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Acta Cryst. (2007). E63, m3058    [ doi:10.1107/S1600536807058138 ]

[5,10,15,20-Tetrakis(2,6-dimethoxyphenyl)porphyrinato]zinc(II) dichloromethane tetrasolvate

D. Conrad, J. DeCoskey, S. Mock, B. C. Noll, J. Petrovic and E. P. Zovinka

Abstract top

The crystal structure, electronic spectroscopy and 1H NMR data for the title compound, [Zn(C52H44N4O8)]·4CH2Cl2, are reported. The asymmetric unit consists of 0.5 zinc-porphyrin and two molecules of dichloromethane. The zinc ion is at a crystallographic inversion center and is four-coordinate with a planar porphyrin ligand.

Comment top

ortho-Functionalized porphyrins have generated interest for a variety of reasons. While ortho functionalization can prevent aggregation and unwanted reactions (Wagner et al., 1994), Suslick used the title compound as a starting material for the construction of porous molecular solids (Suslick, 2005). As part of our continued investigations into the active site of hydroxylamine oxidoreductase (HAO) in Nitrosomonas europea, we report the solid state structure of tetra(2',6'-dimethoxyphenyl) porphyrin complexed with zinc. The compound is of interest as a non redox active control model of the active site of HAO. The characterized metalloporphyrin is stable to both air and moisture in both the solid and solution environments.

The compound is prepared by the reaction of zinc acetate with the ligand in refluxing glacial acetic acid. After purification by column chromatography, zinc tetra (2',6'-dimethoxyphenyl) porphyrin was dissolved in dichloromethane and layered with hexanes. This yielded crystals suitable for X-ray diffraction. The crystallographically determined structure is shown in Figure 1. The asymmetric unit consists of 0.5 zinc porphyrin and 2 molecules of dichloromethane. The zinc ion is at a crystallographic inversion center and is four coordinate with a planar porphyrin ligand. The nitrogen core is flat with Zn—N bond lengths of 2.0324 (13) Å and 2.0368 (13) Å which is slightly shorter than the median Zn—N bond distance of 2.046 Å for zinc porphyrins found in a search of the CSD (Allen, 2002). A closely related molecule, zinc tetra (2',6'-dihydroxyphenyl)porphyrin Zn[T(2',6'-DHP)P](EtOAc)2 has a slightly longer average Zn—N bond distance of 2.043 Å in comparison to the title compound (Bhryappa, 1997). The ether C—O bonds are asymmetric, shorter to the aryl group, and longer to the methyl group. The Ar—O average bond distance is 1.366 (2) Å, comparable to the 1.366 (17) Å distance found from MOGUL (Bruno et al., 2004). The average Me—O length is 1.428 (2) Å, which is consistent with 1.42 (4) Å found from MOGUL. Further studies are underway to examine the structural and solution properties of chloro iron (III) tetra (2',6'- dimethoxyphenyl) porphyrin and other metallo derivatives of tetra (2', 6'- dihydroxoxyphenyl) porphyrins.

Related literature top

For details of the synthesis, see: Tsuchida, et al. (1990). For related ortho-substituted porphyrins, see: Bhryappa et al. (1997) For related literature, see: Allen (2002); Bruno et al. (2004); Rothemund & Menotti (1948); Suslick et al. (2005); Wagner et al. (1994).

Experimental top

The ligand, 5,10,15,20 Tetra (2',6'-dimethoxyphenyl) porphyrin [(H2T-2',6'- DMP)P] was synthesized following literature methods (Tsuchida et al., 1990). Standard porphyrin metal insertion methods were used to obtain the title compound (Rothemund & Menotti, 1948). H2T(2',6'-DMP)P (70 mg, 8.2×10 −5 mol) was dissolved in glacial acetic acid (10 ml). Zinc acetate (180 mg, 8.2×10- 4 mol) was added after all of the ligand dissolved and then the solution was refluxed at 100–130 °C for one h. The solvent was removed by vacuum filtration and the crystals were rinsed three times with water. The resulting purple crystals were dissolved in dichloromethane and the solution was chromatographed on a dry alumina column using dichloromethane as the eluent. (67% Yield); Rf (Alumina, DCM) 0.36; I.R·(KBr): 2933, 1431, 1335, 1249 [νas (C—O—C)], 1110, and 998 [ν (C—H)] cm-1; λmax(DCM): 419, 546, and 579 nm; ε: 4.1×105, 7.1×103, and 6.6×102 cm−1M-1. 1HNMR(CDCl3): 3.5(–OMe), 7.0–7.5(aromatic), and 8.8(pyrrole) p.p.m.;

