Natural Bond Orbital Evaluation of AM1-Predicted C−HO Hydrogen

Feb 8, 2003 - Department of Chemistry, University of Missouri-Kansas City, 5100 Rockhill ... Midwest Research Institute, 425 Volker Boulevard, Kansas ...
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Natural Bond Orbital Evaluation of AM1-Predicted C-HsO Hydrogen Bonds in Dimers of 1,5,7,11-Tetraoxaspiro[5.5]Undecane C. David Harris* and Andrew J. Holder

CRYSTAL GROWTH & DESIGN 2003 VOL. 3, NO. 2 239-246

Department of Chemistry, University of Missouri-Kansas City, 5100 Rockhill Road, Kansas City, Missouri 64110

J. David Eick School of Dentistry, University of Missouri-Kansas City, 25th and Holmes Street, Kansas City, Missouri 64108

C. C. Chappelow Midwest Research Institute, 425 Volker Boulevard, Kansas City, Missouri 64110 Received October 23, 2002;

Revised Manuscript Received December 23, 2002

ABSTRACT: Spiroorthocarbonates have potential utility as components of low-shrinkage polymeric materials. Density functional theory, ab initio Hartree-Fock theory, and natural bond orbital (NBO) analysis have been used to characterize AM1-predicted individual C-HsO intermolecular interactions in calculated gas-phase van der Waals dimers of different conformations of 1,5,7,11-tetraoxaspiro[5.5]undecane (TOSU). NBO theory is employed to identify and evaluate individual charge-transfer interactions in a multi-interaction environment. Relative contributions to the stabilization energy arising from charge transfer for any C-HsO close contacts predicted in the calculated geometries are approximated and compared. Emphasis is placed on identification of and differentiation between short-range intermolecular internuclear distances that represent hydrogen bonds and those that represent forced close contacts. C-HsO intermolecular interactions in the unsubstituted TOSU were found to provide maximum energy stabilization in the S4 conformation. Introduction Polymerization shrinkage has been identified as a significant obstacle to the design of new polymer-based dental restorative materials.1 Shrinkage during the polymerization process causes large stresses within the matrix which are often relieved either by the formation of voids or microcracks in the composite, or by an adhesive failure. Alternatively, physical processes coinciding with expansion in volume, such as the freezing of water, result in significant enhancement of adhesion properties.2,3 Accordingly, expanding monomers have received a great deal of attention by designers of dental restorative materials. Monomers that consist of multiple rings and undergo multiple ring openings during polymerization have received much of this attention.4,5 Polymerization shrinkage is thought to result from atoms with internuclear distances at the van der Waals distance in the monomer state closing to covalent distances in the polymer state.6 It was proposed that a monomer that can undergo double ring opening would contribute two pairs of atoms expanding from their covalent internuclear distances in the monomer state to a van der Waals distance in the polymer state, thereby attenuating or even reversing the volume reduction usually expected in polymerization reactions.6 Spiroorthocarbonates, a class of monomers that undergoes quantitative double ring opening polymerization * Address correspondence to C. D. Harris, University of MissouriKansas City, Department of Chemistry, 5100 Rockhill Rd., Kansas City, MO 64110, telephone: 816-235-2287, fax: 816-235-5502, email: [email protected].

with expansion of volume, especially the derivatives of 1,5,7,11-tetraoxaspiro[5.5]undecane (TOSU, 1, Figure 1), have been the subject of considerable study pursuant to use as a constituent of an expanding or nonshrinking matrix resin for dental composites.7 The double ring opening model does not explain the polymerization expansion of monomers that undergo single ring opening polymerizations such as cyclic carbonates8 and benzoxazine resins.9 Ishida and Low proposed that disappearance of intermolecular hydrogen bonds in the monomer followed by formation of intramolecular hydrogen bonds resulting in regions of free volume in the polymer as the cause of nonshrinking polymerizations of benzoxazine monomers.9 Endo et al. hypothesized that the polymerization expansion of the cyclic carbonate was due to strong intermolecular forces in the monomer which were no longer present in the polymer, and a correlation was drawn between calculated dipole moments and net polymerization expansion.8 Previous computational results indicate that 1 may exhibit C-HsO intermolecular hydrogen bonds, and that these intermolecular attractions and the resulting close packing of monomers may contribute to volume expansion upon their elimination during polymerization.10 Previous results also indicate a significant population of a “twist” conformer in the distribution of conformational states of an asymmetric spiroorthocarbonate.11 A similar conformation in TOSU could lead to a highly symmetric system, which could also provide for the existence of increased close packing in the

