## 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.

Download## Mentions in the media:

**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...
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**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).
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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.
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**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.
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## Recent studies conducted with SuSMoST:

**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.

**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.