An accurate analytic H4 potential energy surface

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The interaction potential energy surface (PES) of H4 is of great importance for quantum chemistry as a test case for molecule–molecule interactions. It is also required for a detailed understanding of certain astrophysical processes, namely collisional excitation and dissociation of H2 in molecular clouds, at densities too low to be accessible experimentally. The 6101 ab initio H4 energies reported in 1991 by Boothroyd et al. demonstrated large inaccuracies in analytic H4 surfaces available at that time. Some undesirable features remained in the more accurate H4 surfaces fitted to these energies by Keogh and by Aguado et al., due in part to the relatively sparse coverage of the six-dimensional H4 conformation space afforded by the 6101 ab initio energies. To improve the coverage, 42 079 new ab initio H4 energies were calculated, using Buenker’s multiple reference (single and) double excitation configuration interaction program. Here the lowest excited states were computed as well as the ground state, and energies for the original 6101 conformations were recomputed. The ab initio energies have an estimated rms “random” error of ∼0.5 millihartree and a systematic error of ∼1 millihartree (0.6 kcal/mol). A new analytical H4 PES was fitted to these 48 180 ab initio energies (and to an additional 13 367 points generated at large separations), yielding a significant improvement over previous H4 surfaces. This new PES has an rms error of 1.43 millihartree relative to these 48 180 ab initio energies (the fitting procedure used a reduced weight for high energies, yielding a weighted rms error of 1.15 millihartree for these 48 180 ab initio energies). For the 39 064 ab initio energies that lie below twice the H2 dissociation energy, the new PES has an rms error of 0.95 millihartree. These rms errors are comparable to the estimated error in the ab initio energies themselves. The new PES also fits the van der Waals well to an accuracy of about 5%. For relatively compact conformations (energies higher than the H2 dissociation energy), the conical intersection between the ground state and the first excited state is the largest source of error in the analytic surface. The position of this conical intersection forms a somewhat complicated three-dimensional hypersurface in the six-dimensional conformation space of H4. A large portion of the position of the conical intersection has been mapped out, but trying to include the conical intersection explicitly in an analytic surface is beyond the scope of the present paper.