**6. How to run a basic simulation**

Setting up the run is probably the part of the MD simulation that a novice finds most intimidating. This requires several steps: creation of an initial configuration for the system, choice of physical conditions as defined by an ensemble and a temperature for the run; and some numerical parameters necessary for the integration of the equations: time-step, simulation time, integrator and thermostat.

#### **6.1 Creation of the initial geometry**

We have to create an initial geometry for the system, that is, to position the atoms and molecules in three dimensions so the calculation can proceed. A simple random placement is not useful, because we must be careful to avoid placing two atoms at the same coordinates, or closer than the sum of their atomic radii. This situations, known as bad contacts, tend to destabilize the numerical algorithms used in the determination of the trajectory (the integration step). Most MD packages, such as GROMACS or AMBER, provide their own utilities for building starting configurations.

For the creation of a starting configuration, we can use programs such as Ghemical, Avogadro(Avogadro, 2011) or Gabedit. Both Avogadro and Ghemical have polished graphic interfaces, and they are very easy to use for building single molecules. Gabedit is still somewhat lacking in this regard, as its interface is harder to use than that of Ghemical or Avogadro. For building clusters, use of a graphical interface quickly becomes tedious and prone to errors. PACKMOL(Martínez, 2009) seems particularly convenient for building any kind of cluster due to its ability to add a given number copies of a molecule, water or any other at the user's choice. For the specific case of water solvation, Ghemical provides a function to build a water box or a water sphere around any compound previously loaded in Ghemical's memory, although the number of water molecules added is less intuitive, because it depends on both the dimensions of the box and of the molecule to be solvated.

Our preferred tools for building systems are packages with graphical user interface, like Ghemical, Avogadro or Gabedit. For running MD simulations we have used, with varying degrees of success Ghemical, MOPAC2009 and Gabedit. PACKMOL is very well suited for the construction of clusters because it lets the user specify the structures of the molecules of interest and how many of them are to be added. Ghemical is less flexible in this regard, because it has tools only for building solvation shells, and the number of water molecules added is not specified directly by the user, but by the volume specified for the water box. Adding a precise number of water molecules in Ghemical can be a hit-and-miss experience.

#### **6.2 Choice of physical conditions**

10 Will-be-set-by-IN-TECH

a low level of theory (Hartree-Fock) and, second, optimization of the obtained structures using the Local Density Approximation. Takayanagi(Takayanagi, 2008) studied clusters of solvated glycine using the PM6 Hamiltonian. Their semiempirical MD simulations were performed at 300 K, and the initial geometries were taken from previously reported higher-level results and reoptimized using PM6. They observed dissociation of the proton from a carboxylate group, although could not observe formation of the zwitterion. In our group we have studied calcium carbonate clusters(Rosas-Garcia, 2011), and we have explored the configurational space by means of semiempirical MD simulations, using the PM6 Hamiltonian in MOPAC2009. Pang et al.(Pang, 1994) studied inclusion compounds in cycloalkanes by simulated annealing using HyperChem using the MM+ force-field (a variant of MM2. We cannot recommend the use of MM+ due to the lack of a published description of the modifications) and varying the temperature from 300 to 1000 K in 100 K increments. The dynamics revealed that there was orientational flexibility within the cycle and that the interconversion barriers were as low as 1

Setting up the run is probably the part of the MD simulation that a novice finds most intimidating. This requires several steps: creation of an initial configuration for the system, choice of physical conditions as defined by an ensemble and a temperature for the run; and some numerical parameters necessary for the integration of the equations: time-step,

We have to create an initial geometry for the system, that is, to position the atoms and molecules in three dimensions so the calculation can proceed. A simple random placement is not useful, because we must be careful to avoid placing two atoms at the same coordinates, or closer than the sum of their atomic radii. This situations, known as bad contacts, tend to destabilize the numerical algorithms used in the determination of the trajectory (the integration step). Most MD packages, such as GROMACS or AMBER, provide their own

