J . Phys. Chem. 1991, 95, 8948-8955
8948
Molecular Packhg and Other Structural Properties of Crystalline Oxohydrocarbons A. Gavezzotti Dipartimento di Chimica Fisica ed Elettrochimica e Centro CNR, Uniuersitb di Milano, Milano, Italy (Received: April 19, 1991)
The crystal structures of 590 oxohydrocarbons, here meaning organic molecules containing C, H, and 0 atoms without O-H.-O hydrogen bonding, have been retrieved from the Cambridge Structural Database. Hydrogen atoms have been placed in calculated positions by an automatic procedure based on the geometry of the C-atom coordination sphere. Two sets of literature parameters for the calculation of packing energies are compared. Statistical analyses of molecular and crystal parameters have been performed, in comparison with those of hydrocarbon compounds. Correlations between molecular size and shape and calculated packing energies are proposed; deviations appear, pointing to electrostatic and partial H-bond contributions in oxohydrocarbons. Schemes for the prediction of sublimation energies are given. The crystal density increases with oxygen content; as shown by principal component analysis, molecular size and shape, so important for hydrocarbon crystals, do not mix into this correlation. Packing coefficients are just slightly lower than for hydrocarbons, showing no clear sign of breakdown of close packing. The presence of short-range 0..H and 0..Cattractive interactions is detected by a survey of deviations from the average atomic contributions to the lattice energy for each species (homomeric principle). A supplementary attractive term in the crystal potential is derived to account for these interactions.
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1. introduction In previous work' several properties of crystalline hydrocarbons were analyzed by using a sample of 391 crystal structures retrieved from the Cambridge Structural Database2 (CSD). The aims of such work are to find the general principles of the molecular self-recognition that determine the solid-state structure of organic compounds and to correlate molecular structure with crystal structure, aiming at the control and prediction of organic crystal s t r ~ c t u r e . ~This task is more difficult when directional forces are weak, but its accomplishment for the basic building blocks of organic chemistry must provide the groundwork for more general applications. Empirical crystal potentials are more easily derived, and hence more readily available, for moderately polar substances, so that we have chosen to start from the least polar compounds and to proceed toward increasing molecular polarity. The first extension of the work on hydrocarbons' is to consider ternary compounds, and this paper describes a statistical analysis of the crystal properties of oxohydrocarbons not forming hydrogen bonds (a restricted sample of monoketones and mononitriles has already been studied4). The next steps will be a parallel analysis of compounds containing nitrogen and, eventually, the establishment of combination rules to deal with systems containing C, H,N, and 0. Given the spectacular impulse of research in the field of molecular recognition and drug design, such studies are very promising, since the forces that preside over these phenomena are not dissimilar from those at work in crystal packing.
TABLE II: Averages and Ranges of Some Molecular Properties within the Database
range property"
W,,,, Da Sm, A2 Vm, A' ~a,,
~~
~~
max
576 605 529 88 0.500 0.661 1.105
of carbon to oxygen atoms larger than 5, with some exceptions, were excluded and, for the larger molecules with more than three oxygen atoms, an upper limit of 0.05 was imposed on the conventional R factor. Hydrogen atom positions were often unavailable, and are always unreliable when determined by X-ray diffraction. The problem was solved in a general way, using geometrical criteria to determine automatically the valence sphere of each carbon atom on the basis of standard C-C and C 4 bond distancess and hence the number of hydrogens to be assigned to each carbon atom; the actual placement was then carried out according to previously described'" geometrical criteria. The procedure is a significant improvement over the one adopted for hydrocarbonsia (details are given in Appendix I). The final data set consisted of 590 crystal structures; by definition, it contains any combination of ether, epoxide, ester, anhydride, lactone, aldehyde and peroxide functional groups. Table I (supplementary material) collects the CSD refcodes. No subdivision into structural groups (as defined for hydrocarbons) was attempted here, since the focus is on the effect of the inclusion of heteroatoms, the effects of gross molecular shape and of chemical nature having already been studied, to the extent possible, with hydrocarbon crystals. Table I1 summaries the size and stoichiometry of the compounds included in the data set. 3. Calculation of Molecular and Crystal Properties A number of molecular and crystal properties can be calculated for each compound, starting from the basic structural data (cell parameters, space group symmetry, and atomic coordinates). Most of them are defined in ref 1 ; Appendix I1 gives a summary. In
~~
( I ) (a) Gavezzotti, A. J. Am. Chem. Soc. 1989,111, 1835. (b) Gaveuotti, A. Acra Crysrallogr., Secr. B 1990, 46, 215. (2) Data for the present work are from the 1989 release. See: Allen, F. H.; Bellard, S.;Brice, M.D.; Cartwright, C. A.; Doubleday, A,; Higgs, H.; Hummelink, T.; Hummelink-Peters, B. J.; Kennard, 0.;Motherwell, W. D. S.;Rodgers, J. R.; Watson, D. G.Acta Crysrallogr.,Secr. B 1979, 35, 2331. (3) (a) Desiraju, G.R. Crysrol Engineering Elsevier: Amsterdam, 1989. (b) Gavezzotti. A. J. Am. Chem. Soc. 1991, 113, 4622. (4) Gavezzotti, A. J. Phys. Chem. 1990, 94, 4319.
( 5 ) Allen, F. H.; Kennard, 0.;Watson, D. G.; Brammer, L.; Orpen, A. G.; Taylor, R. J. Chem. Soc., Perkin Trans. 2 1987, SI. (6) Taylor, R.; Kennard, 0. J. Am. Chem. Soc. 1982, 104, 5063.
0022-365419 , 1 ,12095-8948502.5010 0 1991 American Chemical Societv I
min 87 97 72 9 0.02 1 0.020 0.061
NP SP ZP "See the Appendix for the definition of symbols.
