research communications
of 2,3-dimethylmaleic anhydride: continuous chains of electrostatic attraction
aDepartment of Chemistry and Biochemistry, Oberlin College, Oberlin, Ohio 44074, USA, and bDepartment of Chemistry, Youngstown State University, Youngstown, Ohio 44555, USA
*Correspondence e-mail: Ren.Wiscons@oberlin.edu
In the 6H6O3, the closest non-bonding intermolecular distances, between the carbonyl C and O atoms of neighboring molecules, were measured as 2.9054 (11) and 3.0509 (11) Å, which are well below the sum of the van der Waals radii for these atoms. These close contacts, as well as packing motifs similar to that of the title compound, were also found in the of maleic anhydride itself and other 2,3-disubstituted maleic Computational modeling suggests that this close contact is caused by strong electrostatic interactions between the carbonyl C and O atoms.
of 2,3-dimethylmaleic anhydride, CCCDC reference: 1412475
1. Chemical context
Maleic anhydride and its symmetrically 2,3-disubstituted derivatives are standard reagents found in nearly all chemical stockrooms due to their importance as metal-organic framework post-synthetic modifiers (Wang & Cohen, 2009), biomolecule catalysts (Puigserver & Desnuelle, 1975), synthesis reagents (Moad et al., 2003), and temperature and pH-reversible co-polymer grafts (Gao et al., 2009). Although they are seemingly ubiquitous, comparisons of interactions in the solid state of maleic anhydride (Lutz, 2001) and its disubstituted derivatives have not been discussed. Determination of the structure of the title compound, 2,3-dimethylmaleic anhydride by single-crystal X-ray diffraction was completed and is reported herein. Computational modeling was also used to determine the intermolecular interactions present in the title compound as well as in other 2,3-disubstituted derivatives.
2. Structural commentary
The title compound 2,3-dimethylmaleic anhydride (Fig. 1) is a 5-membered cyclic anhydride with a double bond between carbon atoms C2 and C3. The double bond locks the molecule in a planar conformation and stabilizes the acid anhydride against hydration. The lengths of the C—C single bonds between C1 and C2, and C3 and C4 are 1.4841 (11) and 1.4848 (11) Å, respectively, and that of the C=C bond between C2 and C3 is 1.3420 (12) Å, suggesting that the alkene region of the molecule is not delocalized with the carbonyl groups and that the molecule is non-aromatic. The of a molecule in the gas phase was calculated as 4.8999 D from DFT B3LYP with a 6-311G(d,p) basis set using GUUSSIAN03 (Frisch et al., 2004). All bond lengths and angles are consistent with the molecular structure of unsubstituted maleic anhydride (Lutz, 2001).
3. Supramolecular features
In the title compound, close intermolecular carbonyl–carbonyl contacts with d(δ+C⋯δ−O) ranging from 2.9054 (11) to 3.0509 (11) Å in length are present, which is well below the sum of the carbon and oxygen van der Waals radii of 3.22 Å (Bondi, 1964), suggesting a strong attractive interaction between these two atoms. Close carbonyl–carbonyl interactions, in which d(δ+C⋯δ−O) is < 3.6 Å, persist in 15% of carbonyl-substituted small molecule crystal structures surveyed from the Cambridge Structural Database (CSD) by Allen and colleagues in 1998 (Allen et al., 1998). Three carbonyl–carbonyl approach geometries, characterized by specific ranges in angles between the van der Waals radius-overlapped ketonic carbon and oxygen nuclei, were found to describe 71.2% (945 structures) of the observed interactions in the 1,328 crystal structures identified as having close carbonyl–carbonyl contacts: the anti-parallel, perpendicular, and sheared parallel motifs (Fig. 2). Orthogonality of the interacting ketonic nuclei was found to be correlated with multiplicity using ab initio calculations to quantify interaction strength (Allen et al., 1998). Doubly C⋯O connected anti-parallel carbonyl–carbonyl interactions (Fig. 2a) approached strengths of −22.3 kJ mol−1, which is competitive with weak-to-medium-strength classical hydrogen bonds, while singly C⋯O connected perpendicular (Fig. 2b) and sheared parallel interactions (Fig. 2c) were found to have interaction strengths reaching −7.6 kJ mol−1, which is on a par with strong aromatic stacking interactions (Allen et al., 1998). In addition to the interaction multiplicity, the anti-parallel geometry is strengthened by π–π interactions, lengthening the mean separation distance between carbonyl–carbonyl contacts relative to those observed in singly connected geometries.
