Novel Computation Enables Best-yet Estimate of Ground State of Neutral Helium
November 2001
ITL computational scientist James Sims, in collaboration with Stanley
Hagstrom of Indiana University, has computed the nonrelativistic
energy for the ground 1S state of neutral helium to be -2.9037 2437
7034 1195 9829 99 a.u. This represents the highest accuracy
computation of this quantity to date. Comparisons with other
calculations and an energy extrapolation yield an estimated accuracy
of one part in 10-20.
Exact analytical solutions to the Schrdinger equation, which
determines such quantities, are known only for atomic hydrogen and
other equivalent two-body systems. Thus, solutions must be
determined numerically. In an article submitted to the International
Journal of Quantum Chemistry, Sims and Hagstrom discuss how this best
calculation to date was accomplished. To obtain a result with this
high a precision, very large basis sets must be used. In this case,
variational expansions of the wave function with 4,648 terms were
employed, leading to the need for very large computations. Such
large expansions also lead to problems of linear dependence, which
can only be remedied by using higher precision arithmetic than is
provided by standard computer hardware. For this computation,
192-bit precision (roughly 48 decimal places) was necessary, and
special coding was required to simulate hardware with this
precision. Parallel processing was also employed to speed the
computation, as well as to provide access to enough memory to
accommodate larger expansions. NIST's Scientific Computer Facility
cluster of 16 PCs running Windows NT was utilized for parallel
computation. Typical run times for a calculation of this size about
are 8 hours on a single CPU, but only 30 - 40 minutes on the parallel
processing cluster.
This work employs a very novel wave function, namely, one consisting
of at most a single r12 raised to the first power combined with a
conventional non-orthogonal configuration interaction (CI) basis. The
researchers believe that this technique can be extended to
multielectron systems. Work is in progress, for example, to see what
precision can be obtained for atomic lithium, which is estimated to
require a 6000-fold increase in CPU requirements to reach the same
level of precision, making the use of parallel programming techniques
even more critical.
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