J. Phys. Chem. 1992,96, 5819-5824
5819
Molecular Orbltal Studies of Crystal Formation: The Aggregatlon and Nucleation of
UszM Turi and J. J. Damenberg* Department of Chemistry, City University of New York-Hunter College and The Graduate School, 695 Park Avenue, New York, New York 10021 (Received: December 30, 1991)
Ab initio and semiempirical (AM1) molecular orbital calculations are reported on the relative energies of the tautomers and conformations of 1,3-cyclohexanedione(CHD) and 1,3-propanedione (PPD) used as a model, as well as their energies of association. Small basis set HF calculations make predictions of the relative energies of the monomers that differ from the larger HF and MP2 calculations. The AM1 calculations are in general agreement with the better ab initio results for the monomers. H-bonding interactions have been calculated using HF/6-3 lG, HF/6-3 lG(d,p), and AM1 for aggregates containing up to eight (AMI), four (HF/6-31G), and three (HF/6-31G(d,p) monomeric units. Dimers were also calculated at the MP2/6-31G, MP2/6-31G(d,p)//HF/6-31G(d,p), and MP2/6-31G(d,p)//MP2/G-31G levels. Both the H-bonding interactions and the geometries of the monomeric units are calculated to change due to a significant cooperative interaction. The best values for the H-bonding interactions in the dimers (10 kcal/mol) increase to 13.8 kcal/mol as extrapolated to the infinite chain of the crystal (after correction for zero-point vibrational energy and basis set superposition errors). The with benzene has been calculated using AM 1, while a model 6: 1 aggregate reported 6: 1 cocrystal of 1,3-~yclohexanedione using PPD has been calculated at the HF/6-31G level, as well. From comparison of the best ab initio and AM1 results with each other and a preliminary experimental report, we conclude that the AM1 H-bonding energies need to be scaled by a factor of 1.9 for these systems. The strength of the H-bond between an infinite chain of 1,3-cyclohexanedionesand another molecule is predicted to be 12.7 kcal/mol. The crystal structures for 1,3-cyclohexanedione and its 6:l cocrystal with benzene can be explained using the calculated interaction energies. The effect of cooperativity is central to understanding both the relative energies and structural details, such as 0-0 distances, in these crystals.
The intermolecular interactions of @-dicarbonylcompounds, in general, and 1,3-diones, in particular, is a subject of considerable interest. These compounds normally have energetically accessible enol forms which have been reported to have unusually strong hydrogen bonds. In addition, 1,3-~yclohexanedione(CHD) is known to crystallize in two different forms, including an unusual 6: 1 stoichiometric cocrystal with benzene.' The normal crystal is formed from the anti-enol, which is the least stable of the easily accessible forms (keto, syn-enol, and anti-enol). The availability of extensive crystallographic data on these diones provides us with an excellent opportunity to further test the applicability of the available molecular orbital methods to modeling hydrogen-bonding and crystal structure. The mechanism of nucleation is an important consideration in crystal formation. Presumably the crystal must start as a dimer, become a trimer, and continue to add individual units or small aggregates until it has acquired enough three-dimensional supermolecular structure to be considered a crystal. In order for this process to occur, it ,seems necessary that cooperativity play an important role in the interaction energies of adding individual units to the growing aggregate. Thus, the interaction energy between two individual molecules must be less enthalpically stabilizing than between an aggregate and an individual molecule. If this were not true, many small aggregates (dimers, trimers, etc.) would form, rather than fewer larger crystals, as the former would be entropically favored. Furthermore, one should expect the extent of the wperativity to increase as the aggregate grows, eventually asymptotically reaching the interaction energy of a single unit with an established crystal. In principle, this kind of behavior should obtain for growth in all three crystal directions; however it is possible (even likely) that one or two direction of growth might dominate the other@). In the case of the 1,3-cyclohexanedione,cooperativity of interaction might also play an important role in providing the driving force for overcoming the activation necessary to convert the monomeric keto molecules to the enol forms observed in the crystal structures. For these reasons, empirical force field calculations, which generally rely on two-body intermolecularinteractions,are unlikely to be useful for the study of crystal nucleation. The size of the aggregates that must be calculated makes accurate ab initio calculations an impossible alternative for the complete study. In
