Molecular orbital studies on brominated diphenyl ethers. Part I—conformational properties

Chemosphere 59 (2005) 1033–1041 www.elsevier.com/locate/chemosphere

Molecular orbital studies on brominated diphenyl ethers. Part I—conformational properties ˚ ke Bergman c, Erkki Kolehmainen d, Jiwei Hu a, Lars Eriksson b, A d Juha Knuutinen , Reijo Suontamo d, Xionghui Wei a,* a

Department of Applied Chemistry, College of Chemistry and Molecular Engineering, Peking University, 100871 Beijing, PR China b Department of Structural Chemistry, Arrhenius Laboratory, Stockholm University, S-106 91 Stockholm, Sweden c Department of Environmental Chemistry, Wallenberg Laboratory, Stockholm University, S-106 91 Stockholm, Sweden d Department of Chemistry, University of Jyva¨skyla¨, SF-40351 Jyva¨skyla¨, Finland Received 28 April 2003; received in revised form 2 March 2004; accepted 12 November 2004

Abstract Polybrominated diphenyl ethers (PBDEs) are widely used as additive flame retardants and quantities in the environment are on the rise. Because they are structurally related to polychlorinated biphenyls and also to thyroid hormones, there is serious concern that PBDEs may pose a danger to human health. Knowledge of their conformational properties is key to assessing their environmental fate and risk. The conformational properties of PBDEs were investigated by quantum chemical methods including semiempirical self-consistent field molecular orbital (SCF-MO), ab initio SCF-MO and density functional theory (DFT). Conformational analyses of model congeners 2,2 0 ,4,6 0 -tetrabromodiphenyl ether and 2,3,4,4 0 ,5,6-hexabromodiphenyl ether, based on energy maps calculated by semiempirical AM1 method, may indicate that all PBDE congeners except those with the tetra-ortho-bromination are conformationally flexible (or soft) due to low energy barriers for interconversion of stable conformers. The results of the conformational analyses are in conformity with recently published X-ray crystallographic data. For comparison with the results of the semiempirical method, higher level ab initio and DFT models were applied as well. The optimized geometries all lie well inside low energy regions on the maps and thus also ascertain the semiempirical calculations. According to computed geometric parameters and net atomic charges, the model B3LYP/321G* seemed to give better results than B3LYP/6-31G* and HF/6-31G*.
2004 Elsevier Ltd. All rights reserved. Keywords: Brominated diphenyl ethers; Semiempirical studies; Ab initio and DFT studies; Energy maps; Conformational properties

1. Introduction Large quantities of polybrominated diphenyl ethers (PBDEs) are added as flame retardants to many kinds

*

Corresponding author. Tel./fax: +86 10 6275 1529. E-mail address: [email protected] (X. Wei).

of polymers, which become part of computers, TV sets, textiles and cars. As a result of their migration from these polymers, PBDEs have been found to exist in various environmental samples (Pijnenburg et al., 1995; Sellstro¨m et al., 1998; Sergeant et al., 1998; Asplund et al., 1999; She et al., 2001; Sjo¨din et al., 2001; Huwe et al., 2002). In particular, PBDE residues have been found in human blood plasma (Klasson-Wehler et al.,

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2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.chemosphere.2004.11.028

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J. Hu et al. / Chemosphere 59 (2005) 1033–1041

