New math technique improves atomic property predictions to historic accuracy

June 25, 2014
New math technique improves atomic property predictions to historic accuracy
Computational techniques developed by a team from NIST and IU could enable precise computation of atomic properties that are important for nuclear medicine, as well as astrophysics and other fields of atomic research. Credit: © Paco Ayala (Fotolia)

By combining advanced mathematics with high-performance computing, scientists at the National Institute of Standards and Technology and Indiana University have developed a tool that allowed them to calculate a fundamental property of most atoms on the periodic table to historic accuracy—reducing error by a factor of a thousand in many cases. The technique also could be used to determine a host of other atomic properties important in fields like nuclear medicine and astrophysics.

NIST's James Sims and IU's Stanley Hagstrom have calculated the base energy levels for the four in the element beryllium, an accomplishment that has required nearly an entire career's effort on Sims' part. Precise determination of the base energy—crucial for determining the amount necessary to raise an atom from its base to any level higher—has great intrinsic value for fundamental atomic research, but the team's technique has implications far broader than for a single element.

Sims says the technique allowed the calculation of excitation states with eight-decimal accuracy, resulting in a remarkably smooth curve that they expected theoretically but were not sure they would attain in practice. For the vast majority of the elements in the , the calculated results are a thousand times more accurate than previous values. The results, according to Sims, suggest their method could enable computation of other atomic properties—electron affinity and ionization potential, for example—that are important for , astrophysics and other fields of atomic research. A form of cancer treatment now under development called boron neutron capture therapy may benefit from these calculations, he says.

Their method is the culmination of decades of effort aimed at using quantum mechanics to predict base energy levels from first principles. Sims first proposed in the late 1960s that such a quantum approach could be possible, but the complex calculations involved were beyond the reach of the world's best computers. Only in 2006, after the advent of parallel computing—linking many computers together as a unified cluster—were he and Hagstrom able to create workable algorithms for calculating the energies for a two-electron hydrogen molecule more accurately than could be done experimentally. Then, in 2010, they improved the algorithms to bring lithium's three electrons within reach.

Beryllium's four electrons proved a new hurdle, but perhaps the last significant one. Much of the difficulty stems from the fact that mutual repulsion among the electrons, combined with their attraction for the nucleus, creates a complex set of interacting forces that are at least time-consuming, if not practically impossible, to calculate. The complexity grows with the addition of each new electron, but the team found a mathematical approach that can reduce an atom's electron cloud to a group of problems, none of which are more complex than solving a four-electron system.

Calling their approach a shortcut would be in some ways a misnomer. Where the calculation for lithium required a cluster of 32 parallel processors, beryllium required 256, and even then, the cluster needed to operate at extremely high efficiency for days. But the payoff was that they could calculate the energies for all four-electron ground states—meaning not only all of the elements in beryllium's column on the periodic table, each of which has four electrons in its outer shell, but also for all other elements in ionized states that have four electrons, such as boron with one electron missing, carbon missing two, and so forth, on up to the as-yet-unnamed element 113.

Explore further: Theorists Close In on Improved Atomic Property Predictions

More information: J.A. Sims and S.A. Hagstrom. Hylleraas-configuration-interaction nonrelativistic energies for the 1S ground states of the beryllium isoelectronic sequence. Journal of Chemical Physics, DOI: 10.1063/1.4881639, June 11, 2014.

Related Stories

Theorists Close In on Improved Atomic Property Predictions

January 13, 2010

( -- Scientists at the National Institute of Standards and Technology and Indiana University have determined the most accurate values ever for a fundamental property of the element lithium using a novel approach ...

Exploring the magnetism of a single atom

May 8, 2014

Magnetic devices like hard drives, magnetic random access memories (MRAMs), molecular magnets, and quantum computers depend on the manipulation of magnetic properties. In an atom, magnetism arises from the spin and orbital ...

Nuclear-atomic overlap for the isotope thorium-229

February 17, 2014

More than 99.9% of the mass of any atom is concentrated into a quadrillionth of its volume, the part occupied by the nucleus. Unimaginably small, dense and energetic, atomic nuclei are governed by laws quite distinct from ...

Recommended for you

Toward mass-producible quantum computers

May 26, 2017

Quantum computers are experimental devices that offer large speedups on some computational problems. One promising approach to building them involves harnessing nanometer-scale atomic defects in diamond materials.

New technology could revolutionize 3-D printing

May 26, 2017

A technology originally developed to smooth out and pattern high-powered laser beams for the National Ignition Facility (NIF) can be used to 3-D print metal objects faster than ever before, according to a new study by Lawrence ...


Adjust slider to filter visible comments by rank

Display comments: newest first

not rated yet Jun 25, 2014
Thats a nobel prize in chemistry/physics right there. Just give it ten or fifteen years..
5 / 5 (1) Jun 25, 2014
Their method is the culmination of decades of effort aimed at using quantum mechanics to predict base energy levels from first principles

Good theory.

Interesting to note that the Be nucleus, as a specialized quantum arithmetic logic unit, performs the calculations in much less time.

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.