About qCat

KIST's thematic platfroms were built to offer research environment of material simulations, even to the experimentalists and students who never learned simulations. This platform provides computing facilities and all kinds of software for simulations; atomic structure modeling programs, simulation solvers (DFT, MD, MC, and many others), solver GUI and data visualization programs. You don’t need any further software and computers but web browsers.

The qCat is the thematic (or application-oriented) web-platform that provides comprehensive functions for atomistic modeling of catalysts. Various simulation methods such as Monte Carlo (MC), kinetic Monte Carlo (kMC), molecular dynamics (MD) and density functional theory (DFT) are implemented, and almost all parameters were preset so that even unexperienced users can do serious simulations. The qCat is a application-oriented platform (or thematic platform); it is specialized for specific properties or application (e.g. catalysts) of certain types of materials (e.g. metals) but methods are unlimited. The oxygen reduction reaction (ORR) is implemented to the current version of qCat.

The qCat has functions of building atomic structure of catalysts, finding a thermally stable structure, calculating electronic structures of catalysts, calculating adsorption energies of all related chemicals, drawing reaction diagram, checking catalytic poisoning, analyzing stress, and checking chemical stability. All those functions are free to use.

The qCat is consist of Lobby and four Labs. In the Lobby, users check the list of "samples", which are atomisitic models of catalysts, and status of the their own simulations. Examples are also provided. Available functions and simulation procedurs are dependent on the purpose of the sample ("For Activity" or "For Stability"). Check the "How to use?" for more informaiton.

Powered by SimPL!

The qCat was developed using SimPL: the Simulation Platform Creator, which is the contents management system of simulation web software and platforms. Visit the SimPL webpage for detail.

The qCat is the thematic (or application-oriented) web-platform that provides comprehensive functions for atomistic modeling of catalysts. Various simulation methods such as Monte Carlo (MC), kinetic Monte Carlo (kMC), molecular dynamics (MD) and density functional theory (DFT) are implemented, and almost all parameters were preset so that even unexperienced users can do serious simulations. The qCat is a application-oriented platform (or thematic platform); it is specialized for specific properties or application (e.g. catalysts) of certain types of materials (e.g. metals) but methods are unlimited. The oxygen reduction reaction (ORR) is implemented to the current version of qCat.

The qCat has functions of building atomic structure of catalysts, finding a thermally stable structure, calculating electronic structures of catalysts, calculating adsorption energies of all related chemicals, drawing reaction diagram, checking catalytic poisoning, analyzing stress, and checking chemical stability. All those functions are free to use.

The qCat is consist of Lobby and four Labs. In the Lobby, users check the list of "samples", which are atomisitic models of catalysts, and status of the their own simulations. Examples are also provided. Available functions and simulation procedurs are dependent on the purpose of the sample ("For Activity" or "For Stability"). Check the "How to use?" for more informaiton.

Policies

Free to use for registered users. Commercial usage is not allowed.

Please cite qCat if you publish or present results from qCat.

Registration

Register with your business email, and send your information to contact email. You will get an email from us after we upgrade your authority.

Powered by SimPL!

The qCat was developed using SimPL: the Simulation Platform Creator, which is the contents management system of simulation web software and platforms. Visit the SimPL webpage for detail.

Support

The qCat project was supported by Nano·Material Technology Development Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (Grant. NRF-2016M3A7B4024131).

The computing resource is provied by Computational Science Research Center at KIST

Contact

sckim@kist.re.kr

The qCat Team

PI: Dr Seungchul Kim (KIST)

SimPL, front-end web program: Virtual Lab Inc. (Semi Jang, Yerang Ryu, Minho Lee, and Jungho Lee)

Modeling Lab: Virtual Lab Inc. (Semi Jang, Minho Lee, and Jungho Lee)

Sample Analysis Lab: Computational Science Research Center at KIST (Seungchul Kim, Doyeon Kim)

Activity Lab: Korea Instute of Energy Research (Chanwoo Lee's group), Computational Science Research Center at KIST (Seungchul Kim, Doyeon Kim)

Stability Lab: Pohang University of Science and Technology - POSTECH (Byeong Joo Lee's group)

PI: Dr Seungchul Kim (KIST)

SimPL, front-end web program: Virtual Lab Inc. (Semi Jang, Yerang Ryu, Minho Lee, and Jungho Lee)

Modeling Lab: Virtual Lab Inc. (Semi Jang, Minho Lee, and Jungho Lee)

Sample Analysis Lab: Computational Science Research Center at KIST (Seungchul Kim, Doyeon Kim)

Activity Lab: Korea Instute of Energy Research (Chanwoo Lee's group), Computational Science Research Center at KIST (Seungchul Kim, Doyeon Kim)

Stability Lab: Pohang University of Science and Technology - POSTECH (Byeong Joo Lee's group)

Any simulation needs an atomistic model of the materials, which is called "sample".

