## SUrface Science MOdeling and Simulation Toolkit

SuSMoST is a set of computer programs and libraries that are intended to support studies of surfaces with emphasize on adsorption systems and phase transitions. Currently SuSMoST is being actively developed by staff of Computational Chemistry Laboratory of Omsk State Technical University (OmSTU). SuSMoST development is supported by Russian Science Foundation (project No 17-71-20053 for 2017-2020 years). SuSMoST emerged from the decade of computational studies of physico-chemical processes on surfaces conducted by the scientific group lead by Alexander V. Myshlyavtsev in OmSTU.

#### Citing SuSMoST

**SuSMoST: Surface Science Modeling and Simulation Toolkit**, S. S. Akimenko, G. D. Anisimova, A. I. Fadeeva, V. F. Fefelov, V. A. Gorbunov, T. R. Kayumova, A. V. Myshlyavtsev, M. D. Myshlyavtseva, and P. V. Stishenko,
**Journal of Computational Chemistry**, 2020. DOI: 10.1002/jcc.26370.

## Mentions in the media:

**Abstract:** A simple lattice model of the orientational ordering in organic adsorption layers that considers the directionality of intermolecular interactions is proposed. The symmetry and the number of rotational states of the adsorbed molecule are the main parameters of the model. The model takes into account both the isotropic and directional contributions to the molecule-molecule interaction potential. Using several special cases of this model, we have shown that the tensor renormalization group (TRG) approach can be successfully used for the analysis of orientational ordering in organic adsorption layers with directed intermolecular interactions. Adsorption isotherms, potential energy, and entropy have been calculated for the model adsorption layers differing in the molecule symmetry and the number of rotational states. The calculated thermodynamic characteristics show that entropy effects play a significant role in the self-assembly of dense phases of the molecular layers. All the results obtained with the TRG have been verified by the standard Monte Carlo method. The proposed model reproduces the main features of the phase behavior of the real adsorption layers of benzoic, terephthalic, and trimesic acids on a homogeneous surface of metal single crystals and graphite.
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GAZETA.RU: "A model was developed to predict new organometallic structures"

**Abstract:** Supramolecular coordination self-assembly on the solid surface offers great possibilities for creating nanostructures and thin films with unique physicochemical properties. In this work, we present a simple lattice model based on competitive coordination motifs that enables prediction of the phase behavior and thermal stability of metal–organic networks consisting of 1,3,5-tris(pyridyl)benzene (TPyB) and transition metals on Au(111) surface. The main parameter of the model is the ratio between the energies of the two-fold and three-fold metal–ligand coordination defined by the type of the metal center...
View article

**Abstract:** High accuracy and performance of the tensor renormalization group (TRG) method have been demonstrated for the model of hard disks on a triangular lattice. We considered a sequence of models with disk diameter ranging from a to 2√3a, where a is the lattice constant. Practically, these models are good for approximate description of thermodynamics properties of molecular layers on crystal surfaces. Theoretically, it is interesting to analyze if and how this sequence converges to the continuous model of hard disks. The dependencies of the density and heat capacity on the chemical potential were calculated with TRG and transfer-matrix (TM) methods. We benchmarked accuracy and performance of the TRG method comparing it with TM method and with exact result for the model with nearest-neighbor exclusions (1NN). The TRG method demonstrates good convergence and turns out to be superior over TM with regard to considered models...
View article

**Abstract:** In this paper, a complete analysis of the phase diagrams of the model of adsorption of a binary gas mixture on a square lattice in the ground state for all sets of near undirected interactions between particles was performed. Using the principle of minimum of a large thermodynamic potential in a stable phase, the partition of the model parameter space (the energies of lateral interactions) into regions differing by the type of the phase diagram was constructed. Also, for some regions, partial and total coverages as functions of chemical potentials of the gases were calculated through transfer-matrix method and presented. The work is an extension of the work (Fefelov in Phys Chem Chem Phys 20(15): 10359–10368, 2018).
View article

GAZETA.RU: Scientists have come up with how to create triangular bricks using self-assembling molecules"

