Born-Oppenheimer approximation Hylleraas (Hy) variational calculations with up to 7034 expansion terms are reported for the 1 Σ + g ground state of neutral hydrogen at various internuclear distances. The nonrelativistic energy is calculated to be −1.1744 7571 4220(1) hartree at R= 1.4 bohr, which is 4 orders of magnitude better than the best previous Hylleraas calculation, that of Wolniewicz[1]. This result agrees well with the best previous variational energy, −1.1744 7571 4216 hartree, of

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... ek[2], obtained using Explicitly Correlated Gaussians (ECG) [3-5]. The uncertainty in our result is also discussed. The nonrelativistic energy is calculated to be −1.1744 7593 1399(1) hartree at the equilibrium R= 1.4011 bohr distance. This result also agrees well with the best previous variational energy, −1.1744 7593 1389 hartree, of Cencek and Rychlewski[6, 7], obtained using Explicitly Correlated Gaussians (ECG) [3-5]. ground state of the hydrogen molecule (R = 1.4 bohr) expressed in hartrees. Technique Author N Energy(E) in hartrees many alpha Kubacki and Komasa [29] 22 a -1.1744 7477 JC Bishop and Cheung [30] 249 -1.1744 7565 KW Kolos (includes r 3 12 ) [12] 370 -1.1744 7568 5 1 alpha This work (includes r 3 12 ) 3947 -1.1744 7570 6160 2 alpha This work (includes r 3 12 ) 5577 -1.1744 7570 6942 KW Wolniewicz (includes r 6 12 ) [1] 883 -1.1744 7571 3565 ECG Cencek and Kutzelnigg [31] 1200 -1.1744 7571 4037