Investigation of the Structure and Spectroscopy of H 5 + Using Diffusion Monte Carlo Zhou Lin and Anne B. McCoy* Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States * S Supporting Information ABSTRACT: The results of diffusion Monte Carlo (DMC) calculations of the ground and selected excited states of H 5 + and its deuterated analogues are presented. Comparisons are made between the results obtained from two recently reported potential surfaces. Both of these surfaces are based on CCSD(T) electronic energies, but the fits display substantial differences in the energies of low-lying stationary points. Little sensitivity to these features is found in the DMC results, which yield zero-point energies based on the two surfaces that differ by between 20 and 30 cm -1 for all twelve isotopologues of H 5 + . Likewise, projections of the ground state probability amplitudes, evaluated for the two surfaces, are virtually identical. By using the ground state probability amplitudes, vibrationally averaged rotational constants and dipole moments were calculated. On the basis of these calculations, all isotopologues are shown to be near-prolate symmetric tops. Further, in cases where the ion had a nonzero dipole moment, the magnitude of the vibrationally averaged dipole moment was found to range from 0.33 to 1.15 D, which is comparable to the dipole moments of H 2 D + and HD 2 + . Excited states with up to three quanta in the shared proton stretch and one quantum in the in-phase stretch of the outer H 2 groups were also investigated. Trends in the energies and the properties of these states are discussed. ■ INTRODUCTION Protonated hydrogen dimer, or H 5 + , is a molecular ion of long- standing interest since its first laboratory observation. 1 This is due, at least in part, to its importance as an intermediate in the simplest H + exchange reaction in the interstellar medium, specifically the exchange of a proton between molecular hydrogen and H 3 + . 2 This reaction is thought to play a role in the nonstatistical H/D isotopic substitution and ortho/para distributions observed for H 3 + . 3,4 From a theoretical perspective, this molecular ion provides a challenge to standard approaches for studying vibrational energies and wave functions due to the presence of several low energy barriers for the exchange of the positions of two or more hydrogen atoms. 5-8 The equilibrium structure of H 5 + , identified as 1-C 2v in Figure 1, has two outer H 2 units that lie in parallel planes and are rotated by a 90° torsion angle. In this structure, the fifth hydrogen atom is located on the axis that connects the centers of mass of two outer H 2 units, and shifted so it is closer to one of the outer H 2 units. This sets up a double minimum potential. The barrier, for the transfer of the central hydrogen atom between the two H 2 groups, 2-D 2d , is on the order of 60 cm -1 , 7 whereas the anharmonic frequency of this mode in H 5 + is 379 cm -1 . 9 Likewise, there is a barrier in the torsion coordinate, 3-C 2v and 4-D 2h , of roughly 100 cm -1 , whereas the calculated anharmonic frequency of this mode is between 80 and 90 cm -1 . Finally, the barrier for exchange of the central hydrogen atom, with one of the outer ones, 5-C 2v , is roughly 1550 cm -1 . 7,8 The minimum energy structure and the structures of the four lowest-energy transition states are shown in Figure 1 along with their relative energies. The presence of five hydrogen atoms and the associated large zero-point energy make vibrational calculations of H 5 + challenging. At the same time, the presence of only four electrons makes highly accurate electronic structure calculations tractable for this system, and these calculated electronic energies can be used to construct a potential surface. Two such potentials have been reported recently. The first (hereafter referred to as PES-I) was developed by Xie, Braams, and Bowman 7 and is based on a polynomial fit to more than 100 000 electronic energies that were evaluated at the CCSD(T)/aug-cc-pVTZ level of theory/basis. A second potential (PES-II) was developed by Roncero and co-workers. 8 In that work, electronic energies evaluated at the CCSD(T)/ aug-cc-pVQZ level of theory/basis were fit to a model potential, the form of which is based on the triatomics-in-molecules formalism. In addition to detailed knowledge of the potential, a deeper understanding of the chemistry of H 5 + requires the develop- ment of connections between the potential and the spectros- copy of the molecular ion. Several studies have explored the spectroscopy of H 5 + on the basis of PES-I and PES-II with a variety of approaches. These include vibrational configuration- Special Issue: Curt Wittig Festschrift Received: February 9, 2013 Revised: April 4, 2013 Published: April 5, 2013 Article pubs.acs.org/JPCA © 2013 American Chemical Society 11725 dx.doi.org/10.1021/jp4014652 | J. Phys. Chem. A 2013, 117, 11725-11736