First-principles molecular dynamics method

In this section, the density functional theory (DFT) method is reviewed. Other methods applied in the study of electrochemistry, such as the ab initio (or first principle) molecular dynamics method (AIMD), the wave-function-based method, the Monte Carlo method, and the semi-empirical method are reviewed elsewhere [3, 9-13]. 

First-Principles Molecular Dynamics Methods An Overview... 

In the following, we shall focus on first principles molecular dynamics methods. Due to the high computational cost associated with ab initio electronic structure calculations of large molecules, computation of the entire potential energy surface prior to the molecular dynamics simulation is best avoided. A more efficient alternative is the evaluation of electronic energy and nudear forces on the fly at each step along the trajectory. 

Tab. 1.1 Comparison of the properties of quantum chemical electronic structure calculations (QC methods), classical molecular dynamics (Classical MD) based on empirical force fields and first-principles molecular dynamics (ab initio MD) simulations.

In addition to the development in the methodology to compute electronic structures, there have been several attempts to handle the simulation of a chemical event in a system with a large number of degrees of freedom. The Car-Parrinello (CP) approach [5], often referred to as first-principles molecular dynamics (FPMD) method, opened the way to the molecular dynamics simulations based on the first-principles electronic structure calculations. The point of the method is to circumvent the explicit... 

The first principles molecular dynamics simulation has been applied, based on the linearized-augmented-plane-wave (LAPW) method, to Seg and Seg+ clusters. The equilibrium structures have been obtained for Se8 and Se8+ clusters for the ionized cluster Seg-, a remarkable change from that for the neutral cluster has been found, which reflects the strong electron-lattice coupling in the cluster <1997MI1660, 1997MI75, 1997MI472>. 

First principles approaches are important as they avoid many of the pitfalls associated with using parameterized descriptions of the interatomic interactions. Additionally, simulation of chemical reactivity, reactions and reaction kinetics really requires electronic structure calculations [108]. However, such calculations were traditionally limited in applicability to rather simplistic models. Developments in density functional theory are now broadening the scope of what is viable. Car-Parrinello first principles molecular dynamics are now being applied to real zeolite models [109,110], and the combined use of classical and quantum mechanical methods allows quantum chemical methods to be applied to cluster models embedded in a simpler description of the zeoUte cluster environment [105,111]. 

Abstract Theoretical investigations of ionic liquids are reviewed. Three main categories are discussed, i.e., static quantum chemical calculations (electronic structure methods), traditional molecular dynamics simulations and first-principles molecular dynamics simulations. Simple models are reviewed in brief. 

Computational Methods and Techniques First-Principles Molecular Dynamics... 

In this review, I have interpreted the term Car-Parrinello methods in the broad sense to mean those which combine first-principles quantum mechanical methods with molecular dynamics methods. I use this term synonymously with uh initio molecular dynamics, first-principles molecular dynamics, and ab initio simulations. Thus, ways of solving the many-body electronic problem, such as Hartree-Fock and correlation methods, are included, in addition to the projector-augmented plane-wave method. In the original Car-Parrinello method, molecular motion is treated classically via... 

A promising method, developed in recent years, is the use of first principles molecular dynamics as exemplified by the Car-Parrinello technique (8]. In these calculations the interatomic potentials are explicitly derived from the electronic ground-state within the density functional theory in local or non-local approximation. It combines quantum mechanical calculations with molecular dynamics simulations and, therefore, overcomes the limitations of both methods. Actual computers allow only simulations of aqueous solutions of about 60 water molecules for several ps (10 s). This limit is still at least one order of magnitude shorter than the fastest directly measured water exchange rate, k = 3.5 x 10 s for [Eu(H20)8], i.e. one exchange event every (8 x 3.5 x lO s ) = 36 ps [9]. Nevertheless, several publications appeared in the late 1990s on solvated Be [10], K+ [11] and Cu + [12] presenting mainly structural results. 

In some respects the principle behind the first principles molecular dynamics approach to examining induced strain is similar to the static methods outlined above, in that the response of the system s configuration... 

Recently, ab initio or the first-principle molecular dynamics (AIMD), which is based on Car and Parrinello s technique [33], has become a valuable method for study condensed matter structure and dynamics, in particular liquids, surfaces, and clusters. The basic idea underlying AIMD method is to compute the forces acting on the nuclei from electronic structure that are calculated on the fly as the molecular dynamics trajectory is generated [34]. In this way, the electronic variables are not integrated out beforehand, but are considered as active degrees of freedom. Thus, the Car and Parrinello (CP) algorithm overcomes limitations of standard empirical-potential approaches employed in classical molecular dynamics and... 

The development of plane-wave pseudopotential methods for electronic structure calculations of solids (e.g., Payne et al. 1992) has also opened the door to real first-principles molecular dynamics simulations using the algorithm of Car and Parinello (1985). Here, we let the wavefimctions become part of the dynamics of the system. To do this, we introduce a fictitious kinetic energy associated with a dynamical motion of the wavefunction ... 

We show two examples of the combination of statistical mechanics with first principles electronic structure methods. Although first principles molecular dynamics has been applied for some time to the study of relatively simple systems, its application to Earth materials is more recent. These examples illustrate the power of modem density functional theory and the ability that now exists to treat large systems at high temperature. 

Very recently another group has performed first principles molecular dynamics simulations of MgSiOs perovskite using methods similar to ours (Oganov et al. 2001). This group finds that the Pbnm phase is stable throughout the pressure-temperature regime of their study, which overlaps the conditions at which we find a phase transformation. The reason for this discrepancy is not clear, but may be related to differences in pseudopotential construction, run time, initial conditions, or other factors. 

Recent advances in first-principles molecular dynamics (MD) calculations, which follow the Newtonian dynamics of classically treated nuclei, have made electronic-structure calculations applicable to the study of large systems where previously only classical simulations were possible. Examples of quantum-mechanical (QM) simulation methods are Born-Oppenheimer molecular dynamics (BOMD), Car-Parrinello molecular dynamics (CPMD), tight-binding molecular dynamics (TBMD), atom-centered density matrix propagation molecular dynamics (ADMPMD), and wavepacket ab idtb molecular dynamics (WPAIMD). 

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