organic compounds\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

Journal logoCRYSTALLOGRAPHIC
COMMUNICATIONS
ISSN: 2056-9890
Volume 69| Part 10| October 2013| Pages o1547-o1548

2-(2-Methyl­benzo­yl)benzoic acid: catemeric hydrogen bonding in a γ-keto acid

aCarl A. Olson Memorial Laboratories, Department of Chemistry, Rutgers University, Newark, NJ 07102 , USA, and bDepartment of Chemistry, Touro College - Lander College for Men, New York, NY , USA
*Correspondence e-mail: rogerlal@andromeda.rutgers.edu

(Received 29 July 2013; accepted 9 September 2013; online 18 September 2013)

The crystal structure of the title compound, C15H12O3, displays catemeric aggregation involving O—H⋯O hydrogen bonds progressing from the carboxyl group of one mol­ecule to the ketone O atom of another glide-related neighbor. The mol­ecule is twisted, with the toluene 80.61 (3)° out of plane with respect to the phenyl group of the benzoic acid. The acid group makes a dihedral angle of 13.79 (14)° with the attached phenyl ring. The mol­ecules are achiral, but the space group glide planes create alternating conformational chirality in the chain units. The four hydrogen-bonding chains progress along [001] in an AABB pattern (right-to-left versus left-to-right), and are related to each other by the center of symmetry at (0.5, 0.5, 0.5) in the chosen cell. There is one close contact (2.54 Å) between a phenyl H atom and the acid carbonyl from a symmetry-related mol­ecule.

Related literature

For a discussion of highly ordered carboxyl bond distances and angles, see: Borthwick (1980[Borthwick, P. W. (1980). Acta Cryst. B36, 628-632.]). For close contact information, see: Steiner (1997[Steiner, T. (1997). Chem. Commun. pp. 727-734.]). For related structures, see: Abell et al. (1991[Abell, A. D., Trent, J. & Robinson, W. P. (1991). J. Chem. Soc. Chem. Commun. pp. 362-363.]); Barcon et al. (1998[Barcon, A., Brunskill, A. P. J., Lalancette, R. A. & Thompson, H. W. (1998). Acta Cryst. C54, 1282-1285.], 2002[Barcon, A., Brunskill, A. P. J., Lalancette, R. A. & Thompson, H. W. (2002). Acta Cryst. C58, o154-o156.]); Degen & Bolte (1999[Degen, A. & Bolte, M. (1999). Acta Cryst. C55, 1306-1308.]); Hickmott et al. (1985[Hickmott, P. W., Ahmed, M. G., Ahmed, S. A., Wood, S. & Kapon, M. (1985). J. Chem. Soc. Perkin Trans. 1, pp. 2559-2571.]); Kashyap et al. (1995[Kashyap, R. P., Deshpande, M. N., Rajapaksa, D., Marchand, A. P. & Watson, W. H. (1995). J. Chem. Crystallogr. 25, 573-578.]); Song et al. (2008[Song, G.-L., Deng, S.-P., Liu, S. & Zhu, H.-J. (2008). Acta Cryst. E64, o894.]); Thompson et al. (1998[Thompson, H. W., Brunskill, A. P. J. & Lalancette, R. A. (1998). Acta Cryst. C54, 829-831.]); Watson et al. (1990[Watson, W. H., Nagl, A., Kashyap, R. P., Marchand, A. P. & Vidyasagar, V. (1990). Acta Cryst. C46, 1265-1268.]). For preparation of the title compound, see: Newman & McCleary (1941[Newman, M. S. & McCleary, C. D. (1941). J. Am. Chem. Soc. 63, 1537-1541.]). For a description of the Cambridge Structural Database, see: Allen (2002[Allen, F. H. (2002). Acta Cryst. B58, 380-388.]).

