Molecular dynamics classical mechanics

Molecular dynamics itself can be further divided into two classes classical molecular dynamics and ab initio molecular dynamics. Classical molecular dynamics treats molecules as point masses and the interactions between molecules are represented by simple potential functions, which are based on empirical data or fi om independent quantum mechanical calculations. The so-called ab initio molecular dynamics unifies classical molecular dynamics and density-function theory and takes into account the electronic structure when calculating the forces on atomic nuclei. In this entry, we only present a brief summary of the classical molecular dynamics simulation method. Readers interested in Monte Carlo or ab initio molecular dynamics simulation methods is referred to other entry such as Monte Carlo Method. ... 

As in classical mechanics, the outcome of time-dependent quantum dynamics and, in particular, the occurrence of IVR in polyatomic molecules, depends both on the Flamiltonian and the initial conditions, i.e. the initial quantum mechanical state I /(tQ)). We focus here on the time-dependent aspects of IVR, and in this case such initial conditions always correspond to the preparation, at a time of superposition states of molecular (spectroscopic) eigenstates involving at least two distinct vibrational energy levels. Strictly, IVR occurs if these levels involve at least two distinct... 

Tuckerman M E and Hughes A 1998 Path integral molecular dynamics a computational approach to quantum statistical mechanics Classical and Quantum Dynamics In Condensed Phase Simulations ed B J Berne, G Ciccotti and D F Coker (Singapore World Scientific) pp 311-57... 

Equation (C3.5.3) shows tire VER lifetime can be detennined if tire quantum mechanical force-correlation Emotion is computed. However, it is at present impossible to compute tliis Emotion accurately for complex systems. It is straightforward to compute tire classical force-correlation Emotion using classical molecular dynamics (MD) simulations. Witli tire classical force-correlation function, a quantum correction factor Q is needed 5,... 

Bala, P., Grochowsky, R, Lesyng, B., McCammon, J.A. Quantum-classical molecular dynamics. Models and applications. In Quantum mechanical simulation methods for studying biological systems, D. Bicout and M. Field, eds. Springer, Berlin (1996) 119-156. 

The principal idea behind the CSP approach is to use input from Classical Molecular Dynamics simulations, carried out for the process of interest as a first preliminary step, in order to simplify a quantum mechanical calculation, implemented in a subsequent, second step. This takes advantage of the fact that classical dynamics offers a reasonable description of many properties of molecular systems, in particular of average quantities. More specifically, the method uses classical MD simulations in order to determine effective... 

In molecular dynamics applications there is a growing interest in mixed quantum-classical models various kinds of which have been proposed in the current literature. We will concentrate on two of these models the adiabatic or time-dependent Born-Oppenheimer (BO) model, [8, 13], and the so-called QCMD model. Both models describe most atoms of the molecular system by the means of classical mechanics but an important, small portion of the system by the means of a wavefunction. In the BO model this wavefunction is adiabatically coupled to the classical motion while the QCMD model consists of a singularly perturbed Schrddinger equation nonlinearly coupled to classical Newtonian equations, 2.2. 

P. Bala, P. Grochowski, B. Lesyng, and J. A. McCammon Quantum-classical molecular dynamics. Models and applications. In Quantum Mechanical Simulation Methods for Studying Biological Systems (M. Fields, ed.). Les Houches, France (1995)... 

In this paper, we consider the symplectic integration of the so-called Quantum-Classical Molecular Dynamics (QCMD) model. In the QCMD model (see [11, 9, 2, 3, 6] and references therein), most atoms are described by classical mechanics, but an important small portion of the system by quantum mechanics. This leads to a coupled system of Newtonian and Schrddinger equations. 

Rather than solve a Schrodinger equation with the Nuclear Hamiltonian (above), a common approximation is to assume that atoms are heavy enough so that classical mechanics is a good enough approximation. Motion of the particles on the potential surface, according to the laws of classical mechanics, is then the subject of classical trajectory analysis or molecular dynamics. These come about by replacing Equation (7) on page 164 with its classical equivalent ... 

But a computer simulation is more than a few clever data structures. We need algorithms to manipulate our system. In some way, we have to invent ways to let the big computer in our hands do things with the model that is useful for our needs. There are a number of ways for such a time evolution of the system the most prominent is the Monte Carlo procedure that follows an appropriate random path through configuration space in order to investigate equilibrium properties. Then there is molecular dynamics, which follows classical mechanical trajectories. There is a variety of dissipative dynamical methods, such as Brownian dynamics. All these techniques operate on the fundamental degrees of freedom of what we define to be our model. This is the common feature of computer simulations as opposed to other numerical approaches. 

The only feasible procedure at the moment is molecular dynamics computer simulation, which can be used since most systems are currently essentially controlled by classical dynamics even though the intermolecular potentials are often quantum mechanical in origin. There are indeed many intermolecular potentials available which are remarkably reliable for most liquids, and even for liquid mixtures, of scientific and technical importance. However potentials for the design of membranes and of the interaction of fluid molecules with membranes on the atomic scale are less well developed. 

In Chapter 2, I gave you a brief introduction to molecular dynamics. The idea is quite simple we study the time evolution of our system according to classical mechanics. To do this, we calculate the force on each particle (by differentiating the potential) and then numerically solve Newton s second law... 

A more practical approach for larger systems is molecular dynamics. In this method, the properties of bonds are determined through a combination of quantum-mechanical simulation and physical experiments, and stored in a database called a (semi-empirical) force field. Then a classical (non-quantum) simulation is done where bonds are modeled as spring-like interactions. Molecular... 

Multiparticle collision dynamics describes the interactions in a many-body system in terms of effective collisions that occur at discrete time intervals. Although the dynamics is a simplified representation of real dynamics, it conserves mass, momentum, and energy and preserves phase space volumes. Consequently, it retains many of the basic characteristics of classical Newtonian dynamics. The statistical mechanical basis of multiparticle collision dynamics is well established. Starting with the specification of the dynamics and the collision model, one may verify its dynamical properties, derive macroscopic laws, and, perhaps most importantly, obtain expressions for the transport coefficients. These features distinguish MPC dynamics from a number of other mesoscopic schemes. In order to describe solute motion in solution, MPC dynamics may be combined with molecular dynamics to construct hybrid schemes that can be used to explore a variety of phenomena. The fact that hydrodynamic interactions are properly accounted for in hybrid MPC-MD dynamics makes it a useful tool for the investigation of polymer and colloid dynamics. Since it is a particle-based scheme it incorporates fluctuations so that the reactive and nonreactive dynamics in small systems where such effects are important can be studied. 

Lu ZY, Zhang YK (2008) Interfacing ab initio quantum mechanical method with classical Drude os-illator polarizable model for molecular dynamics simulation of chemical reactions. J Chem Theory Comput 4(8) 1237-1248... 

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