2. Retrieval from CSD and Placement of Hydrogen Atoms The CSD was searched for crystal structures containing C, H, and 0 atoms with crystal coordinates for all non-H atoms, at room temperature, without disorder or unresolved ambiguities. Compounds with 0-H bonds, charged residues, or solvate or clathrate molecules were excluded. Structures with more than one molecule in the asymmetric unit were rejected: they pose a small technical problem in many calculations and do not provide significant additional information (the problem of why a molecule takes this option in the crystal is, anyway, too difficult to be addressed at this stage). Since the number of available structures was very large (2636 hits in the primary search), molecules with a ratio ~
av 276 289 247 38 0.133 0.177 0.332
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Properties of Crystalline Oxohydrocarbons addition, indices to describe the extent of oxygenation (polar part of the molecule) were constructed:
Np = N(Ox)/(N(C) + N(H))
z, = Z(OX)/(Z(C) + Z ( W ) where N is the number of atoms of each species and 5' and Z denote the total surface and the total number of valence electrons provided by each species. S, and Z, have a wider range than N,, as seen in Table 11, since each atom is weighted by its surface or number of electrons.
4. Discussion of the Parametrization Many calculated properties of the molecules (volume, surface) and of the crystal (short intermolecular contacts) depend on the choice of atomic radii. The radius for oxygen is in the range 1.4-1.5 A, as already discussed in a packing analysis context.6 We have used 1.4 A as in previous work? but we have calculated an average correction for the molecular volume if 1.5 A is used: over a sample of 33 molecules with 7 to 15 oxygen atoms, this correction was consistently found to be 1 A' per oxygen atom. The crystal packing energies (PE = PPE, packing potential energy) have been calculated by using empirical atom-atom potentials of the 6-exp type, without explicit Coulombic (that is, R 1 ) terms. The parameters' are quite general and therefore particularly appealing for application to a large number of crystals. A cutoff distance of 7 A in the lattice sums was imposed, so that we call this scheme Mirsky-7 A, or M7. A more accurate formulation has been proposed for a restricted set of oxohydrocarbons by Williams and co-workers,* including Coulomb terms and accelerated convergence of lattice sums (we call this scheme Coulomb-convergent Williams, or CCW). Unfortunately this parametrization is not readily transferable and is not applicable to larger molecules, since atomic charges must be evaluated for each molecule by fitting its electrostatic potential as derived from a high-quality ab initio wavefunction. Other empirical schemes for oxygen-containing crystals9 are also not suitable for large-scale application, requiring hardly justifiable transfers of parameters optimized for restricted classes of compounds, or again the evaluation of ad hoc atomic charges,9a and more complex geometric calculations.w This leaves the parameter set used here as an almost compulsory choice. Among its previous uses we may mention a molecular dynamics study of liquid dimethoxyethane, where the heat of vaporization was correctly predicted.I0 The M7 set was checked against the CCW set in two ways. First, the CCW PE was calculated without Coulombic contributions and using a 7-A cutoff, and the ratio of this PE to the M7 PE was computed. The averages were 93% over 20 molecules with one oxygen atom (range 84-IOI), 91% over 24 molecules with two oxygen atoms (range 83-102), and 83% over 18 molecules with more than four oxygen atoms (range 73-93). These results are roughly in agreement with the percentage of PE usually attributed to R'terms;8J1 as long as these terms actually describe the crystal Coulombic energy, these results also demonstrate the the M7 scheme reproduces at least part of this energy, although it does not contain Coulombic terms. Second, the PE of some (7) Mirsky, K.V. In Compuring in Crystallography. Proceedings of an Iniernarional Summer School on Crystallographic Compuring, Schenk, H., Olthof-Hazenkamp, R., Van Koningsveld, H., Bassi, G. C., Eds.; Delft University Press: Twente, The Netherlands, 1978; pp 169-182. The parameters used here for contacts to oxygen are essentially those of Kitaigorodski et al.: Kitaigorodski, A. 1.; Mirskaya, K. V.; Nauchitel, V. V. Sou. Phy8.Crysiallogr. (Engl. Transl.) 1970, 14, 769. (8) Cox, S.R.; Hsu, L. Y.; Williams, D. E. Acra Crystallogr., Sect. A 1981, 37, 293. (9) (a) Hagler, A. T.; Huler, E.; Lifson, S . J . Am. Chem. SOC.1974, 96, 5319. (b) Derissen, J. L.;Smit, P. H. Acra Crysrallogr., Sect. A 1978, 34, 842. (c) Dauber, P.; Hagler, A. T. Acc. Chem. Res. 1980, 13, 105. (d) Berkovitch-Yellin. Z.: Leiserowitz, L. J . Am. Chem. SOC.1982, 104, 4052. (IO) Bressanini. D.;Gamba, A.; Morosi, G. J. fhys. Chem. 1990,94,4299. ( 1 1 ) Williams, D. E.: Starr, T. L. Compur. Chem. 1977, I , 173.
The Journal of Physical Chemistry, Vol. 95, No. 22, 1991 8949 TABLE III: Heats of Sublimation and Calculated Packing Energies: ComDarison of Two Parameter Sets' calcd PE molecule TROXAN TOXOCN SUCANH
CYHEXO BNZQUI
AH,,< M 7 ( e ~ t ) ~ M7(conv)" 13.8 11.8 10.6 15.6 14.0 19.0 19.6 12.2 10.9 13.1 20.2 14.5 16.3 11.0 10.2
CCW' total p ch
11.3 17.2
16.1 15.5 12.6
3.3 5.2 6.3 4.0 2.8
In units of kcal mol-'. bExperimental; see footnote to Table IX for literature references. Estimated as PE/0.8. "Convergence of lattice sums by PCK83,I2 without structure optimization. Without structure optimization; p ch is the Coulombic point-charge part.