this paper, we report the results of semiempirical AM 1 calculations on large aggregates, reinforced by ab initio calculations on various smaller models. Previous molecular orbital (MO) calculations on cooperativity in H-bonding have been reported at various levels of calculation.2 Specific experimental evidence for the effects has also been rep0rted.j Methods Both the AM14 approximation to molecular orbital theory and various levels of ab initio calculations have been used for these studies. The AM1 method overcomes the problems that previous semiempirical methods (notably, MND05) have in describing hydrogen bonds. It has been used with success in several hydrogen-bonding studies: including modeling of the H-bonding between molecules of various nitroanilines in the crystalline state? Ab initio studies of H-bonding systems are very sensitive to basis set and correction for electron correlation,as exemplifed in studies of the water dimer.8q9 Calculations of sufficient accuracy on molecular complexes of the size to be considered here are not practicable using such costly methods. Nevertheless, ab initio calculations were performed on the monomers and several smaller aggregates for comparison and as an aid in interpreting the semiempirical results. In the case of the a b initio calculations, 1J-propandone (PPD) was often used in place of CHD to reduce the calculational complexity. For these calculations, the carbons and oxygens were constrained to be coplanar in the conformation the dione would have if it were part of the CHD. The geometries of the aggregates were optimized completely with the constraints that the geometry of all molecules in each aggregate be the same and that the three carbons and two oxygens involved in the enolic fragment be coplanar with the corresponding atoms in the other molecules. These constraints were removed in several test cases including an aggregate of six diones using AM1. The energy did not differ from the constrained geometry by more than 0.2 kcal/mol. An axis of symmetry was enforced in the models of the 6:l dione:benzene cocrystals. This axis is 6-fold for the 1,3-propanedione (PPD) and 3-fold for the CHD cyclomers (where the pucker of the rings points in opposite directions in adjacent enols). The calculations were performed using AMPAC (AMl), GAUSSIAN88/GAUSSIAN90 (ab initio), and PCMODEL (generation
0022-3654/92/2096-5819$03.00/0 0 1992 American Chemical Society
5820 The Journal of Physical Chemistry, Vol. 96, No. 14, 1992 TABLE I: Relative Energies of the Keto and Enol Forms of Different 1.3-Diones (in kcal/mol)
HF/3-21G HF/6-31G HF/6-3 lG(d,p) HF/6-3 1 lG(d,p) MP2/3-2 1G MP2/6-31G MP2/6-3 lG(d,p) AM 1
enol form keto total energies (hartrees)O svn anti form of most stable form 1,3-Propanedione 0 3.4 2.3 -264.1334 0 2.2 2.4 -265.5034 1.3 3.5 0 -265.6367 0.7 2.8 0 -265.6994 4.6 8.0 0 -264.6555 3.8 5.8 0 -266.0270 0.8 2.9 0 -266.4070 2.6 6.4 0 -10.7
HF/3-21G HF/6-3 1G HF/6-31G(d,p) AM 1
1,3-Cyclohexanedione 2.1 6.6 0 0.5 4.1 0 4.5 7.7 0 4.5 6.9 0
method/basis set
~
AM 1
~
~~~
-379.4623 -381.4237 -381.61 31 -86.7
5,5-Dimethyl- 1,3-~yclohexanedione 4.7 7.0 0 -93.7
"In the case of AM1 results the heat of formations (kcal/mol) are reported .
of input and graphics) on IBM RS/6000 RISC and Ulysses Systems 386/486 workstations. The ab initio optimizations were performed at both the Hartree-Fock (HF), and second-order Moeller-Plesset (MP2) levels using 3-21G and 6-31G and at the H F level only using 6-31G(d,p) and 6-311G(d,p).
Results and Discussion Calculations were performed on aggregates of PPD, CHD, as well as several derivatives of CHD, each in several different geometrical configurations. Calculations were also performed on aggregates of these diones with one molecule of benzene. Monomers. Table I collects the relevant data on the different tautomers and conformations of the isolated molecules. For PPD, AM1, the larger basis set HF, and all the MP2 calculations favor the keto form, while the smaller basis sets (without polarization functions) favor the syn-enol form at the
