PMC

The isosurface lobes (0.003 e/ų) of charge density difference of the Ag adatom adsorbed on (a) the Si(111)-5×5 and (b) the Si(111)-7×7 unit cell. The blue square shows the CH with the Ag adatom. The top view of the charge density difference on the CH of (c) Si(111)-5×5 and (d) Si(111)-7×7 unit cells. The side views of the enlarged charge density difference in the CH of (e) Si(111)-5×5 and (f) Si(111)-7×7 unit cells. Red and blue lobe represents charge gain and charge depletion respectively. The yellow and light-blue balls represent Si and Ag atoms respectively.

A schematic of charge compensation strategies for LaAlO₃:Mn⁴⁺ phosphor. (a) The charge compensation for the unit of Al³⁺-La³⁺ and Mn⁴⁺-Ca²⁺; (b) The charge compensation for the unit of Al³⁺-La³⁺-Al³⁺ and Mn⁴⁺-Na⁺-Mn⁴⁺.

For a sample charge distribution with non-zero net charge (a glutamic acid group within a protein with net charge , where the group includes the associated NH-CH-CO backbone atoms). (a) The original charge distribution with its quadrupole tensor (Eq. (5)) shown below. The atomic partial charges are represented as spheres rendered using VMD . The sphere colors range from red to blue representing the charge range of to . The charge values for partial charges are shown next to the atoms. As a visual reference, the backbone heavy atoms are labeled and covalent bonds are included in the figure. The green square shows the center of charge (COCh). (b) The principal axes, v1, v2, v3 of the original charge distribution with the center of charge as origin (green square). Its quadrupole tensor, with the coordinate system aligned to the principal axes (Eq. (27)), is shown below. Here v1 is the principal axis with the largest principal value. Analogous to the concept of ellipsoid of inertia in Mechanics used to characterize mass distribution, an “ellipsoid of charge” can be imagined here that helps visualize the charge distribution characterized by the quadrupole tensor. (c) The 2-charges of the PPCA (red diamonds) are placed such that the quadrupole moment for the PPCA equals the component of the quadrupole moment for the original charge distribution along v1. The quadrupole tensor produced by the 2-charge PPCA, with the coordinate system aligned to the principal axes, is shown below. The values of charges are in atomic units (), and Å is the unit for the quadrupole tensors.

Charge distribution (a) in the reduced unit cell geometry (with  = 3.37 Å) and (b) in the full unit cell geometry models of the Si(553)-Pb surface. A color code denotes charge density in electrons/bohr units. A side view (along ) of the reduced (c) and full (d) unit cell geometry models. The charge density is averaged over the whole unit cell along . The brown (light blue) circles denote Pb (Si) atoms.