For the creation of a starting configuration, we can use programs such as Ghemical, Avogadro(Avogadro, 2011) or Gabedit. Both Avogadro and Ghemical have polished graphic interfaces, and they are very easy to use for building single molecules. Gabedit is still somewhat lacking in this regard, as its interface is harder to use than that of Ghemical or Avogadro. For building clusters, use of a graphical interface quickly becomes tedious and prone to errors. PACKMOL(Martínez, 2009) seems particularly convenient for building any kind of cluster due to its ability to add a given number copies of a molecule, water or any other at the user's choice. For the specific case of water solvation, Ghemical provides a function to build a water box or a water sphere around any compound previously loaded in Ghemical's memory, although the number of water molecules added is less intuitive, because it depends

Our preferred tools for building systems are packages with graphical user interface, like Ghemical, Avogadro or Gabedit. For running MD simulations we have used, with varying degrees of success Ghemical, MOPAC2009 and Gabedit. PACKMOL is very well suited for the construction of clusters because it lets the user specify the structures of the molecules

on both the dimensions of the box and of the molecule to be solvated.

kcal/mole.

**6. How to run a basic simulation**

**6.1 Creation of the initial geometry**

simulation time, integrator and thermostat.

utilities for building starting configurations.

The set of 'physical' information contains: temperature, pressure, relaxation times, compresibilities, whether the simulation will be at constant temperature or constant pressure and–probably most important of all–the force-field used to evaluate the interactions within a molecule and between molecules. Given that the trajectories should have physical meaning, how do we know what kind of experimental conditions are we simulating? This corresponds to the choice of the ensemble. We should be familiar with three ensembles: the microcanonical ensemble, the canonical ensemble and the isothermal-isobaric ensemble.

The microcanonical ensemble maintains constant number of particles (N), constant volume (V) and constant total energy (E), so it is also known as the NVE ensemble. The canonical ensemble keeps a constant number of particles, constant volume and constant temperature (T), so it is also called the NVT ensemble.

The isothermal-isobaric ensemble keeps constant number of particles, constant pressure and constant temperature, so it is also known as the NPT ensemble. Physically, the NPT ensemble is the most important in chemistry, because many chemical processes are performed under constant pressure and temperature.

For our particular situation, when we deal with so few molecules that even the concepts of pressure and temperature are not well defined, it suffices to say that these ensembles are different ways to give energy to the system and any one of them can accomplish the task of taking the system out of an energy well and into another one.

In our group we typically choose the program defaults, as we are not interested in the physical meaning of the trajectories, but only in the energetic minima resulting from the dynamic search.

#### **6.3 Choice of force-field**

Choosing a force-field can be daunting to a novice, because of all the options available. In terms of the specific strengths and weaknesses of each force-field, the reader is referred to the literature. However, the main roadblock in using molecular mechanics force-fields is that, sooner or later, one wants to study a molecule lacking adequate parameters in any force-field. Here, the user of MD software needs to know that some software packages, particularly the most friendly to the user, sometimes allow a dynamics calculation to run substituting default values for the missing parameters. Such calculations have practically no value at all. Ghemical uses the TRIPOS force-field, but the user should be aware of the error messages because usually many parameters are missing, and Ghemical will substitute default values. Gabedit will not run a dynamics unless all the parameters are defined or one decides to use semiempirical methods. The lack of adequate parameters usually requires doing ab initio calculations on a model compound, so the parameters can be generated. This route is reasonable when the molecules of interest are large compared to the model molecule, but what are we supposed to do if the molecule and the model compound are the same?

models, whether continuum or explicit, in these calculations. After all, a global minimum obtained in the gas phase may or may not resemble the global minimum under the influence of aqueous solvation. In addition, the general performance of semiempirical MD simulations to study the behavior of solvated ions is still unknown. We caution the reader against an uncritical application of this technique for conformational, configurational searches or otherwise, e.g., the ability of semiempirical Hamiltonians to model transition structures has been questioned(Schenker, 2011), so modeling the dynamics of chemical reactions by

Application of Molecular Dynamics Simulation to Small Systems 69

Aleksandrov, A.; Simonson, T. (2006). The tetracycline: Mg2<sup>+</sup> complex: A molecular

Aleksandrov, A.; Simonson, T. (2009). Molecular mechanics models for tetracycline analogs. *Journal of Computational Chemistry*, Vol. 30, No. 2, (January 2009) 243–255 Allinger, N. L. (1977) Conformational analysis. 130. MM2. A hydrocarbon force field utilizing