TABLE IV: Parameters for the Linear Regression PPE = JIX + b or PPE=aX+bY+P x or x,yb (I b c S' 4.3 Nnon-H 1.55 12.9 1.40 18.3 5.9 Wm 0.1 10 13.8 4.5 0.1 12 17.2 5.9 Z" 0.218 14.3 4.7 0.303 16.2 6.0 Vm 0.124 13.4 4.4 0.117 16.3 6.6 sm 0.1 1 1 12.1 4.4 0.114 13.8 7.1 s250 0.109 5.32 4.3 0.119 6.60 6.3 -6.4 4.1 s250, c,,, 0.120 23.2 0.131 28.4 -8.8 5.9 7.4 4.0 s250, z, 0.117 -8.62 a First row, oxohydrocarbons; second row, hydrocarbons.Ib bSee the Appendix for the definition of symbols. Root-mean-square deviation.
compounds used in the derivation of the CCW set (for which atomic charges are available) was computed,'* and the results are shown in Table 111. There is moderate agreement between M7 and CCW energies, except for succinic anhydride, where the M7 value misses a substantial amount of cohesive energy. Both parameter sets fall somewhat short of reproducing the experimental sublimation energies. However, if the crystal structure (cell dimensions and molecular rigid-body positional parameters) is relaxed under the action of the potential, the M7 functions yield deviations from the observed structure much larger than those obtained using the CCW set, which is in this respect clearly superior. The number of short C. e 0 or He. -0interactions increases with increasing oxygen content and bond polarity. For a large portion of our sample, their influence on the calculated packing energy is small, so that the overall statistics are reliable. In contrast, the M7 potentials miss a substantial part of the cohesive energy for small-size compounds with high Z,. The reasons for this are explained in a special section of the paper, dealing with the particular C-He. a 0 and C-0.. .C interactions appearing in these crystals.
5. PPE-Size Correlations Relative to the space-group statistics for general organic comp o u n d ~ , ~there ' is a high percentage of P2, and P212121crystal structures among oxohydrocarbons, but many compounds are natural ones (especially sugars) occurring is resolved form, so that the choice of a non-centrosymmetric space group is a forced one. An analysis of the spatial symmetry in C, H, N, and 0 containing crystals is described in a separate paper.I4 (12) The calculation was done by using program ~ 1 2 ~ 8(QCPE 3 548; Quantum Chemistry Program Exchange, Indiana University, Bloomington, IN) by D. E. Williams; see refs 8 and 1 1 for a detailed description and the parameters used. (13) Mighell, A. D.; Himes, V. L.;Rodgers, J. R. Acfa Crysrallogr. 1983, A39, 737.
8950 The Journal of Physical Chemistry, Vol. 95, No. 22, 1991 CHART I 0
v
u
HYFURN
FOWBAU
CABBIQ 01
TlKlND
SUCANH
CIMNUH
COZREPIO
DMKETO02
HPDALA
BNZWl
MLEICA
TABLE VI: Panmetera of Crystal Compact" no. of Z,range crystals D, D, 0.0-0.2 149 1.226 0.397 0.2-0.4 280 1.289 0.414 101 1.364 0.434 0.4-0.6 0.6-0.8 49 1.372 0.437 11 1.508 0.472 >0.8 all oxohydrocarbons 590 1.297 0.416 all hydrocarbons 391 1.198 0.387
CK
CKb
0.704 0.697 0.690 0.676 0.697 0.696 0.717
0.710 0.708 0.708 0.698 0.724 0.708
'See the Appendix for definitions of the symbols. With an oxygen atomic radius of 1.50 A.
TMVCBO
BlCVlS
Gavezzotti
/\ MDNEF
CORZAK
TABLE V Heats of Sublimation and Calculated Packing Energies for Comwunds Whose Crvstal Structure Is Not Available estimated Mtub' exptl compound AH..,h Zw N-.U 24.5b diphenyl oxalate 24.5 25.5 23.p benzoic anhydride 23.5 24.5 18.W 23.5 dibenzoylmethane 24.5 17.6d 14.5 13.9 cyclobutane-I ,3-dione 13.Ic 14.5 13.9 cyclobutane-1,2-dione 2-oxabicyclo[2.2.2]otan-3~ .one 16.6' 17.6 16.8 bicyclo[2.2.1]heptan-2-one 1 I,?' 16.6 15.8 bicyclo[2.2.l]heptan-7-one 11.3' 16.6 15.8 glycolide 21.2* 16.6 15.8
"From correlations in Table 1V. bCarson, A. S.;Fine, D. H.; Gray, P.; Laye, P. G. J. Chem. Soc. B 1971, 1611. cWood, J. L.; Jones, M. M. J. Inorg. Nucl. Chem. 1967, 29, 113. dChickw, J. S.;Shenvood, D. E.; Jug, K. J. Org. Chem. 1978,43, 1146. cCao, J. R.; Back, R. A. Can. J . Chem. 1985, 63,2945. IAndruzzi, F.; Pilcher, G.; Hacking, J. M.; Cavell, S . Mokromol. Chem. 1980, 181, 923. Weele, W. V. J . Chem. Thermodyn. 1978, 10, 585. hChem. Abstr. 1980, 92, 22892~. Original work unavailable. Glycolide is 1,4-dioxacyclohexane-2,5dione. The calculated PPE correlates with the usual molecular size descriptors (Table IV); the correlation parameters are quite similar to those for hydrocarbons. The heat of sublimation can be estimated from these correlations ad AH(sub) = '/,(PPE/O.B), as proposed earlier.' Chart I shows structural formulas for some (nearly all) compounds for which the PPE predicted by the correlation to S2Mis larger (deviation > 20%) than that actually calculated. They are small-size, high oxygen content compounds. On one hand, as for hydrocarbons, the correlations tend to overestimate the PPE for small molecules; on the other hand, the substances in the scheme may have large electrostatic or pseudo-H-bond contributions to PPE. Table 1V shows that size (as described by S2m)and oxygen content (as described by 2,or S,)work at cross purposes (the signs of their coefficients in the correlation are opposite). The inclusion of Zpmimics the artifact resulting from the missing contributions to cohesive energy in small-size molecules. In the calculation of S250.the oxygen surface is largely overestimated; the lattice energies predicted by the correlation with this quantity (see also the further discussion and Table IX) are rather good approximations to sublimation heats, presumably due to a cancellation of errors. Table V shows the fair agreement obtained (14) Filippini, G.; Gavezzotti. A., submitted for publication.