Turi and Dannenberg HF, but not the MP2 level. The syn-enol is consistently favored by between 1.96 (MP2/6-31G) and 3.85 (AMI) kcal/mol by all methods. CHO was studied using HF up to 6-31G(d,p), but is too large to optimize using MP2. All methods are consistent with the keto form having the lowest energy (although just barely so for 6-31G). The syn form of the enol is again favored over the anti by from 2.4 (AM1) to 4.5 (3-21G) kcal/mol. The relative energies for 5,5-dimethyl-1,3-cyclohexanedione (only calculated using AM 1) were very similar to those for the parent 1,3-~yclohexanedione. Aggregates. Various aggregates of the enol forms of the diones were modeled in these studies. The enols could be syn or anti, and they could hydrogen bond to give either head to head (hh) or head to tail (ht) junctions. If we only consider structures where each monomeric unit has the same conformation, there are four possibilities (illustrated in Figure 2): anti ht (AHT), anti hh (AHH), syn ht (SHT), and syn hh (SHH).'O Two of these are known from crystal studies: AHT is the normal assemblage found in the crystal structures of the pure diones, while SHH is the assemblage found in the 6:l cocrystals of CHD with benzene. The hydrogen-bonding energies for the dimers and higher aggregates studied are collected in Tables I1 and 111. 1,3-Propanedione,Dimem The dimers were studied at several levels of theory to help interpret the AM1 calculation that were performed on the larger aggregates. AM1 consistently gives the weakest hydrogen-bonding interactions, while the smallest basis set HF calculations give the strongest interactions. The best H F calculations (HF/6-31G(d,p)) predict interactions virtually midway between the 6-31G and AM1 values (before correction for zero point vibrational energy, ZPVE). The predicted 0-0 distances are in the inverse order of the stabilization energies, as expected. These range from 2.67 to 2.98 A. The ZPVE was evaluated for the ab initio calculations of the dimers at the H F / 6 3 1G and HF/6-3 lG(d,p) levels. The basis set superposition errors (BSSE) have also been considered. These errors arise from the possibility that the unused basis of one partner can be used to stabilize the other in an aggregate, but not in the isolated molecules. BSSE can be important for small basis sets (it disappears a t the Hartree-Fock limit). The counterpoise method (CP) is the most common method to correct for this error, but
TABLE 11: Incremental Hydrogen-Bonding Energies for the 1,1Propanedione Aggregates at Different Levels of Theory; Energies in kcal/mol SHT aggregates dimer trimer tetramer pentamer hexamer heptamer Octamer
AM 1 -4.6 -4.6 -4.8 -4.8 -4.9 -4.9 -4.9
6-31G -11.5 -13.6 -14.1
AHT 6-31G(d,p) -9.3 -10.6
AM 1 -5.6 -6.6 -6.9 -7.0 -7.1 -7.1 -7.2
6-31G -1 2.4 -14.8 -15.7
6-3 lG(d,p) -10.3 -12.3
SHH AM 1 -3.8 -5.4 -6.2 -3.8 -3.4
AHH AM 1 -5.7 -6.8 -4.3 -7.7 -7.2
TABLE 111: Incremental Hydrogen-Bonding Energies Calculated by AM1 Method for the 1,3-Cyclohexanedioneand S,S-Dimetbyl-l,3-cyclobexanedioneAggregates; Energies in kcal/mol 1.3-cvclohexanedione 5.5-dimethvl-1.3-cvclohexanedione aggregates dimer trimer tetramer pentamer hexamer heptamer
SHT -4.7 -4.6 -4.8 -4.8 -4.9 -4.9
AHT -5.1 -6.3 -6.5 -6.6 -6.7 -6.7
SHH -4.3 -4.6 -4.7 -4.7 -5.3
AHH -5.6 -6.4 -6.7 -6.9 -6.9
SHT -4.7 -4.6 -4.8 -4.8 -4.9 -4.9
AHT -5.7 -6.3 -6.5 -6.6 -6.6 -6.7
SHH -4.4 -4.6 -4.7
AHH -5.6
-4.1
-6.4 -6.6 -6.8 -6.9
HF/6-3 lG(d,p) SHT -9.3 1.1 1.3 2.4 -6.9
AHH -10.4 0.9 1.4 2.3 -8.1
-5.5
TABLE IV: ZPVE and CP Corrections for the Dimers of 1,3-Prop.aedione; Energies in kcal/mol HF/6-3 1G H-bonding energy __ without corrections CP correction ZPVE correction total correction H-bonding energy after corrections
AHT -12.4 0.8 1.5 2.3 -10.1
SHT -11.5 1.2 1.4 2.6 -8.9
AHH -12.3 0.8 1.6 2.3 -10.0
AHT -10.3 0.7 1.3 2.0 -8.3
The Journal of Physical Chemistry, Vol. 96, No. 14, 1992 5821
Aggregation and Nucleation of 1,3-Diones TABLE V Total W c r , (hrrtrees) and Hydrogen-Bodng Eaergiar ( k d / m d ) of AHT Dimers of 1,3-Propaaedioaeat Different Levels of TbeoW total energy
method HF/6-31G HF/6-3 lG(d,p) MP2/6-31G//HF/6-31G MP2/6-31G
MP2/6-3lG(d,p)//HF/6-31G(d,p)
MP2/6-31G(d,p)//MP2/6-31G
-531.0195 -531.2786 -532.0291 -532.0546 -532.7755 -532.7750
energy Hof the bonding monomer energy -265.4998 -265.631 1 -266.0047 -266.0177 -266.3782 -266.3778
-12.4 -10.3 -12.3 -12.0 -12.0 -12.1
