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Research

Simulations of Highly Reactive Systems

Chemical reactions are structural changes of chemical compounds associated with the breaking and formation of bonds. A chemical compound, that is, any kind of matter, consists of electrons and nuclei, and a chemical reaction involves motions of these compounds on the basis of simple physical interactions. The difficulty in predicting reaction mechanisms on physical grounds is due to the enourmous complexity of such a motion of many particles, all interacting with each other. The evolution of quantum chemistry has got to a point where it is not only possible to compute molecular structures, but also to simulate chemical reactions on the basis of the elementary quantum mechanical equations. We investigate ultrafast chemical reactions using first principles molecular dynamics simulations with the Car-Parrinello program package [1, 2, 3] (using the celebrated Car-Parrinello concept: description of the chemically relevant valence electrons with density functional theory in the Kohn-Sham formalism [4, 5, 6] with a plane wave basis set, description of the core electrons with fixed potentials, description of the motion of the nuclei with classical Newton dynamics, moving electrons and nuclei simultaneously, if possible).
From the simulation the full information about the mechanism is obtained (motion of nuclei and orbitals, entropy, reaction time). However, the time scale of molecular motion is the femtosecond time scale. To model vibrations with periods of some ten femtoseconds, very small time steps have to be used in the simulations and total simulation times presently hardly excess the picosecond time scale. If watched at this scale in extreme slow motion (and extreme magnification), molecules turn out to be enervating inactive and chemical reactions appear as very rare events. Even in highly reactive systems, a violent decomposition that is too fast to be followed experimentally, looks like a slow contradance in the simulation. From time to time molecules collide, eventually exchange electrons or protons, bonds may be formed or broken. Hence, if one wants to observe more than unreactive molecular oscillations (which could also be modelled with much cheaper computational approaches), one has to focus on highly reactive, but still chemically meaningful systems.
We use the following approaches for preparing highly reactive systems:

  • Switching to another potential surface (photo chemistry)
  • Pulling two atoms within a larger system apart (mechanically induced chemistry)
  • Mixing of two components (chemistry)

List of quantities which determine the quality of simulations of chemical dynamics (incomplete):

  • Energy
  • The conservation of energy is a valuable check factor if the simulation is done in the NVE ensemble. Deviations from that principle should have experimental reasons (e.g. absorption of energy due to photoexcitation, increase of the total energy while applying mechanical load).
  • Orbitals
  • Orbitals are no observables. The sum over the orbital densities, however, is the physically interpretable total density (but uncharacteristic). The change of the overall density during a reaction is described best by the most strongly changing orbitals.
    The HOMOs and the LUMOs are the relevant quantities in photochemical reactions. For ground state simulations the representation by localized orbitals is advantageous, because they are most suitable to represent the chemistry of the reaction under investigation (lone pairs, binding orbitals etc.). Orbitals should not jump during reactions.
  • Statistics
  • Chemical reactions can be considered as observed, if they are obtained in two to three simulations. For deriving product ratios, at least 100, rather 1000 simulations are necessary.
  • Comparison
  • It is important to compare the results of the simulations to other quantum chemical methods. For very complex reactions, where essential factors are not reflected by static calculations, the direct comparison between simulation and experiment is the better alternative.

Photoreactions

Theoretical description of photoreactions is particularly challenging: since calculating electronically excited states is usually more demanding than calculating the ground states and since the reaction coordinates are often unknown.

Using the ROKS method (Restricted Open-shell Kohn-Sham), we perform molecular dynamics in the first excited singlet state.[7, 8, 9] There, the atomic nuclei move (according to the laws of classical mechanics) in an electronic potential which is calculated using quantum chemical methods. With this approach we investigated for example photoreactions of small, organic molecules (butadiene, cyclohexadiene), as well as the photoreaction of azobenzene, a molecular rotor and of rhodopsin (the latter in combination with QM/MM).

Movie 1 shows the photoreaction of oxirane: immediately after excitation the C-O bond breaks in agreement with experimental results, subsequent hydrogen migration leads to an aldehyde. A large amount of the released energy is transfered to the vibrational degrees of freedom.

Photochemical excitation of diphenyloxirane leads to cleavage of the C-C bond in a complicated disrotatory motion, as shown in movie 2.



Movie 1 (0,4 MB) Movie 2 (0,4 MB)

An other reaction type induced by electronic excitation is the photodissociation. Movie 3 shows the cleavage of the N-H bond in the pyrrole molecule. The anti-binding orbital of the excited state is converted into a spherical hydrogen orbital.

The reaction is modified in the presence of solvents. The dissociation is prevented in a pyrrole•3H2O cluster (movie 4). Instead an electron transfer to the water molecules is observed (orange orbital). Movie 5 shows a pyrrole•3NH3 cluster. In this more basic system the electron transfer is followed by the transfer of the proton.