TABLE VII: Commition of the Factorsa factor components eigenvalue of matrix C D. D1 . W- Z. C,W F, ox. 3.09 0.95 0.95 -0.75 hyd 3.23 0.61 0.57 0.92 0.89 -0.49 -0.33 ox. 2.49 0.96 0.97 hyd 1.35 -0.77 -0.80 0.24 0.30 -0.51 0.22 0.34 0.94 ox. 1.15 hyd 1.06 0.15 0.15 0.52 0.86 ~
R. 0.83 0.74
Z. 0.13
0.78 0.36 0.33 -0.15 0.26
"Coefficients smaller than 0.1 have been omitted. Ox, oxohydrocarbons; hyd, hydrocarbons. See the Appendix for definitions of the symbols. 1.80
-
1.60
-
1.00
+ r & m + m "
0.20
0.40
0.
a 0.80
1.00
!O
Figure 1. A scatter plot of the crystal density (g/cm3) against Z, (see text for its definition). Horizontal bars mark the average value for each section. The dashed line is the lower threshold (see text for its equation).
between calculated PE and sublimation heats for some compounds whose crystal structure and S250are unavailable. A discussion on the details of the discrepancies is not warranted, since the solids may be affected by disorder or other anomalies. 6. Close Packing in Oxobydrocarbons Table VI reports the observed crystal densities and other packing parameters for oxohydrocarbons. There is a clear increase in crystal density on increasing oxygen content, as expected since oxygen is heavier. Figure 1 shows that the crystal density cannot be less than 0, = 0.42, 1.O g/cm3. Much less clear-cut is the case of C,. A decrease appears on increasing Z,,but only if the oxygen atomic radius is taken as 1.40 A. If 1.SO is used, and the volumes are corrected as previously described, the average C, in oxohydrocarbons closely approaches that for hydrocarbons. Thus, there is no compelling reason to believe that non-hydrogen-bonded oxygen-containing compounds deviate significantly from close packing in crystals. Actually, the few molecules with Z , 7 0.8 have some of the highest packing coefficients of the whole sample, while a reason for the slight drop in CKfor 0.6 < Zp< 0.8 may be that many polyacetylated sugars fall in this category, and
+
The Journal of Physical Chemistry, Vol. 95, No. 22, 1991 8951
Properties of Crystalline Oxohydrocarbons TABLE VIIk Average Volumes and Surfaces for Atoms in Molecules and Atomic Contributions to PPE no. E(i ) of hits" V,A3 S, A2 ox. atom hyd 0.64 0.67 6.58 10738 2.3 H oxygen atoms
n
l a
~~
=o
-0-
-0-o-
1062 1444 20
6.6 3.7 6.1
13.1 7.24 8.96
1.59 1.39 1.41
688 751 889 357 897 25 367 1346 86 549 136 65 128 318
13.6 10.9 8.3 17.7 15.3 16.5 14.1 11.9 13.0 10.7 8.5 9.6 7.3 5.2
10.1 7.56 5.28 14.7 11.9 11.5 8.88 6.87 5.79 4.79 3.56 2.09 1.76 0.96
1.62 1.58 1.42 2.20 1.88 2.29 1.78 1.64 1.49 1.42 1.32 1.34 1.18 1.03
-z W
carbon atomsb
(oocc)c (0CCC)C (CCCC)C
1.32 1.74
I .69 Ei
1.32 160
I
A B C
I I1
"In oxohydrocarbons. bCentral one in each scheme.
t
3000
lZO
2000 40
h LU
Y
z lo00
I d 1.2
0 0
0.4
(
Ei (HI Figure 2. Histogram of atomic contributions to PPE from H atoms (see Appendix 11 for the definition; kcal/mol units). The first slot at the left counts also atoms with an overall repulsive (positive) contribution. dangling COCH3residues usually have very high thermal factors in crystal^.'^ One often overlooked aspect of close-packing is that the amount of space occupied by atomic groups must also take into account the space required to allow intramolecular libration. Table VI1 shows the results of a principal-component analysis of molecular and crystal properties. D, and Del are high for a compact crystal; W,,, and 2"represent molecular size; C,, is high for a regular shape; R, is small for spherical objects; F, is high for cylindrical molecules. 2,represents the oxygen content. From the factor loadings corresponding to the highest eigenvalue, one sees covariant size and R, and contravariant C,; larger molecules deviate from regular or spherical shape. For hydrocarbons, the (1 5) A striking example is provided by phyllanthosehexaacetate (CSD refcode CAVBEGIO N a s i m k n i , R. L.; Niven, M. L.; Cragg, G. M.; Pettit, G. R. Acto Crystollogr. 1985. CII, 728). a disaccharide where the average Uq for the 12-ring atoms is 0.044(range 0.039-0.0S3),while the average for the 18 atoms of the COCH, groups is 0.081 (range 0.052-0.121).
0
L
-
I
0
0.4
(
1.2
2.0
2.4
Ei
Figure 3. Histogram of the oxygen contributions to PPE. The vertical bars are the averages for different numbers of non-H atoms bound to the two atoms attached to oxygen: 6-7, 4-5, and 2-3 atoms for A, B, and C, respectively. Dashed areas: repulsive contacts in the 2-3-A shell around the atom are present, although the overall contribution is still attractive. same eigenvector contains contributions from D, and Del,while for oxohydrocarbons the correlation to crystal compactness is mostly absorbed by Z,,as seen from the loadings in the second eigenvector. In the simplest interpretation, therefore, dense hydrocarbon crystals require large molecules of regular shape (a typical example are planar polyaromatics), while in oxohydrocarbons this effect is swept out by the overwhelming influence of the number of heavier atoms.