Refinement top

Hydrogen atoms were placed at calculated geometries and allowed to ride on the position of the parent atom. Parameters for thermal motion were set to 1.2× the equivalent isotropic U of the parent atom, 1.5× for methyl H atoms.

Computing details top

Data collection: APEX2 (Bruker, 2006); cell refinement: APEX2 and SAINT (Bruker, 2006); data reduction: SAINT and XPREP (Sheldrick, 2003); program(s) used to solve structure: XS (Sheldrick, 2001); program(s) used to refine structure: XL (Sheldrick, 2001); molecular graphics: XP (Sheldrick, 1998); software used to prepare material for publication: enCIFer (Allen et al., 2004).

Figures top
[Figure 1] Fig. 1. Thermal ellipsoid plot showing the title compound and the dichloromethane of solvation. Zn1 is at a crystallographic center of symmetry. Symmetry equivalent atoms are shown with open ellipsoids. Ellipsoids are drawn at 50% probability.
[5,10,15,20-Tetrakis(2,6-dimethoxyphenyl)porphyrinato]zinc(II) dichloromethane tetrasolvate top
Crystal data top
[Zn(C52H44N4O8)]·4CH2Cl2F000 = 1292
Mr = 1257.99Dx = 1.545 Mg m−3
Monoclinic, P21/nMo Kα radiation
λ = 0.71073 Å
Hall symbol: -P 2ynCell parameters from 7854 reflections
a = 13.5090 (5) Åθ = 2.7–30.1º
b = 15.0743 (6) ŵ = 0.91 mm−1
c = 14.1788 (4) ÅT = 100 (2) K
β = 110.547 (1)ºNeedle, translucent dark red
V = 2703.67 (17) Å30.38 × 0.15 × 0.15 mm
Z = 2
Data collection top
Bruker X8-APEXII CCD
diffractometer		6691 independent reflections
Monochromator: graphite5979 reflections with I > 2σ(I)
Detector resolution: 8.33 pixels mm-1Rint = 0.029
T = 100(2) Kθmax = 28.3º
φ and ω scansθmin = 1.8º
Absorption correction: multi-scan
(SADABS; Sheldrick,2006)		h = −17→18
Tmin = 0.726, Tmax = 0.874k = −20→19
63198 measured reflectionsl = −18→18
Refinement top
Refinement on F2Secondary atom site location: difference Fourier map
Least-squares matrix: fullHydrogen site location: inferred from neighbouring sites
R[F2 > 2σ(F2)] = 0.032H-atom parameters constrained
wR(F2) = 0.087  w = 1/[σ2(Fo2) + (0.0375P)2 + 3.1885P]
where P = (Fo2 + 2Fc2)/3
S = 1.05(Δ/σ)max = 0.001
6691 reflectionsΔρmax = 0.51 e Å−3
353 parametersΔρmin = −0.63 e Å−3
Primary atom site location: structure-invariant direct methodsExtinction correction: none
Crystal data top
[Zn(C52H44N4O8)]·4CH2Cl2V = 2703.67 (17) Å3
Mr = 1257.99Z = 2
Monoclinic, P21/nMo Kα
a = 13.5090 (5) ŵ = 0.91 mm−1
b = 15.0743 (6) ÅT = 100 (2) K
c = 14.1788 (4) Å0.38 × 0.15 × 0.15 mm
β = 110.547 (1)º
Data collection top
Bruker X8-APEXII CCD
diffractometer		6691 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick,2006)		5979 reflections with I > 2σ(I)
Tmin = 0.726, Tmax = 0.874Rint = 0.029
63198 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.032353 parameters
wR(F2) = 0.087H-atom parameters constrained
S = 1.05Δρmax = 0.51 e Å−3
6691 reflectionsΔρmin = −0.63 e Å−3
Special details top

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. The asymmetric unit contains 1/2 Zn porphyrin and 2 molecules of dichloromethane. Zn is at a crystallographic inversion center.

Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > 2σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R– factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Zn10.00000.00000.50000.00956 (7)
N10.06157 (10)0.05965 (9)0.63681 (10)0.0104 (3)
N20.12358 (10)0.04630 (9)0.46349 (10)0.0102 (3)
O10.22057 (10)0.31144 (8)0.63177 (10)0.0190 (3)
O20.41183 (10)0.04560 (9)0.71699 (10)0.0192 (3)
O30.08075 (10)0.09141 (8)0.14607 (9)0.0179 (3)
O40.16191 (10)−0.18907 (8)0.29078 (10)0.0189 (3)
C10.01573 (12)0.06372 (11)0.70917 (11)0.0107 (3)
C20.08169 (13)0.11473 (11)0.79364 (12)0.0134 (3)
H20.06810.12710.85370.016*
C30.16680 (13)0.14180 (11)0.77160 (12)0.0133 (3)
H30.22440.17620.81340.016*
C40.15313 (12)0.10831 (11)0.67259 (12)0.0108 (3)
C50.22122 (12)0.12685 (11)0.62006 (12)0.0108 (3)
C60.20585 (12)0.09792 (10)0.52196 (12)0.0105 (3)
C70.27827 (13)0.11453 (11)0.46963 (12)0.0121 (3)
H70.34040.14990.49280.015*
C80.24066 (12)0.06996 (11)0.38082 (12)0.0120 (3)
H80.27230.06740.33070.014*
C90.14385 (12)0.02726 (11)0.37699 (11)0.0102 (3)
C100.08105 (12)−0.02571 (11)0.29750 (11)0.0106 (3)
C110.31887 (13)0.17954 (11)0.67393 (12)0.0123 (3)
C120.31687 (13)0.27228 (12)0.67927 (12)0.0147 (3)
C130.40815 (15)0.32015 (13)0.72980 (14)0.0199 (4)
H130.40630.38310.73200.024*
C140.50133 (14)0.27500 (13)0.77673 (14)0.0213 (4)
H140.56380.30760.81120.026*
C150.50609 (14)0.18380 (13)0.77490 (13)0.0192 (4)
H150.57070.15370.80850.023*
C160.41458 (13)0.13623 (12)0.72301 (12)0.0146 (3)
C170.21042 (17)0.40184 (13)0.65734 (16)0.0265 (4)
H17A0.23080.40730.73060.040*
H17B0.13690.42100.62490.040*
H17C0.25660.43920.63400.040*
C180.50458 (16)0.00004 (14)0.77865 (16)0.0254 (4)
H18A0.56370.01500.75670.038*
H18B0.4921−0.06410.77250.038*
H18C0.52160.01800.84900.038*
C190.12417 (12)−0.04911 (11)0.21652 (12)0.0121 (3)
C200.12455 (13)0.01095 (12)0.14153 (12)0.0147 (3)
C210.16797 (14)−0.01253 (13)0.06877 (13)0.0198 (4)
H210.16960.02890.01890.024*
C220.20830 (14)−0.09676 (14)0.07062 (13)0.0214 (4)
H220.2378−0.11280.02120.026*
C230.20713 (14)−0.15862 (13)0.14214 (13)0.0190 (4)
H230.2340−0.21670.14130.023*
C240.16557 (13)−0.13396 (12)0.21564 (12)0.0148 (3)
C250.05780 (16)0.14806 (13)0.06016 (13)0.0216 (4)
H25A0.12390.16530.05130.032*
H25B0.02110.20130.07030.032*
H25C0.01270.11640.00000.032*