In this page, we will construct several samples with VLatoms in Modeling Lad as a practice.

About VLAtoms

VLAtoms is the visualizer in qCat. If you click right side of your mouse, there is tool box which helps you customize your visualizer.Supported format: VLAtoms in qCat is the minimum version, and it support VASP-POSCAR, cif and xyz format. If your atomic structure file is in other format, you can convert it to POSCAR using other free SW, such as VESTA. Or you may use full version of VLAtoms in https://www.materialssquare.com/

Example 1 : Surface modeling

In this paragraph, Pt FCC crystal structure will be created with crystal builder and Pt (111) surface will be constructed with several options.
Example 2 : Particle modeling

Save sample

Save your sample by setting the calculation option as “For Activity” for DFT calculation or “For Stability” for MC and MD calculation. Also, set proper periodic boundary condition.Pt-based catalysts have been considered the most efficient catalysts for the oxygen reduction reaction (ORR) but exorbitant cost of Pt and designing DOS profiles for efficiency have leaded to alloy catalyst materials research.[1] Moreover, the research has been accelerated with recent result from nanosize effect that offers a chance to find alloy systems that are the immiscible type under ambient conditions in bulk system.[2] Sample Analysis Lab in qCat provides GUI for calculating optimized structure and electronic properties for catalytic materials.

How to use?

1. In "Structure Stabilizer" tab, select the relaxation option depends on the character of the sample system and get the optimized structure by clicking run button.2. Since the platform automatically gets electronic structure information from optimized structure, click "Electronic Structure" tab and visualize or download the electronic properties information. It offers Density of states (DOS), d band center map, and local potential map.

Structure Stablizer

Every structure should go through structure relaxation. From the stable structure, electronic structure will be calculated. There are two options to get optimized structure. First, "Variable cell relax" which is the option that sets for 'vc-relax' in Quantum ESPRESSO and both cell and atoms are changed to fine optimum energy status and atomic structure. Use this option when there is a possibility of considerable cell size change. For instance, modified structure from the default which is offered by qCat, like Pt3Co1 alloys. The other is "Fixed cell relax" which is equivalent to "Relax" option in QE. To be specific, the unit cell is fixed but only atoms there are moving. Use this option when cell size or lateral lattice constant is well known.

For more specific information about calculation setting, please check "Computational detail".

Electronic Structures

First, atomic structure of material should be optimized in “Structure Stabilizer” tab and if the sample reaches energetically stable structure, you can check its electronic properties through “Electronic structure” tab.Density of State (DOS)

Designing the electronic structure of materials is one of the best ways to tune the material properties because not only physical properties such as magnetic and electrical properties but also chemical properties such as catalytic properties are closely related to the density of states (DOS) of solids.[3][4] In particular, for catalytic reactions, the local DOS (LDOS), which is a projection of DOS to each atom, of the surface atoms is supposed to be more important than the total DOS of a bulk solid because reactants interact with atoms on a solid surface, and the catalytic activity is crucially affected by the binding energy of reactants on the catalyst surface.[5]Therefore, qCat offers LDOS diagram of the optimized sample and the UI can selectively visualize LDOS depends on each orbitals or atoms. To be specific, selecting “DOS” in selection tab and clicking the “Run” button will generate the dos visualizer and the pop-up massage. If the massage shows that DOS is ready, choose the atoms by clicking the tabs in “Select", right below the atomic structure visualizer and click “Add” button.

d-band Center Map

Since the binding energy of OH and OOH has linear relation with O binding energy, it is important to find proper determinant that represents adsorption energy of O with material.
Figure 1. Comparison of DFT-based oxygen chemisorption energies, E(O/surface) - 1/2E(O2) - E (surface) (PW91), experimental values, and model estimates of the bond strengths for the various close-packed transition and noble metal surfaces. Data represented by open circles were determined by using the Newns–Anderson model. The experimental values are from Toyoshima and Somorjai[6]. (Bottom) The calculated adsorption energies correlate well with the d band center ed.[6]

