An Experimental and Theoretical Search for Polymorphs of Barbituric

CRYSTAL GROWTH & DESIGN

An Experimental and Theoretical Search for Polymorphs of Barbituric Acid: The Challenges of Even Limited Conformational Flexibility

2004 VOL. 4, NO. 5 979-987

Thomas C. Lewis, Derek A. Tocher, and Sarah L. Price* Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, UK Received November 7, 2003

ABSTRACT: An experimental study of barbituric acid found a new P21/c polymorph with two conformations of barbituric acid in the asymmetric unit, one molecule adopting an envelope conformation and the other refining as planar. The new Form ii involves different hydrogen bond acceptors to Form i. An ab initio conformational analysis study found that barbituric acid can change its envelope conformation by over 20° from planar with a small energy change that can be compensated for by packing forces, so that the new Form ii is predicted to have a lower lattice energy than Form i. A computational search for minima in the lattice energy found many hypothetical structures of barbituric acid within the energy range of possible polymorphism, with a variety of hydrogen bonding acceptors and motifs. The search was found to be very sensitive to the assumed molecular structure of barbituric acid, so further plausible low energy variations in the molecular conformation would produce even more low energy crystal structures. Thus, the combined experimental and theoretical studies show that barbituric acid can pack in such a variety of low energy structures that further polymorphs seem possible. Introduction Polymorphism, the ability of a compound to crystallize in more than one crystal structure, has been a focus of research in both the pharmaceutical industry and the academic scientific community over the past decade or so.1 Polymorphism can affect the melting point, solubility, bioavailability, stability, and morphology of the solid, so, for example, the pharmaceutical industry wishes to find all crystal structures of a drug in development. A method for computationally predicting the polymorphs of a given compound would thus greatly aid pharmaceutical development. However, despite over a decade of methodology development and faster computers, computational polymorph prediction still presents a fundamental challenge. The two blind tests on theoretical crystal structure prediction2,3 showed that no one method or program has the ability to successfully predict the crystal structures of several small, mainly rigid, organic molecules. Indeed, Gavezzotti4 and more recently Dunitz5 have both concluded that theoretical crystal structure prediction is still far from being able to predict polymorphs of a particular compound given just the molecular diagram. Although crystal structure prediction studies have been carried out on a few hundred molecules,6 a major limitation to such studies is the uncertainty as to whether more polymorphs exist. Indeed, a survey showed only 321 molecules7 with more than one polymorph are present in the Cambridge Structural Database,8 despite other indications that a significant proportion of organic molecules are polymorphic.9 Hence, it is highly desirable to combine an experimental search * To whom correspondence should be addressed. Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, UK; tel: +44 (0)20 7679 4622; fax: +44 (0)20 7679 7463; E-mail: [email protected]; Web: http://www.chem.ucl.ac.uk/people/ slprice/index.html.

Scheme 1

with a computational search to aid our understanding of polymorph prediction. We have carried out a joint experimental and theoretical study of the possible polymorphs of barbituric acid (1; Scheme 1), as a molecule where the sequence of hydrogen bond donors and two distinct acceptors gives potential for a variety of hydrogen bonding motifs. When barbituric acid is substituted at C* (1; Scheme 1), this gives the barbiturate family of hypnotic, sedative, and anticonvulsant drugs, such as barbital (2; Scheme 1) and phenobarbital (3, Scheme 1). Polymorphism within the barbiturate family is widespread,10 with most barbiturate crystal structures having a carbonyl group that does not participate in hydrogen bonding.10 It is of fundamental interest, because of its relevance to the physiological activity,11 as to whether the N-H‚‚‚OdC hydrogen bonds arising from the barbiturate group are weak, or whether the occurrence of unused hydrogen bonding acceptors merely results from packing limitations. The only reported12 crystal structure of barbituric acid (Form i) uses the unique and one of the nonunique carbonyl acceptors in the hydrogen-bonding motif. Thus, computational and experimental searches were carried out simultaneously to investigate the hydrogen bonding potential of the barbiturate group.

10.1021/cg034209a CCC: $27.50 © 2004 American Chemical Society Published on Web 03/19/2004

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Crystal Growth & Design, Vol. 4, No. 5, 2004

