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Crystal density prediction for cyclic and cage compounds

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj1

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Politzer's approach was extended to predict the crystal densities of cyclic and cage molecules with quantum mechanics (QM) calculated surface electrostatic properties.

Type: Method | Advantage: None | Novelty: New | ConceptID: Met1

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It was found that there is significant improvement in density prediction for cage molecules by replacing the surface area with molecular volume.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con1

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The best rms deviations of calculated values using molecular volume are 0.118 g cm–3 and 0.068 g cm–3 from the experimental values of cyclic and cage compounds respectively.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res1

Introduction

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Knowing the geometry of a molecule, several methods can be used to predict its crystal density.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac1

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The group additivity methods are the simplest, assuming that the volume of a molecule is a linear sum of appropriate atoms and groups.1

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met2

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The possible conformation and packing efficiency are not taken into consideration by these methods.

Type: Method | Advantage: No | Novelty: Old | ConceptID: Met2

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Packing optimization methods are the most sophisticated ones, which build packing arrangements in various space groups.2

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met3

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In a method by Politzer and his co-workers,3 crystal density (ρ, in g cm–3) is correlated with molecular surface electrostatic potential (V(r)) on a 0.001 au isodensity surface (calculated at the HF/STO-5G*//HF/STO-3G* level), characterized by its total variance (σ2tot), where M is molecular mass, and A is the surface area, VS+(ri) and VS–(rj) are the positive and negative value of V(r) on the surface, and V̄S+ and V̄S– are their averages.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met4

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The M/A term reflects the molecular density, and (σ2tot/A) reflects the contribution of packing efficiency to crystal density.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met4

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The M/A term was used in the equation because of its convenience in the calculations and its satisfactory results for the database.3

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met4

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We calculated the density of some cyclic and cage molecules with eqn. (1), and found that replacing the molecular surface area (A) with volume (V) improves the prediction accuracy especially for cage molecules.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con1

Methodology

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Quantum mechanics calculations were carried out with the G98W program.4

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

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Geometries were fully optimized at the HF/STO-3G* level.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

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The optimized geometry was verified to be stable with frequency computation.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

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The electrostatic potential V(r) was obtained from the single point calculations with the HF/STO-5G* basis set on these structures.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

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The average values, V̄S+ and V̄S–, were obtained by averaging the positive or negative values over the points within a shell between the 0.0011 and 0.0009 au isodensity surfaces.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

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The surface area (A) and molecular volume (V) were directly obtained from the isodensity polarized continuum model (IPCM) of self-consistent reaction field (SCRF) calculations in the G98W program.5

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod4

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Curve fitting was performed with an online program, using its 3D polynomial equation simplified linear data modeller (Z = aX + bY + c)6.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod5

Results and discussion

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Compounds in Table 1 are classified into three groups.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res2

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Molecules in Group I are from Politzer's database.3

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

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Except RDX, they are either highly symmetrical small molecules or substituted benzenes.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

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RDX also belongs to Group II.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

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Molecules in Group II are mono- or polycyclic.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

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Most of them are nitramine and they have a variety of molecular shapes.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

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Molecules in Group III have cage structures.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac5

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First, crystal densities of compounds in Group I were calculated using eqn. (1).

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met5

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The calculated σ2tot and surface areas are quite comparable with Politzer's values.3

Type: Result | Advantage: None | Novelty: None | ConceptID: Res3

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The root mean square (rms) deviation of the calculated densities from the experimental values for compounds in Group I is 0.060 g cm–3, which is comparable with that of the original work (0.055 g cm–3).3

Type: Result | Advantage: None | Novelty: None | ConceptID: Res3

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Therefore, our calculations are consistent with that of Politzer.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res3

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The same equation was then used to predict densities of compounds in Group II and Group III.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met6

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It was found that the predictions for compounds in these two groups are poor.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res4

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The rms deviations of the calculated densities from the literature values are 0.153 and 0.126 g cm–3 for compounds in Group II and III respectively.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res5

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Eqn. (1) was then re-parameterized over all molecules in the three groups, and the following equation was obtained: The predictions of crystal densities using eqn. (3) did not improve significantly.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res6

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The rms deviation of the calculated values from the literature values for all molecules in the three groups is 0.110 g cm–3, comparable with 0.126 g cm–3 from eqn. (1) calculations.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res7

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M/A in eqn. (3) was then replaced with M/V, and eqn. (4) was obtained through parameterization over all molecules in the three groups: It is noticed from the rms deviations, that the predictions of eqn. (4) for compounds in Group I are as good as eqn. (1).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res8

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The predictions for compounds in Group II are still very poor.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res9

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However, there is a large improvement for cage molecules in Group III.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res10

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A graphical representation of the calculated and literature densities in Table 1 is given in Fig. 1.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res11

Conclusions

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The predictions of crystal density of cage molecules can be largely improved when replacing M/A in Politzer's equation with M/V.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con1

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For molecules in Group I, the molecular density is well reflected by M/A as well as the M/V term.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res12

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However, for cage molecules in Group III, the molecular density is best reflected by M/V.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res12

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The rms deviations of the calculated values with three equations from the literature values are all very large for compounds in Group II, 0.153, 0.103 and 0.118 g cm–3 respectively.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res13

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The variety of molecular shapes may largely affect molecular packing efficiency.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con2

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Therefore, other terms such as shape descriptors may be included in the relationship in order to give good predictions for compounds in this group for future work.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con2