10564
J. Phys. Chem. 1996, 100, 10564-10569
Molecular Polarizability as a Tool for Understanding the Binding Properties of Polychlorinated Dibenzo-p-Dioxins: Definition of a Reliable Computational Procedure Elena Fraschini, Laura Bonati, and Demetrio Pitea* Dipartimento di Chimica Fisica ed Elettrochimica, UniVersita` degli Studi di Milano, Via Golgi 19, 20133 Milan, Italy ReceiVed: September 28, 1995; In Final Form: April 5, 1996X
Molecular polarizability can be used to gain an insight into the origins of polychlorinated dibenzo-p-dioxins (PCDDs) specific binding to their receptor protein. In this work, the effects of the basis set on the polarizability values calculated at the HF level of benzene, chlorobenzene, and dibenzo-p-dioxin (DD) are analyzed. The geometry optimized with the 3-21G basis set and polarizability calculated with the 6-31G(sd,sp) basis set give reliable values useful for comparing polarizabilities of PCDDs with reduced computational costs. The study for two tetrachlorodibenzo-p-dioxin isomers highlights interesting differences in the molecular polarizability tensors as well as in the polarizabilities of C-Cl bonds related to the different chlorine positions on the aromatic skeleton.
Introduction Molecular polarizability is the response of electron distribution to an externally-applied static electric field. As polarization and dispersion contributions to the intermolecular interaction energy can be expressed in terms of this molecular property,1 it is very useful to establish methods to obtain reliable polarizability values. Recently-developed methods for calculating analytic energy derivatives have made it possible to obtain accurate values of static and dynamic response properties, such as polarizability.2,3 Because of progress in computer technology, these calculations can also be made for medium- and largesized molecules. Techniques for the evaluation of analytic gradients have been developed and implemented for a number of quantum chemical methods from the self-consistent field (SCF) approximation, with the coupled perturbed Hartree-Fock (CPHF) technique,4 to various correlated methods. The effects of correlation energy have been mainly studied for small molecules.2,3,5 The CPHF method seems to be the one most used for large molecules;2,3,6,7 with a careful choice of the basis set, the calculated values systematically underestimate the mean dipole polarizability by no more than 10-15%, which indicates that a good estimate of its trend within a series of homologous molecules can be obtained.3 These calculations give the components of the polarizability tensor at zero frequency. From these, the electronic contribution to the static average polarizability, R, and polarizability anisotropy, ∆R, can be calculated. The best experimental values for testing the accuracy of calculations are those determined in the gas phase. The opticalfrequency polarizability anisotropy, ∆R, can be obtained from dispersion of the gas phase depolarization ratio of Rayleigh scattered light combined with refractive index data.8-11 The static polarizability anisotropy, ∆R°, can be determined from the temperature dependence of the electrooptical Kerr effect in low-density gases or vapors.12-15 In principle, the analysis of the temperature dependence and the knowledge of ∆R (measured at the same wavelength used in the Kerr apparatus) from other experimental data makes it possible to extract the ∆R° value. The static polarizability anisotropy differs from the optical-frequency value not only because of * Corresponding author. E-mail:
[email protected]. Fax: ++39 2 70 63 81 29. X Abstract published in AdVance ACS Abstracts, May 15, 1996.
