J. Phys. Chem. A 2006, 110, 1569-1574
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An ab Initio Based Global Potential Energy Surface Describing CH5+ f CH3+ + H2† Zhong Jin, Bastiaan J. Braams, and Joel M. Bowman* Cherry L. Emerson Center of Scientific Computation and Department of Chemistry, Emory UniVersity, Atlanta, Georgia 30322 ReceiVed: July 13, 2005; In Final Form: August 24, 2005
A full-dimensional, ab initio based potential energy surface (PES) for CH5+, which can describe dissociation is reported. The PES is a precise fit to 36173 coupled-cluster [CCSD(T)] calculations of electronic energies done using an aug-cc-pVTZ basis. The fit uses a polynomial basis that is invariant with respect to permutation of the five H atoms, and thus describes all 120 equivalent minima. The rms fitting error is 78.1 cm-1 for the entire data set of energies up to 30 000 cm-1 and a normal-mode analysis of CH5+ also verifies the accuracy of the fit. Two saddle points have been located on the surface as well and compared with previous theoretical work. The PES dissociates correctly to the fragments CH3+ + H2 and the equilibrium geometry and normalmode analyses of these fragments are also presented. Diffusion Monte Carlo calculations are done for the zero-point energies of CH5+ (and some isotopologs) as well as for the separated fragments of CH5+, CH3+ + H2 and those of CH4D+, CH3+ + HD and CH2D+ + H2. Values of D0 are reported for these dissociations. A molecular dynamics calculation of CH4D+ dissociation at one total energy is also performed to both validate the applicability of the PES for dynamics studies as well as to test a simple classical statistical prediction of the branching ratio of the dissociation products.
I. Introduction The cation CH5+ plays an important role in astrochemistry1-3 and possibly in combustion chemistry. This cation is also of great basic interest because it is known to be highly fluxional. There have been numerous theoretical studies4-16 of CH5+ since its discovery in mass spectrometry experiments in 1950s.17 The first detailed insights into CH5+ obtained from these calculations were that the minimum, denoted Cs(I), is a Cs structure that is characterized as a “CH3 tripod” with an “H2” attached to the carbon. This unusual structure was attributed to three-center twoelectron bonding. In addition two saddle points, denoted Cs(II) and C2V, have been characterized. The most accurate calculations11 report electronic energies of the Cs(II) and C2V saddle points of 33.9 and 286.1 cm-1 relative to the global minimum. The nature of CH5+ causes it to be quite resistant to direct experimental characterization. Results from mass spectrometric experiments by Hiraoka and co-workers18,19 on CH5+ are compatible with the 3-center, 2-electron bonded structure of Cs(I) symmetry. However, this experiment is achieved by attaching methane molecules as the thermochemical sensors to the CH5+ core. CH5+ has complicated IR absorption spectrum. Oka and co-workers recorded the high-resolution infrared spectrum of CH5+ in the range of 2750-3150 cm-1. There are approximately 900 spectral lines20 with considerable spectral congestion and to date these lines have not been assigned. Very recently Asvany et al. reported a low-resolution IR spectrum of CH5+ (at 110 K) in the range 0-3500 cm-1.21 Three broad bands were observed at 1200, 2500, and 3000 cm-1, with nearly continuous absorption in the range 2500-3000 cm-1. The features were captured in a recent classical power spectrum reported by us using a full-dimensional potential energy surface * Corrrsponding author. E-mail address:
[email protected]. † Part of the special issue “William Hase Festschrift”.
based on MP2/cc-pVTZ calculations.14 A very similar finding though directly of the IR spectrum via the dipole correlation function using DFT-based direct dynamics was also reported along with this new spectrum.21 Theoretically, in addition to the electronic structure calculations, several dynamics studies have been reported. The first dynamical study showing the fluxional nature of CH5+ was reported by Marx and Parrinello based on Car-Parrinello dynamics calculations and path-integral simulations.6,8,9 More recently, we reported the zero point properties of CH5+ and isotopologs obtained with classical molecular dynamics and quantum Diffusion Monte Carlo calculations by McCoy13 and power spectra14 of CH5+ using our semi-global potential energy surface. This PES is a fit to ab initio MP2/cc-pVTZ energies, which is made explicitly invariant with respect to any permutation of the five H atoms. It does describe excitation of CH5+ up to fairly high energies; however, it does not describe dissociation. Very recently other semiglobal PES and DMC calculations of the zero-point state were reported, based on CCSD(T)/aug-cc-pVTZ calculations.15 For a study of the important interstellar reaction3
CH3+ + HD f CH2D+ + H2
(1)
the PES of CH5+ must extend to the dissociation limit CH3+ + H2. The geometries used in the previous potentials12-14 were focused in the configuration space around the global minimum of CH5+ and so did not describe its dissociation. Motivated by this, we have developed a new potential energy surface that describes dissociation to fragments CH3+ and H2 and present that surface and some calculations with it here. The surface we describe here is constructed from 36173 CCSD(T) energies obtained with the aug-cc-pVTZ basis set using MOLPRO 2002.6.22 Section II discusses the details of
10.1021/jp053848o CCC: $33.50 © 2006 American Chemical Society Published on Web 10/05/2005
1570 J. Phys. Chem. A, Vol. 110, No. 4, 2006
Jin et al. Finally, fits (described below) were done and redone based on using those additional configurations obtained from doing MD and quantum DMC calculations on preliminary fits. B. Fitting the Potential Energy Surface. The earlier fitting procedures for CH5+,12,14 and an early version of the H3O2PES23 are closely related to the one we describe in this paper. CH5+ has 12 vibrational degrees of freedom, however, to facilitate a description of the PES that is invariant with respect to a permutation of the five H atoms we use all 15 internuclear distances, as done previously.12,14,23 The function describing the PES has the form12
V ) p(x) +
qi,j(x)yi,j ∑ i