**Abstract:** The model of dimers adsorption on hexagonal lattice with different orientations to surface and hard-spheres lateral interactions has been studied at nonzero temperature. The transfer-matrix method was used as the main one and the Monte Carlo method was used for checking of some extreme cases. Adsorption isotherms, dependencies of the entropy from the density of the adsorption layer and of the energy from the system temperature at certain points of the phase space, were computed. It was found that at least the first ten phases of the ground state still persist at nonzero temperatures.
View article

**Abstract:** Complete analysis of phase behavior of an adsorption model of a binary gas mixture on a square lattice was carried out for all possible sets of lateral interactions between nearest adsorbed molecules of the same type and no interaction between adsorbed molecules of different types. The model was completely investigated in the ground state, and it was shown that the phase behavior of the system is conserved at finite temperatures by means of a transfer matrix method.
View article

## Recent studies conducted with SuSMoST:

**Tensor renormalization group study of orientational ordering in simple models of adsorption monolayers**, V. A. Gorbunov, A. I. Uliankina, S. S. Akimenko, and A. V. Myshlyavtsev,

**J. Phys. Rev. E**, 2023. DOI: 10.1103/PhysRevE.108.014133.

**Abstract:**A simple lattice model of the orientational ordering in organic adsorption layers that considers the directionality of intermolecular interactions is proposed. The symmetry and the number of rotational states of the adsorbed molecule are the main parameters of the model. The model takes into account both the isotropic and directional contributions to the molecule-molecule interaction potential. Using several special cases of this model, we have shown that the tensor renormalization group (TRG) approach can be successfully used for the analysis of orientational ordering in organic adsorption layers with directed intermolecular interactions. Adsorption isotherms, potential energy, and entropy have been calculated for the model adsorption layers differing in the molecule symmetry and the number of rotational states. The calculated thermodynamic characteristics show that entropy effects play a significant role in the self-assembly of dense phases of the molecular layers. All the results obtained with the TRG have been verified by the standard Monte Carlo method. The proposed model reproduces the main features of the phase behavior of the real adsorption layers of benzoic, terephthalic, and trimesic acids on a homogeneous surface of metal single crystals and graphite.

**Tensor network construction for lattice gas models: Hard-core and triangular lattice models**, Sergey S. Akimenko,

**J. Phys. Rev. E**, 2023. DOI: 10.1103/PhysRevE.107.054116.

**Abstract:**The representation of complex lattice models in the form of a tensor network is a promising approach to the analysis of the thermodynamics of such systems. Once the tensor network is built, various methods can be used to calculate the partition function of the corresponding model. However, it is possible to build the initial tensor network in different ways for the same model. In this work, we have proposed two ways of constructing tensor networks and demonstrated that the construction process affects the accuracy of calculations. For demonstration purposes, we have done a brief study of the 4 nearest-neighbor (NN) and 5NN models, where adsorbed particles exclude all sites up to the fourth and fifth nearest neighbors from being occupied by another particle. In addition, we have studied a 4NN model with finite repulsions with a fifth neighbor. In a sense, this model is intermediate between 4NN and 5NN models, so algorithms designed for systems with hard-core interactions may experience difficulties. We have obtained adsorption isotherms, as well as graphs of entropy and heat capacity for all models. The critical values of the chemical potential were determined from the position of the heat capacity peaks. As a result, we were able to improve our previous estimate of the position of the phase transition points for the 4NN and 5NN models. And in the model with finite interactions, we found the presence of two first-order phase transitions and made an estimate of the critical values of the chemical potential for them.

**Triangles on a triangular lattice: Insights into self-assembly in two dimensions driven by shape complementarity**, S. S. Akimenko, A. V. Myshlyavtsev, M. D. Myshlyavtseva, V. A. Gorbunov, S. O. Podgornyi, and O. S. Solovyeva,

**J. Phys. Rev. E**, 2022. DOI: 10.1103/PhysRevE.105.044104.

**Abstract:**A series of models for reversible filling of a triangular lattice with equilateral triangles has been developed and investigated. There are eight distinct models that vary in the set of prohibitions. In zeroth approximation, these models allow one to estimate the influence of the particles’ shape and complementarity of their pair configurations on the self-assembly of dense monolayers formed by reversible filling. The most symmetrical models were found to be equivalent to hard-disk models on the hexagonal lattice. When any contact of hard triangles by vertices is prohibited, the dense monolayers are disordered, and their entropy tends to the constant. If only one pair configuration is prohibited, the close-packed layer appears through the continuous phase transition. In other cases, the weak first-order transition resulting in the self-assembly of close-packed layers is observed.

