AIMD simulation method

Most of the AIMD simulations described in the literature have assumed that Newtonian dynamics was sufficient for the nuclei. While this is often justified, there are important cases where the quantum mechanical nature of the nuclei is crucial for even a qualitative understanding. For example, tunneling is intrinsically quantum mechanical and can be important in chemistry involving proton transfer. A second area where nuclei must be described quantum mechanically is when the BOA breaks down, as is always the case when multiple coupled electronic states participate in chemistry. In particular, photochemical processes are often dominated by conical intersections [14,15], where two electronic states are exactly degenerate and the BOA fails. In this chapter, we discuss our recent development of the ab initio multiple spawning (AIMS) method which solves the elecronic and nuclear Schrodinger equations simultaneously this makes AIMD approaches applicable for problems where quantum mechanical effects of both electrons and nuclei are important. We present an overview of what has been achieved, and make a special effort to point out areas where further improvements can be made. Theoretical aspects of the AIMS method are... 

One solution to such problems is provided by ab initio molecular dynamics (AIMD) simulations (11,53-57). These are still very expensive, but they include dynamical aspects and they are thus one of the most powerful tools to investigate bioinorganic systems if many conformations and unexpected events play a role. A necessary prerequisite will always be that inexpensive electronic structure methods such as DFT can be applied to the bioinorganic system of interest. 

Many available codes use this kind of approach in order to carry out AIMD simulations. In fact some codes are not even implemented with the Car - Parrinello methods (e.g., cp2k). About the advantages and disadvantages of BOMD over CPMD the interested reader is referred to the seminal book of Marx and Hutter (57). 

Our AIMD simulations are all-electron and self-consistent at each 0.4 femtoseconds (fs) time step. Variational fitting ensures accurate forces for any finite orbital or fitting basis sets and any finite numerical grid. These forces are used to propagate the nuclear motion according to the velocity Verlet algorithm [22]. The accuracy of these methods is indicated by the fact that during the 500 time-step simulations of methyl iodide dissociation described below, the center of mass moved by less than 10-6 A. 

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. 

We now develop an example of this variational character. We utilize results from ab initio molecular dynamics (AIMD) for that purpose, and estimate fiquid water. The ab initio molecular dynamics simulations were carried out with the VASP (Kresse and Hafner, 1993 Kresse and Furthmiiller, 1996) simulation program, as described in detail in Asthagiri et al. (2003c). Ab initio molecular dynamics of aqueous solutions are recent activities compared with other simulation methods for aqueous solutions, and basic characterization of the new methods is still underway see Grossman et al. (2004) and Schwegler et al. (2004) for initial examples. 

Fock molecular orbital (HF-MO), Generalized Valence Bond (GVB) [49,50] and the Complete Active Space Self-consistent Filed (CASSCF) [50,51], and full Cl methods. [51] Density Functional Theory (DFT) calculations [52-54] are also incorporated into AIMD. One way to perform liquid-state AIMD simulations, is presented in the paper by Hedman and Laaksonen, [55], who simulated liquid water using a parallel computer. Each molecule and its neighbors, kept in the Verlet neighborlists, were treated as clusters and calculated simultaneously on different processors by invoking the standard periodic boundary conditions and minimum image convention. 

AIMD is still a very time-consuming simulation method and has so far mainly been used to study the structure and dynamics of bulk water [14,15], as well as proton transfer [16] and simple Sjv2 reactions in bulk water [17]. AIMD simulations are as yet limited to small system sizes and real simulation times of not more than a few picoseconds. However, some first applications of this technique to interfacial systems of interest to electrochemistry have appeared, such as the water-vapor interface [18] and the structure of the metal-water interface [19]. There is no doubt... 

For recent examples of new methods anployed, those that propagate in time while including the electronic energies, most notably the implementation of AIMD simulations by Leung et al. [ 12,13,30,31] to smdy various properties of EC and its contribution to the SEl, are fascinating. The time-evolution can of course be treated without any electrons, as in classic MD simulations, and still be predictive about the resulting reaction products - while not the direct electrochemistry. An excellent example of the latter is the work by Bedrov et al. [32]. 

Due to the costs associated with the electronic structure calculations, AIMD simulations always suffer from short simulation times see also previous Sect. 3. In 2005, Iftimie and Tuckerman devised a method that allows well-converged results for IR spectra from small AIMD systems and short trajectories [72], The frequency-(v)-dependent Beer-Lambert absorptivity coefficient a(v) is given as... 

The dipole moment of liquid water was investigated by several authors [92-94]. Silvestrelli and Parrinello calculated dipole moments of a single water molecule (1.87 D), a dimer (2.1 D), a trimer (2.4 D), as well as liquid water (2.95 D) [92]. In a subsequent study with refined methods they obtained a dipole moment of 3.0 D for liquid water from AIMD simulations [93]. In 2004, Kuo and Mundy reported a study of the aqueous liquid-vapor interface where water was simulated in such a fashion that in one simulations box the water molecules moved freely from the dense bulk phase into the low density vapor phase, i.e., the number of molecules surrounding a water molecule changed smoothly [94]. In this study, Kuo and Mundy found a molecular dipole moment at the vapor/liquid interphase of approximately 2.4 D which changed smoothly to a value of 3.0 D in the bulk phase. 

This chapter focuses on the theoretical modeling studies of ORR catalysts for PEMFC. Theoretical methods, such as density functional theory (DFT) and ab initio molecular dynamics (AIMD) simulation, are presented. Current understanding of ORR mechanism in acidic medium is briefly discussed. Recent theoretical investigations on oxygen reduction electrocatalysts, such as Pt-based catalysts, non-Pt metal catalysts (Pd, Ir, CuCl), and non-precious metal catalysts (transitional metal macrocyclic complexes, conductive polymer materials, and carbon-based materials), are reviewed. The oxygen reduction mechanisms catalyzed by these catalysts are discussed based on the results. 

Of the various AIMD simulation techniques, we will restrict our discussion only to the most popular methods Bom-Oppenheimer molecular dynamics (BOMD), Car-Parrinello molecular dynamics (CPMD), and tight-binding molecular dynamics (TBMD). They play a central role in the description of dynamic phenomena, using ab initio or empirical level of theory. 

Ab initio molecular dynamics simulations usually describe fluctuations of molecular electronic structures and can broaden knowledge of electric dipole moments, polarization processes, or possible charge-transfer effects, and complement classic MD methods. However, AIMD simulations are computationally demanding, and only relatively small systems of tens of ion pairs can be propagated over short time periods of tenths of picoseconds. These simulations typically begin from liquid state conflgurations that are equilibrated with classic MD using empirical interaction potentials. 

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