Crystal packing energy minimizations

Experimental tilt angles have usually an accuracy of at best 3°, leading to an error of about 0.1 A in cell axes. The calculated third cell axis will show a higher deviation. If possible an internal standard should be used for calibration purposes but a higher accuracy will be obtained with a Pawley fit (e.g. fit forP CuPc in Fig. 6) from x-ray powder diffraction data [11]. Especially for packing energy minimization used for simulation methods it is essential to determine the cell parameters as precise as possible. In the case of polymorphism, it is essential to use x-ray powder diffraction to ensure that bulk and investigated nano crystals represent the same modifications. 

Figure 6. Application of packing energy minimization method to poly(ethylene oxide) (16). (a) Starting model of uniform helix (b) stable crystal structure model obtained by energy minimization calculations and (c) the structure determined by x-ray analysis.

In the case of crystals, both intramolecular (conformational) and packing energies should be taken into account simultaneously. Such a total energy minimization method, with suitable crystallographic constraints, has been applied in different steps of the analysis of crystalline structures of three different synthetic polymers. Structures of these molecules, namely, isotactic trans-1,4-poly-penta-1,3-diene (ITPP), poly-pivalolactone (PPVL), and isotactic cis-1,4-poly(2-methyl-penta-1,3-diene)(PMPD), do not have troublesome features such as charged groups, counterions, and solvent molecules. 

We conclude that a) all degrees of freedom should be unconstrained (including those related to the shape of the sugar rings)/ b) the packing forces can significantly influence the conformation even of a polymer main chain and c) a suitable potential set (with all atoms), used in total energy minimization, can account for these effects. With these considerations in mind, we attempted to model the crystal structures of DeS and an isolated chain of Hep. 

As molecular packing calculations involve just simple lattice energy minimizations another set of tests have focused on the finite temperature effects. For this purpose, Sorescu et al. [112] have performed isothermal-isobaric Monte Carlo and molecular dynamics simulations in the temperature range 4.2-325 K, at ambient pressure. It was found that the calculated crystal structures at 300 K were in outstanding agreement with experiment within 2% for lattice dimensions and almost no rotational and translational disorder of the molecules in the unit cell. Moreover, the space group symmetry was maintained throughout the simulations. Finally, the calculated expansion coefficients were determined to be in reasonable accord with experiment. 

Gibson, K. D. and Scheraga, H. A. (1995). Crystal packing without symmetry constraints. 2. Possible crystal packings of benzene obtained by energy minimization from multiple starts. J. Phys. Chem., 99, 3765-73. [185]... 

The MSI Polymorph Predictor (PP) is based on a four-step method. " " Sampling via Monte Carlo simulated annealing provides a starting set of trial structures. These are clustered to delete similar structures, minimized to create low energy crystal packings, and once more clustered to remove duplicates. Since the method is under continuous development and the current implementation differs significantly in some places from the procedure originally published, we present it below in relative detail. 

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