**Simple lattice model of surface-confined metal–organic networks consisting of linear nitrogen-bearing molecules and transition metals**, Vitaly A. Gorbunov, Anastasiia I. Uliankina, Alexander V. Myshlyavtseva,

**J. Phys. Rev. E**, 2022. DOI: 10.1039/D2ME00199C.

**Abstract:**We propose a generalized lattice model that enables prediction of the phase behavior and thermal stability of surface-confined metal–organic layers consisting of molecules with nitrogen-bearing functional groups (–CN, –Py, ([double bond, length as m-dash]NH)2) of various sizes and transition metal atoms (copper and iron). The coordination energy per molecule is revealed to be a nearly linear function of the coordination number. In the case of three-fold coordination and higher, steric repulsions between the coordinated functional groups play an important role. The lattice model has been parametrized using DFT methods. The ground state phase diagrams have been calculated and verified by GCMC simulation at non-zero temperatures. An increase in the size of the functional group and/or decrease of the coordination capacity of the metal center leads to a greater phase diversity. There are linear metal–organic structures and metal–organic networks consisting of different coordination motifs. Otherwise, close-packed structures with high coordination motifs predominate. The relative thermal stability of the linear and 2D porous metal–organic structures is proportional to the average coordination number of the structure. Thermal destruction of the porous metal–organic structures occurs through breaking the coordination bonds and compacting the layer at the first stage forming the motifs with higher coordination numbers.

**Metal-organic coordination networks on a titanium carbide MXene: DFT based grand canonical Monte Carlo simulation**, Vitaly A. Gorbunov, Anastasiia I. Uliankina, Pavel V. Stishenko, Alexander V. Myshlyavtsev,

**J. Phys. Rev. E**, 2022. DOI: 10.1016/j.apsusc.2022.153834.

**Abstract:**The self-assembly of 2D metal–organic networks comprising 1,3,5-tris (pyridyl)benzene (TPyB) molecules and copper atoms on the oxygen-terminated titanium carbide MXene surface was theoretically investigated. We have developed a lattice model of the TPyB-Cu networks on the energetically heterogeneous Ti2CO2(0001) surface. The model based on DFT calculations of the structure and energy of key adsorption complexes and metal–organic structures. Using the grand canonical Monte Carlo method, we have calculated and analyzed adsorption isotherms, structure, potential energy, and heat capacity of the adlayer. Due to steric hindrances in the three-fold Cu-TPyB junction, metal–organic structures consisting of only two-fold Cu-TPyB coordination motifs predominantly emerge on the Ti2CO2(0001) surface: honeycomb (HON), honeycomb filled with Cu3TPyB (HON + Cu3TPyB) and zigzag (ZZ) phases. These phases differ in the local environment of the copper adatoms. Thermal stability of the phases decreases in the following series: ZZ, HON + Cu3TPyB and HON. Self-assembly of these structures offers the opportunity to stabilize and “tune” properties of the single-atom Cu/Ti2CO2(0001) catalyst. We hope that our results will stimulate further experimental studies of hybrid “metal–organic network/MXene” catalysts.

**Surface hydrogenation of oxygen terminated MXenes M2CO2 (M = Ti, V, Nb)**, Tatyana R. Kayumova a, Ilay P. Kolganov a, Alexander V. Myshlyavtsev a, Pavel V. Stishenko a b, Anastasiia I. Fadeeva a,

**J. Phys. Rev. E**, 2021. DOI: 10.1016/j.susc.2021.121984.

**Abstract:**We have investigated reduction of MXenes M2CO2 (M = Ti, V, Nb) surface by hydrogen using density functional theory and statistical physics methods. We have approximated lateral interactions between adsorbed hydrogen with simple pairwise potential. We have confirmed model stability via cross-validation. Adsorption isotherms are calculated using Metropolis Monte Carlo method. We have built analytical Langmuir-like approximation of calculated isotherms. Ordered phases with 1/3 and 2/3 ML coverage are visually observed at low temperatures. At temperatures above 300 K no obvious plateau is observed, and intermediate phases does not exist. We compared adsorptive properties of MXenes at the same external conditions.

