# Efficient dielectric matrix calculations using the Lanczos algorithm for fast many-body $G_0W_0$ implementations

@article{Janssen2014EfficientDM, title={Efficient dielectric matrix calculations using the Lanczos algorithm for fast many-body \$G\_0W\_0\$ implementations}, author={Jonathan Laflamme Janssen and B. Rousseau and M. C{\^o}t{\'e}}, journal={Physical Review B}, year={2014}, volume={91}, pages={125120} }

We present a $G_0W_0$ implementation that assesses the two major bottlenecks of traditional plane-waves implementations, the summations over conduction states and the inversion of the dielectric matrix, without introducing new approximations in the formalism. The first bottleneck is circumvented by converting the summations into Sternheimer equations. Then, the novel avenue of expressing the dielectric matrix in a Lanczos basis is developed, which reduces the matrix size by orders of magnitude…

## 16 Citations

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A GPU acceleration study of the full-frequency GW method as implemented in the WEST code, showing a substantial speedup of the GPU-accelerated version of WEST with respect to its CPU version.

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- PhysicsThe Journal of chemical physics
- 2020

This work provides a summary of the underlying theory and discusses the details of its implementation based on Gaussian orbitals, including resolution-of-identity techniques and different approaches to the frequency integration of the self-energy or acceleration by offloading compute-intensive matrix operations using graphics processing units in a hybrid OpenMP/Cuda scheme.

### GW100: A Plane Wave Perspective for Small Molecules.

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- 2017

Differences between Gaussian basis sets and VASP for positive electron affinities and quasi particle (QP) resonances above the vacuum level are found to be substantial, tentatively explained by insufficient basis set convergence of the Gaussian type orbital calculations.

### Combining the GW formalism with the polarizable continuum model: A state-specific non-equilibrium approach.

- PhysicsThe Journal of chemical physics
- 2016

The polarizable continuum model within the framework of the many-body Green's function GW formalism for the calculation of electron addition and removal energies in solution opens the way to GW and Bethe-Salpeter calculations in disordered condensed phases of interest in organic optoelectronics, wet chemistry, and biology.

### Speeding up GW Calculations to Meet the Challenge of Large Scale Quasiparticle Predictions

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A powerful and simple-to-implement method that can drastically accelerate fully converged GW calculations for large systems, enabling fast and accurate quasiparticle calculations for complex materials systems is presented.

## 94 References

### GW calculations using the spectral decomposition of the dielectric matrix: Verification, validation, and comparison of methods

- Physics
- 2013

In a recent paper [Phys. Rev. B 85, 081101(R) (2012)] we presented an approach to evaluate quasiparticle energies based on the spectral decomposition of the static dielectric matrix. This method does…

### Turbo charging time-dependent density-functional theory with Lanczos chains.

- PhysicsThe Journal of chemical physics
- 2008

We introduce a new implementation of time-dependent density-functional theory which allows the entire spectrum of a molecule or extended system to be computed with a numerical effort comparable to…

### Efficient calculation of the polarizability: a simplified effective-energy technique

- Physics
- 2012

In a recent publication [J.A. Berger, L. Reining, F. Sottile, Phys. Rev. B 82, 041103(R) (2010)] we introduced the effective-energy technique to calculate in an accurate and numerically efficient…

### Electronic properties of interfaces and defects from many‐body perturbation theory: Recent developments and applications

- Physics
- 2011

We review some recent developments in many‐body perturbation theory (MBPT) calculations that have enabled the study of interfaces and defects. Starting from the theoretical basis of MBPT, Hedin's…

### Quantitative molecular orbital energies within a G0W0 approximation

- Physics
- 2012

Using many-body perturbation theory within a G0W0 approximation, with a plane wave basis set and using a starting point based on density functional theory within the generalized gradient…

### GW method with the self-consistent Sternheimer equation

- Physics
- 2010

We propose an approach to quasiparticle GW calculations which does not require the computation of unoccupied electronic states. In our approach the screened Coulomb interaction is evaluated by…

### Separable dual-space Gaussian pseudopotentials.

- PhysicsPhysical review. B, Condensed matter
- 1996

The pseudopotential is of an analytic form that gives optimal efficiency in numerical calculations using plane waves as a basis set and is separable and has optimal decay properties in both real and Fourier space.

### Large scale ab initio calculations based on three levels of parallelization

- Computer Science
- 2008

### Efficient approach to time-dependent density-functional perturbation theory for optical spectroscopy.

- PhysicsPhysical review letters
- 2006

Using a superoperator formulation of linearized time-dependent density-functional theory, the dynamical polarizability of a system of interacting electrons is represented by a matrix continued…