10.1021/cg0256024 CCC: $25.00 © 2003 American Chemical Society Published on Web 02/08/2003

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Figure 1. 1,5,7,11-tetraoxaspiro[5,5]undecane (TOSU).

Figure 2. Structure of a bimolecular van der Waals complex 1a/1a(1A) for two molecules of 1a calculated using the AM1 semiempirical molecular orbital method. “1a/1a” denotes a bimolecular complex of two molecules of the 1a conformer, while the “1A” in parentheses refers to the first example of a complex calculated at the AM1 level of theory.

monomer state. These results are consistent with the hypothesis offered by Ishida and Low for the polymerization expansion of benzoxazine,9 and can be interpreted as consistent with the hypothesis offered by Endo, et al. for the polymerization expansion of cyclic carbonate.12 The prediction of the weak hydrogen bonds in TOSU was based on the calculation of four internuclear distances less than 2.7 Å between an oxygen on one molecule and a hydrogen on the other in the calculated structure of a gas-phase dimer of 1. The threshold distance of 2.7 Å represents the sum of the van der Waals radii of the two atoms involved in the long-range attractive interaction. The calculated geometry and the internuclear distances of interest are pictured in Figure 2. The structure of this bimolecular van der Waals complex was produced based on calculations using the AM1 semiempirical molecular orbital method.13 This method includes long-range electronic interactions such as hydrogen bonds by the addition of spherical Gaussian functions to the parameter set of each element. Although the utility and relative accuracy of this method for calculating hydrogen bonds have been accepted for some time, even for weak C-HsO hydrogen bonds,14 there remains uncertainty about the reliability of spherical Gaussians with regard to the directional components of hydrogen bonds, other than those introduced by steric interactions. Also, when identifying the presence of hydrogen bonds only by the HsO internuclear distance, it must be understood that the presence of some intermolecular hydrogen bonds within a structure may forcibly constrain the geometry to include short internuclear distances where there is no actual charge transfer, producing the appearance of a hydrogen bond where there in fact is not one. In the case of a

Harris et al.

structure with several apparent hydrogen bonds, such as in Figure 2, it cannot be known which of the four close contacts represent donor-acceptor activity involving significant charge transfer between oxygen and hydrogen, and which, if any, are being held in close contact by surrounding hydrogen bonds. It has also been suggested that the formation of intramolecular hydrogen bonds within the polymer product can produce structures containing free volume spaces, further contributing to positive volume change during polymerization.15 A computational model of such a polymer product can be expected to contain multiple instances of HsO close contacts, some of which may not actually involve charge transfer. If these weak hydrogen bonding interactions, either between monomer structures or within a product structure, are found to make an actual contribution to polymerization expansion, successful use of molecular modeling techniques for the prediction of volume characteristics will depend on a computational method for identifying which interactions are significant and which structures can be expected to produce them. It is particularly important to evaluate the reliability of semiempirical methods with respect to the prediction of weak hydrogen bonds based on the presence of donor-acceptor close contacts in calculated geometries. Computed models of polymer product structures are routinely too large for correlated ab initio methods to be of practical utility for production screening of candidate structures in a large molecular design endeavor. The natural bond orbital (NBO) analysis method16 has been used to accurately determine the relative significance of individual intermolecular interactions in the context of a donor-acceptor model.17,18 NBO analysis expresses the SCF-HF wave function in terms of localized one- and two-center orbitals transformed from the delocalized Hartree-Fock molecular orbitals. This results in a set of orbitals more closely recognizable as s, p, and d orbitals and various hybrids. Instead of virtual molecular orbitals that are expressly unoccupied, NBO analysis expresses virtual orbital space in terms of antibonding and Rydberg orbitals that can be partially occupied. Small occupancies by these orbitals represent departures from a classic unperturbed Lewis structure containing completely localized and doubly occupied bonding and lone pair orbitals. These departures can be thought of as delocalizations of the electron density relative to that idealized unperturbed Lewis representation of the density. The amount of stabiliza(2) tion energy ∆E*nσ provided by a typical n f σ* delocalization can be approximated by the formula