Allinger, N. L.; Yuh, Y. H.; Lii, J. H. (1989). Molecular mechanics. The MM3 force field for

Allouche, A.-R. (2011). Gabedit-A graphical user interface for computational chemistry softwares. *Journal of Computational Chemistry* Vol. 32, No. 1, (January 2011) 174–182 Atilgan, C.; Aviyente, V. (2007). Hybrid Usage of Computational Tools in Drug Synthesis. *Current Computer-Aided Drug Design* Vol. 3, No. 2, (June 2007) 149–159 Avogadro: an open-source molecular builder and visualization tool. Version 1.0.0 URL:

Berendsen, H. J. C.; van der Spoel, D.; van Drunen, R. (1995). GROMACS: A message-passing

Bombasaro, J. A.; Masman, M. F.; Santágata, L. N.; Freile, M. L.; Rodríguez, A. M.; Enriz, R. D.

Brooks, B. R.; Brooks III, C. L.; Mackerell, A. D.; Nilsson, L.; Petrella, R. J.; Roux, B.; Won, Y.;

Case, D. A.; Cheatham, T.; Darden, T.; Gohlke, H.; Luo, R.; Merz Jr., K. M.; Onufriev, A.;

Case, D. A.; Darden, T. A.; Cheatham III, T. E.; Simmerling, C. L.; Wang, J.; Duke, R. E.; Luo, R.;

*Physical Chemistry A* Vol. 112, No. 32, (July 2008) 7426–7438.

*Chemistry*, Vol. 30, No. 10, (July 2009) 1545–1615

parallel molecular dynamics implementation *Computer Physics Communications* Vol.

(2008) A Comprehensive Conformational Analysis of Bullacin B, a Potent Inhibitor of Complex I. Molecular Dynamics Simulations and Ab Initio Calculations. *Journal of*

Archontis, G.; Bartels, C.; Boresch, S.; Caflisch, A.; Caves, L.; Cui, Q.; Dinner, A. R.; Feig, M.; Fischer, S.; Gao, J.; Hodoscek, M.; Im, W.; Kuczera, K.; Lazaridis, T.; Ma, J.; Ovchinnikov, V.; Paci, E.; Pastor, R. W.; Post, C. B.; Pu, J. Z.; Schaefer, M.; Tidor, B.; Venable, R. M.; Woodcock, H. L.; Wu, X.; Yang, W.; York, D. M.; Karplus, M. (2009). CHARMM: The Biomolecular simulation Program, *Journal of Computational*

Simmerling, C.; Wang, B.; Woods, R. (2005). The Amber biomolecular simulation programs. *Journal of Computational Chemistry*, Vol. 26, No. 16, (December 2005)

Walker, R. C.; Zhang, W.; Merz, K. M.; Roberts, B.; Wang, B.; Hayik, S.; Roitberg, A.;

mechanics force field. *Journal of Computational Chemistry* Vol. 27, No. 13, (October

V1 and V2 torsional terms. *Journal of the American Chemical Society* Vol. 99, No. 25,

hydrocarbons. 1. *Journal of the American Chemical Society* Vol. 111, No. 23, (November

semiempirical means may be dangerous, at best.

(December 1977) 8127–8134.

http://avogadro.openmolecules.net/

91, No. 1-3, (September 1995) 43–56

2006), 1517–1533

1989) 8551–8566.

1668–1688

**8. References**

Inasmuch as a MD simulation will evaluate thousands of structures, it may still be worth doing the work of generating molecular mechanics parameters, although this may need a collaboration with a computational chemist. Another option would be to use dynamics not based on molecular mechanics. As previously mentioned, Ab Initio Molecular Dynamics, such as Car-Parrinello, is a specialist technique well beyond the scope of this review but there is a middle ground, in terms of complexity and computational requirements: semiempirical MD simulations. Computational packages exist that are able to use semiempirical methods, such as AM1(Dewar, 1985), PM3(Stewart, 1989) or PM6(Stewart, 2007), for energy evaluation without the need to determine molecular parameters. The user must exercise due care when using semiempirical methods because, at temperatures high enough, the molecules can break apart. This is because semiempirical methods calculate the electronic structure so, even the strongest covalent bonds can break if the temperature is high enough. In our studies of ionic clusters, it was all too easy to destroy the species by giving too much kinetic energy to the system.

