Related papers: Ultra-large-scale electronic structure theory and …
Qubit models and methods for improving the performance of software and hardware for analyzing digital devices through increasing the dimension of the data structures and memory are proposed. The basic concepts, terminology and definitions…
Evaluation of basic integrals over Gaussian functions, traditionally utilized for electronic structure computations on molecules and solids, is discussed in a pedagogical form.
In recent years, an abundance of new molecular structures have been elucidated using cryo-electron microscopy (cryo-EM), largely due to advances in hardware technology and data processing techniques. Owing to these new exciting…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…
We present a set of efficient techniques in first-principles electronic-structure calculations utilizing the real-space finite-difference method. These techniques greatly reduce the overhead for performing integrals that involve…
The last two decades, in particular, have witnessed a large volume of research revolving around structure-property correlation in Carbon based nanocomposites, synthesized by several methods.In the simplest of terms, the electronic…
Using a real-space high order finite-difference approach, we investigate the electronic structure of large spherical silicon nanoclusters. Within Kohn-Sham density functional theory and using pseudopotentials, we report the self-consistent…
This paper outlines how modern first-principle calculations can adequately address the needs for ever higher levels of numerical accuracy and high-performance in large-scale electronic structure simulations, and pioneer the fundamental…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
The electronic band structures of two-dimensional materials are significantly different from those of their bulk counterparts, due to quantum confinement and strong modifications of electronic screening. An accurate determination of…
This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.
We propose a descriptor for molecular electronic structure that is based solely on the one- and two-electron integrals but is translationally, rotationally, and unitarily invariant. Then, directly exploiting size consistency, we train and…
Fundamentals of energy density functional in nuclear physics are presented. Much attention is paid to a mathematically rigorous treatment of deriving the energy density functional. The specific features of the density functional used in…
An extremely scalable linear-algebraic algorithm was developed for quantum material simulation (electronic state calculation) with 10$^8$ atoms or 100-nm-scale materials. The mathematical foundation is generalized shifted linear equations…
In the previous papers (quant-ph/0204037), (quant-ph/0204134) on the basis of Dirac's equation we have considered the electromagnetic interpretation of the quantum theory of electron. Here we continue the electron structure study. Since the…
Maximally embedding dimension (MED) numerical semigroups are a wide and interesting family, with some remarkable algebraic and combinatorial properties. Associated to any numerical semigroup one can construct a MED closure, as it is well…
This is a replacement paper. There are 6 chapters. The first two chapters are introductory. The third chapter is on extremal graph theory. The fourth chapter is about algebra in graph theory. The fifth chapter is focused on algorithms. The…
This chapter introduces the main ideas and the most important methods for representing the electronic wavefunction through machine learning models. The wavefunction of a N-electron system is an incredibly complicated mathematical object,…
The idea that gauge theory has 'surplus' structure poses a puzzle: in one much discussed sense, this structure is redundant; but on the other hand, it is also widely held to play an essential role in the theory. In this paper, we employ…
The computational pipelines of single-particle cryo-electron microscopy (cryo-EM) and cryo-electron tomography (cryo-ET) include an early particle-picking stage, in which a micrograph or tomogram is scanned to extract candidate particles,…