Methods Experimental. The experimental search for polymorphs of barbituric acid attempted crystallization by slow evaporation from a variety of solvents (water, methanol, ethanol, acetone, acetonitrile, propanol, butanol) at room temperature and 0 °C, and by varying the concentration and surface area of the solution (Table 6 of the Supporting Information). Barbituric acid is only slightly soluble in chloroform and diethyl ether, so vapor-diffusion of these solvents into methanol, ethanol, and acetonitrile solutions was attempted to induce crystallization. Powder diffraction patterns were used to determine whether a new solid form had been obtained. Crystallography. Single-crystal X-ray diffraction data collection was performed on a Bruker SMART APEX diffractometer equipped with graphite-monochromatized Mo-KR radiation (λ ) 0.71073 Å) and a nominal crystal-to-area detector distance of 60 mm. The intensities were integrated using SAINT +13 and the absorption correction was applied with SADABS.14 The structure was solved with direct methods (SHELXS97) and refined against F2 (SHELX97).15 The hydrogen atoms were either added geometrically and refined using a riding model, or refined independently. All non-hydrogen atoms were refined with anisotropic displacement parameters. Details of the crystallographic data are given in Supporting Information. Computational. A “gas phase” model for the barbituric acid molecule was obtained by optimization of the MP2/6-31G** energy using the program GAUSSIAN98.16 Corresponding wave functions were calculated for all the X-ray determined molecular structures, with the N-H bond length elongated to the standard neutron value of 1.01 Å.17 In each case, a distributed multipole analysis (DMA)18,19 of the ab initio charge density of the molecule was performed to provide an accurate description of the electrostatic contribution to the lattice energy in the rigid molecule crystal structure modeling. These atomic multipolar electrostatic models automatically represent the electrostatic effects of lone pair and π electron density, and so give a realistic representation of the relative energies and directional preferences of hydrogen bonds.20,21 The model for the all the nonelectrostatic intermolecular contributions to the lattice energy was an empirical repulsiondispersion model of the form:

U)

∑

i∈1,k∈ 2

1/2

(AιιAκκ)

exp(-(Bιι + Bκκ)Rik/2) -

Lewis et al. Table 1. Comparison of the Unit Cell Dimensions (Å) between the Previous 298 K12 and New Determination (150 K) of the Form i Crystal Structure of Barbituric Acid a (Å)

b (Å)

c (Å)

β (°)

V (Å3)

previous12 6.817(5) 14.310(5) 6.248(5) 118.57(1) 535.284a 298 K this work 6.7305(18) 14.029(4) 6.2309(16) 116.368(4) 527.1(2) 150 K a

No ESD given.

(CιιCκκ)1/2 Rik6

where atom i in molecule 1 is of type ι, and atom k in molecule 2 is of type κ. Parameters for atomic types N, O, and Hc (nonpolar) were taken from the work of Williams22,23 and HN from the derivation of the FIT potential24 where this DMAbased potential modeling scheme was extended to hydrogen bonding crystals. The corresponding carbon repulsion potentials proved to be too repulsive for the interplanar packing, as already noted for parabanic acid.25 Changing the parameter ACC to 277 180 kJ/mol was found to give a reasonable reproduction of the crystal structures of barbituric acid, parabanic acid, urazole, alloxan, and cyanuric acid. The hypothetical crystal structures for barbituric acid were generated by MOLPAK,26 which performs a systematic grid search on orientations of the rigid central molecule in 29 common coordination geometries of organic molecules, belonging the space groups P1, P1 h , P21, P21/c, Cc, C2/c, P21212, P212121, Pca21, Pna21, Pbcn, and Pbca, with one molecule in the asymmetric unit. Approximately 50 densest packings in each coordination type are then used as starting points for lattice energy minimization by DMAREL27 using the DMAbased model potential. The minimizations were constrained by the space group symmetry, but if this resulted in a negative eigenvalue of the second derivative matrix, indicating a transition state, the symmetry was lowered until a true minimum was found. The distinct low energy minima within 7 kJ/mol of the global minimum were established by consider-

Figure 1. Thermal ellipsoid plots (50%) level of (a) the barbituric acid molecule in Form i; (b) the molecules in the asymmetric unit of Form ii of barbituric acid, showing the planar and the envelope conformations of the molecules; and (c) 5-isopropylidene-barbituric acid. ing the reduced cell parameters28 (using PLATON29) and graph-set analysis30-34 to establish the hydrogen bonding motif.

Results Single crystals of Form i of barbituric acid, of a platelike morphology, were obtained from a saturated solution of ethanol crystallized at 0 °C in a sealed environment for several days. These were used to redetermine the crystal structure at 150 K (Table 3, Supporting Information) to give better data for the theoretical modeling (Table 1). The conformation of barbituric acid in Form i is an envelope as previously reported12 (Figure 1a), with the

Search for Barbituric Acid Polymorphs

Crystal Growth & Design, Vol. 4, No. 5, 2004 981

Table 2. Comparison of the Hydrogen Bonding for Two Determinations of Form i, and Form ii of Barbituric Acid hydrogen bonds (Å)

hydrogen bond angles (°)

form 298K

N(1)‚‚‚O(2) 2.90(1) N(3)‚‚‚O(6) 2.80(1)

∠N(1)H(1)O(2) ∠N(3)H(3)O(6) 149.7a

Form i 150 K

N(1)‚‚‚O(2) 2.8799(16) N(3)‚‚‚O(6) 2.8561(16)

∠N(1)H(1)O(2) 169.9(18) ∠N(3)H(3)O(6) 171.1(18)

Form ii

N(1A)‚‚‚O(4B) 2.854(2) N(3A)‚‚‚O(6A) 2.807(2) N(3B)‚‚‚O(6B) 2.868(2) N(1B)‚‚‚O(4A) 2.833(2)

∠N(1A)H(1A)O(4B) 169(3) ∠N(3A)H(3A)O(6A) 174(2) ∠N(3B)H(3B)O(6B) 166(2) ∠N(1B)H(1B)O(4A) 170(2)

i12

a

155.9a

graph setb

hydrogen bond motif

C1, 1(6) R2, 2(8) R4, 4(16) C1, 1(6) R2, 2(8) R4, 4(16) D1, 1(2) C1, 1(6) C1, 1(6)

infinite ribbons, two molecules wide infinite ribbons, two molecules wide sheet structure, with both molecules in the asymmetric unit contributing to each sheet

No ESD given. b For the first three levels only. Calculated using PLUTO.35 Table 3. Angles and ab Initio Energies for Various Conformations of Barbituric Acida Experimental Solid State Molecular Structures

“Gas Phase” Optimized

Form i X-ray (envelope)

Form ii A envelope

Form ii B planar

Form ii planar transition state

minimum envelope

14.094

22.627

1.244

0.044

21.107

10.791 7.535 9.689

10.423 9.346 10.670

0.530 2.530 20.924

0.000 0.00 1.185

15.620 15.750 0.000

angleb between mean planes C(6)C(5)C(4) and C(6)N(1)C(2)N(3)C(4) (°) dihedralb angle C(2)N(1)C(6)C(5) (°) dihedralb angle C(2)N(3)C(4)C(5) (°) relative energy ∆E/kJ mol-1

a Relative ab initio energies calculated at MP2/6-31G** level using Gaussian98.16 The experimental structures had been adjusted for the systematic foreshortening of bonds to hydrogen in X-ray structures. b Atomic labeling shown in Figure 1a.

Table 4. Reproduction of the Known Crystal Structures, by Lattice Energy Minimization Using DMAREL27a X-ray crystal structure molecular structure a/Å b/Å c/Å β/° cell volume/Å3 cell density /g cm-3 F valueb lattice energy kJ/mol

lattice energy minima

X-ray

Form i

Form i

Form i

6.731 14.029 6.231 116.368 527.125 1.614

expt 6.935 (3.03%) 14.223 (1.38%) 6.019 (-3.40%) 116.446 (0.07%) 537.919 (2.05%) 1.582 (-1.98%) 20.1 -103.672

opt 7.024 (4.35%) 14.148 (0.85%) 6.204 (-0.43%) 117.125 (0.65%) 548.757 (4.10%) 1.550 (-3.97%) 26.7 -98.815

lattice energy minima

Form ii

Form ii

Form ii

8.083 12.583 9.764 96.150 987.356 1.723

expt 8.019 (-0.79%) 12.479 (-0.83%) 9.998 (2.40%) 95.64 (-0.53%) 995.770 (0.85%) 1.709 (-0.82%) 14.9 -110.704

opt + planar transition state 8.142 (0.73%) 12.481 (-0.81%) 10.080 (3.24%) 95.302 (-0.88%) 1019.970 (3.30%) 1.668 (3.19%) 30.0 -102.905

a The % errors between the associated X-ray structure and the lattice energy minima are shown in brackets. All lattice energy minimizations used the same model potential (the FIT potential22-24 with the carbon repulsion potentials decreased by 25%). The electrostatic contribution to the lattice energy was obtained by summing all terms in the atom-atom multipole expansion37 up to R-5, using Ewald summation for the charge-charge, charge-dipole, and dipole-dipole contributions and direct summation over entire molecules whose centers were separated by up to 15 Å for the higher multipole interactions. b “Figure of shame”36 defined as F ) (∆θ/2)2 + (10∆x)2 + (100∆a/a)2 + (100∆b/b)2 + (100∆c/c)2 + ∆R2 + ∆β2 + ∆γ2, where ∆θ ) total rigid-body rotational displacement after minimization (°); ∆x ) total rigid-body translational displacement (Å); the other six terms depend on the changes in cell parameters (Å and °). The 0.5, 10, and 100 weighting factors bring the contributions from the different displacements to a comparable scale.

crystal structure consisting of infinite ribbons of pairs of hydrogen bonded molecules. In the new determination of the Form i structure of barbituric acid, the perpendicular distance between parallel ribbons is approximately 2.97 Å, compared to 3.03 Å reported previously.12 The closest approach between any pairs of atoms between the parallel ribbons is 2.84 and 3.15 Å for the new and old structures, respectively. The hydrogen bonds are similar in length in both structures (Table 2); however, in the lower temperature structure, the two hydrogens involved in the hydrogen bonding are closer to planar with the ring. A new polymorph of barbituric acid (Form ii) was crystallized, with platelike crystals with a prismatic habit, by slow evaporation over a number of weeks from either methanol or acetonitrile solution. Superior crystals were obtained from the slower crystallization from acetonitrile solution and a typical one used in the crystal structure determination (Table 4, Supporting Information). Form ii contains two crystallographically independent molecules in the asymmetric unit, one (A) with

Figure 2. The different conformations of barbituric acid in crystal structures and in ab initio calculations on the isolated molecule. Pink: Expt Form i; green: Expt Form ii envelope (A); blue: Expt Form ii planar (B); black: Expt dihydrate planar;38 purple: Ab initio optimized; red: optimized transition state, modeling Form ii planar.

