Molecular dynamics simulation with periodic boundary conditions

To illustrate the solvent effect on the average structure of a protein, we describe results obtained from conventional molecular dynamics simulations with periodic boundary conditions.92,193 This method is well suited for a study of the global features of the structure for which other approaches, such as stochastic boundary simulation methods, would not be appropriate. We consider the bovine pancreatic trypsin inhibitor (BPTI) in solution and in a crystalline environment. A simulation was carried out for a period of 25 ps in the presence of a bath of about 2500 van der Waals particles with a radius and well depth corresponding to that of the oxygen atom in ST2 water.193 The crystal simulation made use of a static crystal environment arising from the surrounding protein molecules in the absence of solvent. These studies, which were the first application of simulation methods to determine the effect of the environment on a protein, used simplified representations of the surround-... 

In a normal molecular dynamics simulation with repeating boundary conditions (i.e., periodic boundary condition), the volume is held fixed, whereas at constant pressure the volume of the system must fluemate. In some simulation cases, such as simulations dealing with membranes, it is more advantageous to use the constant-pressure MD than the regular MD. Various schemes for prescribing the pressure of a molecular dynamics simulation have also been proposed and applied [23,24,28,29]. In all of these approaches it is inevitable that the system box must change its volume. 

Force field calculations often truncate the non bonded potential energy of a molecular system at some finite distance. Truncation (nonbonded cutoff) saves computing resources. Also, periodic boxes and boundary conditions require it. However, this approximation is too crude for some calculations. For example, a molecular dynamic simulation with an abruptly truncated potential produces anomalous and nonphysical behavior. One symptom is that the solute (for example, a protein) cools and the solvent (water) heats rapidly. The temperatures of system components then slowly converge until the system appears to be in equilibrium, but it is not. 

The molecular dynamics simulation was performed using the MOTECC suite of programs [54] in the context of a microcanonical statistical ensemble. The system considered is a cube, with periodic boundary conditions, which contains 343 water molecules. The molecular dynamic simulation of water performed at ambient conditions revealed good agreement with experimental measurements. The main contribution to the total potential energy comes from the two-body term, while the many-body polarisation term contribution amounts to 23% of the total potential energy. Some of the properties calculated during the simulation are reported in Table 3. 

In the present chapter, we will focus on the simulation of the dynamics of photoexcited nucleobases, in particular on the investigation of radiationless decay dynamics and the determination of associated characteristic time constants. We use a nonadiabatic extension of ab initio molecular dynamics (AIMD) [15, 18, 21, 22] which is formulated entirely within the framework of density functional theory. This approach couples the restricted open-shell Kohn-Sham (ROKS) [26-28] first singlet excited state, Su to the Kohn-Sham ground state, S0, by means of the surface hopping method [15, 18, 94-97], The current implementation employs a plane-wave basis set in combination with periodic boundary conditions and is therefore ideally suited to condensed phase applications. Hence, in addition to gas phase reference simulations, we will also present nonadiabatic AIMD (na-AIMD) simulations of nucleobases and base pairs in aqueous solution. 

In contrast to fhe static methods discussed in the previous section, molecular dynamics (MD) includes thermal energies exphcitly. The method is conceptually simple an ensemble of particles represents fhe system simulated and periodic boundary conditions (PBC) are normally apphed to generate an infinite system. The particles are given positions and velocities, fhe latter being assigned in accordance with a... 

As the last example we mention the study of Takemura and Kitao. They studied different models for molecular-mechanics simulations on water. To this end, they studied the dynamics of a ubiquitin molecule solvated in water. They performed molecular-dynamics simulations for a system with periodic boundary conditions. At first they considered pure water without the solute and studied boxes with 360, 720, 1080, and 2160 water molecules. It turned out that even for these fairly large systems, finite-size effects could be recognized. Thus, the translational diffusion constant was found to depend linearly on where V is the volume of the repeated unit. 

Recent years have seen the extensive application of computer simulation techniques to the study of condensed phases of matter. The two techniques of major importance are the Monte Carlo method and the method of molecular dynamics. Monte Carlo methods are ways of evaluating the partition function of a many-particle system through sampling the multidimensional integral that defines it, and can be used only for the study of equilibrium quantities such as thermodynamic properties and average local structure. Molecular dynamics methods solve Newton s classical equations of motion for a system of particles placed in a box with periodic boundary conditions, and can be used to study both equilibrium and nonequilibrium properties such as time correlation functions. 