**Simple lattice model of self-assembling metal–organic layers of pyridyl-substituted porphyrins and copper on Au(111) surface**, Anastasiia I. Fadeeva, Vitaly A. Gorbunov, Alexander V. Myshlyavtseva,

**J. Phys. Rev. E**, 2021. DOI: 10.1039/D1CP03111B.

**Abstract:**A simple lattice model of metal–organic adsorption layers self-assembling on a Au(111) surface and based on pyridyl-substituted porphyrins differing in the number of functional groups and their position has been proposed. The model has been parameterized using DFT methods. The ground state analysis of the considered model demonstrates the variety of surface-confined metal–organic networks (SMONs) containing square, linear, and discrete elements appearing in the adsorption layer depending on the partial pressure of the components. The SMONs comprising more symmetrical molecules with a greater number of pyridyl substituents in the porphyrin core exhibit more diverse phase behavior. Structures of the phase diagrams were verified at nonzero temperatures using Grand Canonical Monte Carlo simulations. It was found that the continuous SMONs have higher thermal stability at relatively low partial pressures of the organic component, while the linear and discrete SMONs are more thermally stable at high pressure. Depending on the partial pressure of the organic component, thermal destruction of continuous SMONs occur either through the formation of defects/islands having structures of the linear SMONs, or through the sublimation of individual structural elements. Melting of linear SMONs reveals the appearance of 2D pores or islands of a purely organic phase. The latter fact is confirmed by the experimentally observed coexistence of these phases.

**Melting of Fe-terephthalate layers on Cu (1 0 0) surface with randomly distributed point defects**, Anastasiia I Fadeeva, Vitaly A Gorbunov, Pavel V Stishenko, Sergey S Akimenko, Alexander V Myshlyavtsev,

**J. Phys. Chem. C**, 2021. DOI: 10.1016/j.apsusc.2021.148989.

**Abstract:**In this theoretical work, we study the influence of the concentration and type of randomly distributed point defects on crystalline solid surfaces on the possibility of self-assembly and thermal stability of surface confined metal-organic networks (SMON). As an example, we chose fundamentally different and well-studied SMONs of Fe-terephthalate on Cu(1 0 0) surface: cloverleaf and single-row structures. Using parallel tempering Monte Carlo simulation, we have determined the concentration thresholds for various types of defects above which the SMONs self-assembly is unfavorable. It is shown that the SMONs melting temperatures decrease equally with an increase in the surface concentration of point defects, regardless of the SMON type. Maximum decrease in the SMON melting temperature relative to the homogeneous surface reaches 15–23%, depending on the defect type. Melting of a more “rigid” single-row structure formed only by the coordination bonds is found to occur through the first-order phase transition, while the cloverleaf structure, stabilized mainly by weak hydrogen bonds and long-range substrate mediated interactions, is a continuous phase transition.

**Homologous Series of Flower Phases in Metal–Organic Networks on Au(111) Surface**, A. I. Fadeeva, V. A. Gorbunov, O. S. Solovyeva, P. V. Stishenko, and A. V. Myshlyavtsev,