A survey of thirteen previously determined 2,3-disubstituted maleic anhydride crystal structures demonstrates the persistence of the unsubstituted maleic ). These 2,3-disubstituted maleic anhydride crystal structures and 2,3-dimethylmaleic anhydride were characterized in the context of the parameters described by Allen et al. (Table 1 to 3). Computational modeling of electrostatic potential and optimized geometric configurations in homomolecular maleic anhydride complexes suggest that non-covalent carbonyl–carbonyl interactions further polarize the interacting nuclei, reinforcing the electrostatic attraction, while also polarizing the neighboring anhydride carbonyl, and propagating the carbonyl–carbonyl interactions. The shortest contacts between any two non-H atoms of two molecules are those between the two carbonyl oxygens and the carbonyl C atoms of neighboring molecules. Both anti-parallel and perpendicular motifs are present in the (Fig. 3a). Though the attraction strength for anti-parallel interactions is predicted to be greater than that of the perpendicular motif (Allen et al., 1998), the shortest two contacts belong to the perpendicular interactions of O2 and O1 with d(δ+C⋯δ−O) = 2.9054 (11) Å and a C=O⋯C angle of 152.88 (6)° for C1=O2⋯C4iii, and d(δ+C⋯δ−O) = 3.0509 (11) Å and a C=O⋯C angle of 143.24 (6)° for C4=O3⋯C2i [symmetry code: (i) −x, y + , −z + , (iii) −x + , y − , z]. The two anti-parallel interactions are arranged pairwise between the two carbonyls rather than between carbonyls of the same type (i.e., they are not related by inversion symmetry) and they have d(δ+C⋯δ−O) values of 3.220 (11) and 3.259 (11) Å and C=O⋯C angles of 100.86 (5) and 98.89 (5) for C1=O2⋯C4iv and C4=O3⋯C2v, respectively [symmetry codes: (iv) x + , y, −z + ; (v) x − , y, −z + ]. The greater d(δ+C⋯δ−O) value for the anti-parallel motif relative to the perpendicular motif may be attributed to the π–π interactions between the doubly connected carbonyl groups that accompany the δ+C⋯δ−O interactions.
carbonyl–carbonyl contacts against steric and electrostatic perturbation (CSD, accessed June 2015; Groom & Allen, 2014
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The perpendicular interactions and pairwise anti-parallel interactions connect neighboring molecules to form several interaction motifs (Fig. 3). Each 2,3-dimethylmaleic anhydride molecule participates in four perpendicular interactions, of which each two are symmetry equivalent: as an electron-density acceptor (through the carbonyl C atom) in two of the four interactions and in the other two as an electron-density donor (through the carbonyl O atom). The perpendicular carbonyl–carbonyl interactions associated with both the 2.9054 (11) and 3.0509 (11) Å δ+C⋯δ−O distances give rise to pleated chains of 2,3-dimethylmaleic anhydride molecules that extend parallel to the b-axis. There are two parallel chains that arise from the two perpendicular interactions with the 2.9054 (11) and 3.0509 (11) Å δ+C⋯δ−O separations (C1=O2⋯C4iii and C4=O3⋯C2i; Fig. 3a). The interactions join parallel chains and combined they create layers perpendicular to the c-axis direction. Molecules within these layers are further connected through the pairwise anti-parallel carbonyl interactions and π-stacking, as well as C—H⋯O interactions between methyl atom H6A and atom O1 (Table 4). Only weak intermolecular interactions are found between parallel layers of 2,3-dimethylmaleic anhydride molecules, the most pronounced one being between methyl atom H6B and atom O3 (Fig. 3b).