S0022-3654(95)02888-7 CCC: $12.00
the frequency dependence of the latter but also because in zerofrequency fields the vibrational contributions to the static polarizability are not negligible. A static ∆R value can be easily extrapolated from optical frequency ∆R, measured at frequencies, ω, that are small relative to the electronic absorption frequencies. In order to compare this value with the optical ∆R value, the vibrational contribution needs to be taken into account. If gas phase measurements are not available, the Kerr constant values determined for the molecule in a nonpolar solvent must be used.16,17 From the above considerations, the comparisons between calculated and experimental data have to be performed carefully. Our goal is to use polarizability as an index of the effectiveness of medium- and short-range interactions in the binding process of polychlorinated dibenzo-p-dioxins (PCDDs). PCDDs belong to a group of halogenated aromatic hydrocarbons which produce a wide variety of species-specific toxic and biological effects, mediated by the specific binding to an intracellular protein.18-20 In our previous works21-23 to rationalize the binding affinities of a number of PCDDs with their receptor, we analyzed their molecular electrostatic potential (MEP) characteristics. These results suggested that two different polarization behaviors of the PCDD electronic distribution influence the PCDD-receptor recognition process. For some PCDDs, named “set A” molecules,23 high affinities are connected with the electron polarization along the prime molecular axis. This polarization causes a concentration of MEP negative values at the lateral sides of the molecule and a depleted electronic charge above and below the aromatic rings. In this set, PCDDs with symmetric chlorination on the lateral sides of the aromatic skeleton and/or with high chlorination are present. For other PCDDs, named “set B”, the electrostatic requirements for high affinity, related to an asymmetric electron polarization, are high MEP values on one side of the prime molecular axis and low MEP values on the opposite one. In this set, there are present PCDDs with an asymmetric chlorination on the lateral sides of the aromatic skeleton or there is a lack of chlorine in these positions. Accordingly, this work aims to do the following: (i) Select a reliable method for calculating accurate polarizability values for the PCDDs at the HF level. Benzene, chlorobenzene, and DD, the PCDD parent compound, are used © 1996 American Chemical Society
Binding Properties of PCDDs
J. Phys. Chem., Vol. 100, No. 25, 1996 10565 From the theoretical (zero-frequency) components of the polarizability tensor along the principal axes, Rxx, Ryy, and Rzz, the following quantities were calculated:
the electronic contribution to the average polarizability, R, R ) (1/3)(Rxx + Ryy + Rzz)
(1)
and to the polarizability anisotropy ∆R ) {1/2[(Rxx - Ryy)2 + (Ryy - Rzz)2 + (Rzz - Rxx)2]}1/2 (2) Figure 1. Molecular schemes of 2,3,7,8-TCDD and 1,4,6,9-TCDD in the system of polarizability tensor principal axes. Numbering of the atoms is also indicated.
as test molecules due to the availability of experimental values.9,10,15,24-26 The performance of different basis sets in the calculation of polarizability values with the CPHF method is tested. Energy- and electrical-property-optimized basis sets are included in our analysis. The effects of molecular geometries obtained with different basis sets are also considered. (ii) Study the effects of different chlorine substitution patterns on polarizability. Among the PCDD homologues, two tetrachlorodibenzo-p-dioxins (TCDDs) that present opposite substitution patterns of the four chlorine atoms are considered: 2,3,7,8-TCDD for set A and 1,4,6,9-TCDD for set B. Their molecular structures are shown in Figure 1. For these TCDDs, the polarizability tensor principal components, the mean polarizability, and the polarizability anisotropy are discussed, along with the contributions of the C-Cl bond polarizability in the ortho 1, 4, 6, and 9, and meta 2, 3, 7, and 8 positions. The possible physical origin of the differences observed and the relationships with the binding properties are discussed. Method The polarizability tensor component calculations were carried out with the CPHF method3 implemented in the Gaussian 9227 program, on the Convex 3820 at the CILEA Computing Center and on the Cray C90 at the CINECA Computing Center. Molecular geometries were optimized at the HF level with 3-21G and 6-31G* basis sets. The HF-6-31G** molecular geometry reported in the work of Hinchliffe et al.28 was used for benzene. Four AO basis sets were tested for the calculation of polarizability: the 6-31+G** and 6-311+G** energy optimized basis sets;29 the 6-31G(sd,sp) basis set, developed by Spackman,30 in which the polarization function exponents are optimized with respect to the calculated polarizability tensor of hydride molecules; and the double ζ polarized basis set for the calculation of low-order electrical properties, developed by Sadlej,31 with exponents of Gaussian functions determined by the basis set polarization method.32 In this basis set the double ζ contraction scheme is [5.4/3.2] for the H atom, [10.6.4/5.3.2] for C and O atoms, and [13.10.4/7.5.2] for the Cl atoms. In the following, this basis set is indicated as [10.6.4/5.3.2]. The valence densities of 2,3,7,8-TCDD, 1,4,6,9-TCDD, and DD were calculated with the 6-31G(sd,sp)//6-31G* basis set in the molecular planes over regular grids of 0.2 Å spaced points. Since superimposition of the DD molecular skeleton of the three molecules showed nearly coincident geometries, density-difference maps between each TCDD and the DD molecule were obtained by subtracting the corresponding density values point by point.
