Related papers: Comment on "Minimal Basis Iterative Stockholder: A…
Atomic partial charges appear in the Coulomb term of many force-field models and can be derived from electronic structure calculations with a myriad of atoms-in-molecules (AIM) methods. More advanced models have also been proposed, using…
The aim of this paper is to analyze from a mathematical perspective some existing schemes to partition a molecular density into several atomic contributions, with a specific focus on Iterative Stockholder Atom (ISA) methods. We provide a…
The recently developed iterated stockholder atoms (ISA) approach of Lillestolen and Wheatley (Chem. Commun. {\bf 2008}, 5909 (2008)) offers a powerful method for defining atoms in a molecule. However, the real-space algorithm is known to…
Partition Density Functional Theory (P-DFT) is a density embedding method that partitions a molecule into fragments by minimizing the sum of fragment energies subject to a local density constraint and a global electron-number constraint. To…
In this work, we introduce several approximations of the Iterative Stockholder Analysis (ISA) method based on exponential basis functions. These approximations are categorized into linear and non-linear models, referred to as LISA and NLIS,…
A new method of the phase determination in X-ray crystallography is proposed. The method is based on the so-called "minimum charge" principle, recently suggested by Elser. The electron density function $\rho$ is sought in the form…
Recently we have developed a robust, basis-space implementation of the iterated stockholder atoms (BS-ISA) approach for defining atoms in a molecule. This approach has been shown to yield rapidly convergent distributed multipole expansions…
A new particle-based sampling and approximate inference method, based on electrostatics and Newton mechanics principles, is introduced with theoretical ground, algorithm design and experimental validation. This method simulates an…
In the following work, we described the problems of porosity analysis of cement materials using backscattered electron images. We noticed that despite its great utility, the overflow porosity segmentation method allows for the introduction…
We illustrate the main features of a recently proposed method based on ensemble density functional theory to divide rigorously a complex molecular system into its parts [M.H. Cohen and A. Wasserman, J. Phys. Chem. A 111, 2229 (2007)]. The…
The so-called matrix-element method (MEM) has long been used successfully as a classification tool in particle physics searches. In the presence of invisible final state particles, the traditional MEM typically assigns probabilities to an…
In this paper, we develop an iterative scheme to construct multiscale basis functions within the framework of the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for the mixed formulation. The…
A double-index atomic partitioning of the molecular first-order density matrix is proposed. Contributions diagonal in the atomic indices correspond to atomic density matrices, whereas off-diagonal contributions carry information about the…
Fredholm integral equations of the first kind are the prototypical example of ill-posed linear inverse problems. They model, among other things, reconstruction of distorted noisy observations and indirect density estimation and also appear…
The embedded atom method (EAM) is one of the most widely used many-body, short-range potentials in molecular dynamics simulations, particularly for metallic systems. To enhance the efficiency of calculating these short-range interactions,…
We show that both confined atoms and electron-atom scattering can be described by a unified basis set method. The central idea behind this method is to place the atom inside a hard potential sphere, enforced by a standard Slater type basis…
The electron density of a molecule or material has recently received major attention as a target quantity of machine-learning models. A natural choice to construct a model that yields transferable and linear-scaling predictions is to…
Micro-Electro-Mechanical Systems (MEMS) normally have fixed or moving structures with cross-sections of the order of microns ($\mu m$) and lengths of the order of tens or hundreds of microns. These structures are often plates or array of…
The perturbative approach for describing the underdense plasma--ultrarelativistic electron bunch system is developed, using the ratio $\frac{n_0}{n_b}$ as a small parameter ($n_b$--bunch,$n_0$--plasma electron densities). Focusing of the…
We introduce a system-independent method to derive effective atomic C$_6$ coefficients and polarizabilities in molecules and materials purely from charge population analysis. This enables the use of dispersion-correction schemes in…