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Exponentially correlated Hylleraas‐configuration interaction nonrelativistic energy of the 1 S ground state of the helium atom
Author(s) -
Sims James S.,
Padhy Bholanath,
Ruiz María Belén
Publication year - 2021
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.26470
Subject(s) - wave function , ground state , helium atom , physics , configuration interaction , exponential function , electronic correlation , quantum mechanics , kinetic energy , atomic physics , electron , mathematical analysis , mathematics , excited state
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 r ij of an Hy‐CI wave function is generalized to a form of the generic type r ij ν ije − ω ij r ij, is explored. This type of correlation, suggested by Hirshfelder in 1960, has the right behavior in the vicinity of both the r ij cusp as r ij goes to 0 and as r ij goes to infinity; this work explores whether wave functions containing both linear and exponential r ij 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 r ij ν ije − ω ij r ijfactor 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 1 S state of the neutral helium atom, with a resultant nonrelativistic energy of −2.9037 2437 7034 1195 9831 1084 hartree for the best expansion.