The interaction between the rotational degrees of freedom of a diatomic molecular impurity and the phonon excitations of a two-dimensional atomic matrix commensurate with a substrate is investigated theoretically. It is shown, that the translational-rotational interaction changes the form of the rotational kinetic energy operator as compared to the corresponding expression for a free rotator, and also renormalizes the parameters of the crystal field without change in its initial form. The contribution of the impurity rotational degrees of freedom to the low-temperature heat capacity for a dilute solution of diatomic molecules in an atomic two-dimensional matrix is calculated. The possibility of experimental observation of the effects obtained is discussed.

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