## What is/are Atomistic Thermodynamics?

Atomistic Thermodynamics - Periodic spin unrestricted DFT+U calculations joined with atomistic thermodynamics and model catalytic experiments (TPD-O2, 18O2/16O4 exchange, N2O decomposition, CO and CH4 oxidation) were used to study the structure, stability and reactivity of various surface oxygen species and oxygen vacancies, produced under different thermodynamic conditions on the (1 1 1) surface exposed by the cobalt spinel nanooctahedra.^{[1]}A mean-field kinetic theory under the steady-state approximation, combined with atomistic thermodynamics and Wulff construction, was developed to study the interplay between oxygen chemisorption, electrode potential, and particle size on the dissolution of Pt nanoparticles.

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## density functional theory

Through the combination of density functional theory calculations and ab initio atomistic thermodynamics modeling, we demonstrate that atomically dispersed platinum species on ceria can adopt a range of local coordination configurations and oxidation states that depend on the surface structure and environmental conditions.^{[1]}The program involves using density functional theory to predict stable surface phases under various conditions by way of ab initio atomistic thermodynamics.

^{[2]}We have used ab initio density functional theory together with ab initio atomistic thermodynamics, and in situ x-ray absorption near edge spectroscopy (XANES) experiments, to study the oxidation of sub-nanometer clusters of Cu n O x supported on a hydroxylated amorphous alumina substrate in an O2-rich environment.

^{[3]}The ground state electronic structure is very accurately calculated via density functional theory with hybrid functionals, whereas the finite T and $${{\boldsymbol{p}}}_{{{\bf{O}}}_{{\bf{2}}}}$$ pO2 effects are captured by ab initio atomistic thermodynamics under harmonic approximations.

^{[4]}This paper examines the thermodynamics of PtO2 stripes formed as intermediates of Pt(111) surface oxidation as a function of the degree of dilation parallel to the stripes, using density functional theory and atomistic thermodynamics.

^{[5]}Water adsorption and dissociation on clean and oxygen pre-covered Ni(111) surfaces have been computed systematically by using density functional theory and ab initio atomistic thermodynamics.

^{[6]}Our approach employs density-functional theory (DFT) combined with ab initio atomistic thermodynamics, where the free energy of formation due to vibration of phonons is duly considered under harmonic approximation.

^{[7]}Due to its importance in energy related catalytic reactions, H2O dissociative adsorption on clean and O pre-covered Ni(100) and Ni(110) surfaces has been computed systematically on the basis of periodic density functional theory and ab initio atomistic thermodynamics.

^{[8]}Here, we performed a thorough study to provide understanding of the influence of CO adsorption on theoretically established Ru nanoparticle models through an approach combining density functional theory, Wulff construction, and ab initio atomistic thermodynamics.

^{[9]}This is achieved by evaluating the free energy of the clusters and O2 analytically (via the ideal-gas approximation as implemented in ab initio atomistic thermodynamics) with Density Functional Theory (DFT) input.

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## Initio Atomistic Thermodynamics

By employing equilibrium ab initio atomistic thermodynamics and phonon spectra analysis a dynamically stable configuration have been found.^{[1]}Through the combination of density functional theory calculations and ab initio atomistic thermodynamics modeling, we demonstrate that atomically dispersed platinum species on ceria can adopt a range of local coordination configurations and oxidation states that depend on the surface structure and environmental conditions.

^{[2]}The program involves using density functional theory to predict stable surface phases under various conditions by way of ab initio atomistic thermodynamics.

^{[3]}We have used ab initio density functional theory together with ab initio atomistic thermodynamics, and in situ x-ray absorption near edge spectroscopy (XANES) experiments, to study the oxidation of sub-nanometer clusters of Cu n O x supported on a hydroxylated amorphous alumina substrate in an O2-rich environment.

^{[4]}The ground state electronic structure is very accurately calculated via density functional theory with hybrid functionals, whereas the finite T and $${{\boldsymbol{p}}}_{{{\bf{O}}}_{{\bf{2}}}}$$ pO2 effects are captured by ab initio atomistic thermodynamics under harmonic approximations.

^{[5]}Water adsorption and dissociation on clean and oxygen pre-covered Ni(111) surfaces have been computed systematically by using density functional theory and ab initio atomistic thermodynamics.

^{[6]}Our approach employs density-functional theory (DFT) combined with ab initio atomistic thermodynamics, where the free energy of formation due to vibration of phonons is duly considered under harmonic approximation.

^{[7]}The low-energy isomers are further analyzed via ab initio atomistic thermodynamics to estimate their free energy of formation at a realistic temperature T and partial pressure of oxygen pO2.

^{[8]}Due to its importance in energy related catalytic reactions, H2O dissociative adsorption on clean and O pre-covered Ni(100) and Ni(110) surfaces has been computed systematically on the basis of periodic density functional theory and ab initio atomistic thermodynamics.

^{[9]}Here, we performed a thorough study to provide understanding of the influence of CO adsorption on theoretically established Ru nanoparticle models through an approach combining density functional theory, Wulff construction, and ab initio atomistic thermodynamics.

^{[10]}The effects of carburization conditions in surface stability as well as catalyst morphology have also been researched by ab initio atomistic thermodynamics method.

^{[11]}This is achieved by evaluating the free energy of the clusters and O2 analytically (via the ideal-gas approximation as implemented in ab initio atomistic thermodynamics) with Density Functional Theory (DFT) input.

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## atomistic thermodynamics method

With the atomistic thermodynamics method, the equilibrium phase diagrams were built to show the relationship of stable CO concentration with temperature and CO partial pressure on each surface.^{[1]}Hydrogen adsorption configurations and stable concentrations on a group of MoP surfaces [(001), (100), (101), (102), (110), (111), (112)] at different conditions have been theoretically investigated with DFT and atomistic thermodynamics methods.

^{[2]}The effects of carburization conditions in surface stability as well as catalyst morphology have also been researched by ab initio atomistic thermodynamics method.

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