〈n|F|σ*〉2 σ* - n

(2) ∆E*nσ ) -2

(1)

where F is the Fock operator and σ* and n are NBO orbital energies.16 NBO analysis is often used to demonstrate and quantify σ f σ* and n f σ* electronic interactions such as those involved in hyperconjugation, the anomeric effect,19,20 and intermolecular charge transfer in hydrogen bonding.17,18 The purpose of this study is to use density functional theory, ab initio Hartree-Fock theory, and NBO analysis to further characterize the C-HsO

Orbital Evaluation of C-H-O Hydrogen Bonds

Crystal Growth & Design, Vol. 3, No. 2, 2003 241 Table 1. Relative Energies of Conformers Identified as Local Minima (kcal/mol)

Figure 3. Representations of the conformational isomers of 1 identified by AM1, RHF/6-31+g(d), and RB3LYP/6-31+g(d,p) geometry optimization calculations.

intermolecular interactions in calculated gas-phase van der Waals dimers of different conformations of 1 (Figure 3), and to approximate and compare the relative contributions to the stabilization energy arising from charge transfer for any C-HsO close contacts predicted in the calculated geometries. Calculations Semiempirical calculations at the AM1 level of theory were performed using the AMPAC 6.55 with Graphical User Interface21 suite of semiempirical quantum mechanical programs. Initial guesses for molecular geometries of 1 were based on all possible combinations of chair, boat and twist-boat conformations for both rings of the spirocyclic structure. Transition state geometries were validated by frequency calculations producing a single negative eigenvalue. Correspondence of the negative eigenvalue to the transition vector was ensured by subsequent geometry optimizations of transition structures perturbed in both directions of the transition vector. Calculations were repeated at the RHF/6-31 g(d) and RB3LYP/631+g(d,p)22 levels of theory implemented in the Gaussian 94 suite of computational tools.23 Geometries of van der Waals dimer complexes were determined by AM1 energy minimization calculations on pairs of optimized structures of 1 in different conformations. Multiple different orientations of each pair were attempted until repeated attempts failed to produce new structures representing stationary points. Each optimized structure was submitted as an initial guess for a subsequent geometry optimization at the RB3LYP/6-31+g(d,p) level of theory. It has previously been demonstrated that the RB3LYP hybrid functionals produce acceptable optimized structures for intermolecular hydrogen bonds.24,25 The Hartree-Fock electron densities of the DFT structures were then analyzed using NBO theory for intermolecular non-Lewis delocalizations.

Results and Discussion Conformational Analysis. A series of AM1 energy minimization calculations using different starting geometries for 1 resulted in repeated convergence on the set of conformers shown in Figure 3. The conformer that was calculated to have a local minimum with both of its rings in the chair orientation (1a) was found to represent the global minimum on the conformational potential energy surface and to possess C2 symmetry.

