Potential Parameterization

Once a functional form is decided to capture different aspects of the potential curve (1) zero order derivative, (2) first order derivative, (3) second order derivative, and (4) anharmonicity. Free parameters of the potential model are obtained either through fitting them to ab initio data for small clusters or condensed systems, or adjusting the parameters to reproduce known experimental results, or some combination of these methods. In the following, we will selectively choose a few examples to illustrate the commonly used parameterization procedures. 

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An important aspect of empirical potential parameterization is the question of transferability. Are, for example, models derived in the study of binary oxides, transferable to ternary oxides Considerable attention has been paid to this problem by Cormack et al., who have examined the use of potentials in spinel oxides, for example, MgAl204, NiCr204, and so on in addition Parker and Price have made a very careful study of silicates especially Mg2Si04. These studies conclude that transferability works well in many cases. However, systematic modifications are needed when potentials are transferred to compounds with different coordination numbers. For example, the correct modeling of MgAl204 requires that the potential developed for MgO, in which the magnesium has octahedral coordination, be modified in view of the tetrahedral coordination of Mg in the ternary oxide. The correction factor is based on the difference Ar between the effective ionic radii for the different coordination numbers. If an exponential, Bom-Mayer, repulsive term is used, the preexponential factor is modified as follows ... 

Nevertheless, these methods are mostly applied with fixed charges (even if these are chosen in a sophisticated way) and with pairwise additivity approximation as well as with the neglect of nuclear quantum effects. Suggestions for polarizable models appeared in literature mainly for water [23], The quality of potential parameterization varies from system to system and from quantity to quantity, raising the question of transferability. Spontaneous events like reactions cannot appear in simulations unless the event is included in the parameterization. Despite these problems, it is possible to reproduce important quantities as structural, thermodynamic and transport properties with traditional MD (MC) mainly due to the condition of the nanosecond time scale and the large system size in which the simulation takes place [24],... 

The NAST [16, 34] model represents each nucleotide by one pseudoatom at the C3 atom of the ribose group. NAST utilizes MD simulations and a force field parameterized from solved rRNA structures. NAST relies upon information from an accurate secondary structure and can also include experimental constraints. These constraints are modeled by a harmonic energy term. The bonded energy terms of distance, angle, and dihedral are further modeled by a harmonic potential, parameterized according to a Boltzmann inversion. Non-bonded interactions are modeled by a Lennard-Jones potential with a hard sphere radii of 5 A. Due to the low-resolution representation of one pseudoatom per nt, the conversion from the CG model to the all-atom model is complex and may produce steric overlaps. In order to overcome this difficulty, Jonikas et al. developed a program C2A [35] which is able to insert and minimize the all atom structure. 

Replace the core electrons by a potential parameterized by expansion into a suitable set of analytical functions of the nuclear-electron distance, for example a polynomial or a set of spherical Bessel or Gaussian functions. Since relativistic effects are mainly important for the core electrons, this potential can effectively include relativity. The potential may be different for each angular momentum. 

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