Ab-initio Molecular Dynamics

The overall scheme of ab initio molecular dynamics is similar to that of classical molecular dynamics described earlier but instead of using interatomic potentials, the Schrodinger equation is solved to provide the energy and the forces acting on the particles. The computational cost is huge and most studies are limited to small simulation cells ( 100 atoms) and time-scales of a few picoseconds. Within 

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. 

The explanation of classical MD given above was meant in part to emphasize that the dynamics of atoms can be described provided that the potential energy of the atoms, U U(ru. .., r3N), is known as a function of the atomic coordinates. It has probably already occurred to you that a natural use of DFT calculations might be to perform molecular dynamics by calculating U U(r, . r3N) with DFT. That is, the potential energy of the system of interest can be calculated on the fly using quantum mechanics. This is the basic concept of ab initio MD. The Lagrangian for this approach can be written as 

To conclude our brief overview of ab initio MD, we note that the dynamics defined by Eq. (9.16) define a microcanonical ensemble. That is, trajectories defined by this Lagrangian will conserve the total energy of the system. Similar to the situation for classical MD simulations, it is often more useful to calculate trajectories associated with dynamics at a constant temperature. One common and effective way to do this is to add additional terms to the Lagrangian so that calculations can be done in the canonical ensemble (constant N, V, and T) using the Nose-Hoover thermostat introduced in Section 9.1.2. 

The basic idea underlying AIMD is to compute the forces acting on the nuclei by use of quantum mechanical DFT-based calculations. In the Car-Parrinello method [10], the electronic degrees of freedom (as described by the Kohn-Sham orbitals y/i(r)) are treated as dynamic classical variables. In this way, electronic-structure calculations are performed on-the-fly as the molecular dynamics trajectory is generated. Car and Parrinello specified system dynamics by postulating a classical Lagrangian  

In this expression p is a mass parameter associated to the electronic fields, i.e. it is a parameter that fixes the time scale of the response of the classical electronic fields to a perturbation. The factor 2 in front of the classical kinetic energy term is for spin degeneracy. The functional f [ i , ] plays the role of potential energy in the extended parameter space of nuclear and electronic degrees of freedom. It is given by. 

HKs = — r+ V + VH + Vxc is the Kohn-Sham Hamiltonian of Eq. (9) in which VH denotes the Hartree potential. When the ifi are at the minimum of E for a given nuclear configura- 

AIMD is extensively applied in different fields of computational chemistry and, certainly, because cell functions occur at approximately 310 K, its use in life sciences seems particularly appropriate, because of the importance of temperature effects in biological systems. In this respect AIMD, which accounts explicitly for the dynamic behavior at finite temperature, can be considered one of the methods of choice when performing DFT-based simulations in theoretical medicinal chemistry. Further details about AIMD and its applications in biological chemistry are available elsewhere [11]. 

Finally, it must be remembered that DFT and AIMD can be incorporated into the so-called mixed quantum mechanical/molec-ular mechanical (QM/MM) hybrid schemes [12, 13]. In such methods, only the immediate reactive region of the system under investigation is treated by the quantum mechanical approach -the effects of the surroundings are taken into account by means of a classical mechanical force field description. These DFT/MM calculations enable realistic description of atomic processes (e.g. chemical reactions) that occur in complex heterogeneous envir- 

A very prominent development in DFT has been the coupling of electronic structure calculations (which, when the ground state is concerned, apply to zero temperature) with finite-temperature molecular dynamics simulations. Carr and Parrinello published the founding paper in this field in 1985. Carr and Parrinello formulated effective equations of motion for the electrons to be solved simultaneously with the classical equations of motion for the ions. The forces on the ions are calculated from first principles by use of the Hellman-Feynman theorem. An alternative to the Carr-Parrinello method is to solve the electronic structure self-consistently at every ionic time step. Both methods are referred to as ab initio Molecular Dynamics (AIMD). 