and the Kerr constant. The classical statistical mechanical expression for the zerodensity molar Kerr constant, AK, is,12,13 in SI units,15
AK ) (NA/4050){5γK + (kBT)-1[(10/3)µβ + ∆R∆R°] + (kBT)-2µ2∆R} (3) where NA is the Avogadro number, kB the Boltzmann constant, 0 the permittivity of empty space, T the absolute temperature, and µ the molecular electric dipole moment; γK ) [3γRβ,Rβ(-ω;ω,0,0) - γRR,ββ(-ω;ω,0,0)/10 is the second Kerr hyperpolarizability; ∆R and ∆R° are the anisotropies in the optical frequency and static polarizabilities, respectively. In single-temperature solution-phase Kerr constant determinations, if the second hyperpolarizability can be neglected and ∆R = ∆R°, the molar Kerr constant, mK, can be calculated from: mK
)
NA (ϑ + ϑ2) 18 0 1
(4)
where ϑ1 and ϑ2 are defined as
ϑ1 )
ϑ2 )
1 DP [2(∆R)2] 45kBT EP
(5)
1 [(Rxx - Ryy) (µx2 - µy2) + (Ryy - Rzz) (µy2 45kB2T2 µz2) + (Rzz - Rxx) (µz2 - µx2)] (6)
Here, DP and EP are, respectively, the total and electronic polarization; µi are the components of permanent dipole moment with respect to the three principal axes of the polarizability tensor. Results and Discussion Polarizability tensors for benzene and chlorobenzene were calculated, or taken from literature,28,33 with the four 6-31+G**, 6-311+G**, 6-31G(sd,sp), and [10.6.4/5.3.2] basis sets and reported in Table 1. Comparing all of the computational results, a poor effect of the basis set can be observed. This is probably due to the fact that all of the basis sets considered include an amount of polarization functions sufficient to obtain reliable values of polarizability. In particular, the 6-31G(sd,sp) basis set, with polarization functions optimized for polarizability calculations, is also a small enough basis to use for large molecules. In comparison with the others, this basis set overestimates the polarizability anisotropy of these planar molecules. However,
10566 J. Phys. Chem., Vol. 100, No. 25, 1996
Fraschini et al.
TABLE 1: Calculated and Experimental Values of Polarizability Tensors (SI Units, 1040 C m2 V-1) and Molar Kerr Constants (SI Units, 1027 m5 V-2 mol-1) for Benzene, Chlorobenzene, and Dibenzo-p-Dioxin (Geometries Optimized at the HF-6-31G* Level; See the Method Section for Details) Rxxa
molecule benzene
chlorobenzene
dibenzo-p-dioxin
Ryya
Rzza
experimental
6-31+G** 6-311+G** 6-31G(sd,sp)k [10.6.4/5.3.2]l experimental 6-31+G** 6-311+G** 6-31G(sd,sp) [10.6.4/5.3.2] experimental 6-31+G** 6-311+G** 6-31G(sd,sp) 6-31+G**q
R
∆R
b mK
mc
13.2 13.02 12.54 14.87 13.35 193
144 168 132 210
d
7.28f 7.39g
13.05 13.64
13.05 13.64
11.12 11.11e ( 0.01 11.13 11.56
7.10i 6.733j 6.848j 7.00 7.49m 7.77i 8.43n 7.38 7.52 7.94 8.52 15.71p 12.13 12.29 12.21 12.39
13.79 12.245 12.257 12.89 13.07 15.24 14.73 12.94 12.99 13.58 13.89 26.26 31.02 31.15 31.94 31.03
13.79 12.245 12.257 12.89 13.07 18.20 17.73 16.16 16.29 16.89 17.35 24.73 22.20 22.26 22.64 22.25
11.56 10.41 10.45 10.93 11.21 13.74 13.63 12.16 12.27 12.80 13.25 22.23 21.78 21.90 22.26 21.89
5.75 ( 0.01 5.77 6.23 ( 0.19 5.48 ( 0.23h 6.69 5.51 5.41 5.89 5.58 9.31 8.22 7.69 7.68 7.84 7.71 9.87 16.37 16.34 17.10 16.15
180.4o 179.2 182.7 182.2 46.73p 114.9 114.5 125.3 74.51q
162 192 146 235 306 356 258 306
a The polarizability tensor principal axes originate in the center of the molecules. The yz plane is, in all cases, the molecular plane. For chlorobenzene, the z axis is the carbon-chlorine bond axis; for dibenzo-p-dioxin, the z axis is the O-O axis. b All of the measurements are taken at a temperature of 298 K even for calculating mK. The ratio DP/EP stands for 1.05.35 c Number of AOs in the basis set. d Calculated value.11 e Zero-frequency values, extrapolated from data in ref 10. f Zero-frequency extrapolated values.9 g At λ ) 632.8.9,10 h Static polarizability anisotropy, ∆R°.15 i From molar Kerr constant measurements in dilute solutions of CCl4 at λ ) 546 nm. Estimated experimental error on mK is 5%.24 j Values from ref 28. k AO basis set from ref 30. l AO basis set from ref 31. m Values from ref 33. n Values from ref 25. o From calculated polarizability components and experimental dipole moment, equal to 5.07 × 10-30 C m.24 p Polarizability estimates with the bond additivity method; mK from measurements in solution of CCl4.26 q Calculated with nonplanar geometry (folding angle of 160°). Components of the dipole moment with respect to the principal axes (in SI units, C m): µx ) -2.84 × 10-30; µy ) -2.37 × 10-30; µz ) +0.80 × 10-30.