A conformer with one ring having a chair orientation and the other with a twist structure (1b) was calculated to be a local minimum with C1 symmetry. The AM1 calculated heat of formation of 1b is just 0.86 kcal/mol higher than that of 1a. Two other structures were found to be stationary points according to AM1. Both of them consist of two twist-oriented rings. One conformer (1c) was calculated to be a local minimum with heat of formation 2.63 kcal/mol higher than 1a. The hydrocarbon portions of the rings of 1c lie in nearly the same plane, which contains the primary axis of D2 symmetry. Energy minimization of the other conformer (1d) converged on a geometry with the hydrocarbon portion of both rings in orthogonal planes that intersect along the primary axis of the structure’s S4 symmetry. The calculated heat of formation of 1d was 1.72 kcal/mol higher than 1a. The relative energies of the four conformers calculated at the three levels of theory employed in this study are summarized in Table 1. AM1 calculations show 1c to have the highest energy of the four conformers, while HF and DFT results show 1d to have the highest energy. HF and DFT results indicate a larger range in relative energies among the conformers (5.2383 and 5.2083 kcal/mol, respectively) than do the AM1 results (2.63 kcal/mol). These differences might be explained by the minimal basis set employed by the AM1 method, or by artifacts of the parametrization process such as the calculation at finite temperature. Representations of the structures determined by AM1 gradient minimization calculations to be conformational transition states of 1 are shown in Figure 4. These results were validated by AM1 frequency calculations, each of which resulted in a single imaginary frequency along the transition vector between two of the local

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Harris et al. Table 2. Calculated Energies of Conformational Isomers of 1 Identified as Transition Structures; Relative to the Calculated Energy of 1a (kcal/mol)

Figure 4. Representations of the conformational transition structures of 1 identified by AM1, RHF/6-31+g(d), and RB3LYP/ 6-31+g(d,p) gradient minimization calculations.

minimum structures pictured in Figure 3. Two of the calculated conformational transition structures, 1ab and 1ba, are both feasible transition states for the transformations between 1a and 1b. The AM1 heat of formation for 1ab is calculated to be 3.24 kcal/mol higher than that of 1a, the global minimum structure. Transition state 1ba has a calculated heat of formation 3.94 kcal/mol higher than that of conformer 1a. 1bc is the calculated transition structure between 1b and 1c. The heat of formation for 1bc is calculated to be 4.94 kcal/mol higher than that of 1a. 1bd, which is the calculated transition structure between 1b and 1c, has a calculated heat of formation 4.43 kcal/mol higher than that of 1a. The relative energies of the four conformational transition structures calculated at the three levels of theory employed in this study are summarized in Table 2. As in the calculations results for the conformational local minima, HF and DFT results indicate a larger range in relative energies among the conformational transition structures (2.63 and 2.66 kcal/mol, respectively) than do the AM1 results (1.70 kcal/mol). HF and DFT results also demonstrate significantly higher energy barriers for all of the conformational transformations, and a different order when the structures are ranked according to energy. The greatest differences in the results provided by the various methods are found in the calculated conformational energy barriers. The HF and DFT results predict barriers between about 3 and 5 kcal/mol higher than the AM1 results. The AM1 method is known to produce rotational barriers that are consistently too low.26 However, in this study, AM1 energy differences between conformers are also lower than those calculated using HF and DFT. Perhaps the energy calculated using AM1 for the global minimum conformer is too high. If so, this could possibly be explained by the neglect of long-range intramolecular stabilizing interactions for which the addition of spherical Gaussians to the AM1 parameter set were not designed to provide. Calculation of van der Waals Dimer Complexes. Additional AM1 calculations involving two molecules of 1a resulted in the identification of a bimolecular complex with apparent C-HsO hydrogen bonding that is

Figure 5. Structure of a second bimolecular van der Waals complex, 1a/1a(2A), for two molecules of 1a calculated using the AM1 semiempirical molecular orbital method.

different than complex 1a/1a(1A) pictured in Figure 2. This new structure, 1a/1a(2A), represented in Figure 5, also contains four OsH internuclear distances calculated by AM1 that are shorter than 2.7 angstroms. The AM1 calculated stabilization energy for 1a/1a(1A) is -3.25 kcal/mol, and for 1a/1a(2A) is -2.98 kcal/mol. Two of the OsH internuclear distances of interest in the 1a/1a(2A) structure, at 2.62 and 2.67 Å, are longer than those in 1a/1a(1A) and are near the 2.7 Å threshold for C-HsO hydrogen bonding defined by the sum of the two atoms’ van der Waals radii. The other two OsH close contacts, at 2.38 and 2.47 Å, are similar to the internuclear distances for the close contacts of interest in the first structure. The two longer internuclear distances in 1a/1a(2A) could be examples of

Orbital Evaluation of C-H-O Hydrogen Bonds

Figure 6. Structure of the bimolecular van der Waals complex 1d/1d(A) for two molecules of 1d calculated using the AM1 semiempirical molecular orbital method.

