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The interstellar medium (ISM) is far from empty; rather it contains large molecular clouds consisting of dust and gas. It is in these clouds that new stars form—possibly with habitable planets—with molecules playing a crucial role.1,2 At the moment, over 170 different molecules have been detected: stable molecules, radicals, cations, and anions. Many molecules only consist of a few atoms and are familiar to us from a terrestrial point of view, such as water, molecular hydrogen, methanol, formaldehyde, formic acid, and dimethyl ether. Other molecules are more exotic and consist, for instance, of very unsaturated carbon chains. Gas phase chemical models show that these latter molecules can be quite easily formed through gas phase reactions.3 The saturated molecules are however only formed in small quantities through gas phase chemistry, since they require either high temperatures to be formed or three-body reactions, which are both not available in cold molecular clouds. Dust grains can act as a third body, facilitating addition reactions that lead to the formation of saturated molecules. Already in 1949 de Hulst4 realized the importance of grain surface chemistry and he suggested surface formation routes for H2 from two hydrogen atoms and the formation of H2O from O2 with hydrogen peroxide as intermediate.  From various sources of information, we know that approximately 1% of the mass of the material in the ISM, and 10–10% in terms of numbers, consists of small, nanosized silicate and carbonaceous particles called dust grains. Although this seems a small portion of the total amount of matter, dust grains play an important role in the ISM, not only by acting as catalytic sites for molecule formation but also by shielding molecules from dissociating UV radiation. Depending on the physical conditions, the dust grains can be coated with a layer of “dirty” ice consisting of a mixture of different species. Their main components are water, carbon monoxide, and carbon dioxide, but also more complex molecules such as methane, methanol, formaldehyde, and ammonia may be present. Some of the ice species accrete from the gas phase, but as mentioned before, many of the simple important molecules such as H2 and H2O and also several complex organic molecules are not formed in the gas phase, but rather on the grain surfaces themselves. As a result, many modelers have begun to include grain surface processes in their models to describe chemical evolution during, for instance, star formation.1,5,6 Originally, the development of grain surface models was mostly driven from the astrochemical modeling community7−9 without much input from specialists in ice chemistry. Gas phase models were extended with a surface phase and the grain surface chemistry was treated in a way similar to that of gas phase chemistry. This was found to lead to problems in the regime where the surface abundance is low—the so-called “accretion limit”—where formation rates could be orders of magnitude off. Since then, different modeling methods have been applied to tackle this and other modeling problems.  From the physicochemical point of view, refinements have been made as well. Many of the initial expressions and input parameters originated from surface science or were extensions from gas phase experiments. In surface science, mostly metal or semiconductor surfaces are studied on which absorbates are deposited within the monolayer regime, around room temperature. This is quite different from the rough grain surface on which inhomogeneous ice layers of tens of monolayers are formed at very low temperatures. Fortunately, technological developments have now enabled the experimental verification of grain surface chemistry. Many of the assumptions within the models are now put to the test by applying to experimental surface science techniques to real interstellar analogues. With this new experimental information comes the need for detailed surface models to understand the physicochemical processes behind the experimental results and to translate the experimental findings to astrochemical time scales.  Different modeling techniques have been applied to grain surface astrochemistry, covering a large range of time and length scales. More molecular detail comes at the expense of more CPU time to cover the same evolution in real time. How different techniques relate to one other in this respect is indicated in Figure Figure1.1. Molecular dynamics simulations trace the exact location and orientation of the molecules including lattice vibrations and in some cases even the intramolecular movement, but they typically stay within the picosecond to nanosecond time frame. Rate equations on the other hand can easily handle 108 years—much longer than the lifetime of a molecular cloud—but adsorbed molecules are only treated in terms of numbers and their exact locations are not known. The present review aims to discuss the application of the kinetic Monte Carlo technique (KMC) to grain surface chemistry. This method was initially introduced into astrochemistry as a solution to the “accretion” limit, but it is now more and more applied to gain insight into the physicochemical surface processes. The method has, in principle, not a real restriction in how molecules are represented: in terms of number densities or with their exact location and orientation. The different implementations of kinetic Monte Carlo can therefore cover a huge time and length scale range.    Figure 1  Overview of the different simulation methods mentioned in the present review.

The Kinetic Monte Carlo Method as a Way To Solve the Master Equation for Interstellar Grain Chemistry