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When talking about solid materials, the discussion is mainly around crystals – periodic lattices. Here we will discuss a 1D lattice of positive ions. Assuming the spacing between two ions is a, the potential in the lattice will look something like this: The mathematical representation of the potential is a periodic function with a period a.
In an ab initio MD simulation, the total energy of the system is calculated at each time step using density functional theory (DFT) or another method of quantum chemistry. The forces acting on each atom are then determined from the gradient of the energy with respect to the atomic coordinates, and the equations of motion are solved to predict ...
The parameterization of these very coarse-grained models must be done empirically, by matching the behavior of the model to appropriate experimental data or all-atom simulations. Ideally, these parameters should account for both enthalpic and entropic contributions to free energy in an implicit way. [ 58 ]
The hybrid model is a combination of fluid and kinetic models, treating some components of the system as a fluid, and others kinetically. The hybrid model is sometimes applied in space physics , when the simulation domain exceeds thousands of ion gyroradius scales, making it impractical to solve kinetic equations for electrons.
The Bose–Hubbard model gives a description of the physics of interacting spinless bosons on a lattice.It is closely related to the Hubbard model that originated in solid-state physics as an approximate description of superconducting systems and the motion of electrons between the atoms of a crystalline solid.
This model exhibits confinement of the fermions and as such, is a toy model for QCD. A handwaving argument why this is so is because in two dimensions, classically, the potential between two charged particles goes linearly as r {\displaystyle r} , instead of 1 / r {\displaystyle 1/r} in 4 dimensions, 3 spatial, 1 time.
Langevin dynamics mimics the viscous aspect of a solvent. It does not fully model an implicit solvent; specifically, the model does not account for the electrostatic screening and also not for the hydrophobic effect. For denser solvents, hydrodynamic interactions are not captured via Langevin dynamics.
The Bohr model is a relatively primitive model of the hydrogen atom, compared to the valence shell model. As a theory, it can be derived as a first-order approximation of the hydrogen atom using the broader and much more accurate quantum mechanics and thus may be considered to be an obsolete scientific theory .