1997; Sjo¨din et al., 1999), motherÕs milk (Meironyte´ et al., 1998), and adipose tissue (Haglund et al., 1997). Compared with the levels of polychlorinated biphenyls (PCBs), those of PBDEs in human motherÕs milk are generally low, but they have been steadily increasing during the last decades (Meironyte´ et al., 1998). Since PBDEs bear structural similarities to PCBs and thyroid hormones and are generally persistent and lipophilic, there is concern that they may pose a risk to human health. While early reports indicate low toxicity for PBDEs (WHO, 1994), some later studies suggest that they are more harmful than previously believed. For example, 2,2 0 ,4,4 0 ,5-pentabromodiphenyl ether has shown to induce learning disabilities in mice (Eriksson et al., 1998). Some PBDE congeners may also interfere with the aryl hydrocarbon (Ah) receptor exhibiting agonist and antagonist activity (Meerts et al., 1998). Information on the toxicological status of PBDE congeners is still very limited, and overall fate and risk assessments of these compounds have yet to be made. In view of generally high cost of experimental methods, application of quantum mechanics, which governs the electronic structures that are responsible for properties such as conformational properties, reactivity and lipophilicity, offers an attractive alternative approach. The physicochemical parameters that are generated by this approach can be used, in combination with limited experimental results, to obtain useful information about PBDEs. For rather large molecules like PBDE congeners, the current level of computer power makes semiempirical self-consistent field molecular orbital (SCF-MO), ab initio Hartree–Fock (HF) SCF-MO and density functional theory (DFT) appropriate choices among quantum mechanical approaches. Semiempirical methods, neglecting most two-electron integrals and replacing the remaining with experimental parameters, are much faster than ab initio and electron-correlation included DFT methods, in which all integrals are computed. The conformations of diphenyl ethers are described by the torsional angles (u1 and u2) between the C–O– C plane and planes of the phenyl rings. The angles are defined as positive when the rotation is clockwise looking down the C4–C1 and C4 0 –C1 0 axes toward the oxygen (Fig. 1). Conformational properties of variously substituted diphenyl ethers have previously been studied

Fig. 1. Molecular structure of diphenyl ether and definition of torsional angles u1 and u2.

using, for example, dipole moment (Anderson and Smyth, 1965), NMR spectroscopy (Montaudo et al., 1971; Edlund and Norstro¨m, 1977; Schaefer et al., 1988; Hu et al., 1994, 2000; Nevalainen, 1995), semiempirical or ab initio calculations (Kollman et al., 1973; Schaefer et al., 1988; Nevalainen and Rissanen, 1994), and X-ray diffraction (Benjamins et al., 1974; Singh and McKinney, 1980; Rissanen et al., 1988; Rissanen and Virkki, 1989; Nevalainen and Rissanen, 1994). To our knowledge, however, all the studies with regard to diphenyl ethers have essentially not covered PBDEs except several recent investigations. Based on computed electronic descriptors, Chen et al. (2003a,b) and Harju et al. (2002) set up quantitative structure–activity relationship (QSAR) and quantitative structure–property relationship (QSPR) models for calculating bioactivities and properties of these compounds. Eloranta et al. (2000) examined two PBDE congeners at the HF and DFT levels in an attempt to predict their isotropic NMR shielding tensors. Theoretically, there are four possible types of conformations of diphenyl ethers: planar (u1 = u2 = 0), butterfly (u1 = u2 = 90), skew (u1 = 0, u2 = 90) and twist (u1, u2 > 0). A variety of experimental and theoretical studies have shown that diphenyl ether has a twist conformation in that u1 and u2 lie in the vicinity of 25– 50 (Schaefer et al., 1988). It has been shown that the PCDE congeners prefer a skew or twist conformation depending on the number of the ortho-substituents (Nevalainen and Rissanen, 1994). The previous studies have also suggested that the interconversion between the minimum energy conformations of diphenyl ethers may occur by a disrotatory mechanism via the skew transition state or by a conrotatory mechanism via the butterfly transition state (Benjamins et al., 1974; Schaefer et al., 1988; Nevalainen and Rissanen, 1994). Conformational properties of PBDEs are of special importance not only because they may be relevant to such mechanisms as molecular recognition in the macromolecular binding of these molecules, but also because they can lay the necessary foundation of further theoretical studies by facilitating identification of the local and global energy minima. A well-known fact is that a successful geometry optimization does not always locate an energy minimum but possibly a saddle point on a potential energy surface (PES) that has as many dimensions as there are degrees of freedom within the molecule; another fact is that there is usually more than one energy minimum on the surface. The ideal way to identify true energy minima is to calculate some specific one- or two-dimensional PESs, which are easily explored visually. Conformational energy maps (virtually PESs) with respect to two central dihedral angles (u1 and u2) were generated in the present investigation, where standard heat of formation (relative energy) from a semiempirical calculation, rather than total energy from