is somewhat controversial, as it often overcorrects." The calculated ZPVE and CP corrections are assembled in Table IV for the dimers. These values will be applied to the larger aggregates by assuming the ZPVE and CP corrections for each H-bond to be those calculated for the dimers. After taking the ZPVE and CP corrections into account, the ab initio H-bonding stabilizations for AHT would be reduced by 2.25 and 2.0 kcal/mol for the HF/6-31G and HF/6-31G(d,p) basis sets, respectively. In view of the tendency of CP to overestimate the correction, we have arbitrarily decided to use the smaller value of 2.0 kcal/mol to correct the interactions. H F calculations are often insufficient for accurate modeling of H-bonding complexes. For this reason, we performed several calculations at the MP2 level (MP2/6-31G, MP2/6-31G(d,p)/ /HF/6-31G(d,p), MP2/6-31G(d,p)//MP2/6-31G) to assess the accuracy of the H F calculations. Due to the complexity of the calculations, we treated only the AHT dimer. The results are summarized in Table V. With the exception of the HF/6-31G(d,p), all the ab initio methods predict stabilizations between 12.0 and 12.4 kcal/mol. The three most advanced calculations, MP2/6-31G, MP2/6-3 lG(d,p)//HF/6-31G(d,p), and MP2/631G(d,p)//MP2/6-31G predict stabilizations of 12.0 to 12.1 kcal/mol. After correction for ZPVE and BSSE (CP correction) this value would become about 10 kcal/mol. Trimers and Higher Aggregates. The AM 1 method predicts the interaction energies to be somewhat weaker than the ab initio methods. However, the calculation of the many aggregates considered here using ab initio methods is impractical using available facilities. For this reason, we shall scale the AM 1 results as described in the following paragraph. All methods predict the second hydrogen bond to be more stabilizing than the first by similar percent increases. From Table 11, it is clear that the H-bonding stabilization for the last interaction increases asymptotically to the value expected in the infinite aggregate or crystal. One can also see that the ratio between the HF/6-31G(d,p) (after correction for ZPVE and CP) and AM1 stabilizations is roughly constant between 1.5 and 1.7, and that between AM1 and HF/6-31G between 1.8 and 2.0. The best dimer calculations for AHT suggest that the HF/6-31G(d,p) interactions are too weak by 1.7 and that the HF/6-31G interactions are too strong by 0.4 kcal/mol. On the basis of these data, we scale the AM1 interaction energies of aggregates too large to calculate by the ab initio methods by a factor of 1.9. While this value is somewhat arbitrary, small changes in it will not affect
I 2
Ab
3
4
initio 5
6
7
8
infinite
Number of Molecules Figure 1. Comparison of ab initio and AM1 hydrogen-bonding interactions for the fusr H-bond as a function of the size of the AHT aggregate. The AM1 values are multiplied by 1.9, while the ab initio values are taken from eq 1. See text for explanation.
the qualitative conclusions described below. Nevertheless, a plot of the interactions obtained by fitting the exponential function of eq 1 (n = number of molecules) to the HF/6-31G H-bonding
Ei= -3.94
- 10.24(1 - e-(w1))
(1)
energies for AHT (after cOtrectiollS for ZPVE and BSSE) in Table 11, corrected by 0.4 kcal/mol compared with the AM1 values multiplied by 1.9, suggests that the approximation is sound (Figure 1). Quation 1 also indicates that the stabilization of adding another monomer to an infinite chain should be 13.8 kcal/mol (after the 0.4 kcal/mol correction), or about 40% more than for the dimer interaction. Significant geometric changes become apparent as the aggregates grow. These are displayed in Table VI. The 0-0 distances acToss the H-bond become smaller. Geometric changes also occur within the molecules themselves, as the longer bonds shorten, while the shorter ones lengthen. With one exception all the geometrical changes are in the direction necessary to convert the geometry calculated for the isolated molecule to that experimentally observed for the crystal. Even for the exception (the C2-C3distance by AMI), the bond length changes in the same direction as in the ab initio calculations. This trend continues for all cases where tetramers could be studied, as well as for higher aggregates studied only by AM1. The calculations clearly predict that the molecular structures in the gas and crystalline phases should be somewhat different. The calculated behavior of these H-bonds seems similar to the *resonance" interaction suggested by Jeffrey for the aggregation of amides.12 1,3-Cyclohexanediones. Table I11 collects the data on the enthalpies of interaction of the various aggregates studied. Figure 2 illustrates the geometries of the aggregates that have been considered. Due to the sizes of the aggregates, only AM1 calculations have been considered. Since the enols of the cyclohexanediones are not planar due to ring pucker, the aggregates