7. Atomic Contributions to PPE Short-Range Forces Table VI11 reports average atomic increments to molecular volume and surface, as well as the average atomic contributions to PPE, E(i). All averages are slightly higher for carbon atoms bound to oxygen; since oxygen atoms are smaller and have a lower connectivity, 0-C bonds leave carbon atoms more exposed than C-C bonds and hence more available for intermolecular contacts. The correlation between exposed atomic surface and atomic contribution to PPE is remarkably consistent, as the number of oxygen atoms bound to a carbon atom changes. Averages for the same atom in oxohydrocarbons and in hydrocarbons are almost identical. Figure 2 shows a histogram of E(i)'s for hydrogen atoms, and Figure 3 shows the same for two types of oxygen atoms. The
Gavezzotti
8952 The Journal of Physical Chemistry, Vol. 95, No. 22, 1991
0
0
0 0
0
0
0
0
\
\
0
0
0
\p
\
..
110
d,A i 5. Scatter gram of 0 - H C angles versus 0 s - H distance (unique contacts only) for all compounds in the charts. The curve denotes points at which the C and 0 atoms are in contact (R(C...O)= 3.15 A). F
1 k/y9
'7 1 I -
a 050
/'r
s W
0.4
/
RbH).A
Figure 4. Radial density of C. .Hand 0..Hintermolecular contacts in the oxohydrocarbon sample; the curve is the pertinent 6-exp nonbonded potential (energy scale on the right; kcal/mol units). D(R)= N(contacts)/ (4rR2dr).
distribution of E ( i ) for hydrogens shows many scarcely attractive or quite repulsive interactions, many more than in hydrocarbon crystals. Accordingly, the average value is slightly smaller (Table Vlll). The distribution for ether oxygens is rather wide, while that for carbonyl oxygens has a well-developed spike at E = -1.2. Also shown in Figure 3 are the separate averages according to the number of non-H nearest neighbors and hence the degree of intramolecular steric hindrance around the oxygen atom. For ether oxygens, this distinction is significant, atoms with less neighbors having higher atomic contributions, since they are more available for intermolecular contacts; not so for carbonyl oxygens, for which equally uneffective was the distinction into free carbonyls and ester carbonyls (the averages being -1.64 and -1 S6, respectively). The reason for the bimodal distribution in Figure 3a must therefore be intermolecular. Let E ( R ) be the PPE due to a given atom, as a function of the radial distance from it; this quantity can be computed by summing all energies from contacts to that atom between R and R + dR.I6 The dashed areas in the histograms of Figure 3 show the number of cases in which E (2-3 A) is repulsive by more than 0.2 kcal/mol. These repulsions mostly originate from short 0..H contacts, since there are no 0.* e 0 and very few 0.-C contacts below 3 A in our sample (these will be discussed separately). The repulsions are spurious and result from neglecting the moderate hydrogen-bond forces acting between 0 and H atoms, not accounted for by the potentials used here; their distribution peaks just below the spike in the distribution of carbonyl atom energies in Figure 3a. This spike therefore corresponds to C 4 . . .H-C hydrogen-bonded carbonyl oxygens, which can be recognized as having an E ( [ )of
-
-
(16) Bianchi, R.;Gavezzotti, A.; Simonetta, M.J . Mol. Smrct. TheoChem 1W6, 135, 391.
c
0
3.26
3.06 2.86 R (c*iO), A
0 2.66
Figure 6. Same as Figure 4, for C..-0contacts.
about -1.3 and a repulsive potential of 0.2-0.6 kcal/mol in their coordination sphere between 2 and 3 A. The counterpart of this effect, on the side of hydrogen atoms, is evident in the leftmost part of the histogram in Figure 2. There are a few repulsive interactions also within the ether oxygen sample, but their distribution is more spread out. 8. A Closer Look at Short O...H and O*.-C Interactions Figure 4 shows the density of intermolecular 0..H and C. .H contacts in oxohydrccarbons, together with the pertinent potential energy curves. The population of 0..H contacts with energies >0.2 kcal/mol is much higher than that of C...H contacts and is much too high to be due to uncertainties in H-atom positioning. This result is complementary to that shown in Figure 3 and confirms the existence of weak or moderate C-H. v . 0 hydrogen bonds and their importance to crystal packing for these compounds (see also refs 6 and 17). A definition of the type of hydrogen atoms involved in such short contacts was not attempted, since this effect is a complex function of the chemical environment. The C-H. -0hydrogen bond spans the region 2.50 > R(0. *H) > 2.10, corresponding to pseudorepulsions of 0.2-1.3 kcal/mol; this is a continuum from zero to a moderately strong interaction. C-H...O contacts below 2.7 A are ubiquitous in carbonyl structures but frequently involve also ether oxygen atoms. A few crystal structures of special interest in this respect were further retrieved from the CSD (starred refcodes in Chart 11) as a s u p plementary data set. Figure 5 shows the distribution of O...H
-
-
( 1 7) (a) Berkovitch-Yellin, Z.; Leiserowitz, L. Acra Crystallogr.,Sect. B 1984.40, 159. (b) Sarma, J. A. R.P.;Desiraju, G. R.J. Chem. Sm.. Perkin Tram. 2 1987, 1195. (c) Desiraju, G. R.J . Chem. Soc., Chem. Commun.
1990,454.
