Subject Area: Properties of Charge Densities Obtained from Electron Scattering from Nitrogen

Abstract

The charge density may be partitioned into separate contributions from each of the atoms by the method of Stewart. For a diatomic molecule this means that

$$\begin{array}{l} \rho (\vec r) = {\rho _A}(\vec r - {{\vec R}_A}) + {\rho _B}(\vec r - {{\vec R}_B})\\ = {\rho _A}({{\vec r}_A}) + {\rho _B}({{\vec r}_B}) \end{array}$$

where ${{\overrightarrow{R}}_{A}}$ is $\underrightarrow{a}$ vector from the center of mass of the molecule to nucleus A, R_B is $\underrightarrow{a}$ vector from the center of mass of the molecule to nucleus B and r is a vector from the center of mass to a point in the electron charge distribution. The density about each center can be expanded as

$${{p}_{A}}(\overrightarrow{r}-{{\overrightarrow{R}}_{A}})=p({{\overrightarrow{r}}_{A}})=\frac{1}{4\pi }\sum\limits_{n=0}^{\infty }{{{p}_{An}}}({{r}_{A}}){{p}_{n}}(cos{{\theta }_{A}})$$

Further the ρ_An(r_A) may be parameterized as

$${{p}_{An}}({{r}_{A}})=\sum\limits_{K=0}^{M}{{{A}_{nk}}}{{r}^{n+k}}{{e}^{-{{\lambda }_{n{{k}^{r}}}}}}$$

Such a parameterized model has been used by Fink to fit electron scattering data.