Force fields crystal structure

Fig. 3a-e. Supermolecular structures of polymers crystallized in various force fields a structure of the shish-kebab type, b structure formed during crystallization in a capillary with a conical inlet and c structure of a polymer crystallized at hydrostatic compression at 4 x 108 Pa... 

This article reviews progress in the field of atomistic simulation of liquid crystal systems. The first part of the article provides an introduction to molecular force fields and the main simulation methods commonly used for liquid crystal systems molecular mechanics, Monte Carlo and molecular dynamics. The usefulness of these three techniques is highlighted and some of the problems associated with the use of these methods for modelling liquid crystals are discussed. The main section of the article reviews some of the recent science that has arisen out of the use of these modelling techniques. The importance of the nematic mean field and its influence on molecular structure is discussed. The preferred ordering of liquid crystal molecules at surfaces is examined, along with the results from simulation studies of bilayers and bulk liquid crystal phases. The article also discusses some of the limitations of current work and points to likely developments over the next few years. 

It is worth noting that much of the development work for the MM force fields has centred on low energy structures of molecules. Consequently, some of the force constants are less applicable to higher energy molecular structures that can occur in molecular dynamics simulations of liquid crystals. 

Finally, there are groups of liquid crystals where, at the current time, force fields are not particularly useful. These include most metal-containing liquid crystals. Some attempts have been made to generalise traditional force fields to allow them to cover more of the periodic table [40, 43]. However, many of these attempts are simple extensions of the force fields used for simple organic systems, and do not attempt to take into account the additional strong polarisation effects that occur in many metal-containing liquid crystals, and which strongly influence both molecular structure and intermolecular interactions. 

Molecular mechanics force fields have largely been parameterised using the best available data from the gas phase and (in some cases) from liquid phase or solution data. The question therefore arises as to how applicable molecular mechanics force fields are to predicting structures of molecules in the liquid crystal phase. There is now good evidence from NMR measurements that the structure of liquid crystal molecules change depending on the nature of their... 

The rapid rise in computer speed over recent years has led to atom-based simulations of liquid crystals becoming an important new area of research. Molecular mechanics and Monte Carlo studies of isolated liquid crystal molecules are now routine. However, care must be taken to model properly the influence of a nematic mean field if information about molecular structure in a mesophase is required. The current state-of-the-art consists of studies of (in the order of) 100 molecules in the bulk, in contact with a surface, or in a bilayer in contact with a solvent. Current simulation times can extend to around 10 ns and are sufficient to observe the growth of mesophases from an isotropic liquid. The results from a number of studies look very promising, and a wealth of structural and dynamic data now exists for bulk phases, monolayers and bilayers. Continued development of force fields for liquid crystals will be particularly important in the next few years, and particular emphasis must be placed on the development of all-atom force fields that are able to reproduce liquid phase densities for small molecules. Without these it will be difficult to obtain accurate phase transition temperatures. It will also be necessary to extend atomistic models to several thousand molecules to remove major system size effects which are present in all current work. This will be greatly facilitated by modern parallel simulation methods that allow molecular dynamics simulations to be carried out in parallel on multi-processor systems [115]. 

The crystal structure of the zinc complex of 6,13-bis(2-pyridinyl)-1,4,8,11-tetraazacyclotetrade-cane (79) shows an octahedral zinc with minimal distortion which is in close agreement with that expected from force field calculations.690... 

Most of the force fields described in the literature and of interest for us involve potential constants derived more or less by trial-and-error techniques. Starting values for the constants were taken from various sources vibrational spectra, structural data of strain-free compounds (for reference parameters), microwave spectra (32) (rotational barriers), thermodynamic measurements (rotational barriers (33), nonbonded interactions (1)). As a consequence of the incomplete adjustment of force field parameters by trial-and-error methods, a multitude of force fields has emerged whose virtues and shortcomings are difficult to assess, and which depend on the demands of the various authors. In view of this, we shall not discuss numerical values of potential constants derived by trial-and-error methods but rather describe in some detail a least-squares procedure for the systematic optimisation of potential constants which has been developed by Lifson and Warshel some time ago (7 7). Other authors (34, 35) have used least-squares techniques for the optimisation of the parameters of nonbonded interactions from crystal data. Overend and Scherer had previously applied procedures of this kind for determining optimal force constants from vibrational spectroscopic data (36). 

The procedure of Lifson and Warshel leads to so-called consistent force fields (OFF) and operates as follows First a set of reliable experimental data, as many as possible (or feasible), is collected from a large set of molecules which belong to a family of molecules of interest. These data comprise, for instance, vibrational properties (Section 3.3.), structural quantities, thermochemical measurements, and crystal properties (heats of sublimation, lattice constants, lattice vibrations). We restrict our discussion to the first three kinds of experimental observation. All data used for the optimisation process are calculated and the differences between observed and calculated quantities evaluated. Subsequently the sum of the squares of these differences is minimised in an iterative process under variation of the potential constants. The ultimately resulting values for the potential constants are the best possible within the data set and analytical form of the chosen force field. Starting values of the potential constants for the least-squares process can be derived from the same sources as mentioned in connection with trial-and-error procedures. 

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