For an understanding of protein-solvent interactions it is necessary to explore the modifications of the dynamics and structure of the surrounding water induced by the presence of the biopolymer. The theoretical methods best suited for this purpose are conventional molecular dynamics with periodic boundary conditions and stochastic boundary molecular dynamics techniques, both of which treat the solvent explicitly (Chapt. IV.B and C). We focus on the results of simulations concerned with the dynamics and structure of water in the vicinity of a protein both on a global level (i.e., averages over all solvation sites) and on a local level (i.e., the solvent dynamics and structure in the neighborhood of specific protein atoms). The methods of analysis are analogous to those commonly employed in the determination of the structure and dynamics of water around small solute molecules.163 In particular, we make use of the conditional protein solute -water radial distribution function,... 

At present three different codes are widely used for calculations of the structural and spectroscopic properties of H-bonded crystals, for example see Refs. [82-85]. The Car-Parrinello molecular dynamics (CPMD) program [86] and the Vienna ab initio simulation program (VASP) [87, 88] use a plane wave basis set, while an atom centered set is used with periodic boundary conditions in the CRYSTAL... 

Molecular Dynamics Simulations With rapid evaluation of energies and gradients, molecular dynamics (MD) simulations can be carried out. For MD simulations in the gas phase, the complex was first heated to 300 K by 6,000 steps and equilibrated at that temperature for 100 ps. Then, a 5-ns NVE trajectory was generated by free dynamics. The time step was 0.1 fs to follow the fast proton motions. For simulations in explicit solvent, a 46.0 A x 46.0 A x 40.9 A box of CDCI3 was first generated with a density of 1.50 g/cm. The Pt[Cl2(6-DPPon)2l complex was then solvated and periodic boundary conditions were applied. A cutoff of 12 A was applied to the shifted electrostatic and switched van der Waals interactions. Before 1-ns free dynamics simulations, the system was heated to 300 K and then equilibrated for 10 time steps. 

Fig. 7.8 ssDNA (GAG) absorption to graphene nanoribbon, a Initial structure, b Time evolution of temperature, c ssDNA absorption on graphene at room temperature, d Final ssDNA conformation during equilibration at 330 K with three nucleobases absorbed on graphene. Molecular dynamics (MD) simulation performed with periodic boundary conditions [60]... 

We used the results of a molecular dynamics simulation to interpret the II-A isotherms. The evolution of the many-particle system can be described by integrating Newton s equations of motion. To integrate the differential equation system we used the leapfrog method [40]. The simulation of the compression was performed for 1,000 particles in a rectangular cell with periodic boundary conditions. The size distribution of the particles could be set... 

With these benchmark calculations in hand, Laasonen et al. went on to perform ab initio molecular dynamics simulations on liquid water using the CP approach. The simulation had 32 D2O molecules at 300 K in a cubic cell of length 9.6 A with periodic boundary conditions. Deuterated water was used instead of ordinary water to slow down nuclear motion. This decrease makes it easier for the electronic parameters to adjust to nuclear motion and have the... 

The QM/MM Hamiltonian can be used to cany out Molecular Dynamics simulations of a complex system. In the case of liquid interfaces, the simulation box contains the solute and solvent molecules and one must apply appropriate periodic boundary conditions. Typically, for air-water interface simulations, we use a cubic box with periodic boundary conditions in the X and Y directions, whereas for liquid/liquid interfaces, we use a rectangle cuboid interface with periodic boundary conditions in the three directions. An example of simulation box for a liquid-liquid interface is illustrated in Fig. 11.1. The solute s wave function is computed on the fly at each time step of the simulation using the terms in the whole Hamiltonian that explicitly depend on the solute s electronic coordinates (the Born-Oppenheimer approximation is assumed in this model). To accelerate the convergence of the wavefunction calculation, the initial guess in the SCF iterative procedure is taken from the previous step in the simulation, or better, using an extrapolated density matrix from the last three or four steps [39]. The forces acting on QM nuclei and on MM centers are evaluated analytically, and the classical equations of motion are solved to obtain a set of new atomic positions and velocities. 

The RMD simulations used dynamical data generated by three molecular dynamics runs of 10 collisions each. The runs involved 100 identical particles, in a box of side 16o, with periodic boundary conditions. The dynamical initial conditions were identical except for the assignment of particle velocity directions using a different set of random numbers in each run. If =... 

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. 

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