Molecular Dynamics Simulation (part 2) - Computational Chemistry

Molecular dynamics simulation part 2 --- In this paper we are still discussing the basics of simulation DM is about several important concepts such as the PBC (Periodic Boundary Condition), MIC (Minimum Image Convention) and the key concepts, namely DM simulation ensemble. These three things are important to know. The simple question that had been raised at Mr. Lecturer to us is if we are simulating ion in water, whereas the salt cations and anions there while we simulated only cations and anions to Which?

PBC is one of the key concepts in the simulation, a way for simulations using hundreds of atoms can be unlimited so as to approach the real nature. In this paper we are still discussing the basics of simulation DM is about several important concepts such as the PBC (Periodic Boundary Condition), MIC (Minimum Image Convention) and the key concepts, namely DM simulation ensemble. These three things are important to know. The simple question that had been raised at Mr. Lecturer to us is if we are simulating ion in water, whereas the salt cations and anions there while we simulated only cations and anions to Which?

PBC is one of the key concepts in the simulation, a way for simulations using hundreds of atoms can be unlimited so as to approach the real nature.

Picture 1. PBC

In the middle of the box in Figure 1 is a box of our simulations while other boxes are duplicates of the simulation box, as well as particles and speed of the other boxes, as well as a duplicate of our simulation box. The direction of the arrow illustrates that the particles fill all the space box. So? If there are atoms left the box simulation then another atom will go in the opposite direction to replace atoms that go earlier. Therefore, the number of atoms in the simulation box can be maintained. Furthermore, there are no atoms experience a force due to interfacial atoms missing or moved.

MIC is one way to reduce the computing time caused by the calculation of non-bonded interactions between atoms in the simulation. In addition to the MIC, other ways that could be used is to use non-bonded cutoff. In the energy MIC counted only as long as the cutoff distance limits, beyond the cutoff then the energy will be considered 0. In PBC, the distance should not be cutoff from half the size of the box simulations and in practice, most of the close-range interactions are usually unstable and can be ignored outside cutoff ,

Picture 2. MIC

Well, the last but often forgotten is the ensemble. in-depth discussion about the ensemble can be found in the book of statistical mechanics. The basic idea is how to link the microstate to macrostate state so that an overview of the simulation had been able to represent the state of the real system.

Molecular dynamics calculating the real dynamics of a system in which the properties of the system within a certain time retata can be calculated. The value of nature, A, of a system depends on the position and momentum of N particles that make up the system. A price on the spot can be written as A (p ^ N (t), r ^ N (t), where p ^ N (t) and r ^ N (t) describe the momentum and position of N at time t. Thus, , the price of A will vary over time because of the interaction between the particle simulation. In the experiment, the measured value is an average of A all the time calculation so called time average (mean time). If a measurement is made to be unlimited, it is necessary approach to get the "true" average of the value of A can be written as follows:

1.  The mean time equation

To calculate the average value of the properties of the system, thus simulating the dynamic behavior of the system is required. For each arrangement of atoms in the system, the force between atoms that are caused by interactions with other atoms can be calculated with diferential energy function. From the style of each atom can be determined acceleration through the 2nd law of Newton. Integration of the equations of motion will produce a trajectory that provides position, velocity and acceleration of particles in each period and the average of the properties can be determined by Equation 1. The large number of atoms or molecules in macroscopic circumstances make it impossible to determine the initial configuration of the system , Based on statistical mechanics who do Boltzmann and Gibbs, a single system that changes over time can be replaced by a large number of replicas diangggap system moves simultaneously. Average time can be replaced by ensemble averages.

ensemble mean,

2. The average ensemble equation

Ensemble averages or price expectations indicated by angle brackets, is the average of all the properties A replication of the ensemble generated by simulation. Double integral in the equation above shows the integral sign 6N 6N for position and momentum of all the particles. The probability density of the ensemble, ρ (pN, RN) is the probability to find configuration with Momenta P ^ N (t) and position r ^ N (t). In accordance with the hypothesis ergodik, ensemble mean is equal to the mean time. Under conditions of particle number, volume and temperature are fixed, the probability density is Boltzmann distribution:

3. Boltzmann distribution

Where E (p ^ n, r ^ N) is the energy, Q is the partition function, k_B is the Boltzmann constant and T is the temperature. Partition function for the canonical ensemble (ensemble with N, V ​​and T remains) with N identical particles can be described in equation Hamiltonian H,

nvt,

4. canonical ensemble

Hamiltonian, H, can be described as a total energy E (p ^ n, r ^ N), which is the sum of the kinetic energy K (p ^ N) and potential V (r ^ n) of the system. Factors N! arises from the particles which can not be distinguished, and a factor of 1 / h ^ (3N) is required to ensure the partition functions the same as the calculation of quantum mechanics.

In addition to the canonical ensemble, there is still another ensemble is microcanonical and grandcanonical. A discussion of both friends could find in the book of statistical mechanics.