as it is to be expected that this basis-set effect is systematic for all the PCDDs, then our conclusions should not be affected. The polarizability values for the D2h DD structure obtained with the energy-optimized 6-31+G** and 6-311+G** basis sets and with the 6-31G(sd,sp) basis set (Table 1) are very similar, in agreement with the results obtained for benzene and chlorobenzene. The best experimental values for testing the accuracy of theoretical calculations are those determined in the low-density gas phase. As vapor phase and solution experimental values are available only for benzene,9,10,15,24 we use this as the reference molecule. For a nondipolar molecule with an axis of 3-fold or higher symmetry, eq 3 reduces to
AK ) (NA/4050) [5γK + (kT)-1 ∆R∆R°] (7) Literature data for optical-frequency polarizability anisotropy, ∆R, at λ ) 632.8 nm are collected in Table 1 (here, absolute values are reported), together with the zero-frequency extrapolated values. In the case of benzene, it was shown15 that the temperature-independent contribution arising from γ, the second Kerr hyperpolarizability, is very small, indeed almost negligible, (only 2 ( 2% of the AK value) in comparison with the temperature-dependent contribution at normal temperatures; this result is likely to be typical of aromatic or other highly anisotropic molecules. In consequence, the assumption that the second hyperpolarizabilities can be neglected in solution phase measurements appears to be acceptable for these molecules. ∆R°, calculated15 from the slope of the plot of AK (≡mK0) against T-1, and the ∆R value at λ ) 632.8 nm are reported in Table 1. The average polarizability and the polarizability anisotropy of benzene in CCl4, derived from single-temperature Kerr constant measurements, are also reported in Table 1.24 Zerofrequency R and ∆R extrapolated from the vapor phase values are in good agreement with the 6-31G(sd,sp) and [10.6.4/5.3.2] results. As the vibrational contribution to ∆R0 from the vapor
phase Kerr constant is about 15% and of opposite sign with respect to the electronic contribution,15 calculated ∆R are, as expected, higher than ∆R°. The solution-phase value of polarizability anisotropy at λ ) 546 nm is about 14% higher than the zero-frequency value. Similar differences are observed for chlorobenzene by comparing solution-phase and calculated values (Table 1). For DD, the molar Kerr constant values determined from measurements in carbon tetrachloride (mK ) 47 × 10-27 m5 V-2) and benzene (mK ) 42 × 10-27 m5 V-2) solutions at 25 °C are reported.26 It is quite difficult to make a comparison between calculated and experimental results at least for two reasons. The first involves the dipole moment that was determined to be 1.5 × 10-30 C m in CCl4 and 1.7 × 10-30 C m in benzene,26 i.e., different from the expected null value for the structure with the D2h symmetry used for calculations. Consequently, the experimental molar Kerr constants include the contribution of the small but finite dipole moment. On the basis of this dipole moment a folding angle of 163.8° was estimated.34 For a nonplanar DD structure, the anisotropy term ϑ1 is positive while the dipole term ϑ2 is negative;26 thus, the sum (ϑ1 + ϑ2) and the mK derived are expected to be smaller for the nonplanar structure than for the D2h one. The second reason involves the standard or fixed bond approach35 used to derive polarizability anisotropy. To obtain the molecular polarizability ellipsoid, in ref 26 the individual bond tensors were summed, using a planar molecular geometry with standard bond lengths and angles of 120°; the semiaxes were first computed using literature values of the polarizabilities of the constituent bonds, and the exaltation of polarizability was then included as an additional increment. We showed36 that the reliability of such a procedure in conformational studies has not been firmly established as the correct alignment of the exaltations is uncertain.