TABLE VI: Dirtumr (in A) in AHT Fonn of 1,3-RoP.llediolr~.ad 1,fCyclohex.nediow Aggregates at Differeat Lev& of Theory
no. of mom men c1-C~ Cz-C3 1 1.461 1.349 2 1.457 1.349 3 1.455 1.350 4 1.453 1.351 5 1.453 1.351 6 1.452 1.352 7 1.452 1.352 8 1.451 1.352 cxptl
-
1,3-propancdionc AM I Cl=O 1.234 1.236 1.238 1.238 1.239 1.239 1.239 1.240
1,3-~yclohexanedione
HF/6-31G C3-0
1.371 1.368 1.366 1.365 1.364 1.364 1.363 1.363
0-0 C& CZ-C, C1=0 C3-0 0-0 1.455 1.325 1.218 1.360 2.964 1.446 1.330 1.223 1.348 2.747 2.946 1 . 4 4 1 1.333 1.226 1.342 2.706 2.936 1.438 1.335 1.228 1.339 2.684 2.930 2.926 2.923 2.921
ClCz 1.464 1.455 1.450
HF/6-31G(d,p) AM1 CZC3 Cl=O C3-0 0-0 CI-CZ C& Cl=O 1.325 1.192 1.335 1.463 1.351 1.238 1.329 1.198 1.325 2.816 1.460 1.353 1.241 1.332 1.200 1.320 2.779 1.458 1.354 1.242 1.457 1.355 1.243 1.456 1.355 1.243 1.456 1.356 1.244 1.455 1.356 1.244 1.410
1.346
C3-0 1.374 1.371 1.370 1.369 1.368 1.368 1.367
0-0
3.043 3.033 3.027 3.024 3.022 3.020
1.243 1.323 2.561
5822 The Journal of Physical Chemistry, Vol. 96, No. 14, 1992
Turi and Dannenberg
a
do
H/
Y "
H-o
b
Figure 3. Drawing of AM1 optimized AHT tetramer of CHD illustrating the pucker of the rings.
n TABLE VII: Relative Energy (AM1 Results after Correcting by the Factor 1.9) of 1,3-CyclohexanedioneAggregates Compared to the Energy of an Equivalent Number of Noninteracting Mones; Energies in kcal/mol 6: 1
6: 1
SHH: AHH: no. of benzene benzene monomers AHT SHT AHH SHH complex complex 1 2 3 4 5 6 7
infinite
?Q
H
Do /
h
"\
H
0
H-b 0
H
P
'-
A" 0
U Figure 2. Schematicdrawings of the various interactions considered for CHD aggregates: (a) AHT; (b) SHT; (c) AHH; (d) SHH.
can assemble with the pucker in the rings aligned or not (see Figure 3). Calculations showed little difference in energy of interaction dependence on the relative direction of the ring puckering. The crystal structure is reported to be disordered with respect to pucker,' which is consistent with this observation. In the absence of any energy preference, all further calculations were performed on aggregates with alternating pucker. The trends for the aggregates of the CHD are similar to those discussed above for PPD. The known crystal structures suggest that the AHT structure of the enol (predicted to be the least stable monomer) be the most stable in the crystal (however, this is not a requirement since the crystal structure could be determined by kinetics rather than thermodynamics). In order for the AHT structure to be favored,
6.9 1.5 -0.7 -1.9 -2.6 -3.1 -3.5 -5.7
4.5 0.1 -1.4 -2.2 -2.7 -3.0 -3.3 -4.9
6.9 1.6 -0.7 -2.0 -2.8 -5.5
4.5 0.4 -1.2 -2.0 -2.5 -4.6
1.5 -1.7 -3.2 -4.0 -4.7 -5.6
5.0 0.1 -2.0 -3.2 -4.1 -6.7
hydrogen-bonding (or other) interactions must overcome both the unfavorable energy difference between the keto and enol forms, as well as that between the anti- and syn-enols. Since the stabilization of an H-bond is greater than the difference between the keto and enol forms, the first requirement is easily met. The second requirement needs more consideration. In order for it to be met, the H-bonding stabilization of the AHT structure must exceed that of the SHH and SHT structures by at least as much as the syn monomer is favored over the anti. One must use an extrapolated H-bonding stabilization for the AHT and SHT structures for comparison with the average H-bonding energy for the cyclic hexameric structure of SHH. The extrapolated values were obtained by fitting a Morse function to the cooperative part of the H-bonding stabilization using eq 2 where n is the number E , = E , - a(1 - e-b(n-1))
(2)
