Quantum-based interatomic potentials

Within DFT quantum mechanics, first-principles GPT provides a fundamental basis for ab initio interatomic potentials in metals and alloys. In the GPT apphed to transition metals [49], a mixed basis of plane waves and localized d-state orbitals is used to self-consistently expand the electron density and total energy of the system in terms of weak sp pseudopotential, d-d tight-binding, and sp-d hybridization matrix elements, which in turn are all directly calculable from first principles. For a bulk transition metal, one obtains the real-space total-energy functional 

The leading volume term in this expansion, E oh as well as the two-, three-, and four-ion interatomic potentials, V2, V3, and V4, are volume-dependent, but structure-independent quantities and thus transferable to arbitrary bulk ion configurations. The angular-force multi-ion potentials V3 and V4 reflect directional-bonding contributions from partially filled d bands and are important for mid-period transition metals. In the full GPT, however, these potentials are multidimensional functions, so that V3 and V4 cannot be readily tabulated for application purposes. This has led to the development of a simplified MGPT, which achieves short-ranged, analytic potential forms that can be applied to large-scale atomistic simulations [50]. 

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Maiti, A. Sierka, M. Andzebn, J. Golab, J. Sauer, J. Combined Quantum Mechanics Interatomic potential function investigation of rac-meso configurational stability and rotational transition in zirconocene-based Ziegler-Natta catalysts. J. Phys. Chem. A 2000,104, 10932-10938. 

A quantitative surface compositional analysis requires the comparison of the experimental yield of the individual clusters with corresponding yields obtained theoretically this may be done by numerical simulation of the complex collision process but the accuracy of the result cannot yet be ascertained. The accuracy of the compositional analysis depends to some extent on such poorly known factors as the interatomic potential, ionization cross-sections and quantum-mechanical corrections to a treatment based on classical trajectories. 

Although there are many ways to describe a zeolite system, models are based either on classical mechanics, quantum mechanics, or a mixture of classical and quantum mechanics. Classical models employ parameterized interatomic potentials, so-called force fields, to describe the energies and forces acting in a system. Classical models have been shownto be able to describe accurately the structure and dynamics of zeolites, and they have also been employed to study aspects of adsorption in zeolites, including the interaction between adsorbates and the zeolite framework, adsorption sites, and diffusion of adsorbates. The forming and breaking of bonds, however, cannot be studied with classical models. In studies on zeolite-catalyzed chemical reactions, therefore, a quantum mechanical description is typically employed where the electronic structure of the atoms in the system is taken into account explicitly. 

Computationally efficient ab initio quantum mechanical calculations within the framework of DFT play a significant role in the study of plasma-surface interactions. First, they are used to parametrize classical force fields for MD simulations. Second, they provide the quantitative accuracy needed in the development of a chemical reaction database for KMC simulations over long time scales upon identification of a surface chemical reaction through MD simulation, DFT can be used to address in quantitative detail the reaction energetics and kinetics. Third, DFT-based chemical reaction analysis and comparison with the corresponding predictions of the empirical interatomic potential used in the MD simulations provides further... 

Latterly, increasing use has also been made of Quantum Molecular Dynamics (QMD), based on the pioneering work of Car and Parrinello (1985) (see Chapter 8). The Car-Parrinello method makes use of Density Functional Theory to calculate explicitly the energy of a system and hence the interatomic forces, which are then used to determine the atomic trajectories and related dynamic properties, in the manner of classical MD. As an ab initio technique, QMD has the advantage over classical simulation methods that it is not reliant on interatomic potentials, and should in principle lead to far more accurate results. The disadvantage is that it demands far greater computing resources, and its application has thus far been limited to relatively simple systems. 

In Chapter 4, Professor Donald W. Brenner and his co-workers Olga A. Shenderova and Denis A. Areshkin explore density functional theory and quantum-based analytic interatomic forces as they pertain to simulations of materials. The study of interfaces, fracture, point defects, and the new area of nanotechnology can be aided by atomistic simulations. Atom-level simulations require the use of an appropriate force field model because quantum mechanical calculations, although useful, are too compute-intensive for handling large systems or long simulation times. For these cases, analytic potential energy functions can be used to provide detailed information. Use of reliable quantum mechanical models to derive the functions is explained in this chapter. 