J. Hu et al. / Chemosphere 59 (2005) 1033–1041

an ab initio computation, was employed for each grid point. The objectives of the present study were to study PBDEs at different levels of theory so as to clarify the conformational properties and some other interesting aspects of these compounds such as dipole moments and net atomic charges. The conformational analysis of PCDE molecules by Nevalainen and Rissanen (1994), based on energy maps calculated by semiempirical AM1 SCF-MO method, demonstrated good agreement with the X-ray diffraction data, and this prompted our current AM1 investigation of PBDEs. The congeners presently under study are tri-ortho2,2 0 ,4,6 0 -tetrabromodiphenyl ether (BDE-51 according to Ballschmiter et al., 1993) and di-ortho-2,3,4,4 0 ,5,6hexabromodiphenyl ether (BDE-166) (Fig. 2), which represent a group of congeners of great interest because their internal rotation around the ether linkage could be restricted in some way by the fairly large ortho-bromines. Non-ortho-, mono-ortho-, and 2,2 0 -di-ortho-congeners were not examined since their conformational properties were expected to be similar to those of their chlorinated analogues. Ab initio and DFT computations were also applied to some extent since they represent more sophisticated, mathematically better-defined models. Owing to our limited computing resources, however, the basis sets employed for ab initio and DFT calculations were only up to a split-valence polarized basis set 6-31G* level. The DFT computations adopted the

Fig. 2. The two PBDE congeners investigated.

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well-known B3LYP functional consisting of BeckeÕs three-parameters (1993) for the exchange and the functional of Lee et al. (1988) for the correlation part.

2. Methods The semiempirical SCF-MO calculations using an AM1 Hamiltonian (Dewar et al., 1985) with the Mopac package (public domain version 6.00 by Coolidge and Stewart, 1990) were carried out on a Digital Unix/ DEC-3000/600 AlphaStation at the computing center of the University of Jyva¨skyla¨ and on several personal computers with Intel ·86 architecture processors at the Department of Environmental Chemistry and the Department of Structural Chemistry, Stockholm University, and the Department of Chemistry, University of Jyva¨skyla¨. The geometry optimizations were achieved using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton method, which is incorporated into the Mopac program. The all electrons ab initio (HF) SCF-MO and DFT calculations were implemented with Gaussian94 RevB.3 package (Frisch et al., 1995) on the Digital Unix/DEC-3000/600 AlphaStation. The geometry optimizations were achieved by the gradient techniques included in the Gaussian program. All the semiempirical, ab initio and DFT calculations were performed on the molecules of ground state in vacuum. The heats of formation for drawing the conformational maps were computed with AM1 (Mopac), using a starting geometry similar to an optimized geometry and only replacing the two torsion angles (u1 and u2) by values from
180 to 180 on a 10 grid. The geometry was optimized at each grid point so as to obtain a ‘‘relaxed’’ conformation map. Bond distance constraints to chemically equivalent bonds were applied in the Mopac input files. This use of symmetry constraints enhanced the convergence compared to completely unconstrained runs. A small computer program was written to generate all input files for Mopac and automatically ran Mopac after each input file was created. The advantage of grid point generation by this way, instead of using the built-in grid capabilities of Mopac, is that a much more robust calculation is produced when starting from an optimized conformation, with the exception of the two torsion angles (u1 and u2), at each point of the map. No single point of all 1369 included in the map ended in error. Although using the built-in grid function in Mopac sometimes led to unphysical results, very strange trends in energy were not produced on the present maps. A few points of the map (<10) were obviously erroneous, but these could later be corrected due to the translational symmetry of the heat of formation maps. If each of the rings in the molecules has C2 symmetry, the maps by necessity have translational symmetry

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according to E(u) = E(u + 180) where u represents the torsion closest to the ring with C2 symmetry. BDE-166 clearly has the C2 symmetry of both rings and thus the map of heat of formation has the translational symmetry along both directions while the BDE-51 only has one ring with C2 symmetry and thus only has the translational symmetry along one direction. Our 10 grid maps showed much more smooth features than the 30 maps previously used. The total computing time of all 1369 grid points was in the order of 10 h on a 1000 MHz Pentium-III personal computer. The maps were made with the program Easyplot.