Local Potential Map

We offer cube files for the local potential of the sample. if you click the “Run" button local potential map selected, you can download cube files and this can be visualized in VESTAComputational detail

- Theory : Kohn-Sham Density functional theory (DFT)
- Software : Quantum ESPRESSO V.6.6 [11]
- Functional : RPBE [12]
- Pseudopotential: PBE potential from GBRV v1.5 [13, 14] and SSSP efficient [15, 16]
- k-point: k spacing = 0.041 reciprocal lattice (i.e. one kpt in 30 Ang cell)
- Kinetic energy cutoff for wavefunctions : 40 Ry
- Kinetic energy cutoff for electron density: 320 Ry
- Spin : spin-polarized calculation (colinear spin)
- SCF energy tolerance : 1.0e-8 Ry
- Force tolerance for relaxation : 0.025 eV/Ang

- cell_dofree = '2Dxy' : only x and y components are allowed to change
- Pressure tolerance : 0.3 kbar

** An example** of 2x2 of Pt (111) surface relaxation is below.

&CONTROL prefix = 'qCat' restart_mode = 'from_scratch' calculation = 'vc-relax' pseudo_dir = './' outdir = './output/' nstep = 1000 forc_conv_thr = 0.001 verbosity='high' tprnfor = .TRUE. disk_io = 'default' wf_collect = .TRUE. / &SYSTEM ecutwfc = 40, ecutrho = 320 ntyp = 1, nat = 20 ibrav = 0 occupations = 'smearing', smearing='gaussian', degauss = 0.002, nspin=2 nosym = .TRUE. input_dft = 'RPBE' starting_magnetization(1)=0.2 / &ELECTRONS mixing_mode = 'plain' mixing_beta = 0.10 conv_thr = 1.0e-6 electron_maxstep = 300 startingwfc = 'random' diagonalization = 'david' / &IONS ion_dynamics = 'bfgs' upscale = 100 / &CELL cell_dynamics = 'bfgs' cell_dofree = '2Dxy' / ATOMIC_SPECIES Pt 195.078 pt_pbe_v1.4.uspp.F.UPF CELL_PARAMETERS (Angstrom) 5.63156844 0 0 -2.81578398 4.87708092 0 0 0 22 K_POINTS (automatic) 5 5 1 0 0 0 ATOMIC_POSITIONS (angstrom) Pt 1.40789199 0.81284678 10.3615808 Pt 0 0 8.22386742 Pt 0 1.62569368 6.0671711 ...

References

[1]Wang, Xiaoqian, et al. "Review of metal catalysts for oxygen reduction reaction: from nanoscale engineering to atomic design." Chem 5.6 (2019): 1486-1511.

[2]Kusada, Kohei, and Hiroshi Kitagawa. "A route for phase control in metal nanoparticles: a potential strategy to create advanced materials." Advanced Materials 28.6 (2016): 1129-1142.

[3]Kittel, C. "Introduction to Solid State Physics . John Wiley& Sons." Inc., New York (2004).

[4]Hoffmann, R. "Solids and Surfaces: A Chemist's View of Bonding in Extended Structures. VCH Publ." Inc., New York (1988).

[5]Kusada, Kohei, et al. "Emergence of high ORR activity through controlling local density-of-states by alloying immiscible Au and Ir." Chemical science 10.3 (2019): 652-656.

[6]Toyoshima, I., and G. A. Somorjai. "Heat of hydrogen and oxygen adsorption." Catal Rev Sci Eng 19 (1979): 105.

[7]Rossmeisl, Jan, Ashildur Logadottir, and Jens Kehlet Nørskov. "Electrolysis of water on (oxidized) metal surfaces." Chemical physics 319.1-3 (2005): 178-184.

[8]Nørskov, Jens Kehlet, et al. "Origin of the overpotential for oxygen reduction at a fuel-cell cathode." The Journal of Physical Chemistry B 108.46 (2004): 17886-17892.

[9]Hammer, Bjørk, and Jens Kehlet Nørskov. "Theoretical surface science and catalysis—calculations and concepts." Advances in catalysis 45 (2000): 71-129.