[Scheme 1]

Experimental

Crystal data
  • C15H12O3

  • Mr = 240.25

  • Orthorhombic, P b c a

  • a = 10.7450 (2) Å

  • b = 10.1737 (2) Å

  • c = 21.6588 (4) Å

  • V = 2367.66 (8) Å3

  • Z = 8

  • Cu Kα radiation

  • μ = 0.77 mm−1

  • T = 100 K

  • 0.45 × 0.26 × 0.20 mm

Data collection
  • Bruker SMART CCD APEXII area-detector diffractometer

  • Absorption correction: numerical (SADABS; Sheldrick, 2008a[Sheldrick, G. M. (2008a). SADABS. University of Göttingen, Germany.]) Tmin = 0.724, Tmax = 0.862

  • 20799 measured reflections

  • 2143 independent reflections

  • 2075 reflections with I > 2σ(I)

  • Rint = 0.024

Refinement
  • R[F2 > 2σ(F2)] = 0.030

  • wR(F2) = 0.076

  • S = 1.07

  • 2143 reflections

  • 169 parameters

  • H atoms treated by a mixture of independent and constrained refinement

  • Δρmax = 0.24 e Å−3

  • Δρmin = −0.17 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
O3—H3A⋯O1ii 0.932 (18) 1.714 (18) 2.6477 (11) 172.3 (16)
Symmetry code: (ii) [-x+{\script{3\over 2}}, y-{\script{1\over 2}}, z].

Data collection: APEX2 (Bruker, 2006[Bruker (2006). APEX2. Bruker AXS Inc., Madison, Wisconsin, USA.]); cell refinement: SAINT (Bruker, 2005[Bruker (2005). SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]); data reduction: SAINT; program(s) used to solve structure: SHELXTL (Sheldrick, 2008b[Sheldrick, G. M. (2008b). Acta Cryst. A64, 112-122.]); program(s) used to refine structure: SHELXTL; molecular graphics: SHELXTL; software used to prepare material for publication: SHELXTL.

Supporting information


Comment top

This carboxyl-to-ketone catemer (I) is an achiral molecule which generates heterochiral chains due to the glide-related chain members. Normally, these types of catemers involve homochiral chains having either a screw or translational internal relationship (Hickmott et al., 1985; Abell et al., 1991; Kashyap et al., 1995). Rarer are heterochiral chains resulting from glide-plane symmetry, which is the case here (Watson et al., 1990; Barcon et al., 1998, 2002; Thompson et al., 1998).

Fig. 1 shows the asymmetric unit for (I) with its numbering. The molecule has many options for rotation, allowing for the angle between the toluene ring and the phenyl ring of the benzoic acid to be nearly perpendicular at 80.61 (3)°. The acid group [C7—O2—O3] makes a dihedral angle with the phenyl group [C1—C6] = 13.79 (14)°, and the ketone [O1—C8—C2—C9] has a dihedral angle to the phenyl group [C1—C6] = 78.99 (3)°. The acid group [C7—O2—O3] makes a dihedral angle of 74.84 (8)° with the plane of the ketone [O1—C8—C2—C9], and also an angle of 76.65 (7)° with the plane of the toluene ring [C9—C14]. There is one close contact (2.54 Å) between a phenyl H atom (H12) and the acid carbonyl (O2) from a symmetry-related molecule (Steiner, 1997).

The structures of 2-(4-methylbenzoyl)benzoic acid and its hydrate have been published: HOFGAK (Degen & Bolte, 1999) is the p-toluene analog of (I) and MIXTOD (Song, et al., 2008) is the hydrated p-toluene analog [Cambridge Structural Database (CSD, Version 5.28, update of Nov., 2006; Allen, 2002)]. Both of these molecules crystallize as centrosymmetric dimers of the acid groups (Borthwick, 1980), but the hydrated version has two water molecules inserted between the acid dimers. In HOFGAK, the dihedral angle between the toluene and the benzoic acid = 89.8°, and the acid is coplanar [0.00°] with the phenyl ring. In MIXTOD, these same angles are 69.5 and 25.8°, respectively. In (I), the toluene and the ketone are essentially coplanar [dihedral angle = 1.91 (7)°], but in HOFGAK and MIXTOD, this same angle is 20.6 and 10.8°, respectively.