the envelope conformation and the other (B) refining as if planar (Figure 1b). The thermal ellipsoid on C(5B) (Figure 1b), associated with the planar conformation, is slightly elongated perpendicular to the ring. This suggests that a static or a dynamic disorder is present in the crystal structure

982


Figure 3. Crystal structures of Forms i and ii of barbituric acid and their reproduction by the computational model. (a) The Form i experimental structure at 150 K (black) is contrasted with the lattice energy minimum (red) obtained starting from the experimental structure using the ab initio molecular structure (ExptMinOpt), and (b) the Form ii experimental structure at 150 K (black) is contrasted with the lattice energy minimum (red) obtained from the experimental structure using the ab initio envelope and transition state planar molecular structures.

of Form ii. However, the C(6B)-C(5B) and C(5B)-C(4B) bond lengths (1.485(3) and 1.489(3) Å, respectively) show no indication of the foreshortening normally associated with disorder. In the Form ii structure of barbituric acid, the hydrogen bonding consists of sheets, with each molecule lying in the same sheet. The perpendicular distance between each hydrogen bonding sheet in the structure is approximately 2.91 Å, and the closest approach between any pairs of atoms between the sheets is 2.84 Å. Form i and Form ii have different hydrogen bond motifs (Table 2) with the unique hydrogen bond acceptor

Lewis et al.

O(2) not involved in the hydrogen bonding in Form ii. This demonstrates that barbituric acid has the ability to use different hydrogen bond acceptors in its crystal structures, like other barbiturates,10 implying no great difference in the different acceptor strengths. In addition, concomitant polymorphism was observed from the acetonitrile solution, with smaller platelike crystals of Form i of barbituric acid forming on rapid evaporation. This was confirmed by powder X-ray diffraction. This suggests that Form i is the kinetic structure while Form ii is the thermodynamic form of barbituric acid. DSC results obtained from crystals of Form i only show a broad exotherm between 200 and 270 °C, consistent with decomposition of the sample. Evaporation of an acetone solution of barbituric acid gave platelike crystals, with a bladed habit. Solving and refining the crystal structure of this sample showed that 5-isopropylidene-barbituric acid had been formed (Figure 1c) in a previously undocumented reaction. Full crystallographic data on the compound are available in Table 5, Supporting Information. The flexibility of barbituric acid was also apparent from the ab initio calculations (Figure 2 and Table 3). Optimization at the MP2 level gave an envelope structure, which was very similar to the envelope structure of molecule A in Form ii. However, when the molecular structure is optimized as a planar molecule, this results in a transition state less than 1.2 kJ/mol above the optimal envelope conformation. This small energy barrier suggests that the various experimentally observed conformations of barbituric acid in the crystal structures (Figure 2) have virtually the same internal energy, to within a few kJ/mol. Thus, the actual observed envelope conformation and related dynamical flexing motions can be easily influenced by the crystal packing. (The differences in the MP2 energies for the experimental molec-

Figure 4. Plot of lattice energy against cell volume per molecule for all the structures corresponding to lattice energy minima found using the gas phase ab initio molecular structure for barbituric acid in the MOLPAK search. The corresponding minimum for the experimental structure (ExptMinOpt) is shown for comparison. The minima are denoted by the space group of the MOLPAK starting structure.



Table 5. Low Energy Crystal Structures of Barbituric Acida with the ab Initio Optimized Molecular Structure