[10]Demiroglu, Ilker, et al. "A DFT study of molecular adsorption on Au–Rh nanoalloys." Catalysis Science & Technology 6.18 (2016): 6916-6931.

[11]Quantum ESPRESSO: P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. De Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A.P. Seitsonen, A. Smogunov, P. Umari, R.M. Wentzcovitch, QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials, J. Phys. Condens. Matter. (2009). https://doi.org/10.1088/0953-8984/21/39/395502.

[12] B. Hammer, L. B. Hansen, and J. K. Nørskov, "Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals", Phys. Rev. B 59, 7413 (1999).

https://doi.org/10.1103/PhysRevB.59.7413

[13] Kevin F.Garrity, Joseph W.Bennett, Karin M.Rabe, and DavidVanderbilt, "Pseudopotentials for high-throughput DFT calculations", Computational Materials Science 81, 446 (2014)

[14] https://www.physics.rutgers.edu/gbrv/

[15] psuedo-potential: SSSP efficient.

[16] Elements not in GBRV v1.5 but from SSSP: Ar, Bi, Ce, Dy, Er, Eu, Gd, He, Ho, Kr, Lu, Nd, Ne, Pm, Po, Pr, Rn, Sm, Tb, Tm, Xe, Yb

Computation setting and option are explained in "DFT calculation setting".

1. Adsorption Analysis

1-1. Surface atom extraction for various nanostructures

For adsorption energy calculation, we do not have to consider every single atom. Contribution of the atoms covered by others would be much smaller than the surface ones, which are exposed therefore very likely to be adsorption sites. It would be much efficient to deal with only surface atoms.

In order to extract surface atoms on an arbitrary structure, i.e. crystal structures with periodic boundary condition (PBC), nanoparticles in vacuum, even amorphous and wavy 2D structures, we have applied a self-structure analysis using the Voronoi Tessellation in the 3 x 3 x 3 supercell. The periodicity in 3 axes, the maximum internal distance, angles between two neighbor atoms, and distances to the atom over the cell boundary if the neighbor is beyond it were analyzed. Moreover, principal component analysis (PCA) assisted by fast Fourier transformation (FFT) was also applied to detect a local 2-dimensional structure which should be classified as surface atoms.

The surface atom extraction results are visualized in the figure below. Green and red indicate surface atoms and blue represents not surface atoms, i.e. atoms located below the surface.

The current limitation:

Our algorithm has difficulties in detecting large-sized pores of which diameter is ~10 atoms. Some atoms at the innermost layer of multi-walled carbon nanotubes and nanoporous materials could not be detected as surface. (See the figure below of multi-walled tubes.) There was a controversy to classify atoms as surface or not at the development stage, finally we decided to leave it as is. If one has such structures which does not work properly, please request to the developers with the sample structures.

1-2. Automatic selection and screening of molecule adsorption sites

It would be reasonable to assume that the adsorption sites of a given surface can be classified by the local geometry around the considered surface atoms. To screen the unique surface atoms from the all surface atoms, the code makes the list of the chemical species and the bond lengths of the nearest neighbor (NN) atoms from every surface atoms. When we search the NN atoms, we divide NN among surface atoms (NN from surface) and NN among bulk atoms (NN from bulk). As a result, we can obtain the NN information as shown in below example. If two surface atoms have same chemical species and bond lengths are same in descending order of bond lengths, we consider those two atoms have identical local geometries. We confirm that a change of the bond lengths and order can depict the change of the other local geometry features such as angles between bonds, coordination number, etc.

As a result, all surface atoms can be classifies in groups that members of each group have same local geometry. Only one surface atom representing each group is chosen to search the adsorption site. The code selects the representing atom that has highest z-axis position for convenience. The right image of above figure shows an example of the screened 25 unique surface atoms from 328 surface atoms from TiO2 nanoparticle.

Once positions of the unique surface atoms are obtained, the code search three types of possible molecular adsorption site as below:

1) On-top sites : On-top sites are easily defined from the position of unique surface atoms.

2) Bridge sites : From the information of ‘NN from surface’ of each unique surface atoms, the code search all the bridges between the considered surface atom and its NN surface atoms. Then the unique bridges are screened that each screened bridges have different local geometry. The center of a given bridge is used as the bridge site.

