Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

New Method Improves Modeling of Electrons’ Motions

15.03.2011
David Mazziotti has significantly improved a quantum computational method that he introduced in 2004 for efficiently modeling the electrons in atoms and molecules.

Although in principle quantum mechanics can describe the properties of molecules and materials in which the electrons’ motions are strongly correlated, in practice such computations are formidable. Molecules can have from 10 to hundreds or thousands of electrons, and the computational cost of modeling molecules increases exponentially with the number of strongly correlated electrons.

Mazziotti, an associate professor in chemistry at the University of Chicago, has been developing a new approach in which any molecule’s energies and properties can be computed as a function of just two of the molecule’s many electrons. Such a strategy provides accurate approximations for strongly correlated electrons without an exponential computational scaling.

In the Feb. 25 issue of Physical Review Letters, Mazziotti announced a newly improved method that is at least 10 to 20 times faster than previous methods.

Mazziotti’s original approach already has been applied to studies of aromatic rings, which are employed in computer displays, and of the energy-transfer process that enables fireflies to glow in the dark.

“The present advance will enable treatment of larger molecules and materials with strongly correlated electrons,” he said.

In the Physical Review Letters article, Mazziotti applied this method to the metal-insulator transition of metallic hydrogen, which forms under the intense pressure found at the cores of Jupiter and Saturn. Computing the electronic properties of a dissociating chain of 50 hydrogen atoms during this transition would require 10 octillion (1028) variables from traditional quantum solutions, while the world’s largest supercomputers can treat approximately a billion (109) variables. The two-electron approach, however, requires only 9.4 million variables and 3.9 million constraints.

The algorithm in Mazziotti’s method is a member of a special family of algorithms known to mathematicians as semidefinite programming. The advance in the Physical Review Letters article also has applications in engineering, computer science, statistics, finance, and economics.

“Remarkably, behind seemingly unrelated phenomena, there lies a common mathematical thread,” Mazziotti said.

In Mazziotti’s method, the energy of a molecule with many electrons is minimized as a function of two electrons, which are constrained to represent all of the electrons.

“In the same fashion, in finance, one might be optimizing profit over a set that is constrained to represent a certain amount of money or a given inventory of products,” he explained. “Both problems require a search — or optimization —of a quantity subject to real-world constraints. In finance these constraints will follow from the laws of business while in chemistry they will follow from the laws of quantum mechanics.

Citation: “Large-Scale Semidefinite Programming for Many-Electron Quantum Mechanics,” David A. Mazziotti, Physical Review Letters, Vol. 108, No. 8, Feb. 25, 2011.

Funding sources: National Science Foundation, Army Research Office, Microsoft Corporation, Dreyfus Foundation, and David-Lucile Packard Foundation

Steve Koppes | Newswise Science News
Further information:
http://www.uchicago.edu

More articles from Physics and Astronomy:

nachricht What happens when we heat the atomic lattice of a magnet all of a sudden?
18.07.2018 | Forschungsverbund Berlin

nachricht Subaru Telescope helps pinpoint origin of ultra-high energy neutrino
16.07.2018 | National Institutes of Natural Sciences

All articles from Physics and Astronomy >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: First evidence on the source of extragalactic particles

For the first time ever, scientists have determined the cosmic origin of highest-energy neutrinos. A research group led by IceCube scientist Elisa Resconi, spokesperson of the Collaborative Research Center SFB1258 at the Technical University of Munich (TUM), provides an important piece of evidence that the particles detected by the IceCube neutrino telescope at the South Pole originate from a galaxy four billion light-years away from Earth.

To rule out other origins with certainty, the team led by neutrino physicist Elisa Resconi from the Technical University of Munich and multi-wavelength...

Im Focus: Magnetic vortices: Two independent magnetic skyrmion phases discovered in a single material

For the first time a team of researchers have discovered two different phases of magnetic skyrmions in a single material. Physicists of the Technical Universities of Munich and Dresden and the University of Cologne can now better study and understand the properties of these magnetic structures, which are important for both basic research and applications.

Whirlpools are an everyday experience in a bath tub: When the water is drained a circular vortex is formed. Typically, such whirls are rather stable. Similar...

Im Focus: Breaking the bond: To take part or not?

Physicists working with Roland Wester at the University of Innsbruck have investigated if and how chemical reactions can be influenced by targeted vibrational excitation of the reactants. They were able to demonstrate that excitation with a laser beam does not affect the efficiency of a chemical exchange reaction and that the excited molecular group acts only as a spectator in the reaction.

A frequently used reaction in organic chemistry is nucleophilic substitution. It plays, for example, an important role in in the synthesis of new chemical...

Im Focus: New 2D Spectroscopy Methods

Optical spectroscopy allows investigating the energy structure and dynamic properties of complex quantum systems. Researchers from the University of Würzburg present two new approaches of coherent two-dimensional spectroscopy.

"Put an excitation into the system and observe how it evolves." According to physicist Professor Tobias Brixner, this is the credo of optical spectroscopy....

Im Focus: Chemical reactions in the light of ultrashort X-ray pulses from free-electron lasers

Ultra-short, high-intensity X-ray flashes open the door to the foundations of chemical reactions. Free-electron lasers generate these kinds of pulses, but there is a catch: the pulses vary in duration and energy. An international research team has now presented a solution: Using a ring of 16 detectors and a circularly polarized laser beam, they can determine both factors with attosecond accuracy.

Free-electron lasers (FELs) generate extremely short and intense X-ray flashes. Researchers can use these flashes to resolve structures with diameters on the...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

VideoLinks
Industry & Economy
Event News

Leading experts in Diabetes, Metabolism and Biomedical Engineering discuss Precision Medicine

13.07.2018 | Event News

Conference on Laser Polishing – LaP: Fine Tuning for Surfaces

12.07.2018 | Event News

11th European Wood-based Panel Symposium 2018: Meeting point for the wood-based materials industry

03.07.2018 | Event News

 
Latest News

Global study of world's beaches shows threat to protected areas

19.07.2018 | Earth Sciences

New creepy, crawly search and rescue robot developed at Ben-Gurion U

19.07.2018 | Power and Electrical Engineering

Metal too 'gummy' to cut? Draw on it with a Sharpie or glue stick, science says

19.07.2018 | Materials Sciences

VideoLinks
Science & Research
Overview of more VideoLinks >>>