Figure 7. Structure of the bimolecular van der Waals complex 1a/1a(1D) for two molecules of 1a optimized using density functional calculations at the RB3LYP/6-31+g(d,p) level of theory, and with the 1a/1a(1A) structure in Figure 2 as the initial geometry.

forced interactions, held in position by the two stronger attractive interactions. No structure was found to represent a stable bimolecular van der Waals complex for either 1b or 1c. AM1 calculations did identify a stable complex for 1d with four intermolecular OsH close contacts and a calculated stabilization energy of -3.36 kcal/mol. This structure, 1d/1d(A), and the close contacts of interest are represented in Figure 6. The symmetric structure of 1d is also demonstrated in the structure of the complex, which is the only one of the three calculated bimolecular structures that appears to possess a C2 axis. The four OsH close contacts were calculated to have internuclear distances of 2.32, 2.32, 2.52, and 2.53 Å, respectively. These results suggest stronger hydrogen bonding and closer packing for bimolecular complexes involving 1d than for those of 1a. The three bimolecular structures previously optimized at the AM1 level of theory were submitted to geometry optimization calculations using the RB3LYP density functional method and the 6-31+g(d,p) set of basis functions. All three starting structures resulted in stable bimolecular complexes when optimized using DFT. However, all of the calculated intermolecular OsH internuclear distances were significantly longer than the corresponding distances calculated using AM1. Only two

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Figure 8. Structure of the bimolecular van der Waals complex 1a/1a(2D) for two molecules of 1a optimized using density functional calculations at the RB3LYP/6-31+g(d,p) level of theory, and with the 1a/1a(2A) structure in Figure 5 as the initial geometry.

of the resulting structures were computed to contain any close contacts with internuclear distances of less than 2.7 Å. The DFT structure corresponding to the AM1 structure 1a/1a(1A) in Figure 2 is represented as complex 1a/1a(1D) in Figure 7. For purposes of comparison of the relative energies of stabilization from intermolecular interactions within the complexes calculated in this study, the energy of stabilization is computed by taking the difference of the calculated energy of the complex and the sum of the energies of two isolated molecules. Since all calculations involve isomers of the same molecular system with identical basis sets, computational deviations from experimental measurements due to basis set superposition error are not considered. In this manner, the energy of stabilization for the intermolecular interaction represented in the 1a/1a(1D) complex was calculated at the RB3LYP/6-31+g(d,p) level of theory to be -2.4602 kcal/mol. This is 0.79 kcal/ mol lower than the AM1 stabilization energy calculated for the corresponding AM1 complex, 1a/1a(1A), shown in Figure 2. All four of the HsO close contact distances are longer than their AM1 analogues. Two of the distances, at 3.0284 and 2.8452 Å, are outside of the range considered necessary for intermolecular charge transfer. The other two close contact distances, calculated to be 2.63 and 2.63 Å, can be considered candidates for C-HsO hydrogen bonds. The DFT structure optimized starting with the AM1optimized 1a/1a(2A) structure in Figure 5 is represented as 1a/1a(2D) in Figure 8. In this structure, none of the calculated HsO internuclear distances are shorter than 2.7 Å. When ranked according to magnitude, the relative distances are in the same order as those calculated using AM1. The shortest two close contact distances, at 2.75 and 2.72 Å, are in the same positions as the two shortest intermolecular internuclear distances calculated in the corresponding AM1 complex. They are close to 2.7 Å, and might represent opportunities for intermolecular charge transfer. The two longest close contact distances, at 2.95 and 2.87 Å, are also positioned analogously to the AM1 results, but are too long to be considered candidates for intermolecular hydrogen bonds. The calculated energy of stabilization is -2.31 kcal/mol. As in the AM1 results, this is the

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(2) Figure 11. Calculated NBO analysis values for ∆E*nσ corresponding to the four C-HsO interactions in 1a/1a(2D).