AIMD is still a very time-consuming simulation method, and has so far mainly been used to study the stracture and dynamics of bulk water,as well as proton transfer and simple Sn2 reactions in bulk water.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. There is no doubt that AIMD simulations of electrochemical interfaces will become increasingly important in the future, and some interesting first results will be described in Sections HI.7 and HI.8. 

On the other end of the modeling spectrum are quantum-based methods one can use to carry out simulations that treat the energetics of the system even 

Ab initio MD methods are certain to gain popularity as computational power grows, but they are presently too expensive to use to obtain quantitative estimates of properties. Quantum MD is most useful for computing spectra, for helping validate and improve classical force fields, and for studying reactivity in ionic liquids, something classical simulations cannot do. 

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Figure Al.3.30. Theoretical frequency-dependent conductivity for GaAs and CdTe liquids from ab initio molecular dynamics simulations [42].

Alavi A 1996 Path integrals and ab initio molecular dynamics Monte Carlo and Molecular Dynamics of Condensed Matter Systems ed K Binder and G Ciccotti (Bologna SIF)... 

Anta J A, Jesson B J and Madden P A 1998 Ion-electron correlations In liquid metals from orbital-free ab initio molecular dynamics Phys. Rev. B 58 6124-32... 

Jesson B J, Foley M and Madden P A 1997 Thermal properties of the self-interstitlal In aluminum an ab initio molecular-dynamics study Pbys. Rev. B 55 4941-6... 

AokI M I and Tsumuraya K 1997 Ab initio molecular-dynamics study of pressure-induced glass-to-crystal transitions In the sodium system Pbys. Rev. B 56 2962-8... 

Ultimately we may want to make direct comparisons with experimental measurements made on specific materials, in which case a good model of molecular interactions is essential. The aim of so-called ab initio molecular dynamics is to reduce the amount of fitting and guesswork in this process to a minimum. On the other hand, we may be interested in phenomena of a rather generic nature, or we may simply want to discriminate between good and bad theories. When it comes to aims of this kind, it is not necessary to have a perfectly realistic molecular model one that contains the essential physics may be quite suitable. 

Meier, R.J., Van Doremaele, H.J., larlori, S., Buda, F. Ab-initio molecular dynamics study of metallocene-catalysed ethylene polymerization. J. Amer. Chem. Soc. 116 (1994) 7274-7281. 

Van der Spoel,D., Berendsen, H.J.C. Determination of proton transfer rate constants using ab initio, molecular dynamics and density matrix evolution calculations. Pacific Symposium on Biocomputing, World Scientific, Singapore (1996) 1-14. 

Abstract. We present novel time integration schemes for Newtonian dynamics whose fastest oscillations are nearly harmonic, for constrained Newtonian dynamics including the Car-Parrinello equations of ab initio molecular dynamics, and for mixed quantum-classical molecular dynamics. The methods attain favorable properties by using matrix-function vector products which are computed via Lanczos method. This permits to take longer time steps than in standard integrators. 

Car-Parrinello Equations of Ab Initio Molecular Dynamics, Constrained Newtonian Dynamics... 

Applications of Ab-Initio Molecular Dynamics Simulations in Chemistry and Polymer Science... 

The full ab-initio molecular dynamics simulation revealed the insertion of ethylene into the Zr-C bond, leading to propyl formation. The dynamics simulations showed that this first step in ethylene polymerisation is extremely fast. Figure 2 shows the distance between the carbon atoms in ethylene and between an ethylene carbon and the methyl carbon, from which it follows that the insertion time is only about 170 fs. This observation suggests the absence of any significant barrier of activation at this stage of the polymerisation process, and for this catalyst. The absence or very small value of a barrier for insertion of ethylene into a bis-cyclopentadienyl titanocene or zirconocene has also been confirmed by static quantum simulations reported independently... 