**J. Phys. Chem. C**, 2020. DOI: 10.1021/acs.jpcc.0c02527.

**Abstract:**Supramolecular coordination self-assembly on the solid surface offers great possibilities for creating nanostructures and thin films with unique physicochemical properties. In this work, we present a simple lattice model based on competitive coordination motifs that enables prediction of the phase behavior and thermal stability of metal–organic networks consisting of 1,3,5-tris(pyridyl)benzene (TPyB) and transition metals on Au(111) surface. The main parameter of the model is the ratio between the energies of the two-fold and three-fold metal–ligand coordination defined by the type of the metal center. The model reveals a homologous series of flower phases that differ in the metal/ligand composition. Existing ranges of the phases, in terms of the chemical potential (or partial pressure) of the components, are determined by the mentioned ratio. The closer the value of this parameter is to unity the more diverse is the phase behavior of the metal–organic network. This ratio is always greater than unity and increases in the following series Ag, Cu, Ni, Co, Fe. The results of the Monte Carlo and tensor renormalization group calculations well reproduces the published experimental data on the self-assembly of metal–organic networks based on the TPyB linker. As an example, we has calculated the phase diagram of the TPyB–Cu/Au(111) adsorption layer and has estimated thermal stability of the phases. The honeycomb, flower-like and triangular close-packed phases are ascertained to be stable at room temperature. The remaining nanostructures appearing on the scanning tunneling microscopy images of this layer are apparently metastable.

**Classical lattice models with single-node interactions on hierarchical lattices: The two-layer Ising model**, A. V. Myshlyavtsev, M. D. Myshlyavtseva, and S. S. Akimenko,

**Physica A**, 2020. DOI: 10.1016/j.physa.2020.124919.

**Abstract:**A general approach is proposed for renormalization group transformations at arbitrary hierarchical lattices with two root nodes and the presence of single-node interactions (interactions between layers, magnetic field, chemical potential, etc.). The effectiveness of the proposed approach was shown for the two-layer Ising model in a zero magnetic field on the simplest representative of folded square hierarchical lattices. The phase diagram was investigated and the shift exponent (

*φ*) was calculated at various values of the interaction energy in each layer (

*J*) and between the layers (

_{1}, J_{2}*J*). The value

_{3}*φ*≈ 2.41 was obtained for identical interactions in the layers (

*J*). In the remaining cases (

_{1}= J_{2}*J*) the shift exponent turned out to be close to 0.5, which is consistent with the data for the square lattice. The exceptional case is

_{1}≠ J_{2}*J*> 0,

_{1}*J*> 0, and

_{2}*J*, where the transition shift exponent in the second layer takes the value 2.57.

_{1}≠ J_{2}**Tensor renormalization group study of hard-disk models on a triangular lattice**, S. S. Akimenko, V. A. Gorbunov, A. V. Myshlyavtsev, and P. V. Stishenko,

**Physical Review E**, 2019. DOI: 10.1103/PhysRevE.100.022108.

**Abstract:**High accuracy and performance of the tensor renormalization group (TRG) method have been demonstrated for the model of hard disks on a triangular lattice. We considered a sequence of models with disk diameter ranging from a to 2√3a, where a is the lattice constant. Practically, these models are good for approximate description of thermodynamics properties of molecular layers on crystal surfaces. Theoretically, it is interesting to analyze if and how this sequence converges to the continuous model of hard disks. The dependencies of the density and heat capacity on the chemical potential were calculated with TRG and transfer-matrix (TM) methods. We benchmarked accuracy and performance of the TRG method comparing it with TM method and with exact result for the model with nearest-neighbor exclusions (1NN). The TRG method demonstrates good convergence and turns out to be superior over TM with regard to considered models. Critical values of chemical potential (μ

_{c}) have been computed for all models. For the model with next-nearest-neighbor exclusions (2NN) the TRG and TM produce consistent results (μ

_{c}=1.75587 and μ

_{c}=1.75398 correspondingly) that are also close to earlier Monte Carlo estimation by Zhang and Deng. We found that 3NN and 5NN models shows the first-order phase transition, with close values of μ

_{c}(μ

_{c}=4.4488 for 3NN and 4.4<μ

_{c}<4.5 for 5NN). The 4NN model demonstrates continuous yet rapid phase transition with 2.65<μ

_{c}<2.7.

