**1. Introduction**

306 Molecular Dynamics – Theoretical Developments and Applications in Nanotechnology and Energy

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Dissociative adsorption phenomena often occur in various fields of engineering, such as oxidation-reduction reactions, cleaning, adhesion, plating, plasma etching, sputtering, and tribology. These phenomena that involve surface reactions have attracted much attention and are analyzed both experimentally and numerically. However, when the surface has structures on the molecular scale, and the scale is not small enough compared to the system, the characteristics of a surface reaction cannot be sufficiently expressed macroscopically, for example by the rate equation. It is extremely difficult to analyze the characteristics of a nanoscale system experimentally due to the scale. Therefore, analysis by numerical calculation, in which the system structure and its electronic state are treated comprehensively, is more effective.

To analyze the surface reaction of these systems accurately, it is necessary to solve the electronic state by the first principle calculation based on quantum mechanics and to then obtain the energy state. The Molecular Orbital (MO) method is most accurate one. However it takes much calculation time and it is impossible to analyze the dissociation phenomena of gas molecule on metal surface because metal has many electrons. Recently, density functional theory (DFT) is one of the most commonly used methods for this process (Parr & Yang, 1989; Satoko & Onishi,1994). Based on the theory that the state of a system is expressed by the functional of the density distribution of the electron, this method can calculate a system state faster than methods that calculate the wave functions of each electron like MO. In the process of surface reaction analysis, this method is applied in various situations, such as specifying the reaction paths from the potential energy surface obtained by the method and calculating the reaction probability at the surface by the value of the absorption/activation energy and the transition state theory (Steinfeld et al., 1989). However, the effects of the motion of gas molecules impinging on the surface and the motion of surface atoms on the surface reaction cannot be considered because this method is applied under the assumption that the temperature is 0 K (fixed atom). , In order to analyze the flow dynamics, including the surface reaction, accurately, a method that considers the interaction between the electronic state of the system and the motion of atoms or molecules for which the time/space scale is distant, must be used.

Molecular Simulation of Dissociation Phenomena of Gas Molecule on Metal Surface 309

The embedded atom method (EAM) is a scheme that treats the interaction between gas atoms and a metal surface by considering the effects of the surface electrons (Daw & Baskes, 1983; 1984). The method is based on DFT, and the potential energy of the system is expressed as a sum of the energy embedded an atom in the electron density of the surface and pair-interaction energy. In EAM, the electron density of the system can be reflected in the interaction potential, and therefore the motion of an atom on a metal surface can be simulated accurately. Moreover, the method has the advantage of a smaller computational load than quantum molecular dynamics (QMD), which is also based on DFT. EAM has often been used to analyze the motion of atoms on a transient metal surface (Baskes, 1992; Baskes et al., 2007). However, there has been little research of the application of EAM to dissociation phenomena. To apply EAM to the analysis of dissociation probability, incorporating the motion of the metal surface atoms, brings the simulations closer to the real system. Moreover, this method can be easily expanded to a more complicated surface.

In this chapter, the methods used for multi-scale analysis of flow phenomena including a surface reaction are described, and a typical example in which these methods are applied to the analysis of flow phenomena including a surface reaction is presented. In Section 2, the simulation method of Density Functional Theory and Embedded Atom Method are described. In Section 3, the analysis of dissociation phenomena by the EAM is discussed.

This section describes the simulation method which was used in this chapter. Especially Density Functional Theory (DFT) and Embedded Atom Method (EAM) are described.

The density functional theory (DFT) is the method in which various values obtained by wave functions of a system and operators are expressed by the functional of electron density of the system. In this method, the energy of the system is obtained exactly. In the analysis of the surface reaction, macroscopic values such as dissociation probability are obtained from the potential energy surface of the system obtained by this method. Moreover, this method is effective for obtaining the database necessary to determine the parameters for the tight binding method or the embedded atom method mentioned below. In this subsection, the outline of the theory of the method is explained below. For details, the reader should refer to

Let us consider the system that consists of *M* nuclei and *N* electrons. Thus, the nuclei are fixed and only the state of the electron is considered (Born- Oppenheimer approximation).

where Ψ*o* and *Eo* denote a wave function that expresses the ground state of a system without degeneracy and the energy of electron at this state, respectively, and *H* denotes an operator, called the Hamiltonian, that expresses the total energy of the system. The operator is expressed using the kinetic energy of the electron, *K*, the Coulomb interaction between

*H E o oo* (1)

The Schrödinger equation, which expresses the ground state of a system, is given by:

Section 4 summarized the chapter.

