Global Analytical Potential Hypersurface for Large Amplitude Nuclear Motion and Reactions in Methane II. Characteristic Properties of the Potential and Comparison to Other Potentials and Experimental Information

Abstract

The global analytical potential surface for the electronic ground state of methane developed in paper I is analyzed and discussed in detail. A new determination of the experimental potential surface for the CH chromophore in CHD 3 , obtained from more recently measured line positions and integrated absorption coefficients, is also reported. The complete, nine-dimensional calculation of the vibrational ground state by diffusion quantum Monte Carlo on the fully anharmonic potential surface allows the determination of r e ) (1.086 ( 0.002) Å with a high level of certainty from comparison with experimental values of rotational constants for methane and isotopomers. Other results regarding properties of the anharmonic potential surface close to the equilibrium configuration are theoretical values for the vibrationally induced electric dipole moments in CH 3 D, CH 2 D 2 , and CHD 3 , which are obtained in conjunction with a nine-dimensional, vector-valued representation of the electric dipole moment in this molecule and agree well with the experimental data. It is shown that, if equilibrium geometry and harmonic force field are fixed to experimental values, the overtone spectrum of the CH chromophore in CHD 3 can be described in an acceptable way (〈|ν cal -ν obs |〉 ≈ 40 cm -1 up to 18 000 cm -1 (METPOT 3). The agreement can be improved to within 17 cm -1 (METPOT 4), on the average, if the anharmonic part of the model potential is refined with data from the experimentally derived, three-dimensional CH chromophore potential surface from Lewerenz and Quack (J. Chem. Phys. 88). For this purpose, the analytical representation of the potential, mainly along the bending degrees of freedom, must be sufficiently flexible, as shown by the present calculations. The accuracy regarding the description of spectroscopic data pertaining to highly excited vibrational states and the global character of the proposed potential surface representation render it a powerful instrument for the theoretical treatment of chemical reaction dynamics. A relation to reaction kinetics can be established through calculation of the lowest adiabatic channel on the complete nine-dimensional potential hypersurface for methane using quasiadiabatic channel quantum Monte Carlo techniques. It is found that the behavior of this channel, corresponding approximately to an exponential interpolation with a parameter R ≈ 0.7-0.8 Å -1 in the adiabatic channel model, is consistent with empirical results obtained from experiment. Further refinements of the models are feasible and expected, when full dimensional calculations of the solution of the rovibrational Schrödinger equation will be performed.

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

“…From this value, and estimated anharmonic zero point energies (Grev et al 1991), one obtains the zero kelvin reaction enthalpy D 0 = ∆ r H 0 • − = 432.63 kJ mol −1 , which agrees fairly well with the thermo-and photochemically determined value 432.9 ± 0.1 kJ mol −1 (Weitzel et al 1999). Marquardt and Quack (2004) show that zero point energy estimations based on anharmonic force fields may carry uncertainties on the order of 0.5-2 kJ mol −1 . The geometry optimized, absolute electronic energy of methane was calculated by Grev and Schaefer (1992) at the CCSD(T) level in an all electron calculation to be −40.501 E h , q which is roughly 0.06 aJ above a "realistic" value of (−40.514 ± 0.002) E h (Pople and Binkley 1975).…”

High‐Resolution Fourier Transform Infrared Spectroscopy

“…We note that this resolution of a five decade long controversy starting with the paper by Coulson (1942) was obtained using IR intensities from the spectrum shown and combining this with numerous NIR intensity measurements and theoretical results in terms of a multidimensional electric dipole hypersurface (Hollenstein et al 1994, Marquardt and. We refer to the original papers for a more detailed discussion, leading to this now well-established result (see also Marquardt and Quack 2004). …”

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

“…[14] led to an effective Morse parameter β ≈ 2 Å −1 , while the analysis of the anisotropy of the ab initio potential in Ref. [19] gave α ≈ 0.7-0.8 Å −1 (being close to the value of 1 Å −1 suggested long ago in Ref. [23]).…”

“…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]).…”