of H-bonds in the aggregate E,, is the energy of the last H-bond and the parameters a (which represents the additional stabilization due to cooperativity in an infinite aggregate) and b are determined by a least squares fit. At the AM1 level, these extrapolated values (kcal/mol) are 6.66 (AHT) and 4.85 (SHH) for 5,5-dimethyl-l,3-cyclohexanedione, 6.67 and 4.96 for CHD, and 7.27 and 4.94 for PPD. Thus, the differences in the extrapolated cooperative bond enthalpies between the AHT and SHH forms vary from 1.7 to 2.3 kcal/mol, depending upon the dione. These values are slightly less than the AM 1 calculated difference between the syn- and anti- 1,3-cyclohexanediones of about 2.4 kcal/mol. However, if one applies the correction factor of 1.9 that allows the AM1 stabilizations to approximate the ab initio stabilization, these energy differences become between 3.3 and 4.4 kcal/mol, enough to overcome the syn/anti energy difference. The H-bond cooperativity is slightly less for CHD than for the PPD model. The predicted H-bonding stabilization to an infinite chain would be 12.7 vs 13.8 kcal/mol for PPD. The H-bond energies obtained by multiplying the AM1 values by 1.9 are consistent with a recent preliminary report that the heat of sublimation of crystals of CHD is 26 kcal/mol, which is several kcal/mol higher than anticipated for an alcohol of this size.I3
The Journal of Physical Chemistry, Vol. 96, No. 14, 1992 5823
Aggregation and Nucleation of 1,3-Diones
TABLE VIII: Total Energies, Heat of Formations, and Hydrogen-Bonding Energies of AHH and SHH Complexes with and without Benzene; Energies in kcal/mol Except Otherwise Noted 6: 1 6: 1
method heat of formation H-bonding energy H-bonding energy due to benzene total energy (hartrees) H-bonding energy H-bonding energy due to benzene
AM 1
6-31G
heat of formation H-bonding energy H-bonding energy due to benzene
AM 1
1
2
3
4
5
6
7
SHH SHH:benzene cvclic hexamer comvlex 1,3-Propanedione -436.4 -417.4 -27.5 -30.5 -1593.1579 -86.4
AHH cvclic hexamer -421.7 -3 1.6
-3.0 -1823.7889
-1593.1420
-90.4
-89.7
-4.1
1,3-CycIohexanedione -503.0 -521.8 -32.0 -28.9 -3.1
infinite
Number of Molecules
Figure 4. Relative energies per molecule of various aggregates compared to the most stable (keto) form of CHD monomer.
An interesting way to consider the data is depicted in Figure 4 and Table VII, where the energy per molecule of a growing aggregate is considered relative to the energy of an equivalent number of noninteracting diones, with zero defined as the energy of the lowest energy (keto) form. For this model, we use the AM1 calculated energy differences for the monomeric forms and 1.9 times the AM1 energies of the H-bonding interactions. The data show that three molecules must aggregate before the enthalpy of the AHT aggregate dips below the enthalpy of the noninteracting molecules in their keto form. Furthermore, six to seven molecules must aggregate before the AHT becomes energetically equivalent to the SHT form. At infinite chain length, the enthalpy per molecule of the relative free keto form (kcal/mol) is calculated to be -5.1 for the AHT and -4.4 for the SHT forms. We now consider the SHH and AHH structures. .One of these is observed in the remarkable 6:l stoichiometric cocrystal formed with benzene upon crystallization from that solvent. As is evident from Figure 5, these two structures can be interconverted by moving the six H-bonding H’s from one 0 to another. Both AM1 and HF/6-31G predict the S H H structure to be more stable in the case of PPD (Table VIII). AM1 predicts the S H H form of CHD to be more stable than the AHH, but by less than for PPD. The data in Table VI1 indicate that the AHH structure for CHD becomes more stable if one multiplies the H-bonding energies by the factor of 1.9, as the enhanced H-bond cooperativity in the anti form once again overcomes the intrinsic stability of the syn structure. In the 6:l cocrystal with benzene, the preferred SHH structure, with the H-atoms of the benzene attracted to the carbonyl oxygens of the enols, forms a second H-bond to the same oxygen. In the corresponding AHH structure, the benzene H’s would have a (presumably) weaker interaction with the hydroxyl oxygens. The H-bonding aggregate cannot exceed the size of the cyclic structure of six enols and simultaneously preserve the interactions with the central benzene molecule. The average hydrogen-bond energy of the crystal becomes that of the six molecule cyclic aggregate divided by six, rather than the value extrapolated
-517.7 -39.4
AHH:benzene comvlex -403.0 -35.0 -3.3 -1823.7726 -93.5 -3.8
-499.4 -43.1
-3.7