#### **6.4 Computational parameters for the run**

The set of computational information, includes how long the simulation is supposed to run in picoseconds (the simulation time), the length of simulation time elapsed between energy evaluations in femtoseconds (the time-step), the algorithm for integration, from a variety such as Verlet, Leapfrog-Verlet and Beeman, among others (the integrator) and the thermostat, which is the algorithm that enforces the constancy of temperature.

The duration of the simulation is usually split in three steps: heating, equilibration and cooling of the system. For the purposes of conformational searching, it is advisable to take a simulation length longer than the program default, probably two times or three times the default value, depending on the complexity of the system.

#### **6.5 Choice of software**

For the MD-based conformational search, both Gabedit and Ghemical can do it, but Gabedit has a more automated implementation. Gabedit automatically saves a user-defined number of geometries from the trajectory and minimizes their energies, either with molecular mechanics or with a semiempirical method.

### **7. Further efforts**

We hope that this brief introduction to molecular dynamics will pique the interest of other researchers in exploring mechanical or semiempirical molecular dynamics as a useful tool for the study of small chemical systems. Recent progress on inclusion of dispersion and H-bonding interactions in semiempirical Hamiltonians, such as the corrections to the PM6 Hamiltonian by Rezá ˘ c(˘ Rezá ˘ c, 2009) and Korth(Korth, 2010), should prove valuable in this ˘ regard. As we have focused on small molecules, the ability to run calculations in parallel over several computers seems unnecessary.

Work remaining to be done includes some benchmarking/callibration of semiempirical MD simulations against higher-level QM/MM simulations or pure ab initio calculations to find out its realm of applicability, and perhaps some further improvement of the semiempirical Hamiltonians to this end. It is also necessary to ascertain the adequacy of including solvation models, whether continuum or explicit, in these calculations. After all, a global minimum obtained in the gas phase may or may not resemble the global minimum under the influence of aqueous solvation. In addition, the general performance of semiempirical MD simulations to study the behavior of solvated ions is still unknown. We caution the reader against an uncritical application of this technique for conformational, configurational searches or otherwise, e.g., the ability of semiempirical Hamiltonians to model transition structures has been questioned(Schenker, 2011), so modeling the dynamics of chemical reactions by semiempirical means may be dangerous, at best.

#### **8. References**

12 Will-be-set-by-IN-TECH

Inasmuch as a MD simulation will evaluate thousands of structures, it may still be worth doing the work of generating molecular mechanics parameters, although this may need a collaboration with a computational chemist. Another option would be to use dynamics not based on molecular mechanics. As previously mentioned, Ab Initio Molecular Dynamics, such as Car-Parrinello, is a specialist technique well beyond the scope of this review but there is a middle ground, in terms of complexity and computational requirements: semiempirical MD simulations. Computational packages exist that are able to use semiempirical methods, such as AM1(Dewar, 1985), PM3(Stewart, 1989) or PM6(Stewart, 2007), for energy evaluation without the need to determine molecular parameters. The user must exercise due care when using semiempirical methods because, at temperatures high enough, the molecules can break apart. This is because semiempirical methods calculate the electronic structure so, even the strongest covalent bonds can break if the temperature is high enough. In our studies of ionic clusters, it was all too easy to destroy the species by giving too much kinetic energy to the

The set of computational information, includes how long the simulation is supposed to run in picoseconds (the simulation time), the length of simulation time elapsed between energy evaluations in femtoseconds (the time-step), the algorithm for integration, from a variety such as Verlet, Leapfrog-Verlet and Beeman, among others (the integrator) and the thermostat,

The duration of the simulation is usually split in three steps: heating, equilibration and cooling of the system. For the purposes of conformational searching, it is advisable to take a simulation length longer than the program default, probably two times or three times the

For the MD-based conformational search, both Gabedit and Ghemical can do it, but Gabedit has a more automated implementation. Gabedit automatically saves a user-defined number of geometries from the trajectory and minimizes their energies, either with molecular mechanics