Figure 9. Structure of the bimolecular van der Waals complex 1d/1d(D) for two molecules of 1d optimized using density functional calculations at the RB3LYP/6-31+g(d,p) level of theory, and with the 1d/1d(A) structure in Figure 6 as the initial geometry.

(2) Figure 10. Calculated NBO analysis values for ∆E*nσ corresponding to the four C-HsO interactions in complex 1a/ 1a(1D).

smallest stabilization energy of the three bimolecular complexes in this study. The DFT structure for the complex between two molecules of 1d optimized starting with the AM1 geometry in Figure 6 (1d/1d(A)) is shown as 1d/1d(D) in Figure 9. Like in the AM1 results, this structure possesses the shortest intermolecular HsO distances calculated at the same level of theory, and maintains the symmetric distribution of potential hydrogen bonds within the complex. The calculated HsO distances near the exterior of the complex, 2.73 and 2.72 Å, are very close to each other, and to the 2.7 Å van der Waals boundary. The calculated HsO distances for the contracts near the interior of the complex, are also nearly equal to each other (2.62 Å) and are the shortest of any within the complexes calculated at the RB3LYP/6-31+g(d,p) level of theory in this study. The calculated DFT stabilization energy for this complex is -5.17 kcal/mol, in agreement with AM1 that 1d gains more stabilization from intermolecular interaction than does 1a. However, AM1 calculations produce a stabilization energy for 1d/1d(A) 0.11 kcal/mol greater than that of 1a/1a(1A), whereas DFT results show it

to be 2.71 kcal/mol greater for 1d/1d(D) than for 1a/ 1a(1D). These DFT results suggest that the 1d conformer might be more stable in the solid phase than the 1a conformer, when the possibility of multiple cooperative intermolecular interactions for each molecule is considered. Natural Bond Orbital Analysis. NBO population analysis calculations were performed on the HF electron densities of the three DFT complex structures. A value for 1.0 kcal/mol for net binding energies between molecules in small complexes has previously been used as a threshold for distinguishing complexes of donoracceptor type (such as H-bonded complexes) from those in which charge transfer is secondary to electrostatic and dispersion interactions.17 It is therefore postulated (2) that a value for ∆E*nσ (which represents the amount of energy stabilization due to a n f σ* interaction) greater than 1.0 kcal/mol can be associated with significant charge transfer for a single HsO close contact within a complex potentially containing multiple instances of charge-transfer interactions. (2) Calculated values for ∆E*nσ pertaining to the four interactions within complex 1a/1a(1D) are shown in Figure 10. In this complex, the energy stabilization due to charge transfer appears to roughly correlate to the HsO internuclear distance. For the longest calculated HsO distance, 3.0284 Å, the value for ∆E(2) is 0.40 kcal/ mol. The interaction with the next longest distance, 2.8452 Å, is also below the threshold for significant charge transfer with a value for ∆E(2) of 0.61 kcal/mol. The close contact with an internuclear distance of 2.63 Å would be considered a candidate for a C-HsO hydrogen bond based on its HsO distance less than 2.7 Å. However, based on the ∆E(2) value of 0.98 kcal/mol, the significance of charge transfer in this interaction is borderline. Finally, the interaction with the shortest Hs O internuclear distance of 2.63 Å has the highest value for ∆E(2), 1.37 kcal/mol. This interaction meets both criteria for designation as a C-HsO hydrogen bond. Calculated values for ∆E(2) corresponding to the four interactions within complex 1a/1a(2D) are shown in Figure 11. None of the interactions possess a calculated ∆E(2) greater than 1.0 kcal/mol, so according to the criteria invoked in this study, none of the interactions can be designated a hydrogen bond. It is noteworthy that ∆E(2) does not strictly correlate to HsO internuclear distance in this complex. The longest HsO

