Many-Body Methods in Chemistry and Physics

Abstract

Written by two leading experts in the field, this book explores the 'many-body' methods that have become the dominant approach in determining molecular structure, properties and interactions. With a tight focus on the highly popular Many-Body Perturbation Theory (MBPT) and Coupled-Cluster theories (CC), the authors present a simple, clear, unified approach to describe the mathematical tools and diagrammatic techniques employed. Using this book the reader will be able to understand, derive and confidently implement relevant algebraic equations for current and even new multi-reference CC methods. Hundreds of diagrams throughout the book enhance reader understanding through visualization of computational procedures and extensive referencing allows further exploration of this evolving area. With an extensive bibliography and detailed index, this book will be suitable for graduates and researchers within quantum chemistry, chemical physics and atomic, molecular and solid-state physics.

Ab initioBogoliubov coupled cluster theory for open-shell nuclei

“…As a result, a diagrammatic technique is desired. The diagrammatic description at play in standard coupled cluster theory [39] provides guidance for the extension to BCC theory. In fact, the procedure is simplified with fewer diagrams at a given truncation order since particles and holes do not need to be treated separately in BCC.…”

“…We utilize instead an approximate implementation that consists of setting the de-excitation operator Λ = T † , which is exact to first order in perturbation theory, with the potential for improvement by extending to second order in perturbation theory [39]. This approximation is sufficient to converge the system of equations, and will be used to evaluate the variance in Sec.…”

“…While these intermediates can be obtained from a diagrammatic procedure involving the similarity-transformed grand canonical potential (in connection to the coupled cluster effective-Hamiltonian diagrams derived in Shavitt and Bartlett [39]), a more straight-forward procedure will provide greater flexibility in the definition of the intermediates. As seen in the single-excitation amplitude equations of BCCSD, Eq.…”

Electric dipole polarizability: from few- to many-body systems

“…In the coupled-cluster formalism [4] the dipole response function is whereΘ is the dipole excitation operator,T is the cluster operator defined in coupled-cluster theory [5], and 0 L |, |0 R ( n L |, |n R ) are the left and right reference ground states (excited states), respectively. Using Eq.…”

A theoretical approach to electromagnetic reactions in light nuclei

“…However, one can use the LIT approach [3] to reduce the continuum problem to the solution of a bound-state equation. In particular, recently this method was reformulated using coupled-cluster theory [4], obtaining a new approach to extend ab-initio studies of electromagnetic observables to heavier and neutron-rich nuclei [2,5]. In coupled-cluster theory one introduces the similarity transformed Hamiltonian…”