0167a (3) r 2 Z 0:9659; SD Z 0:16; q2 Z 0:9634 Afterwards Eq. (3) was applied to the PCB compounds in group two as well as all other congeners. With this model,

the predicted lg Kow values of all PCB compounds are also listed in Table 2, in which the maximum error of predicted lg Kow values in group two is 0.72 for 2,2 0 ,3,3 0 ,4,5 0 -hexa-CB. For comparison, the maximum error of predicted lg Kow value by Eq. (2) isK0.73 for 2,2 0 ,3,6-tetra-CB. With analysis and validation made above, it is suggested that the QSPR model of the present study is reliable and can be used for predicting lg Kow values of all PCB congeners. 3.3. Comparison with the result from AM1 method As reported in Ref. [19], the three-variable QSPR model of lg Kow and structural parameters for PCBs by AM1 method is expressed as Eq. (4). lg Kow ZK4:617 C 3:498Vm =100 C 6:3p1 K6:6qK;

(4)

r 2 Z 0:9093; SD Z 0:249 where Vm is the molecular van der Waals volume in cubic angstroms, and the polarizability term p1 is derived as the ratio of the molecular polarizability (a) to Vm, and qK is the absolute value of the most negative atomic partial charge. In contrast, the squared correlation coefficient r2Z0.9484 obtained from B3LYP/6-31G* level, is obviously larger than that from AM1 method (r2Z0.9093), while SDZ0.18 of the former is less than the latter (SDZ0.249). This is because usually there is much approximation in AM1 method. As a semiempirical molecular orbital calculation method, not only atomic integral but also diatomic differential overlap is omitted in solving Roothaan equation for AM1. However, there are no simplification and approximation for ab initio method in solving Roothaan equation, and the result from ab initio calculation thus possesses higher precision due to its theoretical strictness. Thus, a high precision prediction model for lg Kow of PCB congeners using DFT in the present study has been carried out successfully.

4. Conclusion Based on the TLSER model, optimized calculation of 209 PCBs congeners was carried out at B3LYP/6-31G* level in GAUSSIAN98 program. And the obtained structural parameters were consequently taken as theoretical descriptors to correlate the three-variable QSPR model for predicting lg Kow of PCBs, of which r2Z0.9484, SDZ0.18 and q2Z0.9455. With observation of the larger t values and the result of method validation for the correlation equation, it is proposed that the new QSPR model for predicting lg Kow of all PCB congeners in the present study possesses high accuracy, and meanwhile it exhibited optimum stability and better predictive power than that reported. This work demonstrated that DFT method could be an effective means in QSPR study of environmental contaminants even with larger data sets, and a series of similar study in our laboratory is under way.

W. Zhou et al. / Journal of Molecular Structure: THEOCHEM 755 (2005) 137–145

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