First principle MD simulations

The range of systems studied by first-principle Molecular Dynamics is vast and the number of applications of first-principle MD is growing every day. Apart from the systems previously mentioned, first-principle MD simulations have been for example performed for molecular [3,48,65-67] or ionic liquids [68-72], surfaces and interfaces [48,73-79], solids [27,80-83] or glasses [84-87] and biological systems [88-96]. 

It was pointed out by Pederson and Jackson [36] that it is very difficult to calculate the second term in the equation (27) in first-principles MD simulations. However, Wentzcovitch et al. [37] introduced the Mermin free energy [38] ... 

In the following, we will present jellium-related theoretical approaches (specifically the shell-correction method (SCM) and variants thereof) appropriate for describing shell effects, energetics and decay pathways of metal-cluster fragmentation processes (both the monomer/dimer dissociation and fission), which were inspired by the many similarities with the physics of shell effects in atomic nuclei (Section 4.2). In Section 4.3, we will compare the experimental trends with the resulting theoretical SCM interpretations, and in addition we will discuss theoretical results from first-principles MD simulations (Section 4.3.3.1). Section 4.4 will discuss some of the latest insights concerning the importance of electronic-entropy and finite-temperature effects. Finally, Section 4.5 will provide a summary. 

Until relatively recently, the use of quantum MD for modeling polymers seemed completely unrealistic. This approach, however, is now applicable to polymeric systems that could only be studied by means of empirical and semiempirical methods a decade ago. First-principles MD simulations have been successfully applied to a wide variety of important problems in polymer physics and chemistry and are now beginning to influence biology as well. ° Representative examples include the simulations of polyethylene (PE) (the prediction of Yoimg s modulus for crystalline material, strain energy storage and chain mpture under tensile load, the... 

Fig. 14.6 Mean-squared displacement (MSD) obtained from the first-principles MD simulations in liquid B2O3. Left oxygen and boron MSD at temperatures of 4000 and 2000 K for a density of 1.84 gcm (corresponding to the glass density at 300 K). Right boron MSD at 2000 K for densities of 1.84 and 1.49gcm. The latter density is that of the liquid at 2000 K...

Ohkubo et study electronic properties structure and transport coefficients (conductivity and self-diffusion) of a molten acLi20-(1 — x)B203 system using first-principles MD simulations performed with their own finite element density functional theoiy code, FEMTECK and PFG NMR measurements. For diffusion the first-principles simulation results were in better agreement with experiment than that obtained from classical simulations. 

Many quantities can be calculated using DFPT. Mentioning only applications in the context of first-principle MD, DFPT has been applied to the calculation of polarizability and Raman spectrum of ice [197], NMR chemical shifts in liquid water [206] or other systems [196, 207-209], chemical hardness [47], atomic polar tensors in liquid water [28] and so on. DFPT is a growing field for ab initio simulations. 

We did not address also other extensions of first-principle MD to free-energy Density Functional Theory for metals [145,256,257], simulations with a variable number of electrons [11,14,67,258-260] (fixed electron chemical potential) or otherwise path-integral Molecular Dynamics in the Car-Parrinello framework [27,43,51,80,81,208,261-268]. We hope however that the present introduction on first-principle MD will give the reader both the background and the enthusiasm to look in this vast literature. 

A group of theoretical methods exists where the electronic wavefuntion is computed, and the atomic nuclei are propagated (using classical equations of motion). The Car-Parrinello MD method is one of this type [22-24]. These methods he between the extremes of the classical and ab initio methods, as they include some (quantum) electronic information and some (classical) dynamics information. These methods are called ah initio or first principles MD if you come from the classical community and semi-classical MD if you come firom the quantum community [9], Ah initio MD methods are far more expensive and cannot simulate as many molecules for as long as the classical simulations, but they are more flexible in that structures are not predetermined and information on the electronic structure is retained. Semi-classical MD can be carried out under periodic boundary conditions and thus the local liquid environment, and any extended bonding network, vyill be present. These methods hold a great deal of promise for the future study of ionic liquid systems, the first such calciilations on ionic liquids were reported in 2005 [21,25]. 

Fig. 11.2 Publication and citation analysis. Squares number of publications with usage of AIMD each year from 1991 to September 28, 2011, which is based on Web of Science database (http // apps.webofknowledge.com) using ab initio and molecular dynamics (or synonym such as first-principle MD and Car-Parrinello simulations ) as the keywords. Diamonds number of publications which cite the 1985 paper by Car and Parrinello [33]...

Figure 6. Compilation of coordination number measurements plotted against temperature (at P = 0 GPa) as reported by different experimental reports, first-principle MD (FPMD) simulations as well as classical simulations results. [From Ansell et al. [73], Kimura et al. [77], Jakse etal. [74], Kim et al. [81], Higuchi etal. [76], Krishnan et al. [75], Morishita ]45], Wang etal. [105] with permission.]...

Figure 13. Equation of state of supercooled silicon obtained from first-principles MD (FPMD) simulations displaying a van der Waals-like loop for T < 1232K. [From Ganesh et al. [23] with permission.]...

First-Principles Simulations In the cases of carbon and silica, computer simulations using classical empirical potentials have shown a liquid-liquid transition [17,92], but first-principle MD (FPMD) simulations [93,94] show results that are not consistent with classical simulations. In silicon, Jakse and Pasturel [22] and independently Ganesh and Widom [23] have reported first-principle simulation results, both of which support the proposed liquid-liquid transition in silicon. In the work of Ganesh and Widom, the authors report the emergence of a van der Waals-like loop (shown in Fig. 13), as signature of a first-order phase transition at temperatures below 1182K. The maximum time span of these simulations is around 40 ps [22], which seems to be very small compared to the relaxation times of LDL (tens to hundreds of nanoseconds see below) obtained from simulations of SW silicon [21]. But the FPMD calculations are computationally very expensive compared to classical MD simulations. Hence, it would be of interest to compare the equilibration times of the system simulated in FPMD and classical MD and also do a systematic study of relaxation processes in these two different methods of simulation. A comparison of properties obtained in different simulations are discussed in a later section. 

In 1985 Car and Parrinello invented a method [111-113] in which molecular dynamics (MD) methods are combined with first-principles computations such that the interatomic forces due to the electronic degrees of freedom are computed by density functional theory [114-116] and the statistical properties by the MD method. This method and related ab initio simulations have been successfully applied to carbon [117], silicon [118-120], copper [121], surface reconstruction [122-128], atomic clusters [129-133], molecular crystals [134], the epitaxial growth of metals [135-140], and many other systems for a review see Ref. 113. 

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.

The greatest limitation of QC methods is computational expense. This expense restricts system sizes to a few hundred atoms at most, and hence, it is not possible to examine highly elaborate systems with walls that are several atomic layers thick separated by several lubricant atoms or molecules. Furthermore, the expense of first-principles calculations imposes significant limitations on the time scales that can be examined in MD simulations, which may lead to shear rates that are orders of magnitude greater than those encountered in experiments. One should be aware of these inherent differences between first-principles simulations and experiments when interpreting calculated results. 

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