Figures 2a and 2b are partial packing diagrams showing the H bonds progressing catemerically between glide-related molecules; the individual members making up each chain have alternating chirality. The handedness of the molecules is differentiated by patterning of the bonds.

Centrosymmetrically-related H-bonded chains can be seen by comparing the A molecule in Fig. 2a with the D molecule in Fig. 2b; the B and C molecules are also centrosymmetrically related.

We characterize the geometry of H bonding to carbonyls using a combination of H···O=C angle and H···O=C—C torsion angle. These describe the approach of the acid H atom to the carbonyl O in terms of its deviation from, respectively, C=O axiality (ideal = 120°) and planarity with the carbonyl (ideal = 0°). In (I), the values for these two angles are 116.5 (5) and 10.0 (6)°.

Related literature top

For a discussion of highly ordered carboxyl bond distances and angles, see: Borthwick (1980). For close contact information, see: Steiner (1997). For related structures, see: Abell et al. (1991); Barcon et al. (1998, 2002); Degen & Bolte (1999); Hickmott et al. (1985); Kashyap et al. (1995); Song et al. (2008); Thompson et al. (1998); Watson et al. (1990). For preparation of the title compound, see: Newman & McCleary (1941). For a description of the Cambridge Structural Database, see: Allen (2002).

Experimental top

1.20 g of Mg and 1 ml of 1-bromo-2-methylbenzene were added to 17 ml of dry diethyl ether, followed by the gradual addition of 4.625 ml of 1-bromo-2-methylbenzene. The resulting Grignard reagent was added over a period of 30 min to a stirred suspension of 6.2 g of phthalic anhydride in 35 ml of dry benzene and 15 ml of dry diethyl ether. The pale orange mixture was stirred for 30 minutes, refluxed for 10 minutes, allowed to stir overnight and refluxed for a further 10 minutes. 7 ml of HCl was added along with a small quantity of ice water. The resulting solution was distilled to dryness. The glassy product was then dissolved in aqueous KOH and filtered through Celite. The filtrate was then acidified with HCl and extracted with ether into several fractions. The fractions not yielding crystals melting between 100–110°C were discarded, and the remaining fractions were combined. These were then passed through an alumina column and the solvent allowed to concentrate, yielding pale yellow crystals. These were then recrystallized from 8.6 ml of methanol and 5 mL of water. The resulting fine needle-like crystals were then recrystallized again from pure ethanol at room temperature, yielding colourless block crystals. (See Newman & McCleary, 1941).

Refinement top

Crystal data, data collection and structure refinement details are summarized in Table 1. All H atoms for (I) were found in electron density difference maps. The hydroxyl H was refined. The methyl H atoms were put in ideally staggered positions with C—H distances of 0.98 Å and Uiso(H) = 1.5Ueq(C). The aromatic Hs were placed in geometrically idealized positions and constrained to ride on their parent C atoms with C—H distance of 0.95 Å and Uiso(H) = 1.2Ueq(C).

Computing details top

Data collection: APEX2 (Bruker, 2006); cell refinement: SAINT (Bruker, 2005); data reduction: SAINT (Bruker, 2005); program(s) used to solve structure: SHELXTL (Sheldrick, 2008b); program(s) used to refine structure: SHELXTL (Sheldrick, 2008b); molecular graphics: SHELXTL (Sheldrick, 2008b); software used to prepare material for publication: SHELXTL (Sheldrick, 2008b).