C260.19103 (17)−0.27915 (13)0.28487 (17)0.0273 (4)
H26A0.1446−0.30510.22140.041*
H26B0.1841−0.31250.34150.041*
H26C0.2645−0.28180.28760.041*
C1S0.96642 (18)0.25153 (15)0.52497 (18)0.0351 (5)
H1S11.02970.24400.50590.042*
H1S20.98710.23940.59800.042*
Cl10.91977 (5)0.36179 (4)0.49994 (4)0.04067 (15)
Cl20.86858 (4)0.17594 (4)0.45730 (4)0.02907 (12)
C2S0.63161 (17)0.09694 (14)0.48441 (16)0.0266 (4)
H2S10.61320.03930.44910.032*
H2S20.70950.09960.51710.032*
Cl30.58869 (5)0.18428 (3)0.39562 (4)0.03135 (12)
Cl40.57272 (4)0.10412 (4)0.57715 (4)0.03187 (12)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Zn10.00849 (12)0.01227 (13)0.00826 (12)−0.00277 (9)0.00337 (9)−0.00213 (9)
N10.0093 (6)0.0126 (6)0.0098 (6)−0.0015 (5)0.0038 (5)−0.0012 (5)
N20.0099 (6)0.0113 (6)0.0093 (6)−0.0010 (5)0.0035 (5)−0.0013 (5)
O10.0168 (6)0.0137 (6)0.0265 (7)−0.0005 (5)0.0075 (5)−0.0029 (5)
O20.0135 (6)0.0170 (6)0.0231 (6)0.0001 (5)0.0017 (5)0.0011 (5)
O30.0250 (7)0.0171 (6)0.0132 (5)0.0007 (5)0.0089 (5)0.0030 (5)
O40.0234 (7)0.0150 (6)0.0203 (6)0.0047 (5)0.0101 (5)0.0014 (5)
C10.0116 (7)0.0115 (7)0.0090 (7)−0.0005 (6)0.0035 (6)−0.0009 (6)
C20.0130 (8)0.0164 (8)0.0105 (7)−0.0023 (6)0.0037 (6)−0.0027 (6)
C30.0130 (7)0.0154 (8)0.0104 (7)−0.0033 (6)0.0028 (6)−0.0033 (6)
C40.0093 (7)0.0118 (7)0.0106 (7)−0.0002 (6)0.0025 (6)−0.0011 (6)
C50.0090 (7)0.0109 (7)0.0118 (7)−0.0007 (6)0.0026 (6)−0.0008 (6)
C60.0095 (7)0.0101 (7)0.0117 (7)−0.0007 (6)0.0036 (6)0.0003 (6)
C70.0104 (7)0.0134 (8)0.0129 (7)−0.0021 (6)0.0047 (6)0.0001 (6)
C80.0115 (7)0.0126 (7)0.0128 (7)−0.0004 (6)0.0055 (6)0.0012 (6)
C90.0094 (7)0.0112 (7)0.0103 (7)0.0010 (6)0.0038 (5)0.0011 (6)
C100.0111 (7)0.0122 (7)0.0090 (7)0.0008 (6)0.0042 (6)0.0012 (6)
C110.0114 (7)0.0163 (8)0.0100 (7)−0.0041 (6)0.0047 (6)−0.0025 (6)
C120.0145 (8)0.0169 (8)0.0147 (7)−0.0033 (6)0.0075 (6)−0.0026 (6)
C130.0209 (9)0.0179 (9)0.0234 (9)−0.0088 (7)0.0109 (7)−0.0066 (7)
C140.0164 (8)0.0279 (10)0.0196 (8)−0.0119 (7)0.0064 (7)−0.0072 (7)
C150.0113 (8)0.0283 (10)0.0161 (8)−0.0046 (7)0.0023 (6)−0.0001 (7)
C160.0137 (8)0.0175 (8)0.0130 (7)−0.0038 (6)0.0052 (6)−0.0015 (6)
C170.0305 (11)0.0169 (9)0.0346 (11)0.0022 (8)0.0145 (9)−0.0060 (8)
C180.0192 (9)0.0251 (10)0.0278 (10)0.0042 (8)0.0029 (8)0.0066 (8)
