Charge image simulation

The main difficulty in these simulations is the long-range nature of the Coulomb interactions, since both mirror-plane images and real charges must be included, and the finite nature of the simulated volume must also be mchided. A more detailed discussion is given by Benjamin [29], and the following conclusions have been reached. 

The first simulation studies of full double layers with molecular models of ions and solvent were performed by Philpott and coworkers [51,54,158] for the NaCl solution, using the fast multipole method for the calculation of Coulomb interactions. The authors studied the screening of a negative surface charge by free ions in several highly concentrated NaCl solutions. A combination of (9-3) LJ potential and image charges was used to describe the metal surface. 

The combination of state-of-the-art first-principles calculations of the electronic structure with the Tersoff-Hamann method [38] to simulate STM images provides a successful approach to interpret the STM images from oxide surfaces at the atomic scale. Typically, the local energy-resolved density of states (DOS) is evaluated and isosurfaces of constant charge density are determined. The comparison between simulated and measured high-resolution STM images at different tunneling... 

There are problems with using both of these methods in the simulation of inhomogeneous systems. Because the periodicity of the system is lost in the direction normal to the interface (unless one uses image charges with the flat wall model, which effectively results in a 3D periodic system implementation of the ES method is not straightforward for certain type of systems. Hautman and Klein have presented a modified Ewald sum method for the simulation of systems that are periodic in two... 

Figure 6.18. (Top) STM image of the flfe-plane of TTF-TCNQ taken at 63 K (Ft = 50 mV, /t = 1 nA). The image area is 5.3 nm x 5.3 nm. Reprinted with permission from Z. Z. Wang, J. C. Girard, C. Pasquier, D. Jerome and K. Bechgaard, Physical Review B, 67,121401 (2003). Copyright (2003) by the American Physical Society. (Bottom) Simulation of the STM image of the afe-plane of TTF-TCNQ, obtained with DFT calculations in the GGA performed with the Siesta code (Soler et al, 2002) using the Tersoff-Hamann approximation (see Section 4.2). The value of the charge density is 2 x 10 electrons/a.u., which is about 0.2 nm above the surface. Courtesy of Drs P. Ordejon and E. Canadell.

Fig. 6.4. Image profile with a Na-atom tip. (a) Geometry of the simulation. Two flat and. structureless jellium surfaces, each with an extra Na atom adsorbed on it, represent the tip and the sample, respectively. The net current from these Na atoms is kept constant while moving the Na atoms across each other. The path is generated numerically, (b) The simulated image (.solid curve) is in good agreement with the contour of the bermi-level LDOS and the total-charge-dcnsity contour. The apparent radius, as determined from the curve, is about 12 A. (After Lang, 1986.)...

Fig. 2. (a) Periodic images surrounding the simulation box. Interactions are computed with respect to the nearest image which is indicated by the circle, (b) Violation of the minimum image convention resulting from the interaction of QM particle with point charge 1. 

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