However, the drawback of ab initio calculations is that they usually refer to the athermal limit (T = 0 K), so that pressure but not temperature effects are included in the simulation. Although in principle the ab initio molecular dynamics approach[13] is able to overcome this limitation, at the present state of the art no temperature-dependent quantum-meehanieal simulations are feasible yet for mineral systems. Thus thermal properties have to be dealt with by methods based on empirical interatomic potential functions, containing parameters to be fitted to experimental quan-tities[14,15, 16]. The computational scheme applied here to carbonates is that based on the quasi-harmonic approximation for representing the atomic motion[17]. 

I tested the GAP models on a range of simple materials, based on data obtained from Density Functional Theory. I built interatomic potentials for the diamond lattices of the group IV semiconductors and I performed rigorous tests to evaluate the accuracy of the potential energy surface. These tests showed that the GAP models reproduce the quantum mechanical results in the harmonic regime, i.e. phonon spectra, elastic properties very well. In the case of diamond, I calculated properties which are determined by the anharmonic nature of the PES, such as the temperature dependence of the optical phonon frequency at the F point and the temperature dependence of the thermal expansion coefficient. Our GAP potential reproduced the values given by Density Functional Theory and experiments. 

Lastly, any underlying atomistic model can be used, whether quantum mechanically or classically based. In practice, semi empirical interatomic potentials such as EAM ° and Stillinger-Weber (three-body interaction) potentials have usually been used to model the atomistic regime. 

The last two decades have witnessed a dramatic rise in computational resources that has facilitated tremendous progress in computational science. In particular, this progress has enabled the application of quantum-based methods such as Flartree-Fock (FIF) theory and density functional theory (DFT) to compute the potential energy surfaces of numerous complex reactions that are critical to understanding catalytic reactions. These approaches provide high fidelity because of their explicit treatment of electronic structure however, their computational cost increases rapidly with system size. Therefore, they are limited to a relatively small number of atoms (<500). To overcome this limitation, classical empirical methods (also known as interatomic potentials) that model molecules and materials at the atomic scale without explicitly treating electrons have been developed and have been employed in molecular dynamics (MD) and Monte Carlo (MC) simulations. Such simulations have been employed to examine catalysis at length and time scales beyond the reach of quantum-based approaches. 

Recently, this problem was treated by a rigorous quantum chemistry calculation by Bakalov et al. [28], First, the authors calculated ab initio the interatomic interaction V(R,r, ) between an atomcule pHe- and a He atom based on the Born-Oppenheimer approximation. Since the rotational frequency of the p (of order of 1015 s-1) is much higher than the collision frequency (of order of 1012 s-1), the angular dependence is smeared out, and typically, the Van der Waals minimum occurs around R 5.5 a.u., and the repulsive barrier starts around R 5 a.u. The potential V(R) depends on (n,l), and thus, a small difference AV(R) occurs between an initial state and a final state. It is this difference that causes pressure shifts and broadening in the resonance line. 

Finally, we refer to a quite recent paper where a first- principles molecular dynamics simulation of amorphous and liquid Si02 was performed [14]. This work confirmed that computer simulation based on the quantum-mechanical calculation of interatomic energy gives basically the same atomic structure of amorphous Si02 as mentioned above simulations based on semiempirical potential of Eq. (1). 

Most of the work done to date is based on classical effective potentials that describe with sufficient accuracy the relevant interatomic and intermolecular forces, in particular the vdW couplings between hydrogen molecules and the various carbon structures considered (mainly graphite and nanotubes). An important point to note is that, since the electrons are not explicitly treated in such models, the computational cost of the simulations is relatively small, which makes it possible to perform, for realistic model systems composed of hundreds of atoms, sophisticated statistical calculations in the grand-canonical ensemble, and thus compute the amount of hydrogen that can be stored at particular temperature and pressure conditions, and even consider the quantum effects associated to the hydrogen molecules. Useful reviews of the most important results and literature can be found in Hirscher and Becher, Meregalh and Parrinello and Simonyan and Johnson. ... 

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