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

Johannes Kästner and Eckhart Arnold

1 Introduction
2 Similarities and Differences between Simulations and Experiments
3 Case Study: Simulation of H-2-Formation in Outer Space
    3.1 Introductory Remarks on Simulations in Chemistry
    3.2 The Role of Quantum Mechanics as Comprehensive Background Theory
    3.3 The Motivation for Simulating the H-2-Formation in Outer Space
    3.4 Modeling Techniques and their Credentials
        3.4.1 Abstractions
        3.4.2 Modeling Techniques
        3.4.3 Validation
    3.5 Experiment-likeness
4 Summary and Conclusions

3.4.3 Validation

The tunneling rates calculated by (Goumans/Kaestner 2010) cannot, at least with the techniques currently available, directly be tested by experiment. Thus, they serve as real theoretical predictions. Limiting or similar cases, can be validated, though.

The approximations used can be divided into two classes: (1) instanton theory as an approximation to full quantum mechanics. (2) Density functional theory, the basis set, and the computer codes involved to describe the potential energy surface. The latter is needed as input to instanton theory.

Instanton theory, as mentioned above, was shown previously (by other scientists) to be accurate in a broad class of chemical reactions. Thus, the authors assume that it is also accurate enough for the chemisorption of hydrogen on benzene.

The rate of the chemisorption of hydrogen on benzene was measured experimentally at higher temperature than relevant for the interstellar medium (300-600~K). In this temperature interval, tunneling does not play a role, which facilitates the simulation of rates. (Goumans/Kaestner 2010) therefore were able to use the computationally expensive CCSD(T)/CBS method to calculate the rate in this temperature interval. They compared it to the experimental values (Goumans/Kaestner 2010, Figure S2 of the Supporting Information) and found satisfactory agreement. Additionally, they calculate the rate with a number of density functionals, and found again satisfactory agreement with the MPWB1K functional. The rate at these high temperatures (300-600~K) depends only on a small part of the potential energy surface. The part is crucial for the tunneling rate at low temperatures as well, though. Then they calculated the potential energy surface at the whole tunneling path both with the CCSD(T)/CBS reference method and the MPWB1K functional used for the tunneling rates. The agreement between these surfaces adds credibility to the tunneling simulations.

Thus, although direct empirical validation was impossible for this simulation, different means for indirect validation were available and have been made use of.

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