Charge deformation, definition

Conventional implementations of MaxEnt method for charge density studies do not allow easy access to deformation maps a possible approach involves running a MaxEnt calculation on a set of data computed from a superposition of spherical atoms, and subtracting this map from qME [44], Recourse to a two-channel formalism, that redistributes positive- and negative-density scatterers, fitting a set of difference Fourier coefficients, has also been made [18], but there is no consensus on what the definition of entropy should be in a two-channel situation [18, 36,41] moreover, the shapes and number of positive and negative scatterers may need to differ in a way which is difficult to specify. 

Figure 3. Definition of the ionization energy I for an isolated atom (A) and an atom in a molecule (B). In the first case, the electron is moved to infinite distance and does not interact with the cation. In the latter case, the charge of the electron is distributed in the vicinity of the cation. This results in a deformation of the electron cloud (in this case a tetrahedral one). The definition of an atom-in-molecule electron affinity is analogous.

Figure 5.2 i Anisotropy of various contributions to the 3-body forces for the cyclic water trimer . See Fig. 5.19 for definition of a. HL refers to Heitler-London term which prohibits modification of the charge clouds of each molecule in the presence of the others, and SCF-def to the result of such deformation, both at the SCF level. Three-body induction is computed directly via perturbation theory. 

The coincidence of the topological and quantum definitions of an atom means that the topological atom is an open quantum subsystem, free to exchange charge and momentum with its environment across boundaries which are defined in real space and which, in general, change with time. It should be emphasized that the zero-flux surface condition is universal— it applies equally to an isolated atom or to an atom bound in a molecule. The approach of two initially free atoms causes a portion of their surfaces to be shared in the creation of an interatomic surface. Atomic surfaces undergo continuous deformations as atoms move relative to one another. They are, however, not destroyed as atoms separate. 

The deformed charge distribution is generally axially symmetrical and this fact has an important consequence. It permits to characterize the charge distribution asymmetry by means of only one quantity, Q (called the quadrupolar moment), even if the quadrupolar operator, is a 3x3 matrix (in classical physics, a quadrupole is a second rank tensor). The definition of Q and the explicit form of are given in references 2 and 3. 

---