3) Hollow sites : Starting from the bridges already screened, the 3-ring and 4-ring connections between NN atoms are searched for each bridges. The center of 3-ring or 4-ring atoms is defined as the hollow site. Again the unique hollow sites are screened that consisting atoms have different local geometry.

The below figures show the example of screened bridges and hollows.

For each adsorption sites, the adsorption vector (direction and length) must be decided. To determine the most perpendicular vector from the various types of surface (nanoparticles, wavy thin film, amorphous, etc), the code calculate the adsorption unit vector as shown in below figure.

For the length of adsorption vector, the code use the sum of covalent radii of the surface atom and edge atom of adsorbent. For each type of sites below criteria is used to roughly consider the different local geometry of on-top, bridge, and hollow sites.

- On-top site : (r_{a}+r_{b})*0.95

- Bridge site : (r_{a}+r_{b})*0.75

- Hollow site : (r_{a}+r_{b})*0.55

, where r_{a} and r_{b} are covalent radii of two adjacent atomns.
For orientation of the adsorbed molecule, the code automatically rotate the molecule with respect to the adsorption vector. For ORR, initial orientations of the considered molecules are set to make bond with oxygen. Below figures show the example adsorption structures.

2. Reaction Diagram

2-1. Reaction Mechanism of ORR

The oxygen reduction reaction (ORR) is a fundamental reaction utilized in a broad range of technological applications such as metal dissolution, biology or energy conversion. Recently, ORR has attracted a huge attention in energy converting systems, e.g. fuel cells or lithium ion batteries due to the fact that the slow kinetics of the ORR limits applications of fuel cells or lithium ion batteries. Thus, it is important to understand the mechanism of the ORR on various catalysts in order to develop new catalysts with better performance. However, the mechanism of the electrochemical ORR remains still unclear since the ORR is known to be a quite complicated process, which involves many intermediates. Thus, our qCAT platform is designed to predict and provide catalytic performance of various kinds of catalysts with an efficient way.

ORR mainly occurs in two pathways; the direct 4-electron reduction pathway from O

(1)

In this platform, the free energy of each ORR step and its final ORR energy diagram is determined by the so-called computational hydrogen electrode (CHE) model suggested by Nørskov [1]. The free energy of each ORR step in which an electrochemical proton-electron transfer occurs is a function of the applied electrical potential and 0 V is defined where the electrochemical proton-electron transfer reaction, is defined to be in equilibrium at 0 V, at all values of pH, at all temperatures, and with H

(2)

2-2. DFT Calculations for ORR Energy Diagram

The free energy of each ORR step can be directly obtained by calculating total energies from DFT calculations as shown in Eqs. (3).

(3)

(4)

where * indicates the surface of catalysts, thus O* means the system where O is adsorbed on the surface. The free energy as a function of an applied potential and pH is defined as and , respectively. The overpotentials are defined as

(5)

Finally, the 4-electron ORR energy diagram can be obtained by simply using the qCat plaform. The figures below are examples from the platform. Note that the total enegies are taken from Ref. [2-4].

[1] J. K. Nørskov et al., J. Phys. Chem. B 108, 17886 (2004).

[2] H. A. Hansen, et al., Phys. Chem. Chem. Phys. 10, 3722 (2008).

[3] M. Li, et al., J. Catal. 314, 66 (2014).

[4] I. C. Man, et al., Chem. Cat. Chem. 3, 1159 (2011).

How to use?

Second nearest-neighbor modified embedded-atom-method (2NN MEAM)

Second nearest-neighbor modified embedded-atom-method (2NN MEAM) potential is a semi-empirical interatomic potential, which enable atomistic simulation with over millions of atoms, commonly used in metal systems. It describe the atomic potentials of various elements with various crystal structures using single formalism.

F is the embedding function, ρ is the background electron density, S is screening function and φij(R) is the pair interaction between atoms i and j at a distance R.

Several approaches have been proposed the form of the embedding function and the pair potential and the calculating method of the background electron density, and various potential models such as EAM, MEAM, and 2NN MEAM are defined. 2NN MEAM include angular term in background electron density and screening function for second nearest neighbor atoms screened by first nearest atoms.

Detailed formalism can be found in the following reference papers[1-2].