We hope that this brief introduction to molecular dynamics will pique the interest of other researchers in exploring mechanical or semiempirical molecular dynamics as a useful tool for the study of small chemical systems. Recent progress on inclusion of dispersion and H-bonding interactions in semiempirical Hamiltonians, such as the corrections to the PM6 Hamiltonian by Rezá ˘ c(˘ Rezá ˘ c, 2009) and Korth(Korth, 2010), should prove valuable in this ˘ regard. As we have focused on small molecules, the ability to run calculations in parallel over

Work remaining to be done includes some benchmarking/callibration of semiempirical MD simulations against higher-level QM/MM simulations or pure ab initio calculations to find out its realm of applicability, and perhaps some further improvement of the semiempirical Hamiltonians to this end. It is also necessary to ascertain the adequacy of including solvation

system.

**6.5 Choice of software**

**7. Further efforts**

or with a semiempirical method.

several computers seems unnecessary.

**6.4 Computational parameters for the run**

which is the algorithm that enforces the constancy of temperature.

default value, depending on the complexity of the system.


Seabra, G.; Kolossváry, I.; Wong, K. F.; Paesani, F.; Vanicek, J.; Liu, J.; Wu, X.; Brozell, S. R.; Steinbrecher, T.; Gohlke, H.; Cai, Q.; Ye, X.; Wang, J.; Hsieh, M.-J.; Cui, G.; Roe, D. R.; Mathews, D. H.; Seetin, M. G.; Sagui, C.; Babin, V.; Luchko, T.; Gusarov, S.; Kovalenko, A.; Kollman P. A. (2010). AMBER 11. University of California, San Francisco.

*Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with*

Comparison of simple potential functions for simulating liquid water. *Journal of*

simulations] potential functions for proteins, energy minimizations for crystals of cyclic peptides and crambin. *Journal of the American Chemical Society* Vol. 110, No. 6,

and Dynamics of C8H8, Si8H8, and Ge8H8 Molecules. *Journal of Physical Chemistry A*

liquid-metal-amorphous-semiconductor transition in germanium. *Physical Reviews B*

semiconductors using a plane-wave basis set. *Computational Materials Science* Vol. 6,

calculations using a plane-wave basis set. *Physical Reviews B* Vol. 54, No. 16, (October

clusters with magic numbers of atoms by data of molecular dynamics. *Colloid Journal*

properties of Al-doped Si*<sup>n</sup>* (n=2-21) clusters: FP-LMTO-MD calculations. *Journal of*

simulation and trajectory analysis . *Journal of Molecular Modelling*, Vol. 7, No. 8,

for building initial configurations for molecular dynamics simulations. *Journal of*

G.; Hendrickson, T.; Still, W. C. (1990). MacroModel - an Integrated Software System for Modeling Organic and Bioorganic Molecules Using Molecular Mechanics, *Journal*

and eight-membered cycloalkanes in tris(5-acetyl-3-thieny1)methane inclusion compounds. *Canadian Journal of Chemistry* Vol. 72, No. 11, (November 1994) 2318–2325

Ferguson, D.; Seibel, G.; Kollman, P.A. (1995). AMBER, a package of computer programs for applying molecular mechanics, normal mode analysis, molecular

Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. (1983).

Application of Molecular Dynamics Simulation to Small Systems 71

Jorgensen, W. L.; Tirado-Rives, J. (1988). The OPLS [optimized potentials for liquid

Kiliç, Ç.; Yildirim, T.; Mehrez, H.; Ciraci, S. (2000). A First-Principles Study of the Structure

Korth, M.; Pitonák, M.; ˘ Rezá ˘ c, J.; Hobza, P. (2010) ˘ *Journal of Chemical Theory and Computation*

Kresse, G.; Hafner, J. (1993). Ab initio molecular dynamics for liquid metals. *Physical Reviews*

Kresse, G.; Hafner, J. (1994). Ab initio molecular-dynamics simulation of the

Kresse, G.; Furthmüller, J. (1996). Efficiency of ab-initio total energy calculations for metals and

Kresse, G.; Furthmüller, J. (1996). Efficient iterative schemes for ab initio total-energy