The Journal of Physical Chemistry, Vol. 95, No. 22, 1991 8953
Properties of Crystalline Oxohydrocarbons
CHART I1
4.0
OLGYAH *
a & 00NZpU'
PHTHAO
WMOAN
I 1
I
I
I
.i1
1
2.0
7
CYHEXO' BPnENO 10
I
ANTOUO 07
NAPMU*
ZZZlYE 01'
I \ \
J
4
BENZlL 02
2.0
2.5
3.0
3.5
4.0
R(@H), 8, Figure 7. (a) The 6-exp 0.a.H nonbonded curve. (b) The corrective Morse potential for A = 0.9. Energies in kcal mol-'. DBZFUR 11
TROXAN*
TOXOCN
PTOXEC
properties depend on its physical interpretation. If it is taken as a chemical bond potential, it should involve only two atoms, have a deep minimum, and rise quickly at short distances from it; if it is to describe a supplementary electrostatic effect, it should be more diffuse and ideally fall off as the inverse first power of interatomic distance. Taking an intermediate approach, we write the potential in the Morse form, as
DBEZKP OMTPAL
&4m3 COUMAR 10
MNAPAC
apyw3
E,,,, = A ( l - exp[-B(R - R O ) ] )-zA
0
GIHZEC
distances below 2.6 A as a function of the C-H.0.O angle (including those in the supplementary data set); the directional selectivity is very weak, as noted in previous work6 interactions are apparently limited only by the 0..C distance of closest approach (about 3 A). The appearance of these interactions may depend on electrostatic or steric effects; for example, carbonyl oxygens are always more exposed to intermolecular interactions than ether oxygens, as demonstrated by the statistics in the previous sections; or oxygen atoms in cyclic structures are obviously more prone to C--*Oand O.-.H short interactions. Figure 6 shows the distribution of C...O contacts. A detailed survey of the contacts below 3.06 A (including those of the supplementary data set) reveals 34 independent C=O-..C=O contacts, 15 of which are in cyclic anhydrides, seven in vicinal polyketones, five in lactones, three in p-quinones, three in esters, and one in an aldehyde; 10 independent ether O..-C contacts, mostly in cyclic ethers; and nine C--O.-C(H,) contacts, mostly in esters. A study of the directional properties of O=C*..O interactions was not attempted, since previous work'* has shown that the 0 - C . -0 angle spans a considerable range, while directionality needs to be explained in terms of complex geometrical descriptors involving incipient reactivity-a task outside the scope of the present work. The survey of short O . . C and 0.a.H contacts shows that the M7 6-exp functions are inadequate to describe these interactions. While some of the long-range electrostatic crystal energy is simulated by these potentials, the short-range effects that lead to localized attractions are missing. In fact, reducing the repulsion steepness parameter in the 6-exp functions is not sufficient to reproduce the heats of sublimation. It is therefore necessary, as pointed out in previous work? to add an attractive potential, whose
-
(18) (a) Buergi, H.-B.; Dunitz, J. D.; Shefter, E. Acta Crystallogr.,Sect.
B 1974, 30, 1517. (b) Bernstein, J.; Cohen, M. D.; Leiserowitz, L. In The Chemistry of Quinonoid Compounds; Patai, S., Ed.; Wiley: London, 1974; Part I, pp 37-1 10. (c) Cossu, M.; Bachmann, C.; "Guessan, T. Y.; Viani, R.; Lapasset, J.; Aycard, J.-P.; Bcdot. H. J . Org. Chem. 1987, 52, 5313.
&was taken as 3.05 and 2.50 A for C...O and H.a.0 interactions, respectively, as the threshold distance at which repulsions arise (see Figures 4 and 6); B, the well-width parameter, was taken as 4.0 A-' for both interactions, somewhat smaller than in a true chemical bond, but ensuring that the supplementary attractive potential disappears at longer distances. The A parameters were obtained as A, = DiDi, Di and Dj being coefficients to be assigned for each atom type; presumably, they correlate with the local electrostatic charge. Best values were, in (kcal/mol)'/2, 0.9 for carbonyl carbon, 1.0 for carbonyl oxygen, 0.8 for all other oxygens, and 0.9/n for hydrogens, n being the number of H atoms attached to the same carbon. The observables for the calibration of the parameters are sublimation enthalpies, mostly sensitive to the D,'s, and cell parameters, sensitive to B and Ro. The B, Ro,and D, values were optimized by trial and error; the cell parameters were varied one at a time, leaving cell angles unchanged, and a cubic fit to the energies for variations up to 0.4 A was done to determine the optimum value. These procedures are admittedly approximate, but we found them to be quite indicative of the performance of the parametrization and sufficient for the present purposes. Figure 7 shows a typical result; the deep (compared with the 6-exp function) well of the Morse potential is evident. Table IX summarizes other numerical results. 9. Discussion
On one hand, this work demonstrates that oxygen-containing compounds without 0-He. -0hydrogen bonds are quite similar to hydrocarbons with respect to their solid-state structures. The crystal density increases as expected from stoichiometry; close packing is not affected by the presence of the heteroatoms. Ordinary potential functions of the dispersion-repulsion (6-exp) type are sufficient to describe the gross features of the packing of these compounds, as demonstrated by the correct prediction of sublimation heats for the larger molecules (Table IX). On the other hand, for some classes of small size, high oxygen content molecules-notably vicinal diketones, quinones, anhydrides and cyclic ethers or esters-the crystal packing is complicated by large electrostatic effects and special interactions of hydrogen-bond type. The ordinary potentials do not account for them, but standard PPE calculations clearly reveal their presence, when
8954 The Journal of Physical Chemistry, Vol. 95, No. 22, 1991 TABLE I X Heats of Sublimation, Cakulated Packing Energies (kcal mol-'), Cell Parameter Variations, and Rotational Displacements from Eauilibrium u s u b
compound SUCANH MLElCA DLGYAH PHTHAO PYMDAN FOWBAU av AE BNZQUI NAPHQU ANTQU007 ZZZlYEOl CYHEXO DMKETDO2 BENZILO2 BPHENOIO OBNZQU DOZREPI 0 CIMNUH TlKlND BODCOM HYFURN av AS TROXAN TOXOCN PTOXEC DBZFURll av AS DMEOXA DMTPAL PHBENZ DBEZPO MNAPAC GlHZEC BlCVlS DEDNEF COU MA R 1 0 av A8
exptl 19.6d 16.4d 20.1d 21.1'
24f
(15.03 16.3h 21.7h 27.1'
25.V 20.2d 17.3'' (23.5') 20.3' 22.6'"
13Ad
19.0" 18.3" 11.3P
21.lq
23.7' 23.4'
estd' 15.3 15.2 14.1 18.7 23.6 16.1 14 16.2