1.Thermal Stabilizer

1.1 Monte Carlo Method and Metropolis algorithm

The Monte Carlo method is a method to find the highest probability state by introducing the concept of probability, which is used in various fields as well as the material field. In this stability lab, the Monte Carlo method finds the equilibrium structure by describing the diffusion as stochastic progression of the position exchange between nearest neighbor atoms. The method arbitrarily selects two nearest neighbor atoms, exchanges the positions of atoms with small displacement and calculates the energy difference from the exchange. The energy difference is replaced with the probability according to the following equation, Metropolis algorithm, and whether the exchange proceeds or not is determined by comparison with a random number.

In this way, you can see how the atomic distribution and surface segregation with the slab or particle of alloy system.

In addition, the overall shape of the particle does not change if the exchange of existing atoms is only considered. Therefore, additional vacancy sites on surface are created and considered as selectable site in the Monta Carlo method.

1.2 Limitation and Caution

(1) Thermal stabilizer only supports the FCC structure because the code finding vacancy sites on surface is only available for FCC structure yet.

(2) Before using the stability lab, make sure that the desired alloy is supported.

Stability Lab supports unary, binary and ternary systems of "Pt, Pd, Al, Co, Cu, Fe, Mo, Ni, Ti, V" excepting for the systems containing Pt and Pd.

(3) Before starting the simulation, make sure that the periodic boundary conditions (PBC) are set correctly.

For particles, do not apply PBC in all directions. For slabs, PBCs in all directions other than the surface direction must be applied.

(4) Phase transformation is hardly observed in this Monte Carlo simulation.

1.3 Example images

slab

particle

2.Stress Analyzer

2.1 Von Mises Stress Analysis

It has been found that durability of nano partilces is strongly related to von Mises stress (its mean value and distribution). See the reference[3] for the detail.

2.2 How to calculate Von Mises Stress in this module.s

In this stability laboratory, LAMMPS, the most widely used molecular dynamics program, and 2NN MEAM, the interatomic potential, are used to provide the Von Mises stresses of the desired alloy structure. Six stress tensor components are calculated for each atom and the stress is obtained from the stress tensor divided by the atomic volume. The actual atomic volume is approximated by the atomic volume of each element in a unary bulk system because it is difficult to calculate the exact atomic volume in an alloy system containing a surface. The stress analyzer provides the average Von Mises stress of the sample and the distribution of the Von Mises stress along the x, y, z or radial direction.

For more information on how to calculate the stress tensor in LAMMPS, please refer to the link below.

lammps.sandia.gov/doc/compute_stress_atom.html

3 Dissolution Test.

3.1 kinetic Monte Carlo method

The Monte Carlo simulation method (Metropolis algorithm in this case) has the advantage of reaching an equilibrium state, but also has the disadvantage that the process is unrealistic and the Monte Carlo step, which is the simulation time, is a virtual concept. To cover this, the proportions and probabilities of events were introduced[4]. The calculated rates of all events determine the probability weight of all events. The event determined by the weighted probability and random number is performed, and the event time is determined by the following equation. This method is called kinetic Monte Carlo method. It shows the realistic process and real-time scale.

3.2 Rate equation in this lab.

We employed kinetic Monte Carlo algorithm to simulate dissolution. It is most important to determine the event and rate of event in the kinetic Monte Carlo method. Dissolution and diffusion are considered as events in this dissolution test. The rate equations used in this lab are following equations for dissolution and diffusion, respectively.

The energy barrier was assumed in the form of a sigmoid function of energy difference before and after an event occurred in dissolution. The dissolution rate equation was adjusted to fit the results of the dissolution rate experiment of platinum nanoparticles [5]. The energy difference in the dissolution rate equation took into account the redox potential, applied voltage, and pH, as well as the difference in atomic potential energy from dissolution. The diffusion rate equation adopted the order of atomic oscillation frequencies for prefactor and the energy change in midway between the initial and final states for energy barrier.

Reference

[1] B.-J. Lee and M.I. Baskes, Phys. Rev. B 62, 8564 (2000) DOI : 10.1103/PhysRevB.62.8564

[2] B.-J. Lee, et al., CALPHAD, 34, 510 (2010) DOI : 10.1016/j.calphad.2010.10.007

[3] Sung-Yup Kim, Hong Woo Lee, Sung Jin Pai, and Sang Soo Han., ACS Appl. Mater. Interfaces, 10, 26188−26194 (2018) DOI : 10.1021/acsami.8b05070

[4] K.A. Fichthorn and W. H. Weinberg, J. Chem. Phys. 95 1090 (1991) DOI : 10.1063/1.461138