Figures top
[Figure 1] Fig. 1. A view of the asymmetric unit of (I) with its numbering scheme. Displacement ellipsoids are drawn at a 40% probability level for non-H atoms.
[Figure 2] Fig. 2. Partial packing diagrams for (I). In each part, two different chains of glide-related H-bonding molecules are shown, connected by O—H···O hydrogen bonds (dashed lines). The handedness of the molecules alternates along each individual chain, and is shown by alternate shading of the bonds. The chain marked A has its centrosymmetric counterpart labeled D in the 2nd figure. The chain labeled B (with opposite H-bonding direction to A) has its centrosymmetric counterpart shown as C generated through the center of symmetry. H atoms not involved in hydrogen bonding have been omitted for clarity.
2-(2-Methylbenzoyl)benzoic acid top
Crystal data top
C15H12O3F(000) = 1008
Mr = 240.25Dx = 1.348 Mg m3
Orthorhombic, PbcaCu Kα radiation, λ = 1.54178 Å
Hall symbol: -P 2ac 2abCell parameters from 9881 reflections
a = 10.7450 (2) Åθ = 4.1–69.4°
b = 10.1737 (2) ŵ = 0.77 mm1
c = 21.6588 (4) ÅT = 100 K
V = 2367.66 (8) Å3Block, colourless
Z = 80.45 × 0.26 × 0.20 mm
Data collection top
Bruker SMART CCD APEXII area-detector
diffractometer
2143 independent reflections
Radiation source: fine-focus sealed tube2075 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.024
ϕ and ω scansθmax = 69.7°, θmin = 4.1°
Absorption correction: numerical
(SADABS; Sheldrick, 2008a)
h = 1212
Tmin = 0.724, Tmax = 0.862k = 1211
20799 measured reflectionsl = 2625
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)] = 0.030H atoms treated by a mixture of independent and constrained refinement
wR(F2) = 0.076 w = 1/[σ2(Fo2) + (0.0323P)2 + 0.9262P]
where P = (Fo2 + 2Fc2)/3
S = 1.07(Δ/σ)max < 0.001
2143 reflectionsΔρmax = 0.24 e Å3
169 parametersΔρmin = 0.17 e Å3
0 restraintsExtinction correction: SHELXTL (Sheldrick, 2008b), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
Primary atom site location: structure-invariant direct methodsExtinction coefficient: 0.00145 (14)
Crystal data top
C15H12O3V = 2367.66 (8) Å3
Mr = 240.25Z = 8
Orthorhombic, PbcaCu Kα radiation
a = 10.7450 (2) ŵ = 0.77 mm1
b = 10.1737 (2) ÅT = 100 K
c = 21.6588 (4) Å0.45 × 0.26 × 0.20 mm
Data collection top
Bruker SMART CCD APEXII area-detector
diffractometer
2143 independent reflections
Absorption correction: numerical
(SADABS; Sheldrick, 2008a)
2075 reflections with I > 2σ(I)
Tmin = 0.724, Tmax = 0.862Rint = 0.024
20799 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0300 restraints
wR(F2) = 0.076H atoms treated by a mixture of independent and constrained refinement
S = 1.07Δρmax = 0.24 e Å3
2143 reflectionsΔρmin = 0.17 e Å3
169 parameters
Special details top

Experimental. 'crystal mounted on a Cryoloop using Paratone-N'