3. Results and discussion In this study, tri-ortho- and 2,6-di-ortho-brominated model congeners, i.e., BDE-51 and BDE-166, were selected for conformational analysis including a topological consideration. The selection of these two congeners as model compounds was primarily made on the basis of the availability of quality synthetic single crystals from which detailed structural information could be extracted by X-ray diffraction and so verifies the present theoretical results. Analysis of the conformational energy maps that were drawn (Figs. 3 and 4) revealed that a planar conformation (u1 = 0, u2 = 0) is energetically forbidden as energy maxima (peaks) are indicated in the area

Fig. 3. Conformational energy map of 2,2 0 ,4,6 0 -tetrabromodiphenyl ether (BDE-51) as function of two torsion angles u1 and u2. Contours are drawn at every 5 kcal/mol (55, 60, 65, 70, 75 and 80 kcal/mol). A and B represent global minima (lowest energy points on the map) and local minima respectively. Highest energy points (energy peaks) on the map are at (0, 0) and (0, ±180).

Fig. 4. Conformational energy map of 2,3,4,4 0 ,5,6-hexabromodiphenyl ether (BDE-166) as function of two torsion angles u1 and u2. Contours are drawn at every 4 kcal/mol (66, 70, 74, 78 and 82 kcal/mol). A represents global minima (lowest energy points on the map). Highest energy points (energy peaks) on the map are at (0, 0) and (0, ±180).

around this conformation. Moreover, there are fairly large low-energy regions (valleys) around the energy minima, with the valleys in the map of BDE-51 clearly steeper than those in the map of BDE-166. For BDE51, the local energy minima are found at u1 = ±47.1, u2 = ±60.6 (±119.4) and the global minima at u1 = ±138.6, u2 = ±59.2 (±120.8) (Fig. 3). The energy of the local minima is only 0.8 kcal higher than that of the global minima, however. The interconversion barrier between the global and local minima is 3.7 kcal/mol if occurring via a skew transition state, while that for interconversion between the global minima is 8.7 kcal/ mol if occurring via a butterfly transition state. For BDE-166, two equivalent low-energy regions are found at u1 = ±92.4, u2 = ±1.7 (±178.3) (Fig. 4). Interconversion via a butterfly transition state (barrier 4.0 kcal/ mol) is somewhat favored over that via a skew conformation (barrier 4.6 kcal/mol). The results for BDE-166 are comparable with those of a previous study (Nevalainen and Rissanen, 1994), according to which, through analysis of the AM1-calculated conformational maps, the interconversion barrier via a butterfly transition state is 2.4 kcal/mol for a 2,6-dichlorinated diphenyl ether and 3.2 kcal/mol for a 2,6-diiodated ether. The latter is a conformationally important moiety of thyroid hormones, e.g., T4 and T3 (see Part II (Hu et al., in press) for their structures and more discussions). The low barriers imply that both tri-ortho BDE-51 and di-ortho BDE-166 are free to thermally interconvert at room temperature through synchronized motions of

J. Hu et al. / Chemosphere 59 (2005) 1033–1041

two phenyl groups. Although no experimental results are available in direct support of this conclusion, intuitively it seems plausible. If thyroid hormones such as T4 and T3 were conformationally rigid (or hard) in some degree, their molecular volumes would be fairly large considering a perpendicular conformation plus bulky iodo-substituents. These hormone molecules would then be unlikely to polarize themselves to avoid the various resistances encountered during the binding to macromolecular targets such as transporting protein transthyretin (TTR) and eventually to the nuclear receptors (TR) of target cells (e.g., cells for regulating cellular growth and apoptosis). A flexible (or soft) molecule with free internal motion, such as obtained in the present AM1 calculations, seems therefore to be a reasonable model for these hormones. A series of crystal structures of BDEs including BDE-51 and 166 were recently determined by Eriksson and Hu (2001, 2002a,b) via single crystal X-ray diffraction study, while the structures of some imperfect BDE crystals are being determined either by averaging structural data collected from several small crystals or by applying synchrotron radiation (at the Swedish synchrotron source Maxlab). Selected X-ray geometric parameters for BDE-51 and 166 are listed in Table 1. The crystal conformations of BDE-51 and 166 are found to lie at u1 = 26.3, u2 =
104.6 for BDE-51 (Eriksson et al., 2002), which is close to a twist conformation, and u1 = 104.2, u2 =
15.7 for BDE-166 (Eriksson and Hu, 2002a), which is near a skew conformation. Both these molecular structures are located well inside the low-energy regions near the energy minima and this indicates a good agreement between the theoretical and experimental results. The discrepancy can be attributed in part to the intermolecular forces in the crystals, since