4. Computational modeling
To better understand the intermolecular interactions that allow the close contact between the carbonyl C atom and the carbonyl O atom, the anti-parallel carbonyl–carbonyl interaction between two molecules of 2,3-dimethylmaleic anhydride was modeled computationally. The perpendicular carbonyl interaction is not a geometric minimum in the gas phase and thus was not modeled due to the unknown contributions from additional solid-state interactions. Geometry optimizations were performed for one molecule of 2,3-dimethylmaleic anhydride and a dimer of 2,3-dimethylmaleic anhydride using DFT B3LYP with the 6-31G(d) basis set using GAUSSIAN03 (Frisch et al., 2004). Geometry optimization of the two-molecule complex revealed a strong interaction between the carbonyl O atom and carbonyl C atom with a short d(δ+C⋯δ−O) of 3.178 Å, which is consistent with the value from the [3.220 (11) Å] and is below the sum of the van der Waals radii for O and C (3.22 Å). The Mulliken atomic charges of the carbonyl O atom (−0.4496) and carbonyl C atom (+0.5116) suggest that this interaction is likely electrostatic in nature (Fig. 4a). Comparison of the computed Mulliken atomic charges of the two-molecule complex with that of a single molecule indicates that both the carbonyl C atom (+0.6142) and carbonyl O atom (−0.4677) atoms participating in the anti-parallel interaction (Fig. 4b) are further polarized relative to the free molecule (Fig. 4a). More interestingly, in the two-molecule complex, even the carbonyl C atom not directly involved in the electrostatic attraction is further polarized, with a calculated Mulliken atomic charge of +0.5883 versus +0.5116 in the single-molecule model. These data suggest that the carbon–oxygen electrostatic interaction on one end of the anhydride draws electron density from the carbonyl C atom on the other and enables 2,3-dimethylmaleic anhydride to better interact with a neighboring carbonyl O atom.
Induced polarization reinforces the overall strength of the carbonyl–carbonyl network within the
both between molecules, forming chains through perpendicular interactions, and between anti-parallel chains, forming sheets. Based on these calculations, it can be predicted that with increased polarization of the carbonyl carbon and oxygen nuclei, the strength of the intermolecular interaction between carbonyls would increase and the shortest contact between the interacting nuclei would decrease. Additional inductive effects of dimerization include an increase in the average Mulliken atomic charge of the methyl H atoms (+0.1859) relative to that of the free molecule (+0.1499), which would have the effect of slightly strengthening the weak C—H⋯O attractions that connect layers of molecules associated through the carbonyl–carbonyl interactions.5. Database survey
The Mulliken atomic charges for thirteen 2,3-disubstituted maleic d(δ+C⋯δ−O) and geometries (Tables 1, 2 and 3). The expected trend is most apparent amongst the set of sheared-parallel carbonyl–carbonyl interactions in which the participating nuclei are isolated from additional non-covalent interactions, unlike those found in anti-parallel and perpendicular motifs. This trend supports the prediction that d(δ+C⋯δ−O) decreases with increased carbonyl polarization. The expected trend in anti-parallel d(δ+C⋯δ−O) is disrupted by YUYMIO, a 2,3-diphenylmaleic anhydride, whose packing is also guided by edge-face aromatic interactions [d(C—H⋯centroid] of 3.187 Å). Because of the packing frustration presented by these two competing interactions in 2,3-diphenylmaleic anhydride, its disruption of the d(δ+C⋯δ−O) trend may be disregarded. These data suggest that C2 and C3 functionalization can affect the carbonyl–carbonyl interaction distance for a particular interaction geometry (anti-parallel, perpendicular, and sheared-parallel) through polarization of the carbonyl group. The persistence of the major interactions in maleic acid indicates that electrostatic distribution and intermolecular interaction-induced polarization of the carbonyls contribute strongly to the molecular packing and are competitive with other common supramolecular moieties, such as hydrogen-bonding and aromatic stacking.
found in the CSD were calculated and their crystal structures analyzed for6. Synthesis and crystallization
Crystals were grown by dissolving 2 g of 2,3-dimethylmaleic anhydride in 100 mL of deionized H2O at 373 K. Once dissolved, the solution was slowly cooled to 277 K, crystallizing colorless plates.
