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WIREs Comput Mol Sci
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Hierarchies of quantum chemical descriptors induced by statistical analyses of domain occupation number operators

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Abstract 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
Overview of the k + lth order orbital and domain densities ρ(k + l)(r1, …, rk, Ωa, …, Ωl) that can be derived from the reduced density generating function ℳ[g, t]. Solid arrows indicate successive differentiations of that generating function, whereas dotted arrows indicate multiple successive differentiations. The respective successive differentiation is listed next to these arrows. Curly lines are used to indicate commonly used names for the resulting descriptors
[ Normal View | Magnified View ]
Overview of the k + lth order density cumulants κ(k + l)(r1, …, rk, Ωa, …, Ωl) that can be derived from the reduced density cumulant generating function . Solid arrows indicate successive differentiations of that generating function, whereas dotted arrows indicate multiple successive differentiations. The respective successive differentiation is listed next to these arrows. Curly lines are used to indicate commonly used names for the resulting descriptors
[ Normal View | Magnified View ]
Overview of the k + lth order fluctuation densities ρ′(k + l)(r1, …, rk, Ωa, …, Ωl) that can be derived from the reduced central density generating function [g, t]. Solid arrows indicate successive differentiations of that generating function, whereas dotted arrows indicate multiple successive differentiations. The respective successive differentiation is listed next to these arrows. Curly lines are used to indicate commonly used names for the resulting descriptors
[ Normal View | Magnified View ]

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