Ab initio Thermochemistry and Kinetics of Molecules with Coupled Large-Amplitude Motions

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Large fields of energy conversion and chemical engineering benefit from analysis and prediction capabilities of chemical models. These models rely on thermochemical and kinetic data for the species involved. These data are often hard (or expensive) to measure; in this case data for modeling comes preferably from theoretical (e.g. ab initio) methods. The accurate theoretical determination of thermochemical properties requires both an accurate description of the electrons and an accurate description of the nuclei of the molecules. Electronic structure methods have made great progress in the last decades and can provide electronic energies with an uncertainty in the order of 1 kJ/mol. In contrast, the motion of the nuclei -- especially in case of coupled anharmonic motion -- often is described with an uncertainty rather in the order of 10 kJ/mol. This clearly wastes the accuracy of the previous electronic energy computation. The proposed project aims at overcoming this bottleneck by a new method involving exact and approximate Hamilton operators. The Hamilton operator is composed of a potential and a kinetic energy term. While the potential energy is meaningfully expressed in internal coordinates, i.e. bond lengths, angles and dihedrals, this in turn makes the kinetic energy a complicated functional containing the inverse Jacobian of the transformation from Cartesian to internal coordinates. This has so far hampered calculations involving the exact Hamilton operator. We already have shown that, on the one hand, the Jacobian can be factored into matrices that are easy to invert. On the other hand, because the elements of the Jacobian are all of the same functional form, we can solve integrals over these functions analytically. In the herein proposed project, we will use these properties to apply the exact Hamilton operator to small systems and obtain thermochemical and kinetic data with benchmark accuracy. We will derive and investigate approximations to the exact Hamilton operator that allow to predict thermochemistry and kinetics of larger systems of current interest, e.g. biofuels or solvent molecules and complexes.