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Calculation of Tunneling Splittings of Vibrational Eigenstates of Malonaldehyde

Principal Investigator: Hans-Dieter Meyer, Institute of Physical Chemistry, Universität Heidelberg (Germany)
HPC Platform: Hermit of HLRS
Date Published: March 2015

Spectroscopic investigations often reveal a great deal of information about the structure of a molecule, especially if the molecule is small and only a few atoms are involved. For instance, some characteristic features in the spectra directly point to the chemical bonds and atoms involved. One can identify which atoms a molecule is composed of and how its constituents interact by these features. Unfortunately, this clear identification of spectroscopic features is not always possible. In these situations simulations can help to understand not only the spectroscopic features but also the inner structure of the molecule which causes them.

The challenge of simulating objects on the atomic scale is due to the fact that the quantum nature of the particles cannot be neglected. It is essential to carefully model the quantum behavior of all involved particles if accurate results should be obtained. Since in the quantum world the particles are not point-like but blurred objects and cannot be treated independently, one needs to keep track of all possible quantum mechanic particle locations for all possible combinations of particles involved. This is known as a description in terms of a quantum mechanical wave-function. The numerical modeling of a wave-function requires an enormous amount of data to be stored and processed. Even for small molecules this grows quickly beyond the capabilities of regular computers.

The Heidelberg based scientists developed the Heidelberg MCTDH program package[1] which is designed to treat precisely these kind of quantum mechanical problems. It utilizes a special data reduction scheme which is tailored to treat exactly the above mentioned large quantum mechanical wave-functions of multiple particles. But even with data reduction the numerical demands are in many cases quite high - supercomputing power is required to tackle these problems.

The researchers investigated the spectral properties of malonaldehyde using the HPC ressources of HLRS in Stuttgart. Malonaldehyde is a molecule consisting of 9 atoms, see Fig. 1. The backbone of the molecule is formed by a horseshoe shaped chain of carbon atoms and with one oxygen atom attached to each end. The spectroscopically interesting features are generated by a single hydrogen atom that is located between the two oxygen atoms. This hydrogen atom can be transferred from one oxygen to the other, thereby changing the chemical bonds within the backbone of the molecule. Within a classical picture, this process is forbidden by energy restrictions, but quantum mechanically it is still allowed and known as tunneling. A tunneling process leads to characteristic splittings within the vibrational spectra and has been experimentally observed in malonaldehyde.[2]

Calculation of Tunneling Splittings of Vibrational Eigenstates of MalonaldehydeFig. 1: Chemical structure of malonaldehyde. The proton on the left (a) is transfered via a transition state (b), to the oxygen atom on the righ. During the transfer the single- and double-bonds between the oxygen and carbon atoms are interchanged and the molecule forms a mirror image of the original.
Copyright: Institute of Physical Chemistry, Universität Heidelberg

With the simulations on the Cray XE6 supercomputer at the HLRS the scientists calculated low-lying vibrational states of malonaldehyde and their characteristic splittings induced by the hydrogen tunneling.[3, 4] With these results the researchers were able to confirm experimental assignments of vibrational states that have been measured before as well as results of other researchers. Strong correlations between the involved particles that arise from the changes in the chemical structure of the backbone were also observed. These correlations made the calculations so difficult.

[1] M. H. Beck, A. Jäckle, G. A. Worth, and H.-D. Meyer, Phys. Rep 324, 1 (2000).
[2] N. O. B. Lüttschwager, T. N. Wassermann, S. Coussan, and M. A. Suhm, Phys. Chem. Chem. Phys. 14, 2211 (2013).
[3] M. Schröder, F. Gatti, and H.-D. Meyer, J. Chem. Phys. 134, 234307 (2011).
[4] M. Schröder and H.-D. Meyer, J. Chem. Phys. 141, 034116 (2014).

Markus Schröder and Hans-Dieter Meyer
Institute of Physical Chemistry
Universität Heidelberg
Im Neuenheimer Feld 229, D-69120 Heidelberg/Germany

March 2015