Premium
Hierarchies of quantum chemical descriptors induced by statistical analyses of domain occupation number operators
Author(s) -
Acke Guillaume,
De Baerdemacker Stijn,
Martín Pendás Ángel,
Bultinck Patrick
Publication year - 2019
Publication title -
wiley interdisciplinary reviews: computational molecular science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.126
H-Index - 81
eISSN - 1759-0884
pISSN - 1759-0876
DOI - 10.1002/wcms.1456
Subject(s) - domain (mathematical analysis) , hilbert space , operator (biology) , computer science , quantum , space (punctuation) , cumulant , structuring , wave function , quantum chemical , theoretical computer science , statistical physics , mathematics , pure mathematics , quantum mechanics , physics , chemistry , statistics , mathematical analysis , biochemistry , finance , repressor , molecule , transcription factor , economics , gene , operating system
As approximations to the wave functions governing quantum chemical systems become more and more complex, it is becoming increasingly important to devise descriptors that help understand the practical results of those approximations by condensing information in insightful ways. Quantum chemical descriptors that are able to capture the statistical signatures of quantum chemical interactions provide such conceptual building blocks. Central to an understanding of these descriptors is the concept of a “domain occupation number operator,” which allows the so‐called “real space” and Hilbert space partitionings to be treated on the same footing. Many of the existing descriptors can be expressed as the (central) densities and density cumulants associated with the domain operators. These densities can be obtained by successive differentiation of generating functions, effectively structuring domain associated densities into hierarchies. Not only do the resulting hierarchies indicate how many of the previously reported descriptors are related, they also show which areas have not yet been explored. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods