Adapting gas-phase electron scattering $R$-matrix calculations to a condensed-matter environment

We investigate how gas phase $R$-matrix calculations for electron collisions with the water molecule can be efficiently used in a condensed environment. The electron band structure of cubic ice being fairly well studied, we try to reproduce it using a generalization of the Korringa-Kohn-Rostoker band calculation method. We find two cutoffs have to be applied to the $R$-matrix elastic scattering results in condensed matter: one on the range of the molecular dipole and another in the angular momentum components of the scattering matrix. Their origins and physical meaning are discussed.

Figure 1

Total elastic cross section for electron-gas phase ${\mathrm{H}}_2\mathrm{O}$ collisions for different values of the cutoff radius $a_c$.

Figure 2

Bloch eigenmode energy as a function of the wave number in the [111] crystal direction for $R$-matrix data from a partial wave expansion up to $l\le 4$ using $a_c=6\text{a.u.}$

Figure 3

Bloch eigenmode energy as a function of the wave number in the [111] crystal direction for $R$-matrix data obtained restricting the partial wave expansion to $l\le 2$ and using $a_c=6\text{a.}\mathrm{u}$.

Figure 4

Effective mass $m^{*}$ in terms of the free electron mass $m_0$, circles, and energy $E_{CB}$, squares, at the bottom of the conduction band as a function of the cutoff radius $a_c$, i.e., the range of the dipole field.