The Ground State of the Hydrogen Molecule

Abstract

The method used by Hylleraas in treating the He atom has been extended to the H2 molecule. The method consists of setting up a wave function as a series in the five variables required, electronic separation being introduced explicitly as one of the variables. The coefficients are then determined so as to produce the lowest energy. The energy found is within 0.03 v.e. of the most probable experimental value, while the form and location of the potential energy curve

Theory and application of explicitly correlated Gaussians

“…Other basis sets lead to integrals which are too difficult to compute even for manyelectron diatomic molecules. The only successful applications of other explicitly correlated bases to molecules are those using the JC (James and Coolidge, 1933) and GJC (Kołos and Wolniewicz, 1965) bases for H 2 and other two-electron diatomics. Only in the late 1980s, the first successful applications of Gaussian bases with a linear r 12 factor appeared (Kutzelnigg, 1985;Kutzelnigg and Klopper, 1991); however, in contrast to the ECG basis sets, one has to use several approximations in calculating molecular integrals.…”

“…For almost 30 years after the pioneering work of James and Coolidge (1933), the GJC functions were the only explicitly correlated basis set applied to molecular systems, but such applications were limited to H 2 and isoelectronic diatomic species like HeH þ . One well-known milestone of the GJC approach was the prediction of the ground state dissociation energy of H 2 (Kolos and Wolniewicz, 1968) that later proved to be more accurate than the concurrent experimental data (Herzberg, 1970).…”

“…Generalizations of the James and Coolidge (GJC) functions (James and Coolidge, 1933) have been used for calculations of the hydrogen molecule. The GJC functions have the form…”

Perspective: Explicitly correlated electronic structure theory for complex systems

“…Some 50 years after his death, the Hylleraas Symposium 13 the combined CI and Hylleraas (CI-Hyl) methods, have been proposed for the study of multielectron atoms and diatomic molecules. [14][15][16][17][18][19][20][21] However, these expansions require the computations of difficult integrals involving products of correlation factors such as r µ 12 , r µ 12 r ν 13 , r µ 12 r ν 13 r λ 23 , r µ 12 r ν 13 r λ 14 , and so on. The complexity of these integrals has hindered applications to many-electronic and polyatomic systems, especially for the use of Slater-type orbitals.…”

Evaluation of Multicenter Multielectron Integrals Using One-range Addition Theorems in Terms of STOs for STOs and Coulomb-Yukawa Like Correlated Interaction Potentials with Integer and Noninteger Indices

“…[1][2][3][4][5][6] We notice that the CI expansions converge much more slowly than Hy-method expansions. The Hy method first developed by James and Collidge 7 has been used for determination of the ground state energy of H2 molecule 8,9 and is still valid for two-and threeelectron atomic and molecular systems (see, e.g., Refs. [10][11][12] and references quoted therein).…”