to infinity used for the linear AHT and SHT structures. The thermodynamic stabilities of the cyclic structures of six CHDs are calculated to be -5.5 (AHH) and -4.6 (SHH) kcal/mol per enol unit (based on 1.9 times the AM1 interaction energy) relative to the free keto form, both more stable than six enols in the AHT structure. However, in the absence of benzene, these structures may be severely kinetically disfavored. In forming aggregates of the SHH structure, we encountered problems with the optimization, in that small cyclic H-bonding structures would often be most stable, even for dimers. These cyclic structures would have to break at least one of their H-bonds in order to form larger aggregates. Furthermore, the likelihood of forming populations of different sized cyclic aggregates is quite high. It is unlikely that different sized cyclic aggregates could come together to form a stable crystal lattice. Hence, kinetics disfavors the formation of six-membered cyclic aggregates in crystals. The influence of the benzene can be quite important. To evaluate this, we calculated the optimized structures corresponding to the 6:l cocrystal (Figure 5 ) using both AM1 and HF/6-31G with PPD and using only AM1 with CHD. These are compared to analogous calculationson the cyclic hexamer without a benzene. The structures were independently optimized with and without the benzene. Due to the size of the C24012H30 aggregate, the ab initio calculations were too complex to calculate the ZPVE.I4 AM1 calculations were then performed with a benzene molecule and from one to six molecules of enol to obtain the incremental H-bonding energies. The values of Table VI11 indicate the benzene interaction with the cyclic aggregate of 1,3-propanedionesto be 3.0 kcal/mol, or 0.5 kcal/mol per molecule using AM1 and 4.1 kcal/mol and 0.7 kcal/mol per molecule for HF/6-31G. These results are in good agreement, especially if one assumes that the stabilization energy calculated using HF/6-31G should be somewhat less when corrected by the difference in ZPVEs for the cyclic hexamer with and without the benzene. The AM1 value for interaction of six CHD enols with benzene is 3.1 kcal/mol, similar to the value for PPD. The structures of the cyclamers are indicated in Table IX. The structural features of the HF/6-3 1G calculation on PPD agree reasonably well with the experimental values for CHD; the AM1 values are in somewhat poorer agreement. In all cases, the distance between the two carbonyl oxygens opposite each other contracts upon insertion of the benzene, suggesting a geometric response to an attractive interaction. The kinetic effect of the benzene may be even more important. If one imagines the enols aggregating around the benzene molecule, one can easily account for the six-membered structure. No smaller ring size could accommodate the benzene in the center. If the benzene were the template around which the aggregate formed, then no H-bonds need be broken as the aggregate grows. Finally, the benzene in the center could serve the purpose of creating a uniform size enol aggregate. Included in Figure 4 are the energies of the cyclic structure with and without the benzene. For purpose of energetic comparison, a free benzene is assigned a value of zero. The energies of a benzene with from one to six enols arranged as they would be to form the ring structure are
5824 The Journal of Physical Chemistry, Vol. 96, No. 14, 1992
Turi and Dannenberg
TABLE IX: Distances (in A) in AHH and S H H Cyclic Structures with and without Benzene at AM1 and ab INtio 631C Level
structure C,-C2 C2-C3 1,3-propanedione AHH 1.451 1.352 AHH:benzene 1.451 1.352 SHH 1.451 1.350 SHH:benzene 1.450 1.350 1.453 1.357 1,3-~yclohexanedione A H H AHH:benzene 1.454 1.357 1.455 1.354 SHH SHH:benzene 1.454 1.354 1,3-cyclohexanedione SHH:benzene experimental 1.413 1.349
AM 1 C 1 = O C3-0 1.241 1.360 1.241 1.361 1.239 1.355 1.239 1.356 1.246 1.363 1.246 1.363 1.243 1.363 1.244 1.363 1.253 1.318
HF/6-31G
0-0 cavity C,-C2 C2-C3 C l = O C3-0 0-0 cavity 3.010 3.006 3.019 3.015 3.020 3.016 3.009 3.009 2.579
10.213 1.429 10.039 1.429 10.890 1.428 10.155 1.427 10.097 10.001 10.591 10.327 1.413
1.341 1.341 1.345 1.345
1.238 1.237 1.235 1.236
1.323 1.325 1.323 1.323
2.635 2.638 2.639 2.642
1.349
1.253 1.318 2.579
10.875 10.895 11.331 11.237
'Distances between carbonyl oxygens (SHH) or O H oxygens (AHH) on enols opposite to each other. TABLE X: Hydrogen-Bonding Energies of n:l SHHBenzene Complexes (n = 1-6) for 1,3-Propanedione and 1,3-Cyclohexanedione Calculated bv AM1 Method 1,3-propanedione 1,3-~yclohexanedione total total H-bonding energy of the H-bonding energy of the n energy last H-bond energy last H-bond -1.0 -1.1 1 -1.0 -1.1 -5.2 -6.5 2 -6.2 -5.4 3 -11.6 -5.4 -12.2 -5.7 4 -17.1 -5.5 -17.8 -5.6 -7.3 5 -24.4 -24.1 -6.2 -6.1 -32.0 6 -30.5 -7.9 ~
~
~~
?Q Po "b 0
H
0,
0
dOXH Gd H
YJ p J q
H
H
Figure 5. Schematic drawing of the 6:l CHD:benzene complex in the experimentally observed S H H form.