Orbital Evaluation of C-H-O Hydrogen Bonds

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point at 0.98 kcal/mol could also be a forced close contact. However, the lone pairs of this particular oxygen atom are donating electron density into two hydrogen receptor atoms. The resulting dilution of available density may also account for the relatively low stabilization energy corresponding to the single close contact. Calculated values for ∆E(2) for the four interactions between molecules in complex 1d/1d(D) are shown in Figure 13. All four of the close contacts under consideration have ∆E(2) values greater than 1.0 kcal/mol. The two interior interactions with HsO internuclear distances of 2.62 and 2.62 Å provide values for ∆E(2) of 1.44 and 1.43 kcal/mol, respectively. The interactions located toward the exterior of the complex with HsO internuclear distances of 2.73 and 2.72 Å have values for ∆E(2) of 1.10 and 1.09 kcal/mol, respectively. The symmetry expressed in the geometry of the structure is also seen in the ∆E(2) values to two significant figures. Conclusion (2) Figure 12. Relationship between ∆E*nσ and calculated Hs O internuclear distance.

(2) Figure 13. Calculated NBO analysis values for ∆E*nσ corresponding to the four C-HsO interactions in complex 1d/ 1d(D).

distance of 2.95 Å does correspond to the smallest ∆E(2) (0.34 kcal/mol), but the shortest HsO distance of 2.72 Å produces a ∆E(2) value of 0.67 kcal/mol, which is near the median value for this complex. It is hypothesized that a short HsO internuclear distance corresponding to an uncharacteristically low value for ∆E(2) is emblematic of a close contact forced by nearby intermolecular attractions or other structural features. The relationship between all of the values for ∆E(2) calculated in this study and their corresponding HsO internuclear distances are charted in Figure 12. Four of the data points deviate from the apparent correlation. The points at 2.95 and 3.03 Å are well outside the criteria for donor-acceptor behavior and therefore are not expected to correlate. The point at 0.67 kcal/mol results in less stabilization energy than required to reside on the trend line, and is therefore more likely to be a forced close contact. Using similar reasoning, the

The HsO internuclear distances calculated at the RB3LYP/6-31+g(d,p) level of theory that are near the van der Waals radii sum of 2.7 Å correspond to values for ∆E(2) that are near the threshold value of 1.0 kcal/ mol. Therefore, it is concluded that AM1-calculated C-HsO hydrogen bonds result in values for HsO intermolecular internuclear distances that are artificially small. Furthermore, it is difficult to differentiate between short-range intermolecular internuclear distances that represent hydrogen bonds and those that represent forced close contacts. NBO analysis can assist in the identification of individual forced close contacts in an environment with multiple apparent hydrogen bonding interactions. These results suggest that the 1d conformer of 1 is likely to be predominant in the solid phase. A solid composed of units of 1d could be expected to have the greatest energy stabilization from intermolecular charge transfer, tighter and more symmetric molecular packing, and a more periodic electron density than one composed of units of 1a. The S4 symmetry of 1d makes possible a higher degree of close packing than might be expected from a molecule of this size. This finding is consistent with hypotheses that invoke tight molecular packing and strong intermolecular forces to explain the high degree of polymerization expansion observed in 1. Acknowledgment. This research was supported in part by NIH/NIDR Grant Nos. DE08450 and DE09696. References (1) Bailey, W. J. “Cationic Polymerization with Expansion in Volume”; J. Macromol. Sci.-Chem. 1975, 9, 849. (2) Cohen, M. S.; Bluestein, C.; Dunkel, M. “Monomers Which Expand on Polymerization II”, Proc. 30th Natl. SAMPE Symp., Society for the Advancement of Material and Process Engineering, 1985, 1026. (3) Stansbury, J. W.; Bailey, W. J. “Evaluation of Spiro Orthocarbonate Monomers Capable of Polymerization with Expansion as Ingredients in Dental Composite Materials,” In Progress in Biomedical Polymers; Gebelein, C. G. and Dunn, R. L., Eds.; Plenum Press: Boca Raton, 1990; p 133. (4) Byerley, T. J.; Eick, J. D.; Chen, G. P.; Chappelow, C. C.; Millich, F. “Synthesis and Polymerization of New Expanding Dental Monomers”, Dent. Mater. 1992, 8, 345.

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