Influence of the simplest type of multiparticle interactions on the example of a lattice model of an adsorption layer

Self-organization of molecules on a solid surface is one of the promising directions for materials generation with unique magnetic, electrical, and optical properties. They can be widely used in fields such as electronics, optoelectronics, catalysis, and biology. However, the structure and physicochemical properties of adsorbed molecules are influenced by many parameters that must be taken into account when studying the self-organization of molecules. Therefore, the experimental study of such materials is expensive, and quite often it is difficult for various reasons. In such situations, it is advisable to use the mathematical modeling. One of the parameters in the considered adsorption systems is the multiparticle interaction, which is often not taken into account in simulations due to the complexity of the calculations. In this paper, we evaluated the influence of multiparticle interactions on the total energy of the system using the transfer-matrix method and the Materials Studio software package. The model of monocentric adsorption with nearest interactions on a triangular lattice was taken as the basis. Phase diagrams in the ground state were constructed and a number of thermodynamic characteristics (coverage $\theta$, entropy $S$, susceptibility $\xi$) were calculated at nonzero temperatures. The formation of all four ordered structures (lattice gas with $\theta=0$, $(\sqrt{3}\times\sqrt{3})R30^{\circ}$ with $\theta=\frac{1}{3}$, $(\sqrt{3}\times\sqrt{3})R^{*}30^{\circ}$ with $\theta=\frac{1}{3}$ and densest phase with $\theta=1$) in a system with only pairwise interactions, and the absence of the phase $(\sqrt{3}\times\sqrt{3})R30^{\circ}$ when only three-body interactions are taken into account, were found. Using the example of an atomistic model of the trimesic acid adsorption layer by quantum mechanical methods we determined that in such a system the contribution of multiparticle interactions is $11.44\%$ of the pair interactions energy. There are only quantitative differences at such values. The transition region from the $(\sqrt{3}\times\sqrt{3})R^{*}30^{\circ}$ to the densest phase shifts to the right by $38.25\%$ at $\frac{\epsilon}{RT}=4$ and to the left by $23.46\%$ at $\frac{\epsilon}{RT}=-2$.