structure

space group

lattice energy kJ mol-1

free energyb at 298 K kJ mol-1

density g cm-3

a/Å

b/Å

c/Å

angles/°

hydrogen bondd acceptors and motif

reduced cell parametersc

Expt 298 K

P21/c

1.589

6.248

6.691

14.310

γ 116.52

O2,O4

Expt 150 K

P21/c

1.614

6.231

6.731

14.029

γ 116.37

O2,O4

ExptMinOpt

P21/c

AM14 FC11 FC32 AQ30 AM42 CA25

infinite ribbons of dimers infinite ribbons of dimers infinite ribbons of dimers

-98.815

-113.89

1.550

6.204

6.935

14.148

γ 115.64

O2,O4

P21/c P21/c P21/c P212121 P21/c P1 h

-105.027 -104.277 -102.610 -102.302 -102.010 -101.635

-117.76 -116.46 -115.23 -116.08 -116.09 -114.62

1.711 1.709 1.662 1.657 1.663 1.636

4.470 6.482 6.485 6.371 6.048 5.265

9.779 8.000 7.825 7.543 6.955 5.430

11.517 10.141 10.542 10.681 12.685 9.276

β 98.97 R 108.83 R 106.87

O2,O6 O2,O4,O6 O2,O4,O6 O2,O6 O4,O6 O2,O6

chains 3D network sheets 3D network sheets infinite ribbons of dimers

AQ28 AQ13 FC38 BB2_39sg AK30sg DE27sg AH39sg

P212121 P212121 P21/c Pnma P21 P21/c P1 h

-101.586 -101.433 -101.300 -101.096 -100.932 -100.927 -100.849

-113.77 -115.07 -114.05 -115.46 -114.10 -113.77 -113.18

1.713 1.687 1.705 1.754 1.651 1.632 1.619

5.903 4.507 4.742 5.090 6.719 6.837 4.650

7.000 10.310 6.234 7.627 7.041 12.387 6.334

12.021 10.852 16.884 12.494 10.896 12.571 9.703

O2,O4,O6 O2,O6 O4,O6 O2 O2,O6 O4 O4,O6

3D network jagged sheets sheets chains 3D network chains chains

CD12sg DA39 CD26 AF39 AI36 CA26

P21/c Cc Pbcn P21 P21/c P1 h

-100.655 -100.605 -100.244 -99.780 -99.652 -99.404

-114.00 -111.29 -113.91 -111.58 -113.26 -111.28

1.711 1.624 1.734 1.717 1.646 1.700

8.202 6.858 8.255 4.968 6.899 6.398

10.150 7.950 10.723 6.183 8.601 6.675

12.191 9.610 11.070 8.350 8.726 7.021

γ 101.60 R 91.50 γ 93.02 β 105.20 R 93.72 R 108.95 β 103.48 γ 108.18

O2,O6 O4,O6 O2,O6 O4,O6 O4,O6 O2,O6

chains sheets jagged sheets sheets sheets chains

CA48

P1 h

-99.367

-111.76

1.967

5.816

7.082

7.208

R 104.20 β 107.01 γ 108.14

O2,O4

chains

AM49 CA18

P21/c P1 h

-99.362 -99.318

-114.307 -113.213

1.620

6.120 5.357

6.877 6.510

12.619 7.969

γ 98.44 R 92.88 β 96.36 γ 108.93

O4,O6 O2,O6

sheets infinite ribbons of dimers

CB38sg FA31 AI40 AI20 AQ19 AM 8 FC21 CD20 AQ6 DE23 DE8 BD15 CC11 AY2_32sg

P21/c P21/c P21/c P21/c P212121 P21/c P21/c Pbcn P212121 C2/c C2/c Pna21 Pbca P21

-99.296 -99.202 -99.158 -99.143 -99.086 -98.876 -98.83 -98.488 -98.342 -98.244 -98.178 -98.165 -98.119 -98.045

-113.831 -112.548 -112.163 -112.186 -113.288 -113.275 -113.283 -111.806 -111.524 -110.571 -110.469 -111.407 -111.549 -111.663

1.628 1.682 1.607 1.645 1.615 1.598 1.684 1.748 1.616 1.644 1.648 1.662 1.652 1.649

7.624 4.947 6.851 9.776 6.151 6.619 4.750 7.860 4.983 4.431 7.483 4.777 6.853 12.052

10.975 6.262 8.386 7.744 6.829 7.168 5.211 10.921 8.695 12.956 9.734 6.637 7.781 6.225

12.897 17.062 9.216 7.021 12.541 12.354 20.425 11.339 12.150 20.411 14.323 16.145 19.318 6.730

γ 104.34 γ 106.83 R 96.69 β 76.63

O2,O6 O2,O4 O4,O6 O4,O6 O4,O6 O4,O6 O2,O4 O2,O4,O6 O4,O6 O2,O6 O4,O6 O4,O6 O4,O6 O4,O6

3D network jagged sheets sheets sheets sheets chains jagged sheets 3D network chains jagged sheets sheets 3D network jagged sheets chains

γ 106.50 R 90.11 β 96.57 γ 99.23

β 91.778 R 90.73 R 101.61 R 108.39 β 99.67 γ 97.00

γ 114.69 R 91.95 R 107.43 R 98.44 γ 106.20

a All calculated structures are lattice energy minima calculated with the gas phase ab initio molecular model of barbituric acid and the same intermolecular potential. The hypothetical structures are labeled according to the initial MOLPAK coordination geometry and order of density, with “sg” denoting a minimum that required a lowering of the original space group symmetry. b The Helmholtz free energy as estimated from the lattice energy, zero point intermolecular energy, and temperature dependence of the rigid molecule internal energy and entropy, as derived from the k ) 0 second derivative properties.40 c The Niggli reduced cell parameters28 as calculated by PLATON29 are given for comparison. Only the reduced cell angles which are not 90° are tabulated. d O2 is the unique hydrogen bond acceptor, the cutoff for defining hydrogen bonds is 2.5 Å.

ular structures mainly reflect experimentally insignificant variations in bond lengths, which can produce sufficient changes in the total electronic energy to mask the genuine conformational differences.) The experimental crystal structures of the Form i and Form ii of barbituric acid are adequately reproduced

by lattice energy minimizations (Table 4) using the experimental molecular structure and the DMA-based model intermolecular potential. The 1.06% root-meansquare errors in the cell lengths when compared to the 150 K structure of Form i, and 0.3% for the 298 K structure12 are well within the uncertainties associ-

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Lewis et al.