presented in Tables VI1 and X. These values are used in Figure 4 to indicate the relative energies of the aggregates as they form. The energy of the benzene-stabilized cyclic aggregate is lower than the AHT and SHT structure at each step of formation to completion of the ring. Once the ring is formed, no further aggregated H-bonds are possible. However, although the thermodynamic stability of the infinite chain of H-bonds leads to a more stable structure, there does not seem to be an accessible kinetic route from the cyclic structure to AHT. Such a route would require breaking of one H-bond between enols, breaking of six weak bonds between the enols and benzene, and several rotations a b o u t t h e remaining H-bonds. Conclusion The MO calculations presented here indicate that we can un-
derstand the relative energies of several of the possible aggregates that can lead to crystal formation or nucleation. The cooperativity of the hydrogen-bonding network eventually overcomes the energetic barrier@) necessary to transform the monomeric units from the most stable (keto) form to the enol forms observed in the two different crystal structures of CHO. This cooperativity ultimately dictates the form of the crystal.
Acknowledgment. We gratefully acknowledge many helpful conversations with Prof. Margaret Etter (University of Minnesota). We also thank Prof. Chikos (University of Missouri) for providing us with his preliminary data. This work was supported in part by the PSC-BHE, NSF, and IBM Corporation. Registry No. C H D (diketo form), 504-02-9; C H D (monoenol form), 30182-67-3; PPD (diketo form), 542-78-9; PPD (monoenol form), 92776-4.
References and Notes (I) Etter, M. C.; Urbanczyk-Lipkowska, Z.; Jahn, D. A.; Frye, J. S . J . Am. Chem. SOC.1986, 108, 5871. (2) (a) Hodoscek, M.; Kocjan, D.; Hadzi, D. THEOCHEM 1988,42,115. (b) Koehler, J. E. H.; Saenger, W.; Lesyng, B. J . Comput. Chem. 1987, 8, 1090; Remko, M. Z . Phys. Chem. (Munich) 1983,138,223; Del Bene, J. E. J. Chem. Phys. 1980,72,3423;Tse, Y . C.; Newton, M. D. J. Am. Chem. Soc. 1977, 61 1. (3) (a) Steiner, T.; Mason, S.A.; Saenger, W. J . Am. Chem. Soc. 1990, lZ2,6184. (b) Kleeberg, H.; Luck, W. A. P. 2.Phys. Chem. (Leipziq) 1989, 270, 613. (4) Dewar, M. J. S.;Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J . Am. Chem. SOC.1985, 107, 3902. ( 5 ) Dewar, M. J. S.; Thiel, W. J . Am. Chem. SOC.1977, 99,4899. (6) (a) Dannenberg, J. J.; Vinson, L. K. J . Phys. Chem. 1988,92, 5635. (c) Galera, S.; Lluch, J. M.; Oliva, A,; Bertrin, J. THEOCHEM 1988,40, 101. (7) Vinson, L. K.; Dannenberg, J. J. J . Am. Chem. SOC.1989, I l l , 2777. (8) Dannenberg, J. J. J . Phys. Chem. 1988,92,6869; Dannenberg, J. J.; Mezei, M. J . Phys. Chem. 1991, 95, 6396. (9) Smith, B. J.; Swanton, D. J.; Pople, J. A,; Schaefer 111, H. F.; Radom, L. J . Chem. Phys. 1990, 92, 1240. (10) Our nomenclature differs from that employed by Etter, who refers to the positions of the lone pairs (which are not uniquely defined nor experimentally determinable), rather than the H's. (1 1) (a) Schwenke, D. W.; Truhlar, D. G. J . Chem. Phys. 1984,82,2418. (b) Frisch, M. J.; Del Bene, J. E.; Binkley, J. S.;Schaefer, H. F. 111. J. Chem. Phys. 1986.84, 2279. (c) Szalewicz, K.; Cole, S.J.; Kolos, W.; Bartlett, R. J . J. Chem. Phys. 1988, 89, 3662. (1 2) For a discussion see: Jeffrey, G. A,; Saenger, W. Hydrogen Eonding in Eiologicol Structures; Springer-Verlag: Berlin, 1991; p 35. (13) Chikos. J. S.;Hesse, D. G. Private communication. (14) Optimization of this aggregate at HF/6-31G using GAUSSIANBBtook 30 days CPU time on an RS/6000 Model 320H!
