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Publications
Authors
Wanja T. Schulze, Sebastian Schwalbe, Kai Trepte, and Stefanie Gräfe
Abstract
In current electronic structure research endeavors such as warm dense matter or machine learning applications, efficient development necessitates non-monolithic software, providing an extendable and flexible interface. The open-source idea offers the advantage of having a source code base that can be reviewed and modified by the community. However, practical implementations can often diverge significantly from their theoretical counterpart. Leveraging the efforts of recent theoretical formulations and the features of Python, we try to mitigate these problems. We present eminus, an education- and development-friendly electronic structure package designed for convenient and customizable workflows, yet built with intelligible and modular implementations.
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Show supplementary repositoryAuthors
Sebastian Schwalbe*, Wanja T. Schulze*, Kai Trepte, and Susi Lehtola
Abstract
The Perdew–Zunger (PZ) self-interaction correction (SIC) is an established tool to correct unphysical behavior in density functional approximations. Yet, the PZ-SIC is well-known to sometimes break molecular symmetries. An example of this is the benzene molecule, for which the PZ-SIC predicts a symmetry-broken electron density and molecular geometry, since the method does not describe the two possible Kekulé structures on an even footing, leading to local minima [Lehtola et al. J. Chem. Theory Comput. 2016, 12, 3195]. The PZ-SIC is often implemented with Fermi–Löwdin orbitals (FLOs), yielding the FLO-SIC method, which likewise has issues with symmetry breaking and local minima [Trepte et al. J. Chem. Phys. 2021, 155, 224109]. In this work, we propose a generalization of the PZ-SIC─the ensemble PZ-SIC (E-PZ-SIC) method─which shares the asymptotic computational scaling of the PZ-SIC (albeit with an additional prefactor). The E-PZ-SIC is straightforwardly applicable to various molecules, merely requiring one to average the self-interaction correction over all possible Kekulé structures, in line with chemical intuition. We showcase the implementation of the E-PZ-SIC with FLOs, as the resulting E-FLO-SIC method is easy to realize on top of an existing implementation of the FLO-SIC. We show that the E-FLO-SIC indeed eliminates symmetry breaking, reproducing a symmetric electron density and molecular geometry for benzene. The ensemble approach suggested herein could also be employed within approximate or locally scaled variants of the PZ-SIC and its FLO-SIC versions.
Authors
Wanja T. Schulze, Sebastian Schwalbe, Kai Trepte, Alexander Croy, Jens Kortus, and Stefanie Gräfe
Abstract
The behavior of electrons during bond formation and breaking cannot commonly be accessed from experiments. Thus, bond perception is often based on chemical intuition or rule-based algorithms. Utilizing computational chemistry methods, we present intrinsic bond descriptors for the Diels–Alder reaction, allowing for an automatic bond perception. We show that these bond descriptors are available from localized orbitals and self-interaction correction calculations, e.g., from Fermi-orbital descriptors. The proposed descriptors allow a sparse, simple, and educational inspection of the Diels–Alder reaction from an electronic perspective. We demonstrate that bond descriptors deliver a simple visual representation of the concerted bond formation and bond breaking, which agrees with Lewis’ theory of bonding.
Authors
Kai Trepte, Sebastian Schwalbe, Simon Liebing, Wanja T. Schulze, Jens Kortus, Hemanadhan Myneni, Aleksei V. Ivanov, and Susi Lehtola
Abstract
Fermi–Löwdin orbitals (FLOs) are a special set of localized orbitals, which have become commonly used in combination with the Perdew–Zunger self-interaction correction (SIC) in the FLO-SIC method. The FLOs are obtained for a set of occupied orbitals by specifying a classical position for each electron. These positions are known as Fermi-orbital descriptors (FODs), and they have a clear relation to chemical bonding. In this study, we show how FLOs and FODs can be used to initialize, interpret, and justify SIC solutions in a common chemical picture, both within FLO-SIC and in traditional variational SIC, and to locate distinct local minima in either of these approaches. We demonstrate that FLOs based on Lewis theory lead to symmetry breaking for benzene—the electron density is found to break symmetry already at the symmetric molecular structure—while ones from Linnett’s double-quartet theory reproduce symmetric electron densities and molecular geometries. Introducing a benchmark set of 16 planar cyclic molecules, we show that using Lewis theory as the starting point can lead to artifactual dipole moments of up to 1 D, while Linnett SIC dipole moments are in better agreement with experimental values. We suggest using the dipole moment as a diagnostic of symmetry breaking in SIC and monitoring it in all SIC calculations. We show that Linnett structures can often be seen as superpositions of Lewis structures and propose Linnett structures as a simple way to describe aromatic systems in SIC with reduced symmetry breaking. The role of hovering FODs is also briefly discussed.
