# The Calculation of Brillouin Zone Integrals by Interpolation Techniques

• R. L. Jacobs
• D. Lipton
Chapter
Part of the The IBM Research Symposia Series book series (IRSS)

## Abstract

In this paper we present a quasi-analytic technique for calculating Brillouin zone integrals of the form
$$\operatorname{Re} {\chi _o}\left( {\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{q} ,\omega } \right) = {N^{ - 1}}P\sum\limits_k {{{\left( {f\left( {\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{k} } \right) - f\left( {\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{k} + \underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{q} } \right)} \right)} \mathord{\left/{\vphantom {{\left( {f\left( {\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{k} } \right) - f\left( {\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{k} + \underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{q} } \right)} \right)} {\left( {{\varepsilon _{\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{k} }} - {\varepsilon _{\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{k} + \underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{q} }} + h\omega } \right).}}} \right. \kern-\nulldelimiterspace} {\left( {{\varepsilon _{\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{k} }} - {\varepsilon _{\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{k} + \underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{q} }} + h\omega } \right).}}}$$
(1)

## Keywords

Magnetic Susceptibility Energy Band Imperial College Susceptibility Function Interpolation Technique
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

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