Abstract
The GW approximation in electronic structure theory has become a widespread tool for predicting electronic excitations in chemical compounds and materials. In the realm of theoretical spectroscopy, the GW method provides access to charged excitations as measured in direct or inverse photoemission spectroscopy. The number of GW calculations in the past two decades has exploded with increased computing power and modern codes. The success of GW can be attributed to many factors: favorable scaling with respect to system size, a formal interpretation for charged excitation energies, the importance of dynamical screening in real systems, and its practical combination with other theories. In this review, we provide an overview of these formal and practical considerations. We expand, in detail, on the choices presented to the scientist performing GW calculations for the first time. We also give an introduction to the many-body theory behind GW, a review of modern applications like molecules and surfaces, and a perspective on methods which go beyond conventional GW calculations. This review addresses chemists, physicists and material scientists with an interest in theoretical spectroscopy. It is intended for newcomers to GW calculations but can also serve as an alternative perspective for experts and an up-to-date source of computational techniques.
Highlights
Electronic structure theory derives from the fundamental laws of quantum mechanics and describes the behavior of electrons—the glue that shapes all matter
Before we introduce the GW approximation as a tractable computational approach for calculating quasiparticle energies, we will first address the photocurrent, which is the quantity measured in direct photoemission experiments
The accuracy of the Analytic continuation (AC) approach depends on the features of the self-energy on the real axis and on the flexibility of the model function, which continues the self-energy to real frequencies
Summary
Electronic structure theory derives from the fundamental laws of quantum mechanics and describes the behavior of electrons—the glue that shapes all matter. To understand the properties of matter and the behavior of molecules, the quantum mechanical laws must be solved numerically because a pen and paper solution is not possible In this context, Hedin’s GW method (Hedin, 1965) has become the de facto standard for electronic structure properties as measured by direct and inverse photoemission experiments, such as quasiparticle band structures and molecular excitations. Electronic structure theory covers the quantum mechanical spectrum of computational materials science and quantum chemistry. The GW approach is an integral part of electronic structure theory and readily available in major electronic structure codes It is taught at summer schools along side DFT and other electronic structure methods.
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