Figure 5. Plot of lattice energy against cell volume per molecule for all the structures corresponding to lattice energy minima found using the solid-state experimental Form i molecular structure for the barbituric acid in the MOLPAK search. The corresponding minimum for the experimental structure (ExptMinExpt) is also shown for comparison. The minima are denoted by the space group of the MOLPAK starting structure.

ated39 with thermal effects in comparing a 0 K lattice energy minimum with a finite temperature structure. The crystal structures are still reasonably well reproduced when the molecular structures are replaced by the ab initio optimized envelope structure in Form i (1.06% rms error) and Form ii (molecule A) and planar transition state structure for molecule B in Form ii (Figure 3). This is despite the 7° difference between the experimental and ab initio envelope conformations in Form i (Figure 2). The calculated lattice energies (Table 4) show that Form ii is more stable than Form i, by a margin of between 4 and 10 kJ/mol, depending on the molecular model. Since the intramolecular energy loss for Form ii, for having half its molecules planar, appears to be less than 1 kJ/mol from the ab initio estimates, the total 0 K energy (Etot ) Ulattice + ∆Eintra) still favors Form ii. This agrees with the supposition from the experimental search that Form i is the kinetic structure, while Form ii is the thermodynamic form. Since the planar conformation of half the molecules in Form ii is producing a more stable crystal lattice, the molecule that refines as planar could actually be planar. The molecular flexibility of barbituric acid also affects the theoretical search to see whether any energetically feasible crystal structures could be predicted as potential polymorphs. A search for crystal structures corresponding to minima in the lattice energy, using the rigid ab initio gas-phase molecular structure should have found the minimum corresponding to Form i structure (ExptMinOpt), but failed to do so. However, as Figure 4 and Table 5 show, the search found many crystal structures within the 6.2 kJ/mol range in lattice energy between ExptMinOpt and the global minimum. The second computational search with the rigid Form i solidstate molecular structure, also failed to find the minima corresponding to Form i (ExptMinExpt). However, as Figure 5 and Table 6 demonstrate, the energy gap between the observed Form i and the global minimum has reduced to 2.8 kJ/mol, although there are still a

variety of different crystal structures that appear slightly more stable than Form i. Thus the 7° difference in the envelope conformation has a significant effect on the predictions. Despite this difference in the relative energies, there are still considerable similarities between the crystal structures found in the two searches. For example, the global minima in the two searches (AM14 Table 5, AM16 Table 6) are essentially the same crystal structure, differing primarily in the molecular envelope angle. Both searches find low energy structures in which all the carbonyl groups act as hydrogen bond acceptors, structures that use one unique and one nonunique acceptor (as in Form i) and structures in which only both nonunique carbonyls act as hydrogen bond acceptors (as in Form ii). Which of these low energy structures are potential polymorphs? Using estimates of the harmonic motions of the rigid molecules within the different crystal structures, the room temperature free energy gap between Form i and the hypothetical structures is reduced to about 4 kJ/mol for the optimized molecular structure and 1 kJ/mol for the experimental molecular structure. The changes in the intramolecular motions of the molecules in different crystal lattices might make an even more significant energetic contribution, given the low barrier for large changes in the envelope conformation. The majority of crystal structures in Tables 5 and 6 have elastic constants typical of organic molecules.41 However, many of the hydrogen-bonded sheet structures (FC32, AI40, and AM49 from Table 5 and AQ17, AI29, AQ45, and DD44 from Table 6) are predicted to have a low resistance to shearing forces. This may imply that the crystallites would be unlikely to grow. Thus, using this level of modeling the thermodynamic and kinetic factors involved in determining organic crystal structures, we can only eliminate a minority of the low energy crystal structures as unlikely to be observed.



Table 6. Low Energy Crystal Structures of Barbituric Acida Using the Experimental Form i molecular structure free energyb at 298 K kJ mol-1