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the packing of the compounds indicates that there are salient intermolecular interactions within both crystals. Analysis of these two model compounds in fact may indicate that all PBDE congeners are conformationally flexible except those with the tetra-ortho-bromination, which, in view of the results for tetra-ortho-CDE (Nevalainen and Rissanen, 1994), should have some degree of conformational rigidity due to the steric hindrance of the four ortho-bromines. These results are in conformity with the hardnesses of BDEs shown by the energy gaps between frontier orbitals (Hu et al., in press). Evidently, bromination at other positions than the orthos does not significantly affect the conformational properties including rotational barriers for these compounds. So-called buttressing effect caused by vicinal meta-bromines should be too small to give any significant effect. From the above results, we infer that, in order to bind to macromolecules, the torsional motion (or polarization) of the PBDE molecules to required conformers does not consume a large amount of free energy. This is in contradistinction to PCBs, where the non-orthosubstituted congeners can adopt a planar conformation, and the addition of an ortho-substituent significantly increases the steric hindrance (McKinney et al., 1983). The conformationally flexible nature of PBDE molecules could explain why several congeners including the diand tri-ortho-congeners can work as Ah receptor agonists and antagonists (Meerts et al., 1998). For comparison with the AM1 results, we also carried out higher-level ab initio and DFT computations. Both molecules were optimized with HF/STO-3G, HF/ 3-21G*, HF/6-31G*, B3LYP/3-21G* and B3LYP/631G* models to obtain their equilibrium geometries. The geometry optimization of BDE-166 at B3LYP/631G* level several times failed to converge, probably

Table 1 Some computed and observed geometric parameters of BDE-51 and BDE-166 ˚) Congener Model chemistry Bond length (A Bond angle ()

Torsion angle ()

C1–O7

O7–C8

C1–O7–C8

C8–O7–C1–C6

C9–C8–O7–C1

BDE-51

AM1 HF/STO-3G HF/3-21G* HF/6-31G* B3LYP/3-21G* B3LYP/6-31G* X-ray

1.391 1.405 1.385 1.362 1.404 1.380 1.395

1.395 1.407 1.380 1.356 1.398 1.373 1.397

118.9 115.7 123.0 120.8 120.5 119.3 115.7

138.6
0.4 0.1
34.7
0.2 36.5 26.3


59.2 93.0 91.2 102.2 91.7 81.1
104.6

BDE-166

AM1 HF/STO-3G HF/3-21G* HF/6-31G* B3LYP/3-21G* B3LYP/6-31G* X-ray

1.392 1.405 1.373 1.348 1.393 – 1.391

1.395 1.409 1.398 1.371 1.415 – 1.414

116.5 115.6 122.9 121.5 119.9 – 116.7

92.4 92.7 91.3 92.0 91.2

1.7 0.3 0.1
0.2 0.2

– 104.2

–
15.7

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because the scratch space needed for this computation surpassed the disc limit of the AlphaStation. To save computing time, we did not run frequency calculations to determine the nature of the stationary points, but all of them lie in low energy regions on the maps and appear to be true minima judging from the X-ray geometries. Even if some of them are not true minima but first order saddle points, the calculated properties should not differ much except dipole moment, which are generally sensitive to torsional change (Hu et al., in press). From another point of view, these results show that X-ray, DFT, ab initio and semiempirical methods demonstrate a good conformity and indicate reliability of these conformational analyses. Selected geometric parameters of the optimized geometries, computed net atomic charges from Mulliken population and bonding analysis and dipole moments of BDE-51 and 166 are presented in Tables 1 and 2. Table 2 also presents the correlation coefficients between the atomic charges from each of the models and the experi-