**Model of Fe-Terephthalate Ordering on Cu(100)**, A. I. Fadeeva, V. A. Gorbunov, P. V. Stishenko, and A. V. Myshlyavtsev,

**J. Phys. Chem. C**, 2019. DOI: 10.1021/acs.jpcc.9b02834.

**Abstract:**A lattice model of terephthalic acid (TPA) and iron ordering on the Cu(100) surface is proposed and investigated using Monte Carlo simulation in a grand canonical ensemble. We have an evidence that the emergence of all the experimentally observed metal–organic structures cannot be explained in terms of short-ranged interactions such as hydrogen bonding and metal–carboxylate coordination proposed and discussed in earlier papers. The self-assembly of the “cloverleaf” and “interlocked” structures requires the presence of long-ranged TPA–Fe interaction. The unidentate carboxylate–Fe interaction is demonstrated to be 0.6–0.7 times weaker as compared to the bidentate bond. The phase diagram with all the experimentally observed structures is obtained. It has been established that one type of the ladder structures distinguished on scanning tunneling microscopy images is a metastable state and not a phase in the thermodynamic sense. We have found two new metal–organic structures, which are missed in earlier studies, but apparently formed in the TPA–Fe/Cu(100) adsorption layer. The first one comprises the single −Fe–TPA– rows linked with the TPA molecules in dihapto hydrogen bond motif. This phase is characterized by the lowest density of the monolayer. Another phase is formed at high densities and composed of the alternating rows of “cloverleaves” and TPA molecules linked with a pair of Fe atoms.

**SuSMoST: Surface Science Modeling and Simulation Toolkit**, S. S. Akimenko, G. D. Anisimova, A. I. Fadeeva, V. F. Fefelov, V. A. Gorbunov, T. R. Kayumova, A. V. Myshlyavtsev, M. D. Myshlyavtseva, and P. V. Stishenko,

**ChemRxiv**, 2019. DOI: 10.26434/chemrxiv.8068307.v1.

**Abstract:**We offer the scientific community the Surface Science Modelling and Simulation Toolkit (SuSMoST), which includes a number of utilities and implementations of statistical physics algorithms and models. With SuSMoST one is able to predict or explain the structure and thermodynamics properties of adsorption layers. SuSMoST automatically builds formal graph and tensor-network models from atomic description of adsorption complexes. So it can be routinely used for a wide class of adsorption systems. SuSMoST aids ab initio calculations of interactions between adsorbed species. In particular it generates surface samples considering symmetry of adsorption complexes. Using methods of various nature SuSMoST generates representative samples of adsorption layers and computes its thermodynamics quantities such as mean energy, coverage, density, heat capacity. From these data one can plot phase diagrams of adsorption systems, assess thermal stability of self-assembled structures, simulate thermal desorption spectra, etc.

**Complete analysis of phase diversity of the simplest adsorption model of a binary gas mixture for all sets of undirected interactions between nearest neighbors**, V. F. Fefelov, A. V. Myshlyavtsev, and M. D. Myshlyavtseva,

**Adsorption**, 2019. DOI: 10.1007/s10450-019-00043-3.

**Abstract:**In this paper, a complete analysis of the phase diagrams of the model of adsorption of a binary gas mixture on a square lattice in the ground state for all sets of near undirected interactions between particles was performed. Using the principle of minimum of a large thermodynamic potential in a stable phase, the partition of the model parameter space (the energies of lateral interactions) into regions differing by the type of the phase diagram was constructed. Also, for some regions, partial and total coverages as functions of chemical potentials of the gases were calculated through transfer-matrix method and presented. The work is an extension of the work (Fefelov in Phys Chem Chem Phys 20(15): 10359–10368, 2018).

**Bridging the gap between theory and experiment for self-assembly on surfaces**

**15th European Vacuum Conference**, 17-22 June 2018, Geneva, Switzerland.

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**Qualitative DFT study of lateral interactions between nitrogen molecules adsorbed on a V**, T. R. Kayumova and P. V. Stishenko,

_{3}C_{2}MXene sheet**AIP Conference Proceedings**, 2018. DOI: 10.1063/1.5051853.

**Abstract:**In this study, we calculated the lateral interactions of the nitrogen molecule on the V

_{3}C

_{2}surface by the DFT. The calculations were performed using the local density approximation. To calculate the energies of the lateral interactions, we calculated the energy of the cells with different degrees of surface coverage. The results of the calculations showed that lateral interactions are repulsive on the investigated distance range, and their strength decreases monotonically with distance, unlike some other systems with strong binding energy on metals. At distances greater than 2a the mutual orientation of the molecules has little effect on the energy of lateral interactions. Thermodynamic characteristics of the adsorption monolayer has been studied with the SuSMoST code - phase diagram was plotted and adsorption isotherms were analyzed.