Binding Properties of PCDDs
J. Phys. Chem., Vol. 100, No. 25, 1996 10567
TABLE 2: Optimized Geometrical Parameters for 1,4,6,9-TCDD, 2,3,7,8-TCDD, and Dibenzo-p-dioxin (Bond Distances, r, Å; Angles, deg)a 1,4,6,9-TCDD r(Ca-O) r(C1-Ca) r(C2-C1) r(H-C2) r(Cl-C) Cb-O-Ca C1-Ca-O C2-C1-Ca H-C2-C1 Cl-C1-Ca a
2,3,7,8-TCDD
HF-6-31G*
HF-3-21G
1.355 1.382 1.385 1.073 1.730 118.2 119.1 120.0 119.4 119.9
1.381 1.369 1.377 1.069 1.792 119.3 119.9 120.7 119.6 119.2
dibenzo-p-dioxin
HF-6-31G*
HF-3-21G
1.360 1.375 1.386 1.072 1.731 116.8 118.4 120.2 119.2 118.2
1.387 1.371 1.378 1.068 1.797 118.3 118.9 119.4 119.5 117.9
r(Ca-O) r(C1-Ca) r(C2-C1) r(H-C1) r(Cl-C) Cb-O-Ca C1-Ca-O C2-C1-Ca H-C1-Ca Cl-C2-C1
r(Ca-O) r(C1-Ca) r(C2-C1) r(H-C1) r(H-C2) Cb-O-Ca C1-Ca-O C2-C1-Ca H-C1-Ca H-C2-C1
HF-6-31G*
HF-3-21G
1.369 1.375 1.390 1.074 1.075 118.3 119.1 119.7 118.8 119.5
1.390 1.375 1.385 1.070 1.071 118.4 118.9 119.6 118.4 119.7
See Figure 1 for the atom labels.
TABLE 3: Polarizability Tensor (in SI units, 1040 C m2 V-1) for Dibenzo-p-dioxin, 2,3,7,8-TCDD, and 1,4,6,9-TCDD, Calculated with the 6-31G(sd,sp) Basis Set, with Molecular Geometries Optimized with Different Basis Sets molecule
geometry
dibenzo-p-dioxin RHF/3-21G RHF/6-31G* 2,3,7,8-TCDD RHF/3-21G RHF/6-31G* 1,4,6,9-TCDD RHF/3-21G RHF/6-31G*
Rxxa
Ryya
Rzza
R
∆R
12.16 12.21 16.28 16.15 16.27 16.14
31.73 31.94 48.26 47.25 36.43 36.28
22.49 22.64 30.39 30.05 40.02 39.12
22.13 22.26 31.64 31.15 30.91 30.51
16.96 17.10 27.76 26.98 22.17 21.70
a The principal axes of polarizability originate in the center of the molecules; the yz plane is, in all cases, the molecular plane; the z axis is the O-O axis.
