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Analytic projection from plane‐wave and PAW wavefunctions and application to chemical‐bonding analysis in solids
Author(s) -
Maintz Stefan,
Deringer Volker L.,
Tchougréeff Andrei L.,
Dronskowski Richard
Publication year - 2013
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.23424
Subject(s) - wave function , atomic orbital , population , basis set , chemical bond , basis (linear algebra) , orbital overlap , eigenvalues and eigenvectors , basis function , plane wave , electronic structure , projection (relational algebra) , statistical physics , computational chemistry , chemistry , quantum mechanics , physics , computer science , mathematics , molecule , algorithm , geometry , sociology , electron , demography
Quantum‐chemical computations of solids benefit enormously from numerically efficient plane‐wave (PW) basis sets, and together with the projector augmented‐wave (PAW) method, the latter have risen to one of the predominant standards in computational solid‐state sciences. Despite their advantages, plane waves lack local information, which makes the interpretation of local densities‐of‐states (DOS) difficult and precludes the direct use of atom‐resolved chemical bonding indicators such as the crystal orbital overlap population (COOP) and the crystal orbital Hamilton population (COHP) techniques. Recently, a number of methods have been proposed to overcome this fundamental issue, built around the concept of basis‐set projection onto a local auxiliary basis. In this work, we propose a novel computational technique toward this goal by transferring the PW/PAW wavefunctions to a properly chosen local basis using analytically derived expressions. In particular, we describe a general approach to project both PW and PAW eigenstates onto given custom orbitals, which we then exemplify at the hand of contracted multiple‐ζ Slater‐type orbitals. The validity of the method presented here is illustrated by applications to chemical textbook examples—diamond, gallium arsenide, the transition‐metal titanium—as well as nanoscale allotropes of carbon: a nanotube and theC 60fullerene. Remarkably, the analytical approach not only recovers the total and projected electronic DOS with a high degree of confidence, but it also yields a realistic chemical‐bonding picture in the framework of the projected COHP method. © 2013 Wiley Periodicals, Inc.