**Modeling of self-assembling monolayer of terephthalic acid and iron on the copper surface: Intermolecular interactions and the ground state**, A. I. Fadeeva, V. A. Gorbunov, and P. V. Stishenko,

**AIP Conference Proceedings**, 2018. DOI: 10.1063/1.5051848.

**Abstract:**In this paper we investigated the adsorption layer of terephthalic acid molecules and Fe atoms on Cu(100) surface. On the basis of the experimentally obtained structures, a lattice gas model is developed and further analysis of its ground state is carried out. It has been found that various ordered phases appear when the TPA-Fe coordination interactions are at least twice stronger than the TPA-TPA hydrogen bonds. Under this condition, if we change the interaction energy between TPA and Fe, there is no qualitative change in the diagram. In the ground state, we observe all the experimentally found structures, with the exception of one unstable configuration, which is considered to be a mixture of several phases. Knowing the suggested relation between the hydrogen bonds and coordination interactions, we have simulated the adsorption layer using the Monte Carlo method at room temperature. Separate islets of the investigated phases were obtained. The results are in good agreement with the calculated ground state diagram.

**Phase diversity in an adsorption model of an additive binary gas mixture for all sets of lateral interactions**, V. F. Fefelov, A. V. Myshlyavtsev, and M. D. Myshlyavtseva,

**Physical Chemistry Chemical Physics**, 2018. DOI: 10.1039/C7CP08426A.

**Abstract:**Complete analysis of phase behavior of an adsorption model of a binary gas mixture on a square lattice was carried out for all possible sets of lateral interactions between nearest adsorbed molecules of the same type and no interaction between adsorbed molecules of different types. The model was completely investigated in the ground state, and it was shown that the phase behavior of the system is conserved at finite temperatures by means of a transfer-matrix method.

**Remnants of the devil's staircase of phase transitions in the model of dimer adsorption at nonzero temperature**, S. S. Akimenko, V. F. Fefelov, A. V. Myshlyavtsev, and P. V. Stishenko,

**Physical Review B**, 2018. DOI: 10.1103/PhysRevB.97.085408.

**Abstract:**The model of dimers adsorption on hexagonal lattice with different orientations to surface and hard-spheres lateral interactions has been studied at nonzero temperature. The transfer-matrix method was used as the main one and the Monte Carlo method was used for checking of some extreme cases. Adsorption isotherms, dependencies of the entropy from the density of the adsorption layer and of the energy from the system temperature at certain points of the phase space, were computed. It was found that at least the first ten phases of the ground state still persist at nonzero temperatures.

**Cross-impact of surface and interaction anisotropy in the self-assembly of organic adsorption monolayers: a Monte Carlo and transfer-matrix study**, V. A. Gorbunov, S. S. Akimenko, and A. V. Myshlyavtsev,

**Physical Chemistry Chemical Physics**, 2017. DOI: 10.1039/C7CP01863K.

**Abstract:**Using a simple lattice gas model we study the features of self-assembly in adsorption layers where both “molecule–surface” and “molecule–molecule” interactions are anisotropic. Based on the example of adsorption layers of mono-functional organic molecules on the heterogeneous surface with strip-like topography, we have revealed plenty of possible self-assembled structures in this simple system, such as discrete, linear, zigzag, chess board-like, two-dimensional porous and close-packed patterns. However, the phase behavior of the adsorption layer is much richer, if the interactions between functional and non-functional parts of adjacent adsorbed molecules have comparable strength and opposite signs. It is demonstrated that filling of the strips composed of relatively “strong” adsorption sites with the increase of chemical potential can be non-monotonic. This effect is associated with surface anisotropy and results from the changing of the driving force of the self-assembly process – interactions between the adsorbed molecule and the surface dominate at low surface coverages, but intermolecular forces prevail at higher ones. Additionally, when the width of the strip composed of “strong” adsorption sites is two or more times greater than that of the adsorbed molecule, a local assembly of the ordered phases on the “strong” adsorption sites is observed. Our results suggest strategies for controlling the self-assembly in experiments involving mono-functional organic molecules on a strip-like heterogeneous surface.