For analysis of the effects of a folded geometry on the value of mK, the polarizability tensor for a 160°-folding-angle DD structure was calculated (Table 1). It can be seen that the Rxx, Ryy, and Rzz components are similar to those calculated for the planar structure, while the value of mK moves to the experimental value; i.e., the differences observed in the mK values are related to the use of a planar or a folded geometry for DD. From the above considerations we concluded that the calculated R and ∆R values for DD are of similar quality to those for the test molecule, and, accordingly, the 6-31G(sd,sp) basis set was selected for calculations on TCDDs. It is noteworthy that the SCF-HF calculations for DD and the two TCDDs show convergence problems, due to linear dependence of the basis set. These problems are overcome if angular Gaussian AOs are used for the d-type polarization functions, in place of the Cartesian d-functions. Before the polarizability calculations are continued, the effect of geometry on the polarizability values calculated with the 6-31G(sd,sp) basis set was investigated for DD, 2,3,7,8-TCDD, and 1,4,6,9-TCDD; geometries optimized at the HF level with the two basis sets 3-21G and 6-31G* are reported in Table 2. Only slight differences are observed for each compound in the carbon-oxygen and carbon-chlorine bond distances, and in the ∠C-O-C angle. For DD, the geometry optimized by Schaefer et al.34 with the 4-31G basis set shows no differences with the 3-21G optimized geometry. In all of the cases, optimization gives a planar geometry with a flat potentialenergy-surface region around minimum. This agrees with X-ray findings for the DD37 and the 2,3,7,8-TCDD38 as well as with vibrational spectroscopy results;39 in fact both these analyses indicate planar geometries. As expected, the polarizability tensors calculated with the two basis-set-optimized geometries, shown in Table 3, are not significantly different. Thus, improvement of the basis set for geometry optimization does not change the quality of the results. In the following discussion on the effects of chlorine substitution patterns on the molecular polarizability, we refer
to the values for the TCDD isomers calculated at the HF-631G(sd,sp)//HF-6-31G* level (Table 3). For 2,3,7,8-TCDD, the Ryy tensor component, directed along the prime molecular axis (Figure 1), is the largest and is very different from the Rzz component; the situation is reversed for 1,4,6,9-TCDD with a small difference between the two components. The Rxx component, directed along the axis perpendicular to the molecular plane, is very similar for the two molecules. As a consequence, a significant difference between the polarizability anisotropy values is observed, while the mean polarizability values are almost the same. Therefore, the emerging picture of the PCDD electronic distribution is consistent with what was inferred from the MEP characteristics of these molecules. The 2, 3, 7, 8 substitution pattern causes an enhanced polarization of the electronic distribution along the prime molecular axis related to a depletion of the electronic charge on the center of the aromatic rings and to a presence of positive MEP values in this region. The substitution in the ortho positions to the oxygen atoms (as in the case of the 1, 4, 6, 9 substitution pattern) results in an electronic polarization not much more enhanced along the direction of the carbon-chlorine bonds. This causes a slight depletion of the electronic charge in the aromatic ring center and, as a consequence, a presence of negative MEP values in this region. For an explanation of the differences observed for the two TCDD isomers, the contribution to molecular polarizability of carbon-chlorine bond in the 1, 4, 6 and 9 positions with respect to the 2, 3, 7, and 8 positions was studied. The carbon-chlorine bond polarizabilities (bL, directed along the bond axis; bT, perpendicular to the bond axis in the plane of the molecule; and bv out of the molecular plane) are obtained starting from the polarizability values of DD and TCDDs, calculated at the HF-6-31G(sd,sp)//HF-6-31G* level. The contribution of the four (ortho or meta) carbon-hydrogen bonds to the dibenzo-p-dioxin polarizability tensor is subtracted first; the C-H bond contributions are isotropic (0.72 × 10-40 SI units)35 and are assumed to be independent of their position on the aromatic skeleton. The residual polarizability tensor was then subtracted from each TCDD polarizability tensor, to get the contribution of the four equivalent carbon-chlorine bonds. The average values (b) of the bond-polarizability tensors (Table 4) are almost independent of the substitution position, while the anisotropies (∆b) are quite different; for the meta bonds in the 2, 3, 7, and 8 positions ∆b is greater than for the ortho bonds in the 1, 4, 6 and 9 positions. Moreover, for the meta bonds, the difference between the bL and bT components is larger than that for the ortho bonds; the bT component is the smallest for the meta bond. The bV component is almost the same for both bonds.
10568 J. Phys. Chem., Vol. 100, No. 25, 1996
Fraschini et al.
TABLE 4: Values (SI units, 1040 C m2 V-1) of Carbon-Chlorine Bond Polarizability Tensors for the TCDDs Studieda C-Cl
r(C-Cl)
bL
bT
bV
b
∆b
2, 3, 7, 8 1, 4, 6, 9
1.7313 1.7297
5.82 4.84
1.31 1.81
1.71 1.71
2.95 2.79
4.32 3.08
a
See Results and Discussion for details.