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. 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 > σ(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
O10.94221 (8)0.35848 (8)0.62029 (4)0.0310 (2)
O20.77379 (7)0.10436 (8)0.62358 (3)0.0265 (2)
O30.71268 (8)0.03026 (8)0.69973 (4)0.0296 (2)
H3A0.6595 (17)0.0633 (17)0.6695 (8)0.059 (5)*
C10.86743 (10)0.12547 (10)0.72243 (5)0.0192 (2)
C20.96175 (10)0.20965 (10)0.70233 (5)0.0194 (2)
C31.04111 (10)0.26693 (11)0.74557 (5)0.0247 (3)
H31.10600.32360.73220.030*
C41.02588 (11)0.24164 (12)0.80801 (5)0.0285 (3)
H41.08000.28150.83720.034*
C50.93210 (11)0.15848 (12)0.82799 (5)0.0282 (3)
H50.92180.14130.87080.034*
C60.85359 (11)0.10055 (11)0.78538 (5)0.0239 (3)
H60.78960.04320.79910.029*
C70.78069 (10)0.06640 (10)0.67642 (5)0.0205 (2)
C80.97910 (10)0.24909 (10)0.63557 (5)0.0209 (2)
C91.04899 (9)0.16186 (10)0.59332 (5)0.0197 (2)
C101.07236 (10)0.19649 (11)0.53104 (5)0.0220 (2)
C111.14050 (10)0.10824 (12)0.49536 (5)0.0272 (3)
H111.15850.13030.45370.033*
C121.18287 (11)0.01046 (12)0.51844 (5)0.0282 (3)
H121.22780.06890.49250.034*
C131.15975 (11)0.04392 (11)0.57930 (5)0.0257 (3)
H131.18920.12490.59550.031*
C141.09334 (10)0.04195 (10)0.61622 (5)0.0217 (2)
H141.07750.01910.65800.026*
C151.02565 (11)0.32089 (12)0.50152 (5)0.0286 (3)
H15A1.05730.32670.45920.043*
H15B1.05480.39680.52530.043*
H15C0.93450.32010.50090.043*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
O10.0390 (5)0.0237 (4)0.0303 (4)0.0084 (4)0.0099 (4)0.0048 (3)
O20.0248 (4)0.0380 (5)0.0166 (4)0.0045 (3)0.0004 (3)0.0019 (3)
O30.0312 (5)0.0272 (4)0.0303 (4)0.0101 (3)0.0078 (4)0.0056 (3)
C10.0196 (5)0.0190 (5)0.0191 (5)0.0039 (4)0.0003 (4)0.0028 (4)
C20.0198 (5)0.0174 (5)0.0210 (5)0.0046 (4)0.0006 (4)0.0035 (4)
C30.0224 (5)0.0204 (5)0.0312 (6)0.0011 (4)0.0030 (5)0.0047 (5)
C40.0319 (6)0.0269 (6)0.0268 (6)0.0063 (5)0.0105 (5)0.0098 (5)
C50.0365 (7)0.0308 (6)0.0172 (5)0.0085 (5)0.0024 (5)0.0038 (5)
C60.0260 (6)0.0251 (6)0.0206 (5)0.0037 (5)0.0029 (4)0.0004 (4)
C70.0195 (5)0.0208 (5)0.0211 (5)0.0020 (4)0.0023 (4)0.0030 (4)
C80.0177 (5)0.0207 (5)0.0243 (6)0.0020 (4)0.0003 (4)0.0001 (4)
C90.0154 (5)0.0227 (5)0.0210 (5)0.0029 (4)0.0008 (4)0.0026 (4)
C100.0164 (5)0.0292 (6)0.0204 (5)0.0038 (4)0.0026 (4)0.0013 (4)
C110.0223 (6)0.0423 (7)0.0169 (5)0.0007 (5)0.0008 (4)0.0042 (5)
C120.0209 (6)0.0385 (6)0.0254 (6)0.0049 (5)0.0011 (5)0.0120 (5)
C130.0229 (6)0.0260 (6)0.0281 (6)0.0042 (4)0.0031 (5)0.0050 (5)
C140.0204 (5)0.0242 (5)0.0205 (5)0.0012 (4)0.0007 (4)0.0021 (4)
C150.0271 (6)0.0366 (6)0.0222 (5)0.0002 (5)0.0001 (5)0.0053 (5)
Geometric parameters (Å, º) top
O1—C81.2269 (13)C8—C91.4796 (15)
O2—C71.2102 (13)C9—C141.4004 (15)
O3—C71.3251 (13)C9—C101.4165 (15)
O3—H3A0.932 (18)C10—C111.3926 (16)