[5] S. Cherevko, G. P. Keeley, S. Geiger, A. R. Zeradjanin, N. Hodnik, N. Kulyk, K. J. J. Mayrhofer, ChemElectroChem, 2,1471–1478 (2015) DOI : 10.1002/celc.201500098

[6] J. Erlebacher, Michael J. Aziz, Alain Karma, Nikolay Dimitrov, Karl Sieradzki, Nature. 410, 450–453 (2001) DOI : 10.1038/35068529

[7] J. Erlebacher, J. Electrochem. Soc. 151, C614 (2004) DOI : 10.1149/1.1784820

[8] Andraž Pavlisič, Primož Jovanovic, Vid Simon Šelih, Martin Šala, Marjan Bele, Goran Drazič, Iztok Arcon, Samo Hocevar, Anton Kokalj, Nejc Hodnik, and Miran Gabersčeǩ, ACS Catal. 6, 5530–5534 (2016) DOI : 10.1021/acscatal.6b00557

[9] James G. Speight. Lange's handbook of chemistry 16th ed. McGraw-Hill. (2005)

[10] Sang-Ho Oh, Jin-Soo Kim, Chang Seo Park and Byeong-Joo Lee, Compu. Mater. Sci. (2021)

[11] Jaemin Wang and Byeong-Joo Lee, Compu. Mater. Sci. 188, 110177 (2021)

[12] Sang-Ho Oh, Donghyuk Seol and Byeong-Joo Lee, CALPHAD 70, 101791 (2020)

[13] Jaemin Wang, Sang-Ho Oh and Byeong-Joo Lee, Compu. Mater. Sci. 178, 109627 (2020)

[14] Ga-Un Jeong, Chang Seo Park, Hyeon-Seok Do, Seul-Mi Park and Byeong-Joo Lee, CALPHAD 62, 172-186 (2018)

[15] Jin-Soo Kim, Donghyuk Seol, Joonho Ji, Hyo-Sun Jang, Yongmin Kim, Byeong-Joo Lee, CALPHAD 59, 131-141 (2017)

[16] Jaesong Kim, Yangmo Koo and Byeong-Joo Lee, J. Materials Research 21, 199-208 (2006)

- Load the desired sample from the Sample Load tab.
- Set the temperature and step and run the thermal stabilizer before using other functions to get equilibrium state.
- Check the energy curve convergence.
- If the energy converges, run the desired stability test. The stress analyzer provides Von Mises stress and the stress distribution. The dissolution test provides the change of energy and the number of atoms.

Second nearest-neighbor modified embedded-atom-method (2NN MEAM)

Second nearest-neighbor modified embedded-atom-method (2NN MEAM) potential is a semi-empirical interatomic potential, which enable atomistic simulation with over millions of atoms, commonly used in metal systems. It describe the atomic potentials of various elements with various crystal structures using single formalism.

F is the embedding function, ρ is the background electron density, S is screening function and φij(R) is the pair interaction between atoms i and j at a distance R.

Several approaches have been proposed the form of the embedding function and the pair potential and the calculating method of the background electron density, and various potential models such as EAM, MEAM, and 2NN MEAM are defined. 2NN MEAM include angular term in background electron density and screening function for second nearest neighbor atoms screened by first nearest atoms.

Detailed formalism can be found in the following reference papers[1-2].

1.Thermal Stabilizer

1.1 Monte Carlo Method and Metropolis algorithm

The Monte Carlo method is a method to find the highest probability state by introducing the concept of probability, which is used in various fields as well as the material field. In this stability lab, the Monte Carlo method finds the equilibrium structure by describing the diffusion as stochastic progression of the position exchange between nearest neighbor atoms. The method arbitrarily selects two nearest neighbor atoms, exchanges the positions of atoms with small displacement and calculates the energy difference from the exchange. The energy difference is replaced with the probability according to the following equation, Metropolis algorithm, and whether the exchange proceeds or not is determined by comparison with a random number.

In this way, you can see how the atomic distribution and surface segregation with the slab or particle of alloy system.

In addition, the overall shape of the particle does not change if the exchange of existing atoms is only considered. Therefore, additional vacancy sites on surface are created and considered as selectable site in the Monta Carlo method.

1.2 Limitation and Caution

(1) Thermal stabilizer only supports the FCC structure because the code finding vacancy sites on surface is only available for FCC structure yet.