Kuzmin, V. I.; Tytik, D. L.; Belashchenko, D. K.; Sirenko, A. N. (2008). Structure of silver

Li, B.-X.; Wang, G.-Y.; Ye, M.-Y.; Yang, G.; Yao, C.-H. (2007). Geometric and energetic

*Molecular Structure: THEOCHEM* Vol. 820, No. 1-3, (October 2007) 128–140 Lindahl, E.; Hess, B.; van der Spoel, D. (2001) GROMACS 3.0: a package for molecular

Martínez, L.; Andrade, R.; Birgin, E. G.; Martínez, J. M. (2009). Packmol: A package

Mohamadi, F.; Richard, N. G. J.; Guida, W. C.; Liskamp R.; Lipton, M.; Caufield, C.; Chang,

Pang, L.; Brisse, F. (1994) Structural and conformational analysis of six-, seven-,

Pearlman, D.A.; Case, D.A.; Caldwell, J.W.; Ross, W.S.; Cheatham III, T.E.; DeBolt, S.;

*Computational Chemistry* Vol. 30, No. 13, (October 2009) 2157-2164

*of Computational Chemistry* Vol. 11, No. 4, (May 1990) 440–467

*Materials and Atoms* Vol. 249, No. 1-2, (August 2006) 816–819

*Chemical Physics* Vol. 79, No. 2, (July 1983) 926–935

Vol. 104, No. 12, (March 2000) 2724–2728

Vol. 6, No. 1, (January 2010) 344–352

*B* Vol. 47, No. 1, (January 1993) 558–561

Vol. 49, No. 20, (May 1994) 14251–14269

Vol. 70, No. 3, (June 2008) 284–296

(March 1988) 1657–1666.

No. 1, (July 1996) 15–50

(August 2001) 306–317

1996) 11169–11186


14 Will-be-set-by-IN-TECH

Chandrachud, P.; Joshi, K.; Krishnamurty, S.; Kanhere, D. G. (2009) Stability of gold cages

Chen, G.; Peng, Q.; Kawazoe, Y. (2011). First-principles study on Ca8C*<sup>n</sup>* (n≤ 12) and CamC12 (m ≤ 8) metal carbides. *Physics Letters A* Vol. 375, No. 6, (February 2011) 994–999 Clark, M.; Cramer III, R. D.; van Opdenhosch, N. (1989). Validation of the General Purpose

Corbeil, C. R.; Therrien, E.; Moitessier, N. (2009). Modeling Reality for Optimal Docking of

Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. (1985). Development and use of

Doll, K.; Schön, J.C; Jansen, M. (2010). Ab initio energy landscape of LiF clusters. *Journal of*

Engler, E. M.; Andose, J. D.; Schleyer, P. V. R. (2011). Critical evaluation of molecular

Fujima, N.; Oda, T. (2009). Bonding properties and structures of titanium clusters on (10,0)

Granovsky, A. A.; Firefly version 7.1.G, URL: http://classic.chem.msu.su/gran/firefly/

Haile, J. M. (1992) *Molecular Dynamics Simulation. Elementary Methods*, John Wiley & Sons, Inc.

Hassinen, T.; Peräkylä, M. (2001). New energy terms for reduced protein models implemented

Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. (2008). GROMACS 4: Algorithms

Isayev, O.; Furmanchuk, A.; Shishkin, O. V.; Gorb, L.; Leszczynski, J. (2007). Are Isolated

Jimenez-Saez, J.; Perez-Martin, A.; Jimenez-Rodriguez, J. (2006). A molecular dynamics study

*Chemical Theory and Computation* Vol. 4, No. 3, (February 2008) 435–447 HyperChem(TM) Professional 7.51, Hypercube, Inc., 1115 NW 4th Street, Gainesville, Florida

*Journal of Physical Chemistry B* Vol. 111, No. 13, (April 2007) 3476–3480 Jian-Song, Y.; Li, B.-X. (2010). First-principles study of Ga7As7 ionic cluster and influence of

*Chemical Physics* Vol. 133, No. 2, (July 2010) 024107-8

Francisco.

