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This article combines shape optimization and homogenization techniques by looking for the optimal design of the microstructure in composite materials and of scaffolds. The development of materials with specific properties is of huge…
We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane arrangements. Using our decomposition, we bound the number of…
Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined…
We develop convergence acceleration procedures that enable a gradient descent-type iteration method to efficiently simulate Hartree--Fock equations for atoms interacting both with each other and with an external potential. Our development…
In the present work we studied a subfield of Applied Mathematics called Riemannian Optimization. The main goal of this subfield is to generalize algorithms, theorems and tools from Mathematical Optimization to the case in which the…
Donor-based quantum devices in silicon are attractive platforms for universal quantum computing and analog quantum simulations. The nearly-atomic precision in dopant placement promises great control over the quantum properties of these…
In the present letter, we report the extension of our Wannier-function-based ab initio Hartree-Fock approach---meant originally for three-dimensional crystalline insulators---to deal with quasi-one-dimensional periodic systems such as…
An implementation of the Hartree-Fock (HF) method capable of robust convergence for well-behaved arbitrary central potentials is presented. The Hartree-Fock equations are converted to a generalized eigenvalue problem by employing a B-spline…
Phosphorene, a monolayer of black phosphorus (BP), is an elemental two-dimensional material with interesting physical properties, such as high charge carrier mobility and exotic anisotropic in-plane properties. To fundamentally understand…
We propose a framework for optimization of the chemical composition of multinary compounds with the aid of machine learning. The scheme is based on first-principles calculation using the Korringa-Kohn-Rostoker method and the coherent…
In this paper, we propose a topology optimization (TO) framework where the design is parameterized by a set of convex polygons. Extending feature mapping methods in TO, the representation allows for direct extraction of the geometry. In…
The symmetry-projected Hartree--Fock ansatz for the electronic structure problem can efficiently account for static correlation in molecules, yet it is often unable to describe dynamic correlation in a balanced manner. Here, we consider a…
Phosphorene, the single- or few-layer form of black phosphorus, was recently rediscovered as a twodimensional layered material holding great promise for applications in electronics and optoelectronics. Research into its fundamental…
Gradient porous structured materials possess significant potential of being applied in many engineering fields. To accelerate the design process of infill graded microstructures, a novel asymptotic homogenisation topology optimisation…
In this article, we demonstrate the restricted Hartree-Fock electronic structure computation of the molecule $H_3^+$ through computational algebra. We approximate the Hartree-Fock total energy by a polynomial composed of LCAO coefficients…
The formation of graphen-nanotube composites addresses a few basic problems. First, both partners are good donors and acceptors of electrons, which significantly complicates the intermolecular interaction between them leading to a two-well…
The Hartree-Fock (HF) method, supplemented by low-order Moller-Plesset (MP2) perturbation theory, has been utilized to predict the nuclear geometry, assuming planarity, of a low-lying isomer of the free space cluster BOSi$_2$. The planar…
Accurate modeling of conical intersections is crucial in nonadiabatic molecular dynamics, as these features govern processes such as radiationless transitions and photochemical reactions. Conventional electronic structure methods, including…
Defects such as voids are observed at multiple length scales of an additively manufactured composite material. Modeling such defects and their multiscale interaction is crucial for the materials performance prediction. In this work, we…
The lack of reliable atomic data can be a severe limitation in astrophysical modelling, in particular of events such as kilonovae that require information on all neutron-capture elements across a wide range of ionization stages. Notably,…