mentally determined 13C NMR chemical shifts (Hu et al., 2000), where R21 , R22 and R2 are for BDE-51, BDE166 and the combined parameters of the two congeners, respectively. The correlations between the combined net atomic charges obtained from B3LYP/3-21G*, HF/321G* and AM1 calculations and the combined shifts of the two congeners are plotted in Fig. 5. The geometric parameters clearly revealed the effects of the models, and, overall, B3LYP/3-21G*, STO-3G and AM1 yielded the better results than HF/3-21G* and HF/6-31G*. Surprisingly, B3LYP/6-31G* model did not yield satisfactory geometric results for BDE51. According to the calculated dipole moments, BDE51 is a more polar molecule than BDE-166 because it is structurally less symmetrical. The difference in the dipoles of the two congeners, together with varying number of bromine substituents, should relate to their different bioaccumulative potentials. It is noted that dipole moments of PBDEs are subject to conformational changes and further discussions on this based on

Table 2 Computed net atomic charges and dipole moments (l, debye), observed between the charges and shifts (R21 , R22 , R2) for BDE-51 and BDE-166

13

C NMR chemical shifts (ppm) and correlation coefficients

AM1

HF/STO-3G

HF/3-21G*

HF/6-31G*

B3LYP/3-21G*

B3LYP/6-31G*

13

C chemical shift

BDE-51

C1 C2 C3 C4 C5 C6 O7 C8 C9 C10 C11 C12 C13 R21 l

0.103
0.203
0.062
0.185
0.076
0.131
0.147 0.106
0.192
0.080
0.139
0.083
0.167 0.912 1.909

0.133
0.059
0.053
0.054
0.051
0.084
0.229 0.121
0.058
0.058
0.054
0.058
0.058 0.656 3.655

0.463
0.450
0.115
0.416
0.171
0.263
0.758 0.483
0.439
0.182
0.238
0.182
0.439 0.868 4.227

0.435
0.050
0.170
0.014
0.179
0.237
0.699 0.409
0.054
0.186
0.196
0.187
0.034 0.378 4.216

0.344
0.376
0.110
0.341
0.152
0.189
0.573 0.358
0.363
0.157
0.175
0.156
0.363 0.855 3.549

0.344 0.047
0.185 0.090
0.159
0.155
0.551 0.287 0.071
0.167
0.118
0.165 0.045 0.131 3.617

152.18 112.59 136.12 115.08 131.12 115.37 – 148.84 118.40 133.17 128.06 133.17 118.40

BDE-166

C1 C2 C3 C4 C5 C6 O7 C8 C9 C10 C11 C12 C13 R22 l

0.099
0.151
0.124
0.139
0.124
0.152
0.144 0.082
0.184
0.068
0.193
0.076
0.141 0.937 0.531

0.129
0.061
0.049
0.050
0.049
0.061
0.230 0.130
0.069
0.051 0.056
0.049
0.088 0.543 0.274

0.522
0.391
0.329
0.319
0.329
0.391
0.763 0.378
0.254
0.169
0.413
0.169
0.265 0.799 0.436

0.431
0.040
0.005
0.005
0.005
0.040
0.704 0.427
0.236
0.178
0.021
0.176
0.253 0.684 0.570

0.392
0.333
0.306
0.281
0.306
0.333
0.578 0.283
0.188
0.148
0.342
0.147
0.196 0.748 0.582

– – – – – – – – – – – – –

149.59 122.03 129.06 126.59 129.06 122.03 – 154.68 116.84 132.80 115.60 132.80 116.84

0.921

0.595

0.833

0.513

0.799

2

R

–

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Fig. 5. Correlations between combined net atomic charges from B3LYP/3-21G*, HF/3-21G* and AM1 calculations and combined 13C NMR chemical shifts for BDE-51 and BDE-166.