a/Å

b/Å

c/Å

angles/°


Expt 298 K

P21/c

1.589

6.248

6.691

14.310

γ 116.52

O2,O4

Expt 150 K

P21/c

1.614

6.231

6.731

14.029

γ 116.37

O2,O4

ExptMinExpt

P21/c

-103.672

-118.03

1.582

6.092

6.897

14.223

γ 115.81

O2,O4

AM16 FC23 AM2_30 sg

P21/c P21/c P1 h

-106.473 -105.549 -105.381

-119.12 -117.83 -117.96

1.784 1.774 1.729

4.494 6.249 5.204

9.629 7.958 10.000

11.158 10.277 10.625

β 99.12 R 110.21 R 67.02 R 86.05 β 75.29

O2,O4 O2,O4,O6 O4,O6

chains 3D network sheets

AZ42 AK38 AQ22 AB17

P212121 P21/c P212121 P1 h

-104.555 -104.510 -104.343 -103.839

-118.02 -117.08 -116.55 -116.39

1.771 1.772 1.774 1.710

6.733 6.224 5.808 5.235

7.003 7.913 6.925 5.349

10.542 10.360 11.927 9.070

O2,O4 O2,O4,O6 O2,O4,O6 O2,O4

3D network 3D network 3D network infinite ribbons of dimers

AQ32 AQ27 AK31 DB2_16 sg

P212121 P212121 P21/c P1

-103.837 -103.775 -103.735 -103.694

-117.17 -117.14 -117.41 -116.10

1.756 1.765 1.821 1.710

4.870 4.588 5.053 6.825

9.850 10.215 7.566 8.107

10.100 10.284 12.223 10.036

O2,O4 O2,O6 O2 O2,O6

jagged sheets jagged sheets chains infinite ribbons of dimers

AB10

P1 h

-103.687

-117.08

1.718

5.277

6.323

7.914

R 93.44 β 97.02 γ 108.27

O2,O4

infinite ribbons of dimers

DD2_34 sg

P1 h

-103.680

-117.42

1.710

6.825

8.108

9.036

R 92.97 β 94.64 γ 90.41

O2,O4


AB40

P1 h

-103.574

-116.041

1.71

5.291

5.325

8.998

R 94.61 β 90.19 γ 99.98

O2,O6


DA29 AZ47

Cc P212121

-103.126 -102.652

-113.658 -116.302

1.704 1.789

6.773 4.907

7.88 5.014

9.356 19.332

R 91.30

O4,O6 O2,O4

FC40 FC18 FC32 AK21 FA43

P21/c P21/c P21/c P21/c P21/c

-102.635 -102.588 -102.528 -102.512 -102.230

-116.429 -115.262 -115.936 -116.048 -115.341

1.772 1.759 1.69 1.716 1.767

4.793 4.884 6.362 6.799 4.862

5.029 5.982 7.731 8 8.23 6.174

19.935 16.561 10.61 8.868 16.706

R 92.39 β 90.97 R 106.18 R 92.49 γ 106.24

O2,O4 O4,O6 O2,O4,O6 O4,O6 O2,O6

FA33 DA2_45 sg

P21/c P1

-102.015 -101.924

-114.824 -111.982

1.75 1.792

4.636 4.985

6.413 10.127

16.385 10.207

γ 93.27 R 72.49 β 77.82 γ 78.34

O4,O6 O4,O6

sheets infinite ribbons of dimers jagged sheets jagged sheets sheets sheets infinite ribbons of dimers jagged sheets chains

AM40 DC32

P21/c C2/c

-101.780 -101.745

-116.10 -115.78

1.737 1.630

6.209 6.049

7.095 12.294

12.333 14.376

γ 115.65 R 102.51

O4 O2,O4

AQ17 AK24 AM19 AI32 AK20 AF28 AI29 AB26

P212121 P21/c P21/c P21/c P21/c P21 P21/c P1 h

-101.681 -101.618 -101.570 -101.425 -101.392 -101.380 -101.380 -101.265

-116.37 -114.82 -115.02 -115.77 -113.58 -113.22 -114.44 -113.44

1.764 1.776 1.787 1.775 1.773 1.770 1.683 1.710

6.157 6.661 4.118 6.138 5.635 5.009 6.763 4.804

7.397 7.164 9.810 7.395 8.412 6.056 8.100 6.117

10.592 10.255 11.822 10.576 10.737 8.215 9.226 9.169

BD9 CB25 AQ45 CA36

Pna21 Pbca P212121 P1 h

-101.108 -101.056 -101.013 -100.914

-113.81 -114.06 -115.79 -113.57

1.750 1.738 1.681 1.739

4.845 7.265 6.088 5.483

6.449 8.099 6.745 6.334

15.555 16.638 12.326 7.897

AQ18 AI34 CD35 DE47 DD44

P212121 P21/c Pbcn C2/c C2/c

-100.554 -99.989 -99.830 -99.775 -99.626

-113.93 -113.65 -113.40 -112.36 -112.24

1.777 1.753 1.814 1.736 1.770

5.106 6.107 7.809 5.073 6.232

5.505 8.963 10.644 12.026 10.383

17.036 9.658 11.287 16.094 14.883

structure

space group


reduced cellc density g cm-3

R 109.79 R 91.26 β 96.00 γ 99.68

R 90.01 R 110.8 β 105.3 γ 90.37

β 101.74 γ 94.53 β 93.32 R 109.46 β 105.40 R 90.52 R 106.27 β 99.86 γ 99.04

R 77.63 β 77.43 γ 67.45 R 113.13 R 92.84 R 93.63

infinite ribbons of dimers infinite ribbons of dimers infinite ribbons of dimers

O4,O6 O2,O6 O2,O6 O4,O6 O2,O6 O4,O6 O4,O6 O4,O6

chains infinite ribbons of dimers sheets jagged sheets chains sheets 3D network sheets sheets chains

O4,O6 O4,O6 O4,O6 O2,O4

3D network jagged sheets sheets chains

O4,O6 O2,O6 O2,O4,O6 O2,O6 O2,O6

3D network jagged sheets 3D network jagged sheets jagged sheets

986


Lewis et al.

