Structure of malonaldehyde with the proton in the “left” minimum configuration (a), at the transition state (b), and in the “right” minimum configuration (c). Note, that the single- and double-bonds are interchanged after the proton transfer.
Numbering, frequencies, type and physical interpretation of the normal mode coordinates obtained at the transition state. The in-plane modes are of A 1 or B 2 symmetry, out-of-plane modes are of A 2 or B 1 symmetry. The modes which are symmetric with respect to the q 21 = 0 plane are of A 1 or B 1 and the ungerade of A 2 or B 2 symmetry. All energies are in cm−1.
Mode combinations for cluster expansion.
Mode combinations for MCTDH calculations.
Primitive grids: HO – harmonic oscillator DVR; SIN – sine DVR functions using mass and frequency scaled normal modes. For the HO DVR the ranges result from the number of grid points chosen. As mass an frequency scaled normal modes are used, the mass and frequency parameters of the HO-DVR are set to unity.
Extrapolation of the state energies using a small set of SPF as reference. ΔE denotes the difference to the reference state. All energies are in cm−1.
Extrapolation of the state energies as in Table V but with a larger set of SPF. ΔE denotes the difference to the reference state. The last three rows outline the extrapolation with the number of SPF increased in modes 3 and 6 simultaneously. We consider the values given in the last line of the table as our best results. All energies are in cm−1.
Largest direct calculations. The state energies are expected to lie slightly above the extrapolated ones reported in Table VI. All energies are in cm−1. The first three lines allow to extrapolate the energy. However, this extrapolation only includes modes Q 3 and Q 6. A full extrapolation including all modes is expected to lower the ZPE by additionally 0.3–0.6 cm−1, bringing it to very close agreement with the extrapolated values of Table VI. The last line of the table presents the results of our largest calculation.
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