Abstract

This chapter provides introductory material on use of Wannier functions for analyzing chemical bonding in crystalline solids. Wannier functions are obtained by applying a unitary transformation to Bloch functions. In particular, so-called maximally localized Wannier functions (MLWFs) are obtained under the widely used maximal-localization criterion. Although this criterion does not directly reflect chemical intuition other than localization, MLWFs often provide us useful chemical insights. Two simple examples are dealt with to show how to use MLWFs in chemical bonding analyses. In the first example, 2c–2e inter-cluster, 3c–2e inter-cluster, and intra-cluster bonding orbitals in α-rhombohedral boron are extracted as Wannier functions. In the second example, CoCo bonding orbitals in cobalt aluminide (an 18−n compound with n=6) are extracted as Wannier functions.

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