Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:


New Method Improves Modeling of Electrons’ Motions

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:

More articles from Physics and Astronomy:

nachricht Novel light sources made of 2D materials
28.10.2016 | Julius-Maximilians-Universität Würzburg

nachricht OU-led team discovers rare, newborn tri-star system using ALMA
27.10.2016 | University of Oklahoma

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: Novel light sources made of 2D materials

Physicists from the University of Würzburg have designed a light source that emits photon pairs. Two-photon sources are particularly well suited for tap-proof data encryption. The experiment's key ingredients: a semiconductor crystal and some sticky tape.

So-called monolayers are at the heart of the research activities. These "super materials" (as the prestigious science magazine "Nature" puts it) have been...

Im Focus: Etching Microstructures with Lasers

Ultrafast lasers have introduced new possibilities in engraving ultrafine structures, and scientists are now also investigating how to use them to etch microstructures into thin glass. There are possible applications in analytics (lab on a chip) and especially in electronics and the consumer sector, where great interest has been shown.

This new method was born of a surprising phenomenon: irradiating glass in a particular way with an ultrafast laser has the effect of making the glass up to a...

Im Focus: Light-driven atomic rotations excite magnetic waves

Terahertz excitation of selected crystal vibrations leads to an effective magnetic field that drives coherent spin motion

Controlling functional properties by light is one of the grand goals in modern condensed matter physics and materials science. A new study now demonstrates how...

Im Focus: New 3-D wiring technique brings scalable quantum computers closer to reality

Researchers from the Institute for Quantum Computing (IQC) at the University of Waterloo led the development of a new extensible wiring technique capable of controlling superconducting quantum bits, representing a significant step towards to the realization of a scalable quantum computer.

"The quantum socket is a wiring method that uses three-dimensional wires based on spring-loaded pins to address individual qubits," said Jeremy Béjanin, a PhD...

Im Focus: Scientists develop a semiconductor nanocomposite material that moves in response to light

In a paper in Scientific Reports, a research team at Worcester Polytechnic Institute describes a novel light-activated phenomenon that could become the basis for applications as diverse as microscopic robotic grippers and more efficient solar cells.

A research team at Worcester Polytechnic Institute (WPI) has developed a revolutionary, light-activated semiconductor nanocomposite material that can be used...

All Focus news of the innovation-report >>>



Event News

#IC2S2: When Social Science meets Computer Science - GESIS will host the IC2S2 conference 2017

14.10.2016 | Event News

Agricultural Trade Developments and Potentials in Central Asia and the South Caucasus

14.10.2016 | Event News

World Health Summit – Day Three: A Call to Action

12.10.2016 | Event News

Latest News

Steering a fusion plasma toward stability

28.10.2016 | Power and Electrical Engineering

Bioluminescent sensor causes brain cells to glow in the dark

28.10.2016 | Life Sciences

Activation of 2 genes linked to development of atherosclerosis

28.10.2016 | Life Sciences

More VideoLinks >>>