Global analytical potential hypersurfaces for large amplitude nuclear motion and reactions in methane. I. Formulation of the potentials and adjustment of parameters to ab initio data and experimental constraints

Abstract

Analytical representations of the global potential energy surface of XYn molecules are developed and applied to model the potential surface of methane in the electronic ground state. The generic analytical representation allows for a compact, robust, and flexible description of potentials for XYn systems irrespective of the specific nature of the atomic interactions. The functions are global in that structures near several minima of the potential hypersurface as well as saddle points and dissociation limits are well described. Clusters of atoms Yn can be represented as well by this type of function. Care is taken to implement conditions resulting from the symmetric group Sn and to construct positive definite bilinear forms of special functional forms of certain coordinates (such as bond lengths and bond angles), in order to avoid artifacts in exceptional ranges of the potential hypersurface. These special functional forms include intrinsic, symmetry allowed couplings between coordinates such as bending and stretching. We include linear potential terms in bond angle coordinates, which result in effectively quadratic potential terms for highly symmetric structures. True logical multidimensional 01-switching functions Ssw(r) of bond lengths r are used to interpolate between limiting ranges in the hypersurface. The particular form Ssw(r)∼exp(−(rsw/r)nsw) allows us to describe the potential as a multipole expansion representation in the limit of large r(→∞). In the application to methane, first the representations are fitted to data from high level ab initio calculations using multireference configuration interaction techniques. Additional conditions which help to improve the description of experimental data are considered during the fit. Typically, these conditions involve some parameters or parameter groups and refer to the equilibrium geometry and harmonic force field. Other constraints apply to the energies of dissociation channels. We describe the model potentials METPOT 1 to METPOT 4 in the present work.

Global Analytical Potential Energy Surfaces for High‐resolution Molecular Spectroscopy and Reaction Dynamics

“…Here we mention the well-studied system of overtone transitions pertaining to the alkyl CH infrared chromophore in symmetrical CHX 3 (Peyerimhoff et al 1984, Dübal and Quack 1984a, Baggott et al 1985, Segall et al 1987, Carrington et al 1987, Dübal et al 1989, Davidsson et al 1991, Hippler and Quack 1996 and asymmetrical CHXYZ (Dübal and Quack 1984b, Beil et al 1994, Hippler and Quack 1996, Beil et al 1997) compounds (and references cited therein). For methane (CH 4 ), several PESs have been proposed in the past, p among which we mention here the spectroscopically determined quartic force field of Gray and Robiette (1979) and other ab initio potentials (Duchovic et al 1982, Peyerimhoff et al 1984, Duchovic et al 1984, Brown and Truhlar 1985, Hirst 1985, Schlegel 1986, Brodersen and Lolck 1987, Sosa et al 1988, Dübal et al 1989, Wu and McWeeny 1994, Lee et al 1995, Schwenke and Partridge 2001, refined empirically , or semiempirically (Aboumajd 1984, Brodersen and Lolck 1987, Iung and Leforestier 1989, 1994, Halonen 1997, Marquardt and Quack 1998. We give a more detailed discussion of some of these PESs in Section 4.…”

“…In this section, we review some theoretical developments on new, compact analytical forms that were devised to fill this gap (Marquardt and Quack 1998, Cuvelier et al 2004, Marquardt et al 2005, Marquardt and Sagui 2007, Marquardt et al 2010) and discuss applications regarding global analytical representations of molecules of the type XY n , with emphasis on methane Quack 1998, 2004) and ammonia (Marquardt et al 2003a(Marquardt et al ,b, 2005.…”

“…This is so because, in the case of a bond rupture, the analytical forms used to describe the bond stretching potentials of the parent molecule XY n can be formally used to describe the product XY n−1 . The description becomes quantitative if parameters are switched accordingly: (13) Appropriate multidimensional switching functions have been developed by Marquardt and Quack (1998), which fully account for all permutation symmetries and so naturally induce all allowed compositions of irreducible representations in equation (8).…”

From quantum chemistry to dissociation kinetics: what we need to know

“…Examples [13,14] Figures 5-7 illustrate experimental data and modelling results (full curves). The high-pressure limiting behaviour corresponds to a capture of H by CH 3 (for combination) on the potential energy surface of CH 4 (see Refs [15][16][17] and, for more details, see [18][19][20]). The low-pressure behaviour reflects the properties of collisional energy transfer on CH 4 -M potential energy surfaces (see Refs [21,22]).…”

An improved third order dipole moment surface for methane

“…Proposed PES for methane include those of Gray and Robiette [15], Lee, Martin and Taylor [16], Schwenke and Partridge [17,18], Marquardt and Quack [19,20], Oyanagi et al [21], and more recently those of Nikitin, Rey and Tyuterev (NRT) [22] and Yurchenko et al. [25].…”