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Register a new userReproducibility in $G_0W_0$ Calculations for Solids
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Ab initio many-body perturbation theory within the $GW$ approximation is a Greens function formalism widely used in the calculation of quasiparticle excitation energies of solids. In what has become an increasingly standard approach, Kohn-Sham eigenenergies, generated from a DFT calculation with a strategically-chosen exchange correlation functional ``starting point, are used to construct $G$ and $W$, and then perturbatively corrected by the resultant $GW$ self-energy. In practice, there are several ways to construct the $GW$ self-energy, and these can lead to variations in predicted quasiparticle energies. For example, for ZnO and TiO$_2$, reported $GW$ fundamental gaps can vary by more than 1 eV. In this work, we address the convergence and key approximations in contemporary $G_0W_0$ calculations, including frequency-integration schemes and the treatment of the Coulomb divergence in the exact-exchange term. We study several systems,and compare three different $GW$ codes: BerkeleyGW, Abinit and Yambo. We demonstrate, for the first time, that the same quasiparticle energies for systems in the condensed phase can be obtained with different codes, and we provide a comprehensive assessment of implementations of the $GW$ approximation.
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Nonequilibrium electron dynamics in solids is an important subject from both fundamental and technological points of view. The recent development of laser technology has enabled us to study ultrafast electron dynamics in the time domain. First-principles calculation is a powerful tool for analyzing such complex electron dynamics and clarifying the physics behind the experimental observation. In this article, we review the recent development of the first-principles calculation for light-induced electron dynamics in solids by revising its application to recent attosecond experiments. The electron dynamics calculations offer an accurate description of static and transient optical properties of solids and provide physics insight into light-induced electron dynamics. Furthermore, the microscopic decomposition of transient properties of nonequilibrium systems has been developed to extract microscopic information from the simulation results. The first-principles analysis opened a novel path to analyze the nonequilibrium electron dynamics in matter and to provide the fundamental understanding complementarily with the sophisticated experimental technique.
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 while being computationally efficient. We also develop a model dielectric operator that allows us to further reduce the size of the dielectric matrix without accuracy loss. Furthermore, we develop a scheme that reduces the numerical cost of the contour deformation technique to the level of the lightest plasmon pole model. Finally, the use of the simplified quasi-minimal residual scheme in replacement of the conjugate gradients algorithm allows a direct evaluation of the $G_0W_0$ corrections at the desired real frequencies, without need for analytical continuation. The performance of the resulting $G_0W_0$ implementation is demonstrated by comparison with a traditional plane-waves implementation, which reveals a 500-fold speedup for the silane molecule. Finally, the accuracy of our $G_0W_0$ implementation is demonstrated by comparison with other $G_0W_0$ calculations and experimental results.
Kinetic energy (KE) approximations are key elements in orbital-free density functional theory. To date, the use of non-local functionals, possibly employing system dependent parameters, has been considered mandatory in order to obtain satisfactory accuracy for different solid-state systems, whereas semilocal approximations are generally regarded as unfit to this aim. Here, we show that instead properly constructed semilocal approximations, the Pauli-Gaussian (PG) KE functionals, especially at the Laplacian-level of theory, can indeed achieve similar accuracy as non-local functionals and can be accurate for both metals and semiconductors, without the need of system-dependent parameters.
Theoretical calculations of core electron binding energies are important for aiding the interpretation of experimental core level photoelectron spectra. In previous work, the $Delta$-Self-Consistent-Field ($Delta$-SCF) method based on density functional theory has been shown to yield highly accurate 1s and 2p binding energies in free molecules. However, most experimental work is concerned with solids, not gases. In this study, we demonstrate the application of the all-electron $Delta$-SCF method to periodic systems. A consideration of the experimentally accessible points of reference leads to the definition of a core electron binding energy in a solid as the difference between the total energies of two $N-1$ electron systems: one with an explicit, localized core hole, and one with an electron removed from the highest occupied state. The calculation of each of these quantities is addressed. In addition, the analogy between a localized core hole and a charged defect in a solid is highlighted, and the extrapolation of calculated core electron binding energies to the infinite supercell limit is discussed. It is found that the extrapolated values of the core electron binding energies from periodic $Delta$-SCF calculations agree well with experimental results for both metallic and insulating systems, with a mean absolute error of 0.24 eV for the 15 core levels considered in this study.
Thermal expansion in materials can be accurately modeled with careful anharmonic phonon calculations within density functional theory. However, because of interest in controlling thermal expansion and the time consumed evaluating thermal expansion properties of candidate materials, either theoretically or experimentally, an approach to rapidly identifying materials with desirable thermal expansion properties would be of great utility. When the ionic bonding is important in a material, we show that the fraction of crystal volume occupied by ions, (based upon ionic radii), the mean bond coordination, and the deviation of bond coordination are descriptors that correlate with the room-temperature coefficient of thermal expansion for these materials found in widely accessible databases. Correlation is greatly improved by combining these descriptors in a multi-dimensional fit. This fit reinforces the physical interpretation that open space combined with low mean coordination and a variety of local bond coordinations leads to materials with lower coefficients of thermal expansion, materials with single-valued local coordination and less open space have the highest coefficients of thermal expansion.
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