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Register a new userExploring approximations to the GW self-energy ionic gradients
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C. Faber
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The accuracy of the many-body perturbation theory GW formalism to calculate electron-phonon coupling matrix elements has been recently demonstrated in the case of a few important systems. However, the related computational costs are high and thus represent strong limitations to its widespread application. In the present study, we explore two less demanding alternatives for the calculation of electron-phonon coupling matrix elements on the many-body perturbation theory level. Namely, we test the accuracy of the static Coulomb-hole plus screened-exchange (COHSEX) approximation and further of the constant screening approach, where variations of the screened Coulomb potential W upon small changes of the atomic positions along the vibrational eigenmodes are neglected. We find this latter approximation to be the most reliable, whereas the static COHSEX ansatz leads to substantial errors. Our conclusions are validated in a few paradigmatic cases: diamond, graphene and the C60 fullerene. These findings open the way for combining the present many-body perturbation approach with efficient linear-response theories.
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A parameterized tight-binding (TB) model based on the first-principles GW calculations is developed for single layer tin diselenide (SnSe$_2$) and used to study its electronic and optical properties under external magnetic field. The truncated model is derived from six maximally localized wannier orbitals on Se site, which accurately describes the quasi-particle electronic states of single layer SnSe$_2$ in a wide energy range. The quasi-particle electronic states are dominated by the hoppings between nearest wannier orbitals ($t_1$-$t_6$). Our numerical calculation shows that, due to the electron-hole asymmetry, two sets of Landau Level spectrum are obtained when a perpendicular magnetic field is applied. The Landau Level spectrum follows linear dependence on the level index and magnetic field, exhibiting properties of two-dimensional electron gas in traditional semiconductors. The optical conductivity calculation shows that the optical gap is very close to the GW value, and can be tuned by external magnetic field. Our proposed TB model can be used for further exploring the electronic, optical, and transport properties of SnSe$_2$, especially in the presence of external magnetic fields.
The GW method is a many-body electronic structure technique capable of generating accurate quasiparticle properties for realistic systems spanning physics, chemistry, and materials science. Despite its power, GW is not routinely applied to large complex assemblies due to its large computational overhead and quartic scaling with particle number. Here, the GW equations are recast, exactly, as Fourier-Laplace time integrals over complex time propagators. The propagators are then shredded via energy partitioning and the time integrals approximated in a controlled manner using generalized Gaussian quadrature(s) while discrete variable methods are employed to represent the required propagators in real-space. The resulting cubic scaling GW method has a sufficiently small prefactor to outperform standard quartic scaling methods on small systems ($gtrapprox$ 10 atoms) and also represents a substantial improvement over other cubic methods tested for all system sizes studied. The approach can be applied to any theoretical framework containing large sums of terms with energy differences in the denominator.
Recent calculations using coupled cluster on solids have raised discussion of using a $N^{-1/3}$ power law to fit the correlation energy when extrapolating to the thermodynamic limit, an approach which differs from the more commonly used $N^{-1}$ power law which is (for example) often used by quantum Monte Carlo methods. In this paper, we present one way to reconcile these viewpoints. Coupled cluster doubles calculations were performed on uniform electron gases reaching system sizes of $922$ electrons for an extremely wide range of densities ($0.1<r_s<100.0$) to study how the correlation energy approaches the thermodynamic limit. The data were corrected for basis set incompleteness error and use a selected twist angle approach to mitigate finite size error from shell filling effects. Analyzing these data, we initially find that a power law of $N^{-1/3}$ appears to fit the data better than a $N^{-1}$ power law in the large system size limit. However, we provide an analysis of the transition structure factor showing that $N^{-1}$ still applies to large system sizes and that the apparent $N^{-1/3}$ power law occurs only at low $N$.
We show that the equations underlying the $GW$ approximation have a large number of solutions. This raises the question: which is the physical solution? We provide two theorems which explain why the methods currently in use do, in fact, find the correct solution. These theorems are general enough to cover a large class of similar algorithms. An efficient algorithm for including self-consistent vertex corrections well beyond $GW$ is also described and further used in numerical validation of the two theorems.
The Self-Assembly of Nano-Objects (SANO) code we implemented demonstrates the ability to predict the molecular self-assembly of different structural motifs by tuning the molecular building blocks as well as the metallic substrate. It consists in a two-dimensional Grand Canonical Monte-Carlo (GCMC) approach developed to perform atomistic simulations of thousands of large organic molecules self-assembling on metal surfaces. Computing adsorption isotherms at room temperature and spanning over the characteristic sub-micrometric scales, we confront the robustness of the approach with three different well-known systems: ZnPcCl8 on Ag(111), CuPcF16 on Au(111) and PTBC on Ag(111). We retrieve respectively their square, oblique and hexagonal supramolecular tilling. The code incorporates generalized force fields to describe the molecular interactions, which provides transferability and versatility to many organic building blocks and metal surfaces.
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