7. Refinement
Crystal data, data collection and structure . H atoms were positioned geometrically and constrained to ride on their parent atoms, with carbon–hydrogen bond distances of 0.95 Å for C—H, and 0.98 Å for CH3 moieties, respectively. Methyl H atoms were allowed to rotate but not to tip to best fit the experimental electron density. Uiso(H) values were set to a multiple of Ueq(C) with 1.5 for CH3 and 1.2 for C—H.
details are summarized in Table 5Supporting information
CCDC reference: 1412475
https://doi.org/10.1107/S2056989015013419/zs2339sup1.cif
contains datablock I. DOI:Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2056989015013419/zs2339Isup2.hkl
Supporting information file. DOI: https://doi.org/10.1107/S2056989015013419/zs2339Isup3.cml
Data collection: APEX2 (Bruker, 2013); cell
SAINT (Bruker, 2013); data reduction: SAINT (Bruker, 2013); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL2014 (Sheldrick, 2015) and SHELXLE (Hübschle et al., 2011); molecular graphics: Mercury (Macrae et al., 2008); software used to prepare material for publication: publCIF (Westrip, 2010).C6H6O3 | Dx = 1.432 Mg m−3 |
Mr = 126.11 | Mo Kα radiation, λ = 0.71073 Å |
Orthorhombic, Pbca | Cell parameters from 4877 reflections |
a = 10.4087 (18) Å | θ = 3.1–31.3° |
b = 8.5848 (15) Å | µ = 0.12 mm−1 |
c = 13.095 (2) Å | T = 100 K |
V = 1170.1 (3) Å3 | Plate, colourless |
Z = 8 | 0.50 × 0.31 × 0.19 mm |
F(000) = 528 |
Bruker APEXII CCD diffractometer | 1856 independent reflections |
Radiation source: fine focus sealed tube | 1688 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.031 |
ω and phi scans | θmax = 31.5°, θmin = 3.5° |
Absorption correction: multi-scan (SADABS; Bruker, 2013) | h = −15→15 |
Tmin = 0.643, Tmax = 0.746 | k = −12→12 |
16692 measured reflections | l = −19→19 |
Refinement on F2 | Primary atom site location: structure-invariant direct methods |
Least-squares matrix: full | Secondary atom site location: difference Fourier map |
R[F2 > 2σ(F2)] = 0.037 | Hydrogen site location: inferred from neighbouring sites |
wR(F2) = 0.101 | H-atom parameters constrained |
S = 1.07 | w = 1/[σ2(Fo2) + (0.0563P)2 + 0.342P] where P = (Fo2 + 2Fc2)/3 |
1856 reflections | (Δ/σ)max = 0.001 |
84 parameters | Δρmax = 0.53 e Å−3 |
0 restraints | Δρmin = −0.19 e Å−3 |
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. |
x | y | z | Uiso*/Ueq | ||
C1 | 0.21013 (8) | 0.04947 (9) | 0.74377 (6) | 0.01397 (17) | |
C2 | 0.16580 (8) | 0.09029 (9) | 0.84811 (6) | 0.01289 (17) | |
C3 | 0.06175 (8) | 0.18143 (9) | 0.83852 (6) | 0.01265 (17) | |
C4 | 0.03516 (8) | 0.20010 (9) | 0.72780 (6) | 0.01341 (17) | |
C5 | 0.23380 (9) | 0.03114 (10) | 0.93985 (7) | 0.01846 (19) | |
H5A | 0.2334 | −0.0830 | 0.9392 | 0.028* | |
