Related papers: Importance profiles. Visualization of atomic basis…
The projection of the eigenfunctions obtained in standard plane-wave first-principle calculations is used for analyzing atomic-orbital basis sets. The "spilling" defining the error in such a projection allows the evaluation of the quality…
We propose a unique scheme to construct fully optimized atomic basis sets for density-functional calculations. The shapes of the radial functions are optimized by minimizing the {\it spillage} of the wave functions between the atomic…
The performance of basis sets made of numerical atomic orbitals is explored in density-functional calculations of solids and molecules. With the aim of optimizing basis quality while maintaining strict localization of the orbitals, as…
Complete orthonormal sets of exponential-type orbitals with non-integer principal quantum numbers are discussed as basis functions in non-relativistic Hartree-Fock-Roothaan electronic structure calculations of atoms. A method is proposed to…
Electronic structure methods for accurate calculation of molecular properties have a high cost that grows steeply with the problem size, therefore, it is helpful to have the underlying atomic basis functions that are less in number but of…
Band structure unfolding is a key technique for analyzing and simplifying the electronic band structure of large, internally distorted supercells that break the primitive cell's translational symmetry. In this work, we present an efficient…
The projection of the eigenfunctions obtained in standard plane-wave first-principle electronic-structure calculations into atomic-orbital basis sets is proposed as a formal and practical link between the methods based on plane waves and…
Many datasets suffer from missing values due to various reasons,which not only increases the processing difficulty of related tasks but also reduces the accuracy of classification. To address this problem, the mainstream approach is to use…
The need for accurate calculations on atoms and diatomic molecules is motivated by the opportunities and challenges of such studies. The most commonly-used approach for all-electron electronic structure calculations in general - the linear…
A complete discrete set of spherical single-particle wave functions for studies of weakly-bound many-body systems is proposed. The new basis is obtained by means of a local-scale point transformation of the spherical harmonic oscillator…
Finite-range numerical atomic orbitals are the basis functions of choice for several first principles methods, due to their flexibility and scalability. Generating and testing such basis sets, however, remains a significant challenge for…
The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular…
We revisit the problem of estimating the profile (also known as the rarity) in the data stream model. Given a sequence of $m$ elements from a universe of size $n$, its profile is a vector $\phi$ whose $i$-th entry $\phi_i$ represents the…
An accurate description of electron correlation energies in molecules requires either basis set extrapolation or the use of explicitly-correlated wave functions that address the deficiencies of standard determinantal expansions at short…
We introduce an iterative importance truncation scheme which aims at reducing the dimension of the model space of configuration interaction approaches by an a priori selection of the physically most relevant basis states. Using an…
The description of weakly bound electronic states is especially difficult with atomic orbital basis sets. The diffuse atomic basis functions that are necessary to describe the extended electronic state generate significant linear…
A general procedure for the optimization of atomic density-fitting basis functions is designed with the balance between accuracy and numerical stability in mind. Given one-electron wavefunctions and energies, weights are assigned to the…
Basis sets of atomic orbitals are very efficient for density functional calculations but lack a systematic variational convergence. We present a variational method to optimize numerical atomic orbitals using a single parameter to control…
Interpretability studies often involve tracing the flow of information through machine learning models to identify specific model components that perform relevant computations for tasks of interest. Prior work quantifies the importance of a…
The semi-exponential basis set of radial functions (A.M. Frolov, Physics Letters A {\bf 374}, 2361 (2010)) is used for variational computations of bound states in three-electron atomic systems. It appears that semi-exponential basis set has…