G reen's Functions and Propagators for Chemistry

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640

The algebraic diagrammatic construction (ADC) scheme for the polarization propagator provides a series of ab initio methods for the calculation of excited states based on perturbation theory. In recent years, the second-order ADC(2) scheme has attracted attention in the computational chemistry community because of its reliable accuracy and reasonable computational effort in the calculation of predominantly singly excited states. Owing to their size-consistency, ADC methods are suited for the investigation of large molecules. In addition, their Hermitian structure and the availability of the intermediate state representation (ISR) allow for straightforward computation of excited-state properties. Recently, an efficient implementation of ADC(3) has been reported, and its high accuracy for typical valence excited states of organic chromophores has been demonstrated. In this review, the origin of ADC-based excited-state methods in propagator theory is described, and an intuitive route for the derivation of algebraic expressions via the ISR is outlined and comparison to other excited-state methods is made. Existing computer codes and implemented ADC variants are reviewed, but most importantly the accuracy and limits of different ADC schemes are critically examined.

Section: The Origin Of the Methods In Propagator Theorymentioning

confidence: 99%

The algebraic diagrammatic construction scheme for the polarization propagator for the calculation of excited states

Dreuw

Wormit

2014

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640

“…In this review, we will focus on aspects of Green's functions and many‐body perturbation theory that are inspired by their origin in the electron gas and extended systems. Green's functions are widespread also in quantum chemistry, for example, to deal with problems of open shell systems and strong correlation (see, e.g., Refs ), or to analyze total energies (see, e.g., Ref ), but this would be a topic that is complementary to the present discussion (for a recent review, see, e.g., Ref ).…”

Section: From Wavefunctions To Green's Functionsmentioning

confidence: 99%

The GW approximation: content, successes and limitations

Reining

2017

217

209

Many observables such as the density, total energy, or electric current, can be expressed explicitly in terms of the one‐body Green's function, which describes electron addition or removal to or from a system. An efficient way to determine such a Green's function is to introduce a self‐energy, which is a nonlocal and dynamic effective potential that influences the propagation of particles in an interacting system. The state‐of‐the art approximation for the self‐energy is the GW approximation, where the system to (or from) which the electron is added (or removed) is described as a polarizable, screening, medium. This is expressed by the name of the approximation: ‘GW’ stands for the one‐body Green's function G and for W, the dynamically screened Coulomb interaction. The GW approximation is very popular for the calculation of band structures in solids, and increasingly used also to describe nanostructures, clusters, and molecules. As compared to static mean‐field approximations for the effective potential, the dynamical screening of the Coulomb interaction in GW leads to a renormalization of energies, to broadening and/or to the observation of additional excitations. An analysis of the approximations that lead to the GW self‐energy, and of the underlying picture, explains the successes and the limitations of the approach. This article is categorized under: Electronic Structure Theory > Density Functional Theory Electronic Structure Theory > Ab Initio Electronic Structure Methods Theoretical and Physical Chemistry > Spectroscopy Structure and Mechanism > Computational Materials Science

“…The GF method is discussed in several general textbooks 10,15,16. Furthermore, a detailed discussion of the use of GF and other related methods in atomic and molecular physics is discussed in several reviews to which the reader is reffered 1,2,8,9,17. Here, we only briefly present some of the main points of GF theory.…”

Section: Green's Functionsmentioning

confidence: 99%

Green's function methods for calculating ionization potentials, electron affinities, and excitation energies

Danovich

2011

Green's function (GF; electron propagator) methods represent a very useful set of tools for direct calculation of electron detachment (ionization potentials), electron attachment (electron affinities), excitation energies, electron transition probabilities, and other properties. The main idea of GF methods is that for description of various properties of a many-body system, one does not need to describe all the particles of the system but rather needs information about one or two particles belonging to the system. The corresponding required quantities are the one-and two-particle GFs. Within one-or two-particle GF methods, the energy difference between an initial state and a state with one additional or one less electron is calculated directly, thus eliminating errors due to inconsistent treatment of the initial and final states.