Exponentially correlated Hylleraas-configuration interaction nonrelativistic energy of the 1S ground state of the helium atom
Abstract
A generalization of the Hylleraas-configuration interaction
method (Hy-CI) first proposed in a previous study, the exponentially
correlated Hylleraas-configuration interaction method (E-Hy-CI) in which
the single rij of an Hy-CI wave function is generalized to a form of the generic type 
, is explored. This type of correlation, suggested by Hirshfelder in 1960, has the right behavior in the vicinity of both the rij cusp as rij goes to 0 and as rij goes to infinity; this work explores whether wave functions containing both linear and exponential rij
factors converge more rapidly than either one alone. The method of
calculation of the two-electron E-Hy-CI kinetic energy and electron
repulsion integrals in a stable and efficient way using recursion
relations is discussed, and the relevant formulas are given. The
convergence of the E-Hy-CI wave function expansion is compared with that
of the Hy-CI wave function without exponential correlation factors,
demonstrating both convergence acceleration and an improvement in the
accuracy for the same basis. This makes the application of the E-Hy-CI
method to systems with N > 4, for which this formalism with at most a single 
factor per term leads to solvable integrals, very promising. E-Hy-CI
method variational calculations with up to 10,080 expansion terms are
reported for the ground 1S state of the
neutral helium atom, with a resultant nonrelativistic energy of −2.9037
2437 7034 1195 9831 1084 hartree for the best expansion.
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