(2) Before using the stability lab, make sure that the desired alloy is supported.

Stability Lab supports unary, binary and ternary systems of "Pt, Pd, Al, Co, Cu, Fe, Mo, Ni, Ti, V" excepting for the systems containing Pt and Pd.

(3) Before starting the simulation, make sure that the periodic boundary conditions (PBC) are set correctly.

For particles, do not apply PBC in all directions. For slabs, PBCs in all directions other than the surface direction must be applied.

(4) Phase transformation is hardly observed in this Monte Carlo simulation.

1.3 Example images

slab

particle

2.Stress Analyzer

2.1 Von Mises Stress Analysis

It has been found that durability of nano partilces is strongly related to von Mises stress (its mean value and distribution). See the reference[3] for the detail.

2.2 How to calculate Von Mises Stress in this module.s

In this stability laboratory, LAMMPS, the most widely used molecular dynamics program, and 2NN MEAM, the interatomic potential, are used to provide the Von Mises stresses of the desired alloy structure. Six stress tensor components are calculated for each atom and the stress is obtained from the stress tensor divided by the atomic volume. The actual atomic volume is approximated by the atomic volume of each element in a unary bulk system because it is difficult to calculate the exact atomic volume in an alloy system containing a surface. The stress analyzer provides the average Von Mises stress of the sample and the distribution of the Von Mises stress along the x, y, z or radial direction.

For more information on how to calculate the stress tensor in LAMMPS, please refer to the link below.

lammps.sandia.gov/doc/compute_stress_atom.html

3 Dissolution Test.

3.1 kinetic Monte Carlo method

The Monte Carlo simulation method (Metropolis algorithm in this case) has the advantage of reaching an equilibrium state, but also has the disadvantage that the process is unrealistic and the Monte Carlo step, which is the simulation time, is a virtual concept. To cover this, the proportions and probabilities of events were introduced[4]. The calculated rates of all events determine the probability weight of all events. The event determined by the weighted probability and random number is performed, and the event time is determined by the following equation. This method is called kinetic Monte Carlo method. It shows the realistic process and real-time scale.

3.2 Rate equation in this lab.

We employed kinetic Monte Carlo algorithm to simulate dissolution. It is most important to determine the event and rate of event in the kinetic Monte Carlo method. Dissolution and diffusion are considered as events in this dissolution test. The rate equations used in this lab are following equations for dissolution and diffusion, respectively.

The energy barrier was assumed in the form of a sigmoid function of energy difference before and after an event occurred in dissolution. The dissolution rate equation was adjusted to fit the results of the dissolution rate experiment of platinum nanoparticles [5]. The energy difference in the dissolution rate equation took into account the redox potential, applied voltage, and pH, as well as the difference in atomic potential energy from dissolution. The diffusion rate equation adopted the order of atomic oscillation frequencies for prefactor and the energy change in midway between the initial and final states for energy barrier.

Reference

[1] B.-J. Lee and M.I. Baskes, Phys. Rev. B 62, 8564 (2000) DOI : 10.1103/PhysRevB.62.8564

[2] B.-J. Lee, et al., CALPHAD, 34, 510 (2010) DOI : 10.1016/j.calphad.2010.10.007

[3] Sung-Yup Kim, Hong Woo Lee, Sung Jin Pai, and Sang Soo Han., ACS Appl. Mater. Interfaces, 10, 26188−26194 (2018) DOI : 10.1021/acsami.8b05070

[4] K.A. Fichthorn and W. H. Weinberg, J. Chem. Phys. 95 1090 (1991) DOI : 10.1063/1.461138

[5] S. Cherevko, G. P. Keeley, S. Geiger, A. R. Zeradjanin, N. Hodnik, N. Kulyk, K. J. J. Mayrhofer, ChemElectroChem, 2,1471–1478 (2015) DOI : 10.1002/celc.201500098

[6] J. Erlebacher, Michael J. Aziz, Alain Karma, Nikolay Dimitrov, Karl Sieradzki, Nature. 410, 450–453 (2001) DOI : 10.1038/35068529

[7] J. Erlebacher, J. Electrochem. Soc. 151, C614 (2004) DOI : 10.1149/1.1784820

[8] Andraž Pavlisič, Primož Jovanovic, Vid Simon Šelih, Martin Šala