# HPCVG Performs Most Accurate Lithium Atom Computations to Date

## October 2009

Computational scientists at NIST and Indiana University have achieved record levels of accuracy in the development of computational methods for the virtual measurement of fundamental properties of the three electron atom lithium (Li). Their recent results for the nonrelativistic energies for four excited states of the lithium atom represent the highest level of accuracy ever reached (less than 10^{-9} hartree) in atomic quantum computations with more than two electrons. The achievement is described in a forthcoming article in Physical Review A by James Sims of the ITL Mathematical and Computational Sciences Division and Stanley Hagstrom of Indiana University. The exact solution for many body systems of this type can be represented as an infinite sum of terms. In practice, only a finite number can be employed in any calculation, with each additional term contributing a bit more to the accuracy to the result. For all but the simplest systems or a relative handful of terms, however, the calculation becomes impossibly complex. To make the problem computationally practical, they merge two earlier algorithms for these calculations - one which has advantages in ease of calculation, and one which more rapidly achieves accurate results - into a hybrid, the Hylleraas-Configuration Interaction (Hy-CI) method. Perhaps the biggest advantage of this technique is that insights gleaned from both techniques can be utilized in obtaining the best choice of terms in their computations. To obtain high accuracy results it is also necessary to use quadruple precision (30+ digit computations). In addition, they developed improved computer code for a key computational bottleneck, high-precision solution of the large-scale generalized matrix eigenvalue problem, using parallel processing. For a 17190 term wave function they achieved a factor of 30 speedup on 32 processors of the ITL/PL/CNST/OCIO Linux cluster. The resulting computations obtained four excited states of the lithium atom to two orders of magnitude greater than has been done before.

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