Potential molecular dynamics simulation

Famulari, A., Specchio, R., Sironi, M., and Raimondi, M. (1998) New basis set superposition error free ab initio MO-VB interaction potential molecular dynamics simulation of water at critical and supercritical conditions, J. Chem. Phys., 108, 3296-3303. 

Progress in the theoretical description of reaction rates in solution of course correlates strongly with that in other theoretical disciplines, in particular those which have profited most from the enonnous advances in computing power such as quantum chemistry and equilibrium as well as non-equilibrium statistical mechanics of liquid solutions where Monte Carlo and molecular dynamics simulations in many cases have taken on the traditional role of experunents, as they allow the detailed investigation of the influence of intra- and intemiolecular potential parameters on the microscopic dynamics not accessible to measurements in the laboratory. No attempt, however, will be made here to address these areas in more than a cursory way, and the interested reader is referred to the corresponding chapters of the encyclopedia. 

Field, M.J., Bash, P.A., Karplus, M. A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations. J. Comput. Chem. 11 (1990) 700-733. 

Although, the notion of molecular dynamics was known in the early turn of the century, the first conscious effort in the use of computer for molecular dynamics simulation was made by Alder and Wainright, who in their paper [1] reported the application of molecular dynamics to realistic particle systems. Using hard spheres potential and fastest computers at the time, they were able to simulate systems of 32 to 108 atoms in 10 to 30 hours. Since the work of Alder and Wainright, interests in MD have increased tremendously, see... 

A molecular dynamics simulation samples the phase space of a molecule (defined by the position of the atoms and their velocities) by integrating Newton s equations of motion. Because MD accounts for thermal motion, the molecules simulated may possess enough thermal energy to overcome potential barriers, which makes the technique suitable in principle for conformational analysis of especially large molecules. In the case of small molecules, other techniques such as systematic, random. Genetic Algorithm-based, or Monte Carlo searches may be better suited for effectively sampling conformational space. 

How can we apply molecular dynamics simulations practically. This section gives a brief outline of a typical MD scenario. Imagine that you are interested in the response of a protein to changes in the amino add sequence, i.e., to point mutations. In this case, it is appropriate to divide the analysis into a static and a dynamic part. What we need first is a reference system, because it is advisable to base the interpretation of the calculated data on changes compared with other simulations. By taking this relative point of view, one hopes that possible errors introduced due to the assumptions and simplifications within the potential energy function may cancel out. All kinds of simulations, analyses, etc., should always be carried out for the reference and the model systems, applying the same simulation protocols. 

A typical molecular dynamics simulation comprises an equflibration and a production phase. The former is necessary, as the name imphes, to ensure that the system is in equilibrium before data acquisition starts. It is useful to check the time evolution of several simulation parameters such as temperature (which is directly connected to the kinetic energy), potential energy, total energy, density (when periodic boundary conditions with constant pressure are apphed), and their root-mean-square deviations. Having these and other variables constant at the end of the equilibration phase is the prerequisite for the statistically meaningful sampling of data in the following production phase. 

The Morse function rises more steeply ihan ihe harmonic potential at short bonding distances. This difference can be important especially during molecular dynamics simulations, where thermal energy takes a molecule away from a potential minimum. ... 

TIte NCC water model. (After Corongiu G 1992. Molecular Dynamics Simulation fir Liquid Water Using risable and Flexible Potential. International Journal of Quantum Chemistry 42 1209-1235.)... 

The thermodynamic properties that we have considered so far, such as the internal energy, the pressure and the heat capacity are collectively known as the mechanical properties and can be routinely obtained from a Monte Carlo or molecular dynamics simulation. Other thermodynamic properties are difficult to determine accurately without resorting to special techniques. These are the so-called entropic or thermal properties the free energy, the chemical potential and the entropy itself. The difference between the mechanical emd thermal properties is that the mechanical properties are related to the derivative of the partition function whereas the thermal properties are directly related to the partition function itself. To illustrate the difference between these two classes of properties, let us consider the internal energy, U, and the Fielmholtz free energy, A. These are related to the partition function by ... 

There are many variants of the predictor-corrector theme of these, we will only mention the algorithm used by Rahman in the first molecular dynamics simulations with continuous potentials [Rahman 1964]. In this method, the first step is to predict new positions as follows ... 

Just as one may wish to specify the temperature in a molecular dynamics simulation, so may be desired to maintain the system at a constant pressure. This enables the behavior of the system to be explored as a function of the pressure, enabling one to study phenomer such as the onset of pressure-induced phase transitions. Many experimental measuremen are made under conditions of constant temperature and pressure, and so simulations in tl isothermal-isobaric ensemble are most directly relevant to experimental data. Certai structural rearrangements may be achieved more easily in an isobaric simulation than i a simulation at constant volume. Constant pressure conditions may also be importai when the number of particles in the system changes (as in some of the test particle methoc for calculating free energies and chemical potentials see Section 8.9). 

The pressure often fluctuates much more than quantities such as the total energy in constant NVE molecular dynamics simulation. This is as expected because the pressure related to the virial, which is obtained as the product of the positions and the derivativ of the potential energy function. This product, rijdf rij)/drij, changes more quickly with than does the internal energy, hence the greater fluctuation in the pressure. 

The first molecular dynamics simulations of a lipid bilayer which used an explicit representation of all the molecules was performed by van der Ploeg and Berendsen in 1982 [van dei Ploeg and Berendsen 1982]. Their simulation contained 32 decanoate molecules arranged in two layers of sixteen molecules each. Periodic boundary conditions were employed and a xmited atom force potential was used to model the interactions. The head groups were restrained using a harmonic potential of the form ... 

Umbrella sampling attempts to overcome the sampling problem by modifying the potenti function so that the unfavourable states are sampled sufficiently. The method can be use with both Monte Carlo and molecular dynamics simulations. The modification of tf potential function can be written as a perturbation ... 

Field M J, P A Bash and M Karplus 1990. A Combined Quantum Mechanical and Molecular Mechanical Potential for Molecular Dynamics Simulations. Journal of Computational Chemistry 11 700-733. 

To calculate the properties of a molecule, you need to generate a well-defined structure. A calculation often requires a structure that represents a minimum on a potential energy surface. HyperChem contains several geometry optimizers to do this. You can then calculate single point properties of a molecule or use the optimized structure as a starting point for subsequent calculations, such as molecular dynamics simulations. 

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