C1—C61.3948 (15)C10—C151.5041 (16)
C1—C21.3965 (15)C11—C121.3840 (18)
C1—C71.4909 (15)C11—H110.9500
C2—C31.3942 (15)C12—C131.3838 (17)
C2—C81.5120 (15)C12—H120.9500
C3—C41.3863 (17)C13—C141.3828 (15)
C3—H30.9500C13—H130.9500
C4—C51.3851 (18)C14—H140.9500
C4—H40.9500C15—H15A0.9800
C5—C61.3823 (16)C15—H15B0.9800
C5—H50.9500C15—H15C0.9800
C6—H60.9500
H12···O2i2.54
C7—O3—H3A109.8 (11)C14—C9—C10119.58 (10)
C6—C1—C2119.57 (10)C14—C9—C8118.43 (9)
C6—C1—C7120.89 (10)C10—C9—C8121.99 (10)
C2—C1—C7119.51 (9)C11—C10—C9117.47 (10)
C3—C2—C1119.40 (10)C11—C10—C15118.82 (10)
C3—C2—C8117.13 (10)C9—C10—C15123.70 (10)
C1—C2—C8123.38 (9)C12—C11—C10122.35 (10)
C4—C3—C2120.37 (11)C12—C11—H11118.8
C4—C3—H3119.8C10—C11—H11118.8
C2—C3—H3119.8C13—C12—C11119.98 (11)
C5—C4—C3120.26 (11)C13—C12—H12120.0
C5—C4—H4119.9C11—C12—H12120.0
C3—C4—H4119.9C14—C13—C12119.21 (11)
C6—C5—C4119.73 (11)C14—C13—H13120.4
C6—C5—H5120.1C12—C13—H13120.4
C4—C5—H5120.1C13—C14—C9121.41 (10)
C5—C6—C1120.66 (11)C13—C14—H14119.3
C5—C6—H6119.7C9—C14—H14119.3
C1—C6—H6119.7C10—C15—H15A109.5
O2—C7—O3124.28 (10)C10—C15—H15B109.5
O2—C7—C1122.80 (10)H15A—C15—H15B109.5
O3—C7—C1112.91 (9)C10—C15—H15C109.5
O1—C8—C9122.77 (10)H15A—C15—H15C109.5
O1—C8—C2117.31 (9)H15B—C15—H15C109.5
C9—C8—C2119.67 (9)
C6—C1—C2—C30.35 (15)C3—C2—C8—C999.68 (11)
C7—C1—C2—C3178.67 (9)C1—C2—C8—C983.75 (13)
C6—C1—C2—C8176.14 (10)O1—C8—C9—C14176.35 (10)
C7—C1—C2—C82.17 (15)C2—C8—C9—C142.36 (14)
C1—C2—C3—C40.62 (16)O1—C8—C9—C103.38 (16)
C8—C2—C3—C4176.09 (10)C2—C8—C9—C10177.37 (9)
C2—C3—C4—C50.43 (17)C14—C9—C10—C110.57 (15)
C3—C4—C5—C60.04 (17)C8—C9—C10—C11179.15 (10)
C4—C5—C6—C10.31 (17)C14—C9—C10—C15178.13 (10)
C2—C1—C6—C50.11 (16)C8—C9—C10—C152.14 (16)
C7—C1—C6—C5178.18 (10)C9—C10—C11—C121.15 (16)
C6—C1—C7—O2165.34 (10)C15—C10—C11—C12177.62 (11)
C2—C1—C7—O212.94 (15)C10—C11—C12—C131.14 (18)
C6—C1—C7—O314.30 (14)C11—C12—C13—C140.51 (17)
C2—C1—C7—O3167.41 (9)C12—C13—C14—C90.05 (17)
C3—C2—C8—O174.63 (13)C10—C9—C14—C130.00 (16)
C1—C2—C8—O1101.94 (12)C8—C9—C14—C13179.74 (10)
Symmetry code: (i) x+2, y, z+1.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O3—H3A···O1ii0.932 (18)1.714 (18)2.6477 (11)172.3 (16)
Symmetry code: (ii) x+3/2, y1/2, z.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O3—H3A···O1ii0.932 (18)1.714 (18)2.6477 (11)172.3 (16)
Symmetry code: (ii) x+3/2, y1/2, z.
 

Footnotes

This paper is dedicated to the memory of HWT; he was a wonderful mentor, teacher and friend at Rutgers University-Newark for over 44 years.

Acknowledgements

The authors acknowledge support by NSF–CRIF grant No. 0443538.

References

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Volume 69| Part 10| October 2013| Pages o1547-o1548
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