Atomistic structural molecular mechanics models

Empirical energy functions can fulfill the demands required by computational studies of biochemical and biophysical systems. The mathematical equations in empirical energy functions include relatively simple terms to describe the physical interactions that dictate the structure and dynamic properties of biological molecules. In addition, empirical force fields use atomistic models, in which atoms are the smallest particles in the system rather than the electrons and nuclei used in quantum mechanics. These two simplifications allow for the computational speed required to perform the required number of energy calculations on biomolecules in their environments to be attained, and, more important, via the use of properly optimized parameters in the mathematical models the required chemical accuracy can be achieved. The use of empirical energy functions was initially applied to small organic molecules, where it was referred to as molecular mechanics [4], and more recently to biological systems [2,3]. 

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. 

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]. 

There has been an explosion in the application of atomistic and molecular modeling to corrosion and electrochemistry in the past decade. The continued increasing computational power has allowed the development and implementation of atomistic and molecular modeling frameworks that would have been impractical even a short time ago. These frameworks allow the application of fundamental physics at the appropriate scale on assemblies of atoms of a size that provides a more realistic basis than ever before. In some cases, that level is the determination of the electronic structure based on quantum mechanics. Such is the case when determining the energetics of surface structures and reactions. In other cases, the appropriate scale requires the forces between atoms or ions to be calculated, and the effects those forces have on the configuration of atoms and how it changes with time. Surface and solution diffusion are prime examples. 

Part of the power of molecular modeling lies in its ability to isolate aspects of a phenomenon in ways that are simply not possible by experiment. The effects of bond energy on the dissolution or surface diffusion allows one to turn off surface diffusion, for example, to quantitatively determine what effect it has on the dissolution rate and the resulting nanostructure. This example is one of many in which the dependence of critical parameters on the atomistic and molecular composition, as well as the local structure, including defects, can be determined. The insights that such calculations can provide into the overall thermodynamic, mechanical, and kinetic properties of a system are substantial. 

The hybrid methods which combine quantum-mechanical (QM) and classical descriptions are surely one of the mostly well-suited strategies in this context. Two main families of hybrid methods can be defined according to the model used to describe the classical part of the system. Either continuum or atomistic formulations can be introduced where, in the first case, the classical subsystem is described as a dielectric medium while, in the second case, a Molecular Mechanics (MM) formulation is generally adopted. While QM/continuum methods have been largely and successfully applied to molecular solutes in liquid solutions [2-5], QM/MM formulations have been more often used in the field of structured (biological) environments [6-10] even if the study of chemical reaction dynamics in solution represents another important field of applications of the method [11, 12]. 

Within the last two decades, enormous progress has been achieved in the ability to calculate the structures, the properties (e.g., thermodynamic, mechanical, transportation properties), and the reactivity of solids starting from atomistic approaches. The molecular-level models can be classified into three categories. 

Looking at the structure of HMR, it is clear that it occupies several sites on the surface. Some optimized adsorption structures on Pd(lll) surface modeled by molecular mechanics (MM) with the COMPASS (Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies) force field are presented in Fig. 7.9. As the force fields cannot properly model chemisorption and, consequently, exact structures of the adsorbed molecules, the role of the metal surface in the MM calculations was mainly to act as a steric constraint. Depending on the adsorption structure, HMR covers 10-20 Pd surface atoms. 

In another paper in this issue [1], the molecular motions involved in secondary transitions of many amorphous polymers of quite different chemical structures have been analysed in detail by using a large set of experimental techniques (dynamic mechanical measurements, dielectric relaxation, H, 2H and 13C solid state NMR), as well as atomistic modelling. 

---