Sub-microhartree accuracy potential energy surface for H3+ including adiabatic and relativistic effects. I. Calculation of the potential points

Abstract

Sixty-nine points of the Born–Oppenheimer (BO) potential energy surface (PES) for the ground state of H3+ have been computed using explicitly correlated Gaussian wave functions with optimized nonlinear parameters. The calculated points have an absolute error of about 0.02 cm−1 (0.1 microhartree), i.e., they are by at least one order of magnitude more accurate than ever reported. Similarly accurate adiabatic and relativistic corrections have also been evaluated by means of the Born–Handy formula and by direct perturbation theory (DPT), respectively.

Potential energy surface and wave packet calculations on the Li+HF→LiF+H reaction

“…7,26 However, as we have stressed above, this absolute error is not as important as the error in energy differences with respect to a reference zero energy. Since we have computed the very accurate 69 points quoted recently by Cencek et al, 7 it is possible to obtain a root-mean-square ͑rms͒ deviation of our energy differences errors, taken as zero energy value the corresponding energy of the equilibrium geometry both for our energy differences ͑zero energy at Ϫ1.343 100 a.u.͒ as for the exact energy differences ͑zero energy at Ϫ1.343 835 a.u.͒. The resulting rms deviation is less than 17 cm Ϫ1 .…”

“…It should be noted that the assignment is not a simple task, especially at high energies, and we have also used the data from previous assignments. 7,48 In Table VI the eigenvalues for Jϭ0 are compared with those of previous works. The LPESs of Refs.…”

“…If we add to all of these conformations the 69 proposed by Meyer et al 9 and used by Cencek et al 7 in their very accurate H 3 ϩ ground-state calculations, we obtain a total number of 8469 conformations and 36 FCI energy values for each one ͑304 884 energy values that we do not quote here for obvious reasons͒. A file containing the 8469 ground-state H 3 ϩ data points used to obtain the GPES reported in this paper has been placed in the electronic depository EPAPS.…”

“…The single best FCI energy obtained for the H 3 ϩ minimum 9 is about 95 cm Ϫ1 higher than the very accurate result reported recently. 26,7 Nevertheless, when constructing a GPES, we are not interested in total energies but in energy differences, which are usually small quantities. In forming the difference between two large quantities of similar size, we must consider that errors at each term of the difference are similar and will cancel to a large extent, with a final result for the difference that may have a lower error ͑with respect to the exact difference͒ than the absolute error obtained in the calculated total energy.…”

“…6 Local potential energy surfaces ͑LPES͒ on the highest level of sophistication have appeared recently, 7,8 but covering only 69 points on the minimum region of the ground-state potential energy surface, based on previous full configuration interaction ͑FCI͒ calculations due to Meyer et al ͑the so-called MBB LPES͒. 9 Dinelli et al, 10 using high-resolution spectroscopic data for H 3 ϩ , H 2 D ϩ , D 2 H ϩ , and D 3 ϩ , have determined effective mass-dependent LPES for each isotopomer.…”