**2.1 Density Functional Theory (DFT)** 

some references (Parr & Yang, 1989; Satoko & Onishi,1994).

electrons, *V*ee, and the interaction with the external force field, *V*ex, as

**2. Simulation methods** 

Molecular Dynamics (MD) is one of the most suitable method for simulating the motion of atoms. In this method, the force between atoms is first obtained, and then the positions or velocities of the atoms are simulated by a time marching scheme. The quantum molecular dynamics (QMD) method, in which the interaction between atoms of a system is obtained according to the quantum calculation mentioned above, is the most precise method. In particular, the Car-Parrinello method (Car & Parrinello, 1985), in which the potential force of a system is calculated using the DFT to calculate the electronic state, is applied to analyze the process of oxidation-reduction reaction at the platinum surface (Wang & Balbuena, 2004; Jinnouchi & Okazaki, 2003). In general, the Car-Parrinello method is known as a first principle quantum molecular dynamics method. However, despite its precision, the Car-Parrinello method is not practical for analyzing a flow phenomenon as a statistical behavior of numerous motions of atoms or molecules because of the enormous calculation load. For the analysis of flow phenomena with surface reaction, the application of the multiscale method, in which only smaller-scale systems are analyzed by precise quantum calculation and the characteristics that affect surface reaction are modeled, is more appropriate. Flow phenomena with larger-scale surface reactions can then be analyzed by the MD method using this model, rather than treating the entire system using quantum calculation.

The tight binding (TB) method, which greatly improves the computation speed, is contrived by simplifying the first principle quantum molecular dynamics method. Regarding this method, as mentioned later, it has been reported that the computation speed was improved 5,000 times beyond that of the first principle quantum molecular dynamics method by calculating the electronic state using the extended Hückel method (Yonezawa et al, 2001a, 2001b). Since this method enables faster computation and still has the characteristics of calculating the electronic state of a system according to quantum theory, the tight binding method is often applied within the field of chemistry for analyzing the surface reaction dynamics of relatively large systems. Using the tight binding method, the process of the production reaction of water in a fuel cell at the solid-gas interface has been simulated (Ishimoto et al., 2006). In addition, a hybrid method, which combines the tight binding method and the classical molecular dynamics method, is also being developed.

The tight binding method is still not sufficient for large-scale calculations that deal with the "flow" of a system because the calculation procedure is complicated because the electronic state of a system is calculated according to quantum theory. For calculations that deal with the statistical quantity of atomic motion, another method that determines the potential function, which is used in the classical molecular dynamics method using the results of the density functional theory, is also applied frequently. For instance, the potential, which is a function of the position or the orientation of an impinging molecule, is contrived by fitting the potential energy surface of a diatomic molecule on a transient metal surface at various orientations obtained by the density functional theory using an analytic function. The potential is often used to analyze the dissociation phenomena of hydrogen on a Pt or Pd surface (Beutl et al., 1995; Olsen et al., 1999, 2002). In this method, however, the motion of surface atoms cannot be considered, and therefore the effect of thermal motion of surface atoms on dissociation phenomena cannot be analyzed using this method. Owing to this defect, it has often been reported that the dissociation probability obtained by this method cannot be used to reproduce experimentally obtained data (Vincent et al., 2004).

The embedded atom method (EAM) is a scheme that treats the interaction between gas atoms and a metal surface by considering the effects of the surface electrons (Daw & Baskes, 1983; 1984). The method is based on DFT, and the potential energy of the system is expressed as a sum of the energy embedded an atom in the electron density of the surface and pair-interaction energy. In EAM, the electron density of the system can be reflected in the interaction potential, and therefore the motion of an atom on a metal surface can be simulated accurately. Moreover, the method has the advantage of a smaller computational load than quantum molecular dynamics (QMD), which is also based on DFT. EAM has often been used to analyze the motion of atoms on a transient metal surface (Baskes, 1992; Baskes et al., 2007). However, there has been little research of the application of EAM to dissociation phenomena. To apply EAM to the analysis of dissociation probability, incorporating the motion of the metal surface atoms, brings the simulations closer to the real system. Moreover, this method can be easily expanded to a more complicated surface.

In this chapter, the methods used for multi-scale analysis of flow phenomena including a surface reaction are described, and a typical example in which these methods are applied to the analysis of flow phenomena including a surface reaction is presented. In Section 2, the simulation method of Density Functional Theory and Embedded Atom Method are described. In Section 3, the analysis of dissociation phenomena by the EAM is discussed. Section 4 summarized the chapter.
