Related Experiment Video
Updated: Jul 14, 2026
10:52
Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
Published on: April 12, 2019
A hierarchic sparse matrix data structure for large-scale Hartree-Fock/Kohn-Sham calculations
Emanuel H Rubensson1, Elias Rudberg, Paweł Sałek
1Department of Physics and Chemistry, University of Southern Denmark, Odense M, Denmark. emanuel@theochem.kth.se
Journal of Computational Chemistry
|May 16, 2007
Summary
A new hierarchic sparse matrix data structure accelerates Hartree-Fock/Kohn-Sham calculations for large systems. This efficient method enhances matrix operations, proving useful in quantum chemistry and ab initio computations.
Area of Science:
- Computational Chemistry
- Materials Science
- Quantum Mechanics
Background:
- Hartree-Fock/Kohn-Sham calculations are computationally intensive, especially for large systems.
- Efficient matrix manipulation is crucial for performance in quantum chemistry simulations.
Purpose of the Study:
- To introduce a novel hierarchic sparse matrix data structure.
- To improve the speed, ease, and maintainability of matrix operations in large-scale electronic structure calculations.
Main Methods:
- Development of a hierarchic sparse matrix data structure.
- Implementation of algorithms for symmetric matrix square and inverse Cholesky decomposition.
- Benchmarking on water droplets and graphene nanoribbons for ab initio calculations.
Main Results:
- The data structure significantly speeds up matrix manipulations for large systems.
- Performance is maintained without loss of accuracy.
- Demonstrated applicability to ab initio calculations.
Conclusions:
- The hierarchic sparse matrix data structure offers a general and efficient solution for large-scale computations.
- It is applicable beyond Hartree-Fock/Kohn-Sham methods to other fields requiring similar matrix properties.
More Related Videos
Related Concept Videos
02:28Electronic Structure of Atoms
An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum numbers: n, l, ml, and...
03:02The Aufbau Principle and Hund's Rule
To determine the electron configuration for any particular atom, we can build the structures in the order of atomic numbers. Beginning with hydrogen, and continuing across the periods of the periodic table, we add one proton at a time to the nucleus and one electron to the proper subshell until we have described the electron configurations of all the elements. This procedure is called the aufbau principle, from the German word aufbau (“to build up”). Each added electron occupies the subshell of...
01:08Hückel's Rule Diagram of π MOs: Frost Circle
The Frost circle or the inscribed polygon method is a graphical method for determining the relative energies of π molecular orbitals (MOs) for planar, fully conjugated, and monocyclic compounds. This method was first described by A. A. Frost and Boris Musulin in 1953.
A Frost circle is constructed by drawing a polygon whose number of edges is equal to the number of carbons of the given cyclic system, with one of the vertices pointing down. Then, a circle is drawn enclosing the polygon so that...
A Frost circle is constructed by drawing a polygon whose number of edges is equal to the number of carbons of the given cyclic system, with one of the vertices pointing down. Then, a circle is drawn enclosing the polygon so that...
02:37Metallic Solids
Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
All metallic solids exhibit high thermal and electrical conductivity, metallic luster, and malleability. Many...
All metallic solids exhibit high thermal and electrical conductivity, metallic luster, and malleability. Many...
02:22Structures of Solids
Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
01:24One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
On...