the DD molecular skeleton and in the electron concentration around the chlorine atoms. However, it appears that this behavior is enhanced in 2,3,7,8-TCDD, with maximum density differences on chlorines of 4.65 e Å-3 with respect to 1.32 e Å-3 in the 1,4,6,9-TCDD. In addition, the polarization of the former isomer involves a larger space, including all the carbon and the oxygen atoms, while it involves only the central part of the molecule, in the latter isomer. In both the maps (Figure 2a,b) there are minimum-density-difference zones around the chlorinated carbons and on the atoms belonging to the dioxane ring, but only in the 2,3,7,8-TCDD map (Figure 2a) there are minima also around the other carbon atoms. These polarization characteristics may cause the larger polarizability anisotropy of the 2,3,7,8-TCDD, and the topology of the density-difference map explains the prevalence of the Ryy tensor component, directed along the prime molecular axis, in this molecule (Table 3). Conclusions
Figure 2. Maps of the 6-31G(sd,sp)//6-31G* density differences between the following: (a) 2,3,7,8-TCDD and DD; (b) 1,4,6,9-TCDD and DD. Boxes are 15 by 8 Å in the molecular plane. Contours are at 0.2 e Å-3 intervals starting from a minimum value of -2.0 e Å-3 up to 2.0 e Å-3; solid lines are positive and dashed lines negative.
These results prove real differences in the polarizability of the carbon-chlorine bonds due to their positions on the aromatic rings and, related to this, on different conjugation effects that also affect the polarization of the total electron distribution. The difference in carbon-chlorine bond polarizabilities reflects both the enhanced polarizability of the electronic distribution along the prime molecular axis for 2,3,7,8-TCDD and the slight anisotropy for 1,4,6,9-TCDD. For insight into the possible physical origin of the differences observed in both the molecular and the bond polarizabilities of the two isomers, the electron density distributions were also analyzed. For the not-substituted dibenzo-p-dioxin, electron density values on the carbon atoms at the oxygen ortho positions are larger than densities on the meta carbon atoms (12.7 and 3.04 e Å-3, respectively). This suggests that chlorine substitution in the ortho positions may lead to less polarized carbonchlorine bonds. The maps of density differences between the 2,3,7,8-TCDD and the DD (Figure 2a) and between the 1,4,6,9TCDD and the DD (Figure 2b) confirm this hypothesis. The C-Cl bond polarizations in the 2,3,7,8-TCDD and in the 1,4,6,9TCDD are depicted by differences in density of about 4.70 and 1.65 e Å-3 between the maximum on chlorine and the minimum on the attached carbon atom. This highlights the causes of the different C-Cl bond polarizability values, and in particular of the different bL components, in the two TCDDs. Moreover, as seen in Figure 2a,b, in both cases substitution of four chlorine atoms results in a charge-density depletion in
For formulation of a reliable methodology for calculating accurate polarizability tensor values for the PCDDs, with the CPHF method, the effects of four basis sets and the molecular geometry on test molecules were examined. Calculations carried out with energy- and electrical-propertyoptimized basis sets on benzene, chlorobenzene, and dibenzop-dioxin indicate that all of these basis sets give polarizability tensor values in agreement with the experimental data. In particular, a very good agreement is observed with the smallest 6-31G(sd,sp) basis set in which the polarization functions are optimized for polarizability calculations. The geometries of DD and two TCDD isomers optimized at the HF level with two basis sets, 3-21G and 6-31G*, give only slightly different 6-31G(sd,sp) polarizability values. The choice of geometry optimized with the 3-21G basis set and polarizability calculated with the 6-31G(sd,sp) basis set satisfies both requirements of reduced computational costs and the final aim of our work, that is, the comparison of reliable polarizability values within the PCDD class of molecules. The study of polarizability principal components for two TCDDs confirms the differences between PCDDs with or without prevalent substitution in the 2, 3, 7, 8 positions, as observed in our previous studies on MEP. The analysis of the C-Cl bond contributions to molecular polarizability, as well as of the density differences between each TCDD and DD, indicates that the different polarizabilities are associated with differences in the polarization of the C-Cl bonds, due to different chlorine positions on the aromatic rings. However, as the bond contribution from a single, ortho or meta, carbon-chlorine bond may depend on the whole PCDD substitution pattern, i.e., on conjugation effects due to the presence of other ortho and/or meta chlorine atoms, calculation of the total polarizability on the basis of the skeleton and bond contributions must be further investigated. On the basis of this preliminary analysis of two TCDDs we infer that calculated polarizability is a valuable tool for understanding how different chlorination patterns may affect the tendency of PCDDs to give polarization- and dispersiontype interactions with the active site of their receptor protein. Acknowledgment. The authors thank Prof. P. Fantucci and Dr. M. Barzaghi for their helpful consideration. Computational support provided by the CILEA Computing Center (Centro di Modellistica Computazionale) in Segrate and the CINECA Computing Center in Casalecchio di Reno and financial support
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