C190.0097 (7)0.0166 (8)0.0101 (7)−0.0024 (6)0.0037 (6)−0.0029 (6)
C200.0130 (8)0.0192 (8)0.0117 (7)−0.0026 (6)0.0042 (6)−0.0016 (6)
C210.0174 (8)0.0316 (10)0.0124 (8)−0.0035 (7)0.0076 (7)−0.0007 (7)
C220.0150 (8)0.0365 (11)0.0150 (8)−0.0011 (7)0.0084 (6)−0.0071 (7)
C230.0124 (8)0.0257 (9)0.0181 (8)0.0026 (7)0.0044 (6)−0.0076 (7)
C240.0111 (7)0.0190 (8)0.0134 (7)−0.0016 (6)0.0034 (6)−0.0026 (6)
C250.0259 (10)0.0227 (9)0.0155 (8)−0.0010 (7)0.0063 (7)0.0070 (7)
C260.0287 (10)0.0185 (9)0.0348 (11)0.0086 (8)0.0112 (9)0.0018 (8)
C1S0.0282 (11)0.0283 (11)0.0356 (11)0.0042 (9)−0.0050 (9)−0.0046 (9)
Cl10.0454 (3)0.0281 (3)0.0340 (3)0.0073 (2)−0.0042 (2)−0.0048 (2)
Cl20.0257 (2)0.0308 (3)0.0263 (2)−0.00326 (19)0.00364 (19)0.00526 (19)
C2S0.0322 (11)0.0231 (10)0.0276 (10)0.0090 (8)0.0142 (8)0.0092 (8)
Cl30.0422 (3)0.0211 (2)0.0259 (2)0.0049 (2)0.0059 (2)0.00504 (18)
Cl40.0307 (3)0.0339 (3)0.0367 (3)0.0072 (2)0.0189 (2)0.0061 (2)
Geometric parameters (Å, °) top
Zn1—N12.0324 (13)C13—C141.379 (3)
Zn1—N1i2.0324 (13)C13—H130.9500
Zn1—N2i2.0368 (13)C14—C151.377 (3)
Zn1—N22.0368 (13)C14—H140.9500
N1—C41.373 (2)C15—C161.395 (2)
N1—C11.3733 (19)C15—H150.9500
N2—C61.372 (2)C17—H17A0.9800
N2—C91.3775 (19)C17—H17B0.9800
O1—C121.371 (2)C17—H17C0.9800
O1—C171.429 (2)C18—H18A0.9800
O2—C161.368 (2)C18—H18B0.9800
O2—C181.427 (2)C18—H18C0.9800
O3—C201.361 (2)C19—C241.398 (2)
O3—C251.430 (2)C19—C201.398 (2)
O4—C241.365 (2)C20—C211.399 (2)
O4—C261.424 (2)C21—C221.378 (3)
C1—C10i1.400 (2)C21—H210.9500
C1—C21.439 (2)C22—C231.382 (3)
C2—C31.356 (2)C22—H220.9500
C2—H20.9500C23—C241.397 (2)
C3—C41.441 (2)C23—H230.9500
C3—H30.9500C25—H25A0.9800
C4—C51.400 (2)C25—H25B0.9800
C5—C61.402 (2)C25—H25C0.9800
C5—C111.499 (2)C26—H26A0.9800
C6—C71.442 (2)C26—H26B0.9800
C7—C81.359 (2)C26—H26C0.9800
C7—H70.9500C1S—Cl21.754 (2)
C8—C91.441 (2)C1S—Cl11.769 (2)
C8—H80.9500C1S—H1S10.9900
C9—C101.399 (2)C1S—H1S20.9900
C10—C1i1.400 (2)C2S—Cl41.763 (2)
C10—C191.501 (2)C2S—Cl31.773 (2)
C11—C161.397 (2)C2S—H2S10.9900
C11—C121.401 (2)C2S—H2S20.9900
C12—C131.391 (2)
N1—Zn1—N1i180.0C14—C15—H15120.5
N1—Zn1—N2i90.37 (5)C16—C15—H15120.5
N1i—Zn1—N2i89.64 (5)O2—C16—C15123.07 (16)
N1—Zn1—N289.63 (5)O2—C16—C11115.82 (14)
N1i—Zn1—N290.36 (5)C15—C16—C11121.11 (16)
N2i—Zn1—N2180.0O1—C17—H17A109.5
C4—N1—C1106.50 (13)O1—C17—H17B109.5