Table 6 (Continued)

space group


free energyb at 298 K kJ mol-1

density g cm-3

a/Å

b/Å

c/Å

angles/°


AV2_37 sg DD31

Pc C2/c

-99.445 -99.338

-113.72 -113.83

1.817 1.678

6.549 6.865

7.539 7.633

10.182 19.345

γ 111.32 R 90.9

O2,O6 O2,O4

AM24 DE2_14 sg AI42 AP2_36 sg CA14

P21/c P21/c P21/c P21 P1 h

-99.291 -99.275 -99.175 -99.085 -99.058

-113.37 -114.48 -114.57 -113.01 -111.876

1.750 1.734 1.693 1.729 1.775

5.156 4.817 6.452 6.896 5.509

7.541 10.163 6.821 7.074 7.026

12.505 20.408 11.501 10.348 7.292

β 90.50 R 100.71 β 96.84 R 102.89 R 100.28 β 106.92 γ 110.77

O2,O4 O2 O2,O6 O2,O6 O2,O4

structure

reduced cellc

3D network inf inite ribbons of dimers 3D network dimers ribbons jagged sheets chains

a All calculated structures are lattice energy minima calculated with the Form i solid-state molecular model and the same intermolecular potential. The hypothetical structures are labeled according to the initial MOLPAK coordination geometry and order of density, with “sg” denoting a minimum that required a lowering of the original space group symmetry. b The Helmholtz free energy as estimated from the lattice energy, zero point intermolecular energy and temperature dependence of the rigid molecule internal energy and entropy, as derived from the k ) 0 second derivative properties.40 c The Niggli reduced cell parameters28 as calculated by PLATON29 are given for comparison. Only the reduced cell angles which are not 90° are tabulated. d O2 is the unique hydrogen bond acceptor, the cutoff for defining hydrogen bonds is 2.5 Å.

Conclusions The discovery of Form ii of barbituric acid is significant, because it uses different hydrogen-bond acceptors from Form i. It is also unusual in that it has two conformations of barbituric acid in the asymmetric unit, and seems to be the thermodynamically more stable form. The thermal ellipsoids on the molecule that refines as planar suggests static or dynamic disorder within the crystal structure of Form ii of barbituric acid. The ab initio calculations show that a planar molecular structure forms a transition state between two equivalent ∼20° envelope conformations, with a very low energy barrier of a few kJ/mol. The rigid-molecule crystal structure modeling using a planar and envelope molecular structures show that the improved intermolecular interactions in Form ii more than compensate for the intramolecular energy required for a planar molecule. Hence, it is plausible that Form ii may contain a planar molecule, and the thermal ellipsoids indicate genuine vibrations. Barbituric acid is also planar in the dihydrate crystal structure,38,42 although the thermal displacement parameters also show evidence of the flexibility within the molecular structure of barbituric acid observed in Form ii. The flexibility of barbituric acid, observed in both its polymorphs and the gas phase modeling, has been shown to have a major effect on the relative energies of the hypothetical low-energy crystal structures found in the search. The key finding is that there are a wide variety of crystal structures that are very similar in energy, which differ in their hydrogen-bonding motifs and acceptors. Thus, it is unlikely that there is a significant difference in the hydrogen-bonding ability of the unique and equivalent carbonyls. Although we have found a large number of low energy crystal structures of barbituric acid in the searches with two molecular conformations (Tables 5 and 6), there are likely to be many more, given the range of conformations that could be adopted, and the limitations of the search. Dealing computationally with Form ii was outside the capabilities of the search due to having two molecules in the asymmetric unit, let alone one of them being a planar conformation. The searches, although limited by the standards of most current crystal structure predic-

tion work, should have found Form i. The failure may arise from using MOLPAK to generate densely packed structures as starting points for the search, as Form i (as represented by ExptMinExpt or ExptMinOpt) is significantly less dense than the lower energy crystal structures. This density difference may mean that the relative energy ordering may be changed by plausible variations in the model intermolecular potential (particularly the dispersion coefficients) or better modeling of both intra- and intermolecular contributions to the room temperature energy. Even though only one new polymorph of barbituric acid was found in the laboratory, the searches indicate that there could be more potential polymorphs. Indeed, preliminary results with a high-throughput robotic screen43 are promising. Nevertheless, experimentally establishing and understanding the polymorphism of barbituric acid will provide a major challenge to computational polymorph prediction. Acknowledgment. We would like to thank Miguel Calles, Matt Peterson, and O ¨ rn Almarsson of Transform Pharmaceuticals Inc. for some collaborative discussions, and Marianne Odlyha for the DSC analysis. This research was supported by EPSRC funding for T.C.L. and was a preliminary to a Basic Technology Program on polymorphism, funded by the Research Councils U.K. Supporting Information Available: A comparison of the geometrical parameters for the different conformations of barbituric acid found in the crystals structures (Table 1), selected bond lengths and angles of 5-isopropylidene-barbituric acid (Table 2), the crystallographic data for Form i anhydrous barbituric acid (Table 3), Form ii of barbituric acid (Table 4) and 5-isopropylidene barbituric acid (Table 5). The experimental crystallization conditions considered in the search (Table 6). X-ray crystallographic files (CIF) are available for Form i and Form ii of barbituric acid, and 5-isopropylidene barbituric acid. This material is available free of charge via the Internet at http://pubs.acs.org.

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CG034209A

An Experimental and Theoretical Search for Polymorphs of Barbituric

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