Rydberg States of H₄

Abstract

Energies of the 15 lowest Rydberg states of the metastable H4 cluster have been determined using Koopman's theorem at the equilibrium geometry of the parent ion, H4 +. To represent the core orbitals of H4, a 6-31G** basis set has been used at the SCF, MP2, MP4(SDTQ), CI-SD, and CI-SDT levels. The Rydberg orbitals have been modeled using a basis set analogous to that used to model the Rydberg orbitals of H3 in previous theoretical calculations. To test the validity of the calculations for the H4 molecule, ab initio calculations were repeated for the Rydberg orbitals of the H3 molecule at the stable geometry of the H3 + core. Predicted transitions were within 2% of the rotational band spectra of H3 observed by Herzberg. The metastable H4 cluster formed from charge neutralization of H4 + decomposes into two H2 molecules. Previous calculations have predicted that one of the two H2 products will be vibrationally hot while the other will be relatively cold and that a large recoil energy of approximately 9 eV is expected for the relative kinetic energy of the two H2 products. The present work suggests that if Rydberg states are involved in the charge neutralization process, the recoil energy could be reduced due to radiative transitions among the Rydberg states.

Full Dimensional Ab Initio Dynamics Calculations of Electron Capture Processes of the H4+ Ion

“…Instead, an unpaired electron was almost localized on H(1). The binding energies of H to H 3 + were calculated to be 3.0 kcal/mol (HF level) and 4.2 kcal/mol (MP4SDQ level), which are in reasonable agreement with the numeric values obtained previously. ,− The agreement revealed that the dynamics calculations at the HF/6-311G(d,p) level would give reasonable features of the reaction dynamics.

1 Geometrical parameters and schematic structure of the reaction system of H 4 + and H 4 .

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“…Comparison with the Previous Studies. The feature of the product vibrational and rotational states of H 2 obtained from the present dynamics calculations is in good agreement with that predicted by Pan and Borkman using static ab initio MO calculations . The present calculations strongly support the model proposed by them.…”

“…The optimized parameters of H 4 + calculated were r 1 = 1.6097 Å, r 2 = 0.9004 Å, r 3 = 0.8437 Å, θ = 55.9°, and φ = 152.1°. The numerical values of H 4 + were in good agreement with those obtained by Pan and Borkman . To elucidate the electronic states of H 4 + , the charge on each atom was calculated at the MP4SDQ/6-311G(d,p)//HF/6-311G(d,p) level.…”

“…To elucidate the effect of the Rydberg state on the reaction dynamics, preliminary trajectory calculations from a geometrical configuration optimized for the Rydberg 2s state (the lowest Rydberg state) are run. The structure of H 4 at the lowest Rydberg state is optimized at the single excited configuration interaction (S-CI) method with a basis set 6-311G(d,p)+Rydberg orbital 14b. The calculated optimized parameters under C 2 v symmetry are: r 1 = 2.1206 Å; r 3 = 0.9194 Å; φ = 93.1°.…”

“…Studying H 3 + provides information on detailed reaction dynamics in the cloud. The positive ion H 4 + , composed of an even hydrogen atom, has been shown both computationally − and experimentally to be a stable species. Borkman et al carried out accurate ab initio calculations of H 4 + systems. − They showed that H 4 + has a planar C 2 v geometry consisting of a triangle of three H atoms with a fourth H bonded to one vertex.…”