 

Movie 3 (96 KB)Movie 4 (0,7 MB)
Movie 5 (1,2 MB)

Reactions under Mechanical Stress

We investigated the material failure of siloxane materials under mechanical load in cooperation with the Wacker Chemie AG. In contrast to previous models which are based on radical bond rupture, the Car-Parrinello molecular dynamics simulations show an ionic bond rupture. This observation is in accordance with ESR-experiments. Hence the Si-O and C-C bonds exhibit a qualitatively different rupture behaviour while they have comparable bond strenghts. This affects the consecutive reactions: the ionic fragments react quickly with neighbouring chains. Due to this mechanism a crack propagates rapidly.

Movie 1 shows the tearing of a siloxane chain from a silica surface. In movie 2, four siloxane chains under mechanical stress are shown.



Movie 1 (4,9 MB) Movie 2 (7,8 MB)

Motivated by single molecule AFM experiments, we are investigating chemical reactions induced by pulling a disulfide with first principles simulations. Both in the presence (reduction) and in the absence (simple bond rupture) of the reducing agent dithiothreitol, we investigate the force to break the disulfide bond.

The relevant localized orbitals are depicted in short movies. Movie 3 shows the disulfide in the absence of solvent and reducing agent, movie 4 shows the disulfide in ammonia and in the presence of dithiothreitol.



Movie 3 (6,8 MB) Movie 4 (6,2 MB)

Highly Reactive Mixtures

Hypergolic mixtures are compounds that react spontaneously when brought into contact with one another. This characteristic is deployed e.g. in the propellant for the upper stage engine of the European launch vehicle Ariane 5. The bipropellant that is used in this case consists of monomethylhydrazine (MMH) and nitrogen tetroxide (NTO). Complications in the upper stage procedure emerged during a mission to transport two satellites into space in July 2001. A possible reason for this could be undesired reactions in the bipropellant.
We investigate the reactions of the MMH/NTO mixture on a picosecond timescale with Car-Parrinello molecular dynamics.
We observe the sequence of electron (MMH→NTO) and proton transfers (e.g. MMH radical cation→MMH) over a few picoseconds. The proton transfers are shown in movies 1 and 2 which present a timeframe of two picoseconds. The first electron transfer of this sequence is shown in movie 3 (2.0 MB).


Movie 1 (2.4 MB) Movie 2 (2.5 MB)
Movie 3 (2.0 MB)

Electrochemistry

Movie (13.4 MB)

Evolution of molecular oxygen.

Movies created with

gOpenMol:
a) L. Laaksonen, J. Mol. Graphics 10(1992) 33.
b) D.L. Bergman, L. Laaksonen and A. Laaksonen, J. Mol. Graphics & Modelling 15(1997) 301.

Molekel:
a) Molekel 4.2, P. Flükinger, H.P. Lüthi, S. Portmann, J. Weber,
Swiss Center for Scientific Computation, Manno (Switzerland), 2000-2002.
b) S. Portmann, H.P. Lüthi, CHIMIA (2000) 54 766-770.

Literature


[1] R. Car and M. Parrinello,
Unified Approach for Molecular Dynamics and Density Functional Theory
Phys. Rev. Lett., 55, 2471 (1985)

[2] D. Marx and J. Hutter,
Ab initio molecular dynamics: Theory and Implementation
Modern Methods and Algorithms in Quantum Chemistry
Forschungzentrum Juelich, NIC Series, vol. 1, (2000)

[3] J. Hutter et al.,
CPMD,
Max-Planck-Institut für Festkörperforschung and IBM Zurich Research Laboratory, 1995.

[4] P. Hohenberg and W. Kohn,
Inhomogeneous Electron Gas
Phys. Rev., 136, B864 (1964)

[5] W. Kohn and L.J. Sham,
Self-Consistent Equations Including Exchange and Correlation Effects
Phys. Rev., 140, A1133 (1965)

[6] A. Becke,
Density-functional exchange-energy approximation with correct asymptotic behavior
Phys. Rev. A, 38, 3098 (1988)

[7] I. Frank, J. Hutter, D. Marx, and M. Parrinello,
Molecular dynamics in low-spin excited states
J. Chem. Phys., 108, 4060 (1998)

[8] S. Grimm, C. Nonnenberg, and I. Frank,
Restricted open-shell Kohn-Sham theory for pi-pi* transitions. I. Polyenes, cyanines, and protonated imines
J. Chem. Phys., 119, 11574 (2003)

[9] J. Friedrichs, K. Damianos and I. Frank,
Solving restricted open-shell equations in excited-state molecular dynamics simulations
Chem. Phys., 347, 17 (2008)