Solving the Redundant Coordinate Problem

Date & time

1–1.30pm 22 June 2017


Room 3.105


Prof Meredith Jordan

At any given geometric configuration of an N-atom molecule there are 3N – 6 linearly independent local coordinates. To describe the molecule at any point in configuration space, however, we must use a redundant coordinate description, describing the molecule in terms of some set of primitive redundant coordinates. Such descriptions are used in the optimisation routines available in electronic structure codes and in descriptions of global molecular potential energy surfaces. For normal molecules, for example methane, CH4, the ground vibrational state can be described using 3N – 6 local coordinates from this set– for example, the CH4 normal coordinates. This choice, however, is particularly problematic for the protonated water dimer, H5O2+: even large sets of primitive redundant coordinates suffer from linear. Here we introduce a general solution to the redundant coordinate problem and demonstrate that it can be used to develop accurate interpolated molecular potential energy surfaces. We assess our potential energy surface using quantum diffusion Monte Carlo (QDMC) simulations of the H5O2+ ground state, determining its quality of in terms of (i) a test set of configurations (ii) the number of QDMC walkers “killed” as a result of artefacts in the potential, (iii) the H5O2+ zero-point energy and (iv) approximate H5O2+ anharmonic vibrational frequencies. In particular, our solution to the redundant coordinate problem enables us to retain inverse atom-atom distances as primitive redundant coordinates, with a number of inherent advantages. Moreover, our strategy is generally applicable to any case where redundant coordinates are used to describe a system. Time permitting, application to hydrogen absorption materials will also be discussed.

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