rotational PEb max IAa displ, deg 6-exp totC 6-exp tot 6-exp tot 10.8 17.8 -2 -3 2 2 9.3 15.2 -2 -3 1 2 11.8 18.9 -3 -4 15.2 22.5 -5 -6 0 2 18.2 23.4 -2 4 3 3 11.7 20.1 -3 -7 36 6 10.1 13.6 -3 3 7 2
19.4 17.3 22.6 24.0 21.7 22.0 16.7 13.0 19.6 14.4 24.3 20.5
22.7 -1 27.6 -5 24.4 -3 19.5 -2 16.1 -10 24.2 -3
19.4 16.2 11.1 19.1 14.3 16.4 9.3 19.9 14.1 21.2 17.6 15.3 10.3 12 19 13.9 10.5 15.8 13.8 17.6 16.2 20.1 20.0 9 20 17.3 12.2 23.2 21.7 23.3 21.6 26.4 23.6 23.2 20.4 23.7 20.3 18.5 13.7 18.6 13.7 18.5 16.6 20 6
21.8 19.4 17.5 14.3 19.7 29.8 15.3 8 14.5
-4 2
18.0
-4
20.8 20.4 8 16.6 24.5 23.9 29.0 23.1 26.5 13.3 19.2 20.2
-2
22.1
-5 6
-2 -10
2
3
2 3
1
1
-3 -5 -16
4
1
1
2
2
-4
1
0
0 -10
3
I 0 1
5
-2
-3
0
-1
-1
1
-2
-5
-1
-2 -7 -3
-3
-6
-4 -3
-7
-4 -3 0 -2 -5
-4
-5 -5 -4 -1
3 -8
-5
1
3
4
0
1 1 1 0 I 1
0 1 2 1 0 1
3
4
1 1
2
1
22
a Estimated from S250-PPEcorrelation, Table IV. bIncluding all interatomic contacts within the cluster of all molecules with at least one contact shorter than IO A to the reference molecule (convergent). C6-expM7 parameters plus Morse potential (see text). dDeWit, H. G. M.; Van Miltenburg, J. C.; De Kruif, C. G. J . Chem. Thermodyn. 1983, 15, 651. ' C R C Handbook of Chemistry and Physics, 64th ed.; CRC Press: Boca Raton, FL, 1983-84. fChem. Abstr. 1977, 87, 59208~.Original work unavailable. 8 Average of absolute percent (obs - calc)/obs lattice energies. De Kruif, C. G.; Smit, E. J.; Govers, H. A. J. J . Chem. Phys. 1981, 7 4 , 5838. 'Bardi, G.;Gigli, R.; Malaspina, R.; Piacente, V. J . Chem. Eng. Data 1973, 18, 126. Literature survey quotes values from 25.8 to 32.7. 'Ribeiro DaSilva, M. A. V.; Ribeiro DaSilva, M. D. M. C.; Teixeira, J. A. S.;Bruce, J. M.; Guyan, P. M.; Pilcher, G. J. Chem. Thermodyn. 1989, 21, 265. PE calculated for the ordered P2/c phase. Experimental values of 21.9 and 31.5 are also mentioned. kSellers, P. Acta Chem. Scand. 1971, 25, 2291. 'See: Dworkin, A. J. Chem. Thermodyn. 1983, 15, 1029. Average of three values. '"De Kruif, C. G.; Van Miltenburg, J. C.; Blok, J. G. J . Chem. Thermodyn. 1983, 15, 129. "Chem.Abstr. 1975,83, 43841f. Original work unavailable. "Sabbah, R.; Antipine, I. Bull. Chem. SOC.Fr. 1987, 392. PChem. Absrr. 1976, 84, 16396111. Original work unavailable. 4 Chem. Abstr. 1963, 58, 10746d. Original work unavailable. 'Carson, A. S.; Fine, D. H.; Gray, P.; Laye, P. G.J . Chem. SOC. B 1971, 1611. 'Carson, A. S.; Laye, P. G.; Morris, H. J. Chem. Thermodyn. 1975, 7 , 993.
a statistical analysis of appropriately partitioned energies is carried out. Short C.. e 0 interactions appear almost exclusively in small planar molecules, when there are no steric barriers to their formation; C-Ha interactions are more widespread, but only in s . 0
Gavezzotti a few cases appear to be particularly strong. The whole analysis confirms that these are secondary interactions, superimposed to the general bulk and shape effects, which by and large dominate the crystal packing of the compounds examined here. To what extent, however, they can be structure-defining, making the choice between several packing modes of similar energy, cannot be ascertained here. The results of the calculations including the supplementary attractive potentials for 0..C and 0. -Hreveal more. Table IX compares calculated lattice energies with observed heats of sublimation and also shows the effects of the variation of cell parameters and of molecular rigid-body rotation around the minimum. There is a substantial improvement in the agreement between calculated PE and sublimation heats when these corrections are applied to anhydrides or ketones, while for some esters the corrections are quite unnecessary and produce overestimated sublimation energies and undue shortening of lattice parameters, caused by excess attraction (but notice that the 6-exp functions alone generally predict shorter cell parameters, and, when the supplementary attractive potential is added, this malfunction is magnified). In DMEOXA, the excess attraction comes from both C.-.O and H-s.0energies, while in DBEZPO and DMTPAL it comes from He..Oenergies only. This might be caused by more complex directional requirements not accounted for by the radial form of the Morse potential-but this may not be the case, since 0m.H contacts have been shown not to be directional. We propose a more likely explanation, invoking the local polarity of the chemical groups: anhydride groups have large dipoles, and it is commonly recognized in organic chemistry that they are more reactive than esters toward nucleophilic attack. Therefore, in our model, anhydride and ester oxygens should be given different Di values. Note that the net molecular dipole, which is zero in, say, quinone or PYMDAN, is not an important parameter in this discussion. On the other hand, there must be another factor, which may be called steric shielding or enhancement of polar interactions, due to molecular shape. For example, ketone or cyclic ether oxygens are usually more exposed to intermolecular contacts than their ester counterparts; or, in a lactone group or in a vicinal diketone, two oxygens participate in forming a negatively charged region, while in a methyl ester the two negative regions point to opposite sides. One may also remember that DMEOXA, DMTPAL, and DBEZPO molecules are not rigid, so that the solid-state and gas-phase conformations may be different, resulting in calculated packing energies that are overestimated. The dynamic aspects of crystal structure are even more difficult to investigate, within the present model; however, in at least two cases (BNZQUI and TOXOCN) the supplementary attractive term restores the correct position in the crystal with respect to molecular rotation. There is no simple physical interpretation of the parameters of the attractive potential we propose; but the same is true for the interactions it is meant to describe, which oscillate between chemical bonds and Coulombic attraction. A better fit could no doubt be obtained by increasing the number of disposable parameters, but this would probably be pointless, unless the 6-exp part of the potentials is reoptimized at the same time. The derivation of a general and transferable intermolecular force field, using the experience from studies of the kind described in this paper, is the main perspective for future work.