C4—N1—Zn1127.08 (10)H17A—C17—H17B109.5
C1—N1—Zn1126.31 (11)O1—C17—H17C109.5
C6—N2—C9106.52 (13)H17A—C17—H17C109.5
C6—N2—Zn1127.11 (10)H17B—C17—H17C109.5
C9—N2—Zn1126.28 (11)O2—C18—H18A109.5
C12—O1—C17116.42 (14)O2—C18—H18B109.5
C16—O2—C18116.32 (14)H18A—C18—H18B109.5
C20—O3—C25117.38 (14)O2—C18—H18C109.5
C24—O4—C26116.60 (14)H18A—C18—H18C109.5
N1—C1—C10i125.91 (14)H18B—C18—H18C109.5
N1—C1—C2109.62 (14)C24—C19—C20118.53 (15)
C10i—C1—C2124.46 (14)C24—C19—C10119.07 (14)
C3—C2—C1107.25 (14)C20—C19—C10122.40 (15)
C3—C2—H2126.4O3—C20—C19115.06 (14)
C1—C2—H2126.4O3—C20—C21124.19 (16)
C2—C3—C4106.85 (14)C19—C20—C21120.75 (16)
C2—C3—H3126.6C22—C21—C20118.96 (17)
C4—C3—H3126.6C22—C21—H21120.5
N1—C4—C5125.81 (14)C20—C21—H21120.5
N1—C4—C3109.75 (13)C21—C22—C23121.96 (16)
C5—C4—C3124.38 (15)C21—C22—H22119.0
C4—C5—C6124.72 (15)C23—C22—H22119.0
C4—C5—C11117.37 (14)C22—C23—C24118.64 (17)
C6—C5—C11117.89 (14)C22—C23—H23120.7
N2—C6—C5125.63 (14)C24—C23—H23120.7
N2—C6—C7109.85 (13)O4—C24—C23123.67 (16)
C5—C6—C7124.44 (15)O4—C24—C19115.19 (14)
C8—C7—C6106.89 (14)C23—C24—C19121.14 (16)
C8—C7—H7126.6O3—C25—H25A109.5
C6—C7—H7126.6O3—C25—H25B109.5
C7—C8—C9107.15 (14)H25A—C25—H25B109.5
C7—C8—H8126.4O3—C25—H25C109.5
C9—C8—H8126.4H25A—C25—H25C109.5
N2—C9—C10125.63 (14)H25B—C25—H25C109.5
N2—C9—C8109.55 (14)O4—C26—H26A109.5
C10—C9—C8124.82 (14)O4—C26—H26B109.5
C9—C10—C1i125.18 (14)H26A—C26—H26B109.5
C9—C10—C19117.53 (14)O4—C26—H26C109.5
C1i—C10—C19117.14 (14)H26A—C26—H26C109.5
C16—C11—C12118.14 (15)H26B—C26—H26C109.5
C16—C11—C5120.09 (15)Cl2—C1S—Cl1110.72 (12)
C12—C11—C5121.74 (15)Cl2—C1S—H1S1109.5
O1—C12—C13123.13 (16)Cl1—C1S—H1S1109.5
O1—C12—C11115.86 (15)Cl2—C1S—H1S2109.5
C13—C12—C11121.01 (16)Cl1—C1S—H1S2109.5
C14—C13—C12119.10 (17)H1S1—C1S—H1S2108.1
C14—C13—H13120.4Cl4—C2S—Cl3111.31 (11)
C12—C13—H13120.4Cl4—C2S—H2S1109.4
C15—C14—C13121.63 (17)Cl3—C2S—H2S1109.4
C15—C14—H14119.2Cl4—C2S—H2S2109.4
C13—C14—H14119.2Cl3—C2S—H2S2109.4
C14—C15—C16118.99 (17)H2S1—C2S—H2S2108.0
Symmetry codes: (i) −x, −y, −z+1.
Acknowledgements top

This material is based upon work supported by the National Science Foundation under grant No. 0525440. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

references
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