broader data are presented in Part II of this work (Hu et al., in press). According to the correlations with the 13 C NMR chemical shifts (R2 = 0.921, 0.833, 0.799, respectively), B3LYP/3-21G* HF/3-21G* and AM1 yielded satisfactory atomic charges. Again, B3LYP/631G* gave really poor charge results for BDE-51 (R2 = 0.131). Overall, however, all ab initio and DFT models except HF/STO-3G seem to have yielded too pronounced charges on such atoms as C1, O7 and C8, and that seems unreasonable for these neutral, stable molecules that were readily synthesized in our laboratory. These results are compatible with a well-known fact that Mulliken charges are generally dependant on basis set and a new method was therefore proposed to solve this problem (Liu and Li, 1997). The calculated charges are useful for calculating electrostatic potentials, which, together with steric and hydrophobic factors, are key to the binding affinity of ligands. To our knowledge, B3LYP/6-31G* and B3LYP/321G* represent the highest levels of theory so far applied to this class of polyhalogenated compounds and therefore of theoretical significance. Clearly, the model B3LYP/3-21G* delivered good accuracy in the present study. These computed results, together with the previous X-ray studies, show direct ascertainment to AM1 calculated conformational properties of BDEs. Moreover, the present study, consistent with previous investigations by Chen et al. (2003a,b) and Harju et al. (2002), show that the semiempirical method also provided satisfactory accuracy for the BDEs, probably because its high quality parameterization partly offset errors due

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to such factors as basis set effects, electron repulsion and relativistic effects (spin–orbit coupling and scalar relativistic effect, for example). Since PBDE congeners contain rather heavy bromine element that can cause considerable relativistic effect because of fast electron motion, non-relativistic quantum mechanics (i.e., the Schro¨dinger equation), which is generally applicable to light elements and was used in the present study, is inadequate for calculating some of properties for the molecules. This conclusion is consistent with a previous study in which obvious relativistic effects were also encountered in computation of NMR shielding tensors of PBDE congeners (Eloranta et al., 2000). Relativistic quantum mechanics (i.e., the Dirac equation) could be expected to provide more accurate results for these molecules. For the future, therefore, the application of relativistic quantum mechanics might be a better approach for calculations of heavy-atom-containing molecules (Liu et al., 1997, 2003). Such an approach should become feasible as computer technology and methodology advance. On the whole, facing a paucity of experimental data, semiempirical methods such as AM1 and PM3, with advantage of their speeds, are still well suited for facilitating solutions to problems with environmental research, for instance, conformational and QSAR studies of relatively large systems. Because the number of calculations is generally large in these cases, higher level ab initio and DFT methods continue to face obvious challenges. For example, B3LYP/3-21G* and particularly B3LYP/6-31G* are commonly used moderate models for large molecules, and even those computations are heavy. The CPU times needed on the AlphaStation were 6 days 18 h for the full optimization of BDE-166 at the B3LYP/3-21G* level and 15 days 9 h for that of BDE51 at the B3LYP/6-31G* level. That means that, even with much faster computers than the Alpha, it is still too costly to employ such moderate DFT methods for a large number of computations. In conclusion, the present study has set up satisfactory models for clarifying some conformational properties of PBDEs through application of quantum mechanical methods. The same approach can be applied to identify energy minima of other PBDE congeners than the two investigated here (Hu et al., in press). The results are of fundamental significance for assessments of PBDE contaminants. As well, the conformational properties obtained are potentially useful for mapping of receptors possibly involved in the interaction of PBDEs and their analogues with macromolecular targets, and those mapped receptors can then be applied in docking procedures for screening other potential toxic ligands. Finally, this investigation is expected to contribute to the long-standing endeavor of chemists to thoroughly understand internal motion of diphenyl ethers of different kinds, the unique lipophilic structures

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of which may be of significant application prospect in the design of novel pharmaceutical and agrochemical products.

Acknowledgment The authors wish to thank Profs. Wang Xiangyun and Liu Wenjian and Dr. Hu Shaowen, College of Chemistry and Molecular Engineering, Peking University, for many insightful discussions.

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