麻豆淫院

(麻豆淫院Org.com) -- 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鈥� 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鈥檚 energies and properties can be computed as a function of just two of the molecule鈥檚 many electrons. Such a strategy provides accurate approximations for strongly correlated electrons without an exponential computational scaling. In the Feb. 25 issue of 麻豆淫院ical Review Letters, Mazziotti announced a newly improved method that is at least 10 to 20 times faster than previous methods.

Mazziotti鈥檚 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.

鈥淭he present advance will enable treatment of larger molecules and materials with strongly correlated electrons,鈥� he said.

In the 麻豆淫院ical 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鈥檚 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鈥檚 method is a member of a special family of algorithms known to mathematicians as semidefinite programming. The advance in the 麻豆淫院ical Review Letters article also has applications in engineering, computer science, statistics, finance, and economics.

鈥淩emarkably, behind seemingly unrelated phenomena, there lies a common mathematical thread,鈥� Mazziotti said.

In Mazziotti鈥檚 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.

鈥淚n 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,鈥� he explained. 鈥淏oth problems require a search 鈥� or optimization 鈥攐f 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.鈥