In previous work, high precision eigenvalues for all states of
helium up to $n = 10$ and $L = 7$ have been obtained by the use of
double basis sets in Hylleraas coordinates . In the present
work, we show that triple basis sets using three sets of
individually optimized nonlinear parameters for different distance
scales yield an order of magnitude improvement in accuracy for
basis sets of the same size for the Rydberg S-states states of
helium. They also allow an extension of high precision calculations
for the nonrelativistic energies and wave functions up to at least
$n = 16$ with little loss of accuracy. An important advance in
computational technique is the use of David Bailey's
double-quadruple (dq) precision arithmetic (approximately 70
decimal digits) in the optimization of the nonlinear parameters in
the basis set. Except for this, the wave functions have a high
degree of numerical stability, and standard quadruple precision is
sufficient for the evaluation of matrix elements. A comparison with
the best previous calculations for $n > 10$  will be presented.
 G.W.F. Drake and Z.-C. Yan, Phys. Rev. A. 46, 2378 (1992).
 H. Nakashima and H. Nakatsuji, J. Chem. Phys. 128, 154108 (2008).
|Presenter name||Lamies Sati|
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