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.
Contact: James S. Sims