Direct molecular dynamics principles

Wigner rotation/adiabatic-to-diabatic transformation matrices, 92 Electronic structure theory, electron nuclear dynamics (END) structure and properties, 326-327 theoretical background, 324-325 time-dependent variational principle (TDVP), general nuclear dynamics, 334-337 Electronic wave function, permutational symmetry, 680-682 Electron nuclear dynamics (END) degenerate states chemistry, xii-xiii direct molecular dynamics, structure and properties, 327 molecular systems, 337-351 final-state analysis, 342-349 intramolecular electron transfer,... 

Free and Lombardi (FL) models, Renner-Teller effect, triatomic molecules, 618-621 Free electrons, electron nuclear dynamics (END), time-dependent variational principle (TDVP), 333-334 Frozen Gaussian approximation direct molecular dynamics ... 

First-principles (or ah initid) molecular dynamics, the direct combination of DFT with classical molecular dynamics (MD), was introduced in 1985 in a seminal paper by Car and Parrinello [9]. This novel scheme has first been applied to the study of metal clusters [20] and amorphous and liquid silicon [21] but has since moved rapidly into chemistry [22] and biology [23, 24], CP-MD of-... 

The second approach used in first-principles tribological simulations focuses on the behavior of the sheared fluid. That is, the walls are not considered and the system is treated as bulk fluid, as discussed. These simulations are typically performed using ab initio molecular dynamics (AIMD) with DFT and plane-wave basis sets. A general tribological AIMD simulation would be run as follows. A system representing the fluid would be placed in a simulation cell repeated periodically in all three directions. Shear or load is applied to the system using schemes such as that of Parrinello and Rahman, which was discussed above. In this approach, one defines a (potentially time-dependent) reference stress tensor aref and alters the nuclear and cell dynamics, such that the internal stress tensor crsys is equal to aref. When crsys = aref, the internal and external forces on the cell vectors balance, and the system is subject to the desired shear or load. 

The direct simulation of P(z) is possible in principle by following the motion of the ion in a long molecular dynamics trajectory and binning the observed values of the ion position. This method will give reasonable... 

Molecular Dynamics and Monte Carlo simulations have been used to predict the adsorption isotherms and transport diffusivities of Xe adsorbed in A1P04-31. The results of these calculations can be used to predict the properties of Xe diffusing through membranes made from A1P04-31 crystals directly from atomic-scale principles. 

There are alternates to probing diffusion by molecular dynamics or transition state theory. For a diffiisional path than contains a significant constriction or activation barrier, an additional force along the difiusion direction can be applied to enforce lateral difiusion pn the molecule. The hias in quantifying the difiusion that results that such an additional force injects can, in principle, be corrected-for so as to yield an estimate of the translational difiusion coefELdent in the free, unperturbed system. 

The most important information to be extracted from either experiment or theory is structural information. In first-principles methods this information is readily available. Experimentally, it may be extracted directly from diffraction techniques. While X-ray diffraction provides information on solids, which means on frozen structures, other techniques like neutron diffraction can provide statistical information like pair correlation functions that are also easily obtained from a molecular dynamics trajectory. 

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