Scientists at the National Institute
of Standards and Technology (NIST) and Indiana University (IU) have determined*
the most accurate values ever for a fundamental property of the element lithium
using a novel approach that may permit scientists to do the same for other atoms
in the periodic table.
NIST’s James Sims and IU’s Stanley Hagstrom have calculated four
excitation energies for the lithium atom approximately 100 times more accurately
than any previous calculations or experimental measurements. Precise determination
of excitation energy—the amount necessary to raise an atom from a base
energy level to the next higher—has intrinsic value for fundamental research
into atomic behavior, but the success of the method the team employed has implications
that go beyond lithium alone.
The theorists have overcome major computational and conceptual hurdles that
for decades have prevented scientists from using quantum mechanics to predict
electron excitation energies from first principles. Sims first proposed in the
late 1960s that such a quantum approach could be possible, but its application
to anything more than two electrons required a fiendishly difficult set of calculations
that, until recently, was beyond the capacity of even the world’s fastest
computers. In 2006 the team used a novel combination of algorithms, extended
precision computing and the increase in power brought about by parallel computing
to calculate the most accurate values ever for a simple, two-electron hydrogen
By making improvements to those algorithms, Sims and Hagstrom now have been
able to apply their approach to the significantly more difficult problem of
lithium, which has three electrons. Much of the original difficulty with their
method stems from the fact that in atoms with more than one electron the mutually
repulsive forces among these tiny elementary particles introduces complications
that make calculations extremely time-consuming, if not practically impossible.
Sims says that while the lithium calculation is valuable in itself, the deeper
import of refining their method is that it should enable the calculation of
excitation energies for beryllium, which has four electrons. In turn, this next
achievement should enable theorists to predict with greater accuracy values
for all of the remaining elements in the second row of the periodic table, from
beryllium to neon, and potentially the rest of the periodic table as well. “The
mathematical troubles we have with multiple electrons can all be reduced to
problems with four electrons,” says Sims, a quantum chemist in the mathematics
and computational sciences division. “Once we’ve tackled that, the
mathematics for other elements is not any more difficult inherently—there’s
just more number-crunching involved.”
To obtain their results, the researchers used 32 parallel processors in a NIST
computer cluster, where they are currently working on the calculations for beryllium.
High precision determinations of excitation energies are of interest to scientists
and engineers who characterize and model all types of gaseous systems, including
plasmas and planetary atmospheres. Other application areas include astrophysics
and health physics.
* J.S. Sims and S.A. Hagstrom. Hylleraas-configuration-interaction study of
the 2 2S ground state of neutral lithium and the first five excited 2S states.
Physical Review A, Nov. 19 2009, 10.1103/PhysRevA.80.052507.
** See “Algorithm Advance Produces Quantum Calculation Record,”
NIST Tech Beat, March 16, 2006.