**Adsorption of ethylene on Cu(410): A transfer-matrix and Monte Carlo study**, S. I. Evseeva, V. A. Gorbunov, A. V. Myshlyavtsev, and M. D. Myshlyavtseva,

**Surface Science**, 2017. DOI: 10.1016/j.susc.2017.06.016.

**Abstract:**Using the combination of Monte Carlo and transfer-matrix methods, we study the joint influence of the external (gas phase) pressure and temperature on the structure and thermodynamic properties of the ethylene adsorption layer on Cu(410) surface. It is found that the energies of interactions between the ethylene molecules adsorbed on the step-edge and terrace sites are different. Such interaction anisotropy and the actual heterogeneity of Cu(410) surface lead to the following sequence of the ordered phases in the adsorption overlayer with increase of the gas phase pressure. Phase 1/2S consisting of the alternating π-complexes and empty sites at the step-edge of the terraces (the surface coverage θ equals to 0.125) is formed continuously from the clean surface. Further increase of the pressure leads to the sequential appearance of the S (θ = 0.25) and S + T

_{2}(θ = 0.5) phases, wherein the step-edge and middle rows of the terrace are occupied by the ethylene π-complexes, respectively. We reveal that the adsorption on the middle row of the terrace can be described with 1D Langmuir model.

**Generalized lattice-gas model for adsorption of functional organic molecules in terms of pair directional interactions**, S. S. Akimenko, V. A. Gorbunov, A. V. Myshlyavtsev, and P. V. Stishenko,

**Physical Review E**, 2016. DOI: 10.1103/PhysRevE.93.062804.

**Abstract:**A generalized lattice-gas model that takes into account the directional character of pair interactions between the lattice sites is proposed. It is demonstrated that the proposed model can be successfully used to deeply understand the self-assembly process in adsorption monolayers of functional organic molecules driven by specified directional interactions between such molecules (e.g., hydrogen bonding). To illustrate the idea, representative cases of the general model with different numbers of identical functional groups in the chemical structure of the adsorbed molecule are investigated with Monte Carlo and the transfer-matrix methods. The model reveals that the phase behavior of the adsorption systems considered can be characterized as a hierarchical self-assembly process. It is predicted that in real adsorption systems of this type, the energy of hydrogen bonding sufficiently depends on the mutual orientation of the adsorbed molecules.

**Monte Carlo study of adsorption of additive gas mixture**, V. F. Fefelov, P. V. Stishenko, V. M. Kutanov, A. V. Myshlyavtsev, and M. D. Myshlyavtseva,

**Adsorption**, 2016. DOI: 10.1007/s10450-015-9753-x.

**Abstract:**The monolayer adsorption of binary gas mixture on a square lattice has been investigated through grand canonical Monte Carlo method and transfer matrix technique. Repulsive and attractive lateral interactions have been introduced between the adsorbed particles for one component of the gas mixture and for another, respectively, at the same time the particles of different components of the gas mixture have not interacted. The model has been studied in the ground state and at finite temperatures. Interesting features of the phase behavior of the gas mixture adlayer were observed and discussed. The model shows that a simultaneous increasing of the chemical potentials of both gas components can lead to displacing of particles of one component on the surfaces by particles of another component.

**Potential of lateral interactions of CO on Pt (111) fitted to recent STM images**, A. V. Myshlyavtsev, and P. V. Stishenko,

**Surface Science**, 2015. DOI: 10.1016/j.susc.2015.08.018.

**Abstract:**Monolayers of carbon monoxide (CO) on Pt(111) surfaces are one of the most studied adsorption systems. However, molecular models of this system still do not take into account the reliable potential of lateral interactions between adsorbed CO molecules. Recent advances in experimental technique have brought high-resolution real-space images of CO/Pt(111) monolayers. For example, Yang et al. (J. Phys. Chem. C 117 (2013) 16429–16437) found island structures for coverages from 0.11 to 0.25 ML. In this study we have shown that these island structures can be explained with long-range oscillating lateral interactions. Parameters of the proposed potential were fitted to experimental scanning tunneling microscopy images with a series of Monte Carlo simulations.