Nonperiodic boundary conditions

In order to overcome the limitations of currently available empirical force field param-eterizations, we performed Car-Parrinello (CP) Molecular Dynamic simulations [36]. In the framework of DFT, the Car-Parrinello method is well recognized as a powerful tool to investigate the dynamical behaviour of chemical systems. This method is based on an extended Lagrangian MD scheme, where the potential energy surface is evaluated at the DFT level and both the electronic and nuclear degrees of freedom are propagated as dynamical variables. Moreover, the implementation of such MD scheme with localized basis sets for expanding the electronic wavefunctions has provided the chance to perform effective and reliable simulations of liquid systems with more accurate hybrid density functionals and nonperiodic boundary conditions [37]. Here we present the results of the CPMD/QM/PCM approach for the three nitroxide derivatives sketched above details on computational parameters can be found in specific papers [13]. 

Figure 20.8 The schematic figures relating to periodic and nonperiodic boundary conditions for the Au wire with Au(001) electrodes, (a) and (b) relate to model (I) and (II), respectively, see the text.

Q. Lu and R. Luo. A Poisson-Boltzmann dynamics method with nonperiodic boundary condition. / Chem. Phys., 119(21J 11035-11047,2003. 

The use of nonperiodic boundary conditions is also complicated, especially by the necessity for having a mechanism that effectively and realistically recirculates mobile components (ions and sometimes water molecules) that escape from the computational domain. The injection scheme is trivial in periodic systems, but it is not at all obvious for nonperiodic systems. 

Yeh and Berkowitz [9] proposed a simple and efficient method for treating systems with slab geometries. In their method, the nonperiodic dimension (e.g., the z direction in this case) was first extended to create some empty space, and then the periodic boundary conditions were applied in aU three directions to calculate interparticle forces. Finally, a correction force was added to each particle to remove the artifacts from the image charges due to periodic boundary conditions ... 

Figure 13 Smaller domain (region I) represents the part of the system where the detailed physics is relevant and that is, therefore, described using OFDFT. The larger domain (region II) is the region described by the atomistic classical potential (usually EAM). Region I is embedded into region II and is always nonperiodic, while periodic boundary conditions can be applied to region II.

We introduce new ab-initio real-space method based on (1) density functional theory, (2) finite element method, and (3) environment-reflecting pseudopotentials. It opens various ways for further development and applications restricted periodic boundary conditions in a desired sub-region or in a requisite direction (e.g. for nonperiodic objects with bonds to periodic surroundings), adaptive finite-element mesh and basis playing the role of variational parameters (hp-adaptivity) and various approaches to Hellman-Feynman forces and sensitivity analysis for structural optimizations and molecular dynamics. 

Regarding techniques of data analysis, the most fundamental challenge in QCs is the inabihty to apply periodic boundary conditions. In general terms, there are three possible solutions (i) analyze long-range structure in a nonperiodic manner, (ii) focus on local stmcture in a way that makes boundary conditions unnecessary, or (iii) use periodic approximants as surrogates. 

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