H5B | 0.1902 | 0.0687 | 1.0015 | 0.028* | |
H5C | 0.3227 | 0.0687 | 0.9394 | 0.028* | |
C6 | −0.02176 (9) | 0.25635 (10) | 0.91611 (7) | 0.01814 (19) | |
H6A | −0.0139 | 0.3698 | 0.9108 | 0.027* | |
H6B | 0.0048 | 0.2229 | 0.9845 | 0.027* | |
H6C | −0.1113 | 0.2258 | 0.9043 | 0.027* | |
O1 | 0.12815 (6) | 0.11870 (7) | 0.67262 (5) | 0.01582 (16) | |
O2 | 0.29960 (6) | −0.02770 (8) | 0.71646 (5) | 0.01983 (17) | |
O3 | −0.04983 (6) | 0.26794 (8) | 0.68539 (5) | 0.01860 (16) |
U11 | U22 | U33 | U12 | U13 | U23 | |
C1 | 0.0154 (4) | 0.0128 (3) | 0.0137 (4) | −0.0016 (3) | 0.0001 (3) | −0.0002 (3) |
C2 | 0.0145 (4) | 0.0126 (3) | 0.0115 (3) | −0.0023 (3) | −0.0003 (3) | 0.0003 (3) |
C3 | 0.0151 (4) | 0.0125 (3) | 0.0103 (3) | −0.0020 (3) | 0.0005 (2) | −0.0004 (2) |
C4 | 0.0149 (4) | 0.0125 (3) | 0.0129 (3) | −0.0015 (3) | 0.0005 (3) | −0.0004 (3) |
C5 | 0.0194 (4) | 0.0210 (4) | 0.0150 (4) | −0.0005 (3) | −0.0042 (3) | 0.0030 (3) |
C6 | 0.0185 (4) | 0.0208 (4) | 0.0151 (4) | 0.0014 (3) | 0.0037 (3) | −0.0026 (3) |
O1 | 0.0192 (3) | 0.0177 (3) | 0.0106 (3) | 0.0027 (2) | 0.0002 (2) | −0.0011 (2) |
O2 | 0.0188 (3) | 0.0195 (3) | 0.0212 (3) | 0.0035 (2) | 0.0035 (2) | −0.0018 (2) |
O3 | 0.0186 (3) | 0.0191 (3) | 0.0181 (3) | 0.0011 (2) | −0.0039 (2) | 0.0023 (2) |
C1—O2 | 1.1976 (10) | C4—O1 | 1.3955 (10) |
C1—O1 | 1.3963 (10) | C5—H5A | 0.9800 |
C1—C2 | 1.4841 (11) | C5—H5B | 0.9800 |
C2—C3 | 1.3420 (12) | C5—H5C | 0.9800 |
C2—C5 | 1.4840 (11) | C6—H6A | 0.9800 |
C3—C6 | 1.4837 (11) | C6—H6B | 0.9800 |
C3—C4 | 1.4848 (11) | C6—H6C | 0.9800 |
C4—O3 | 1.1959 (10) | ||
O2—C1—O1 | 120.76 (8) | C2—C5—H5B | 109.5 |
O2—C1—C2 | 130.35 (8) | H5A—C5—H5B | 109.5 |
O1—C1—C2 | 108.90 (7) | C2—C5—H5C | 109.5 |
C3—C2—C5 | 131.32 (8) | H5A—C5—H5C | 109.5 |
C3—C2—C1 | 107.60 (7) | H5B—C5—H5C | 109.5 |
C5—C2—C1 | 121.08 (7) | C3—C6—H6A | 109.5 |
C2—C3—C6 | 131.41 (8) | C3—C6—H6B | 109.5 |
C2—C3—C4 | 107.74 (7) | H6A—C6—H6B | 109.5 |
C6—C3—C4 | 120.84 (7) | C3—C6—H6C | 109.5 |
O3—C4—O1 | 121.09 (8) | H6A—C6—H6C | 109.5 |
O3—C4—C3 | 130.09 (8) | H6B—C6—H6C | 109.5 |
O1—C4—C3 | 108.80 (7) | C4—O1—C1 | 106.95 (6) |
C2—C5—H5A | 109.5 | ||
O2—C1—C2—C3 | 179.19 (8) | C2—C3—C4—O3 | 177.77 (8) |
O1—C1—C2—C3 | −0.43 (9) | C6—C3—C4—O3 | −1.64 (14) |
O2—C1—C2—C5 | −1.17 (13) | C2—C3—C4—O1 | −0.84 (9) |
O1—C1—C2—C5 | 179.21 (7) | C6—C3—C4—O1 | 179.75 (7) |
C5—C2—C3—C6 | 0.48 (15) | O3—C4—O1—C1 | −178.21 (7) |
C1—C2—C3—C6 | −179.93 (8) | C3—C4—O1—C1 | 0.55 (8) |
C5—C2—C3—C4 | −178.84 (8) | O2—C1—O1—C4 | −179.77 (7) |
C1—C2—C3—C4 | 0.75 (9) | C2—C1—O1—C4 | −0.10 (8) |
D—H···A | D—H | H···A | D···A | D—H···A |
C6—H6A···O1i | 0.98 | 2.68 | 3.5004 (12) | 142 |
C6—H6B···O3ii | 0.98 | 2.69 | 3.5445 (13) | 146 |