1989) 982–1012

No. 4, (December 2009) 241–263

Wiley-Interscience, New York

(September 2001) 1229–1242

(June 1985) 3902–3909

8005–8025

2009) 87–90

index.html

32601, USA

Seabra, G.; Kolossváry, I.; Wong, K. F.; Paesani, F.; Vanicek, J.; Liu, J.; Wu, X.; Brozell, S. R.; Steinbrecher, T.; Gohlke, H.; Cai, Q.; Ye, X.; Wang, J.; Hsieh, M.-J.; Cui, G.; Roe, D. R.; Mathews, D. H.; Seetin, M. G.; Sagui, C.; Babin, V.; Luchko, T.; Gusarov, S.; Kovalenko, A.; Kollman P. A. (2010). AMBER 11. University of California, San

(Au16 and Au17) at finite temperature. *Pramana* Vol. 72, No. 5, (August 2009) 845–855

Tripos 5.2 Force Field, *Journal of Computational Chemistry* Vol. 10, No. 8, (December

Small Molecules to Biological Targets. *Current Computer-Aided Drug Design* Vol. 5,

quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model. *Journal of the American Chemical Society* Vol. 107, No. 13,

mechanics. *Journal of the American Chemical Society* Vol. 95, No. 24, (October 2011)

single wall carbon nano capsule. *European Physical Journal D* Vol. 52, No. 1-3, (March

in an off-lattice force field. *Journal of Computational Chemistry*, Vol. 22, No. 12,

for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. *Journal of*

Nucleic Acid Bases Really Planar? A Car-Parrinello Molecular Dynamics Study.

multi-charge on its structure. *Chinese Physics B* Vol. 19, No. 9, (September 2010) 097103

of atomic rearrangements in Cu clusters softly deposited on an Au(001) surface.

*Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms* Vol. 249, No. 1-2, (August 2006) 816–819


dynamics and free energy calculations to simulate the structural and energetic properties of molecules. *Comp. Phys. Commun.* Vol. 91, No. 1-3, (September 1995) 1–41 Ponder, J. (2011). *TINKER* URL: http://dasher.wustl.edu/tinker/

**5** 

*France* 

**Molecular Dynamics Simulations and** 

**Thermal Transport at the Nano-Scale** 

This chapter presents an overview of the Molecular Dynamics (MD) simulation technique to predict thermal transport properties of nanostructured materials. This covers systems having characteristic lengths of the order of a few nanometers like carbon nanotubes, nanowires and also superlattices, i.e. composite materials made of submicronic thickness of solid layers. The common features of these systems is the small ratio between their characteristic system size and the phonon mean free path, which leads to ballistic heat transport and deviations from the classical Fourier law. Also when the density of interfaces gets large, the energy transport properties of the materials can not longer be described solely by the thermal conductivities of the constituents of the material, but depend also on the thermal boundary resistance which measures the transmission of phonons across an interface. In this context, molecular dynamics was proven to be a very useful technique to study heat transport in nanostructured materials. The main reasons are; the length scale probed by the method is in the nanometer range, and it does not make any assumption on

In this contribution, we present two MD methods, the equilibrium and the non-equilibrium method, which are now commonly used to determine both the thermal conductivity and the thermal boundary resistance of nanostructured materials. We focus on superlattices and discuss how the structural features of the interfaces like height, shape, inter-diffusion phenomena and the layer thickness affect the thermal conductivity of the superlattice. We show how these complex phenomena can be predicted by simple models of Lennard-Jones crystals with a mass ratio corresponding to the acoustic impedance ratio of Si/Ge and

The development of molecular simulations began in the early fifties after the considerable development of computer facilities in the United States during World War II. A few years after the first Monte-Carlo simulation, Alder and Wainwright, first introduced in the late 50's the Molecular Dynamics (MD) method (Alder & Wainwright, 1957, 1959). The aim of

**1. Introduction** 

GaAs/AlAs superlattices.

**2. Molecular dynamics** 

the phonons dynamics except their classical nature.

Konstantinos Termentzidis1,2 and Samy Merabia3  *1CETHIL-UMR5008, INSA de Lyon, CNRS, Université Lyon 1,* 

> *2EM2C-UPR288, Ecole Centrale Paris, CNRS, 3LPMCN-UMR5586, Université Lyon 1,*

