# When can a Computer Simulation act as Substitute for an Experiment? A Case-Study from Chemisty

Johannes Kästner and Eckhart Arnold

### 3.3 The Motivation for Simulating the H-2-Formation in Outer Space

The simulation of $H_2$-formation in outer space described in the following is documented in Goumans/Kaestner (2010). The purpose of this simulation is to contribute to the explanation of $H_2$-enrichment in the interstellar medium. The simulation can best be described as a piece in the puzzle to explain this phenomenon. The point where the simulation study picks up the problem is defined by a number of previously established facts and existing astrochemical hypotheses:

1. It has been measured in astronomy that $H_2$ is abundant in the interstellar medium “despite inefficient gas-phase formation routes and $H_2$-destruction by cosmic rays and photons.” (Goumans/Kaestner 2010, p. 7350)

2. To explain this fact, other $H_2$-formation routes must exist. One possible route is the chemisorption of hydrogen atoms (H) on dust grains made mostly of carbon (Casaux et al. 2008). “Astrochemical models require facile chemisorption of H on carbonaceous dust grains at intermediate temperatures” (Goumans/Kaestner 2010, p. 7350). Intermediate temperatures are temperatures approximately between 100~K and 250~K. Such dust grains mainly consist of graphite and its smaller fragments, polycyclic aromatic hydrocarbons.

3. Is has been suggested that the $H_2$-formation rates must exceed $3\times 10^{-17}$ or $2\times 10^{-16}$ cm$^3$molecule$^{-1}$s$^{-1}$. (Habart et al. 2004) (The rate is specified relative to the concentration of dust molecules which catalyse the process.)

4. The chemisorption of the first hydrogen atom to an aromatic hydrocarbon determines the rate. The addition of the second hydrogen atom is known to be much faster (Hornekaer et al. 2006).

5. Hydrogen exists in the form of two stable isotopes, the lighter protium ($^1$H) and the heavier deuterium ($^2$H or D). Observations show that D is much more abundant in atomic hydrogen than in molecular hydrogen ($H_2$ vs. HD) (Casaux et al. 2008). This suggests that atom tunneling is involved in the formation of $H_2$ because deuterium tunnels less efficiently than protium due to its higher mass. “D$_2$ has not been observed to date [in photon dominated regions].” (Casaux et al. 2008, p. 496)

The question that Goumans/Kaestner (2010) seek to answer is whether chemisorption of H and D atoms to polycyclic aromatic hydrocarbons (as a model for dust grains consisting of carbon), and in particular the tunneling effect, can account for the $H_2$-enrichment in the interstellar medium. In order to answer this question the reaction rates of the chemisorption of H and D on benzene, the simple-most aromatic hydrocarbon, need to be determined. The reaction rates of the chemisorption of H and D on benzene can be determined experimentally only for temperatures that are much higher than those in in the interestellar medium in outer space. Therefore, the experimental determination of the reaction rate must be surrogated by numerical calculation. In the given low temperature setting the reaction rates depend crucially on the tunnel effect. If the tunneling rates can be brought into agreement with the observations and suggestions listed above, then this supports both the assumption that $H_2$-formation in outer space is catalyzed by polycyclic aromatic hydrocarbons and that the tunneling effect plays a crucial role in this reaction.

In principle, the tunneling effect can also be observed experimentally, but practically this is well-nigh impossible in the given scenario, because the reaction rates are too low for experimental purposes due to the low temperatures (Goumans/Kaestner 2010, p. 7351). The time scales relevant to the interstellar medium (10$^5$ years) can not even closely be reached in experiments. The more welcome therefore is the possibility to simulate this reaction in the computer. At the same time, because no direct experimental validation of the simulation is available, more strain is put on the justification of the theoretical and technical ingredients of this simulation which will be described in the following.