Symmetry codes: (i) −x, y+1/2, −z+3/2; (ii) x, −y+1/2, z+1/2. |
Molecule | CSD refcode | δ+ C, δ- C | d(C···O) | <C=O···C |
3,4-bis(2,5-dimethylthien-3-yl)furan-2,5-dione | NOYGEN | 0.6602895, -0.432609 | 3.063, 3.063 | 94.98, 94.98 |
bicyclo(2.2.1)hepta-2,5-diene-2,3-dicarboxylic anhydride | DAJXIV | 0.656483, -0.4329365 | 3.088, 3.927 | 135.40, 85.90 |
2,3-diphenylmaleic anhydride | YUYMIO | 0.618440, -0.442542 | 3.575, 3.843 | 75.83, 63.55 |
4,5,6,7-tetrahydroisobenzofuran-1,3-dione | NADCOL | 0.566591, -0.447350 | 3.108, 3.191 | 87.26, 83.39 |
dimethylmaleic anhydride | this work | 0.5116155, -0.449629 | 3.220, 3.259 | 100.86, 98.90 |
dichloromaleic anhydride | LIZCOM | 0.2165505, -0.374174 | 3.211, 3.219 | 103.01, 102.55 |
Molecule | CSD refcode | δ+ C, δ- O | d(C···O) | <C=O···C |
bicyclo(2.2.1)hepta-2,5-diene-2,3-dicarboxylic anhydride | DAJXIV | 0.656483, -0.4329365 | 3.140, 4.747 | 137.15, 50.35 |
3-benzyl-4-phenylfuran-2,5-dione | GUSHOS | 0.640951, -0.4265975 | 2.872, 4.257 | 134.72, 59.61 |
2,3-diphenylmaleic anhydride | YUYMIO | 0.618440, -0.442542 | 2.913, 3.583 | 115.98, 80.11 |
4,5,6,7-tetrahydroisobenzofuran-1,3-dione | NADCOL | 0.566591, -0.447350 | 2.957, 4.360 | 156.23, 68.51 |
4,5,6,7-tetrahydroisobenzofuran-1,3-dione | NADCOL | 0.566591, -0.447350 | 3.148, 4.143 | 124.42, 91.05 |
dimethylmaleic anhydride | This work | 0.5116155, -0.449629 | 2.905, 4.351 | 152.88, 66.53 |
dimethylmaleic anhydride | This work | 0.5116155, -0.449629 | 3.080, 4.258 | 130.02, 67.42 |
4-(4-fluorophenyl)-3-hydroxymaleic anhydride | VEYNIX | 0.263244, -0.457944 | 3.086, 4.271 | 119.16, 59.94 |
dichloromaleic anhydride | LIZCOM | 0.2165505, -0.374174 | 2.888, 4.346 | 149.52, 63.38 |
dichloromaleic anhydride | LIZCOM | 0.2165505, -0.374174 | 3.011, 4.275 | 133.18, 64.81 |
Molecule | CSD entry code | δ+ C, δ- C | d(C···O) | <C=O···C |
bicyclo(2.2.2)octa-2,5-diene-2,3-dicarboxylic anhydride | GIQRAZ | 0.6408315, -0.441006 | 3.184, 4.092 | 107.62, 63.77 |
acenaphthylene-1,2-dicarboxylic acid anhydride | KECPIR | 0.6385225, -0.442158 | 3.242, 4.030 | 102.25, 64.70 |
2-(1,2-dimethylindol-3-yl)-3-(1-propenyl)maleic anhydride | FARQUL | 0.5945155, -0.439755 | 3.243, 4.027 | 92.18, 55.81 |
bicyclo(2.2.1)hept-2-ene-2,3-dicarboxylic anhydride | DAJXOB | 0.5930385, -0.430164 | 3.434, 3.498 | 87.57, 81.57 |
2-phenylmaleic anhydride | ZIVKOE | 0.4664565, -0.437246 | 3.847, 4.151 | 83.27, 97.93 |
Footnotes
‡Dr Jesse Rowsell passed away on January 30, 2015.
Acknowledgements
The X-ray diffractometer was funded by NSF grant 0087210, Ohio Board of Regents grant CAP-491, and by Youngstown State University. The authors would like to thank Oberlin College for funding this research.
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