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10. Summary (1) Five hundred ninety crystal structures of organic substances containing C, H, and 0 atoms without O-H...O hydrogen bonds have been retrieved from the Cambridge Files. A procedure for the systematic assignment of H atoms and renormalization of C-H distances has been devised. (2) Molecular and crystal descriptors have been calculated: these include molecular surface, volume and effective surface, crystal density, packing coefficient, and packing energy. Correlations between molecular size/oxygen content and packing energy have been established; recipes for estimation of sublimation
The Journal of Physical Chemistry, Vol. 95, No. 22, 1991 8955
Properties of Crystalline Oxohydrocarbons energies are given; and the parameters of two crystal force fields for oxygen-containingcrystals have been compared and discussed. (3) The crystal density was studied by computing averages as a function of oxygen content and by principalamponents analysis; the density does not appear to correlate with molecular size or shape, in contrast to hydrocarbons, but it does correlate with oxygen content; average packing coefficients show close-packed crystals for oxohydrocarbons. (4) The presence of short C-Ha -0and C. SOintermolecular contacts is detected by studying the deviations from average atomic contributions to calculated packing energies. C-He -0contacts are scarcely sensitive to the CHO angle and appear preferentially with carbonyl oxygens. C. -0contacts mainly appear in small planar molecules (especially cyclic anhydrides) and involve almost exclusively carbonyl atoms. (5) A supplementary attractive potential has been optimized to account for these interactions. Extensive comparison between calculated packing energies and observed sublimation enthalpies shows that the additional attractive term is needed for small, cyclic molecules but may not be necessary for large molecules and esters, where the ordinary 6-exp functions perform well; both 6-exp and supplemented 6-exp potentials tend to predict shorter cell parameters but reproduce the molecular orientation in the crystal-although the supplemented functions perform better in some cases. (6) The results suggest that, besides the intrinsic polarization of electronic charge, steric shielding factors due to molecular shape or conformation determine the amount of electrostatic attraction in these crystals.
-
-
Appendix I. Assignment and Placement of Hydrogen Atoms For each carbon atom, N is the number of non-H atoms bound to it and S is the sum of the corresponding C-X distances. The following cases are contemplated. (a) N = 3: If S > T, assign one (methyne) H atom. Tis equal to 4.14 plus 0.1 times the number of C atoms bound to the C atom in question. (b) N = 2: If they are both carbon atoms, if S < 2.65, no action; if 2.65 C S < 2.96, assign one (aromatic) H atom; if S > 2.96, assign two (methylenic) H atoms. If one atom is carbon and the other oxygen, if S < 2.60, no action; if 2.60 C S < 2.86, assign one (aromatic) H atom; if S > 2.86, assign two (methylenic) H atoms. (c) N = I : If S > 1.40, assign three (methyl) hydrogens; if 1.40 < S < 1.25, assign two ( = C H H ) hydrogens; if S < 1.25, assign one (acetylenic) H atom.
For what is not specified here, the rules stated in the Appendix and Table I of ref l a apply, except that methyne hydrogens are placed in such a way that the C-H vector forms three equal angles with the C-X vectors (an improvement over the procedure of ref la). All C-H distances were standardized at 1.08 A. Threshold values for S were calculated by using average bond lengths from standard table^.^ Appendix 11. Definition of Symbols (1) 6-exp potentials: The interaction between atoms i and j in the crystal is E = A exp(-BR,,) - CR,jd, where A , B, and C are parameters to be specified for each couple of atomic species; the lattice energy is obtained by appropriate double summations over i and j and is always a negative number, although in the tables the minus sign is omitted for brevity. (2) W, is the molecular weight, S, the molecular van der Waals surface, V, the molecular van der Waals volume, N,,,, the total number of atoms, and Z,the total number of valence electrons in the molecule. S,, is the molecular surface obtained by ignoring H atoms and setting all other atomic radii to 2.50 A (a sort of available outer surface). Cmlfis the self-packing coefficient or the ratio of the molecular volume to the volume of the parallelepiped containing the molecule. (3) DEis the crystal density, Dd is the total number of electrons in the cell divided by the cell volume, and CKis the Kitaigorodski packing coefficient, or total molecular volume in the cell divided by the cell volume. (4) Fc is the cylindrical index, or 0.5 ( M , M 2 ) / M 3 the , Ws denoting the moments of inertia in descending order; Rs is a sphericity index defined as the difference between one-third of an average molecular radius and the volume/surface ratio; since this ratio is just R / 3 for a sphere, deviations of Rs from zero are deviations from sphericity. (5) E ( i ) is the part of PPE that is ascribed to atom i in the molecule, as obtained by an appropriate breakdown of the double sums in the lattice energy. Unless otherwise stated, it is a negative number (in units of kcal/mol), although in tables and figures the minus sign is omitted.
+
Acknowledgment. Partial financial support from Minister0 della Pubblica Istruzione is acknowledged. We thank the Servizio Italian0 per la Diffusione Dati Cristallografici del CNR (Parma) for help in handling the CSD. Supplementary Material Available: Table I, the Cambridge Database Refcodes of the 590 compounds in the sample (3 pages). Ordering information is given on any current masthead page.