Authors
Wanja T. Schulze
Abstract
In this master thesis an educational Python-based plane wave DFT code using the modern DFT++ pragmas has been successfully implemented. The implementation has been tested and offers reproducible and comparable results to various plane wave codes,e.g., JDFTx and PWDFT.jl. Additional features have been implemented and tested, e.g., the calculation of dipole moments to further investigate the properties of orbitals and densities. It has been found that the handling of the Coulomb potential in plane wave codes is important for calculating SIC energies. The usage of a periodic or a truncated Coulomb potential does not change the total energy of the system, but the resulting SIC energies will change. The creation of FLOs has been successfully implemented and tested. The implementation includes an interface to the FOD generator PyCOM. The FLO generation uses a novel idea that utilizes the features of plane waves that allow shifts in reciprocal space. The properties of calculated FLOs have been illustrated. The effect of various domain restrictions on the SIC energies have been discussed. While the current implementation does not allow large speed-ups, a convergence of SIC energies has been found for domains that truncate the real space using spherical and cuboidal domains. This shows that a subset of sampling points can be used to accurately calculate SIC energies. It has been shown that the mesh error of the total density can be used as a measurement of the numerical quality for the SIC energies.
Authors
Wanja T. Schulze
Abstract
In the branch of quantum chemistry, one of the main goals is to determine the nuclear and electronic structure of molecules. This can be done experimentally with the help of spectroscopy, e.g., infra-red (IR), Raman, or photoelectron spectroscopy or theoretically by solving the Schrödinger equation for the system of interest. With the Hohenberg-Kohn theorems and the help of the Kohn-Sham equations, density functional theory (DFT) calculations can be performed to approximately solve said Schrödinger equations by using electronic densities instead of wave functions. PySCF provides a toolbox to carry out quantum chemical calculations and DFT in an efficient way. PySCF is easy-to-use because it is based on Python. One important part of the DFT calculation is the numerical grid. With the needed discretization of the electronic density, one gets into a dilemma. While creating more grid points usually results in a more accurate representation/calculation, the increased number also increases the calculation time. With a variational mesh, grids can be generated that are accurate up to a given threshold. This thesis shows one implementation of a variational mesh that can be used with PySCF. The preset will be a mesh error that is calculated by evaluating the initial-guess density on the grid. Tests for small standardized benchmark sets, i.e., AE6 and BH6 were performed to show the capabilities of the implementation.
Scientific
Key features
- Pythonic implementation of density functional theory
- Customizable workflows and developer-friendly code
- Minimal dependencies and large platform support
- Comparable and reproducible calculations
- Example notebooks showcasing educational usage
Open documentationKey features
- Very simple and educational DFT code
- Implementation of DFT++ pragmas
- Plane wave basis set
- Restricted Kohn-Sham calculations
- Minimal dependencies
- High agreement of results to SimpleDFT codes in other languages
Key features
- Very simple and educational DFT code
- Implementation of DFT++ pragmas
- Plane wave basis set
- Restricted Kohn-Sham calculations
- Minimal dependencies
- High agreement of results to SimpleDFT codes in other languages
Key features
- Optimizes meshes by optimizing the representation of the initial-guess density
- Use a new method that uses different radial grids for different atom species
- Works with PySCF and PyFLOSIC by using the PYSCF grids object
- Additional ERKALE and GAMESS output modes
- Comprehensive tutorials
Key features
- 3D molecular dynamics with periodic boundary conditions
- Lennard-Jones cluster formation of argon atoms
- Fancy visualization
Key features
- Compare different integration techniques
- Display simple example implementations
- Plot the visual representation
Key features
- Calculates and plots band structures for silicon, germanium, and tin
- Simple-cubic, fcc, bcc, and diamond lattice types supported
- Custom band path sampling
- Calculates the total bandgap and the Fermi level
Key features
- Implementation of Dijkstra's algorithm
- Parallelized using Open MPI
- Calculates the shortest path to every node from a starting node
- Test scaling using random graphs
Creative
Key features
- Recreation of handwritten glyphs
- TTF font for initials
- LaTeX examples included
Key features
- Static HTML5 webpage
- Clean and modern UI
- Light and dark mode
- Responsive design
- Functional under modern browsers
- Functional with JavaScript disabled
- Perfect Lighthouse scores
- Accessible
Miscellaneous
Key features
- Merge multiple PDFs into one
- PNG, JPG, and EPS can be used as well
- Landscape option
- Nup option to merge multiple pages into one
- Supports all pdfpages commands
Key features
- Android 4.4.4 and Kernel 3.4.113
- Build with many performance optimizations
- Removed or replaced many proprietary software
- Debloated and hardened build configuration
Abstract
Star Wars: Episode III - Revenge of the Sith is a side-scrolling beat 'em up with charming sprites and beautiful animations released in 2005 for the GBA and the NDS. Since this was one of the games I loved playing in my childhood and it had a huge potential due to a huge skip I decided to make a TAS for this game, and a few RTA viable skips and tricks have been found along the way.