Crystal force field methods

Brodersen S, Wilke S, Leusen FJJ, Engel GE (2005) Comparison of static and fluctuating charge models for force-field methods applied to organic crystals. Cryst Growth Des 5(3) 925—933... 

The various types of successful approaches can be classified into two groups empirical model calculations based on molecular force fields and quantum mechanical approximations. In the first class of methods experimental data are used to evaluate the parameters which appear in the model. The shape of the potential surfaces in turn is described by expressions which were found to be appropriate by semiclassicala> or quantum mechanical methods. Most calculations of this type are based upon the electrostatic model. Another more general approach, the "consistent force field method, was recently applied to the forces in hydrogen-bonded crystals 48> 49>. 

Meso- and D,L-2,3-dimethoxy-2,3-diphenylsuccinonitrile 39 were obtained in a 1 1 ratio by a preparative dimerization procedure. Their configurations were assigned by crystal structure analysis 74). According to nmr both diastereomers have a configuration with the phenyl groups in the anti position. From a conformational analysis by the force field method it was concluded that these conformations remain the preferred ones also for the isolated molecules meso-39 was calculated to be 1.2 kcal mol-1... 

M. G. B. Drew, S. Hollis, and P. C. Yates, / Chem. Soc., Dalton Trans., 1829 (1985). Studies in the Flexibility of Macrocycle Ligands. Calculation of Macrocycle Cavity Size by Force-Field Methods. Crystal and Molecular Structures of [CoLCl][CIO.,], and [CuLlfPFgJ jL = 2,13-Dimethyl-3,6,9,12,18-pentaazabicyclo[12.3.1]octadeca-l(18),i4,16-triene. ... 

The simplest crystal calculation consists of taking the atomic coordinates, cell data and space group for a crystal structure from an X-ray determination, building a static cluster of molecules to represent the crystal, and calculating all the interaction energies by some potential. This can be done by force field methods, Eq. (1.1.25) (time for one calculation a few milliseconds) or by Pixel, Eq. (1.1.34) (time for one calculation a few minutes). Figure 1.1.1 shows that the results are of comparable accuracy (remember that experimental values themselves are no more accurate than 5-10 kj mol-1). The UNI empirical force field [9] uses however about 100 parameters while the Pixel method uses only a few. 

The structure and energy of D-sorbitol has been calculated using an empirical force-field method bond lengths and angles are in reasonable agreement with crystal structure X-ray and neutron... 

The main alternative approach to force field methods that has emerged in the past few years is the application of solid-state (periodic) DFT calculations for the lattice energy minimization and energetic evaluation of predicted crystal structures. The main weakness of DFT is its failure to account for the attractive dispersion interactions between... 

If the nnit cell parameters are known, it is often easy to find a possible arrangement of the molecnles within the nnit cell. Kitaigorodski demonstrated this long ago using a mechanical apparatus. This approach should be readily extendable to force-field methods. It requires that the structure of the molecules in the crystal be known in advance, and hence it is a mnch easier problem than that normally solved in crystallography, where one must determine both the structure of the molecule and that of the crystal at the same time. The structure of the crystal alone should be found relatively easily. Numerous methods for dealing with this problem have become available recently, and are being explored. ... 

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