In this chapter we shall consider four important problems in molecular n iudelling. First, v discuss the problem of calculating free energies. We then consider continuum solve models, which enable the effects of the solvent to be incorporated into a calculation witho requiring the solvent molecules to be represented explicitly. Third, we shall consider the simi lation of chemical reactions, including the important technique of ab initio molecular dynamic Finally, we consider how to study the nature of defects in solid-state materials. 

Fig. 11.38 Lag ejfects in ab initio molecular dynamics. (Figure redrawn from Payne MC, M P Teter, D C Allan, R A Arias and D ] Joannopoidos 1992. Iterative Minimisaticm Techniques for Ab Initio Total-Energy Calculations Molecular Dynamics and Conjugate Gradients. Reviews of Modern Physics 64 1045-1097.)...

Sandre E and A Pasturel 1997. An Introduction to Ab-Initio Molecular Dynamics Schemes. Molecu Simulation 20 63-77. 

Rothlisberger and M Parrinello 1997. Ab Initio Molecular Dynamics Simulation of Liquid Hydroge Fluoride. Journal of Chemical Physics 106 4658-4664. 

TECHNICAL ASPECTS OF AB-INITIO MOLECULAR-DYNAMICS, ESPECIALLY FOR METALS... 

AB INITIO MOLECULAR DYNAMICS SIMULATIONS OF LIQUID ALLOYS ... 

A successful tool to describe and interpret experimental findings of liquids is to perform ab initio molecular dynamics (MD) simulations for the particular systems. We performed such simulations for 5 different compositions of NaSn - ranging from 20% to 80% of sodium - applying the Car-Parrinello technique [5]. 

M. Odelius, M. Kadi, J. Davidsson, and A. N. Tarnovsky, Photodissociation of diiodomethane in acetonitrile solution and fragment recombination into iso-diiodomethane studied with ab initio molecular dynamics simulations. J. Chem. Phys. 121(5), 2208-2214 (2004). 

On the potential energy surfaces thus obtained 2D wavepacket dynamics calculations have been performed in the diabatic state representation. The reduced massses are regarded as those of CH2-ethylene system. The validity was examined by using on-the-fly ab initio molecular dynamics that were supplementarily performed. The dynamics calculations performed are composed of the following steps ... 

The measurement of these angles for a series of [PdClj(NHC) P(OR)3 ] complexes permitted to evidence the remarkable flexibility of NHCs due to rotations aronnd the iV-substituent bonds [82]. This flexibility, captured by the allows NHCs to respond actively to the steric requirements of co-ligands. This is further confirmed by ab initio molecular dynamics simulations aimed at understanding the variability of ( )j and in a series of NHCs containing Ru-complexes relevant to olefin metathesis [83]. 

Rousseau, R. and Marx, D. (2000) The interaction of gold clusters with methanol molecules Ab initio molecular dynamics ofAUn CH3OH and AunCH30H./owmn of Chemical Physics, 112, 761-769. 

In addition to enhancing surface reactions, water can also facilitate surface transport processes. First-principles ab initio molecular dynamics simulations of the aqueous/ metal interface for Rh(l 11) [Vassilev et al., 2002] and PtRu(OOOl) alloy [Desai et al., 2003b] surfaces showed that the aqueous interface enhanced the apparent transport or diffusion of OH intermediates across the metal surface. Adsorbed OH and H2O molecules engage in fast proton transfer, such that OH appears to diffuse across the surface. The oxygen atoms, however, remained fixed at the same positions, and it is only the proton that transfers. Transport occurs via the symmetric reaction... 

Vassilev P, Hartnig C, Koper MTM, Frechard F, van Santen RA. 2001. Ab initio molecular dynamics simulation of liquid water and water-vapor interface. J Chem Phys 115 9815-9820. 

Wang YX, Balbuena PB. 2004 Roles of proton and electric field in the electroreduction of O2 on Pt(lll) surfaces Results of an ab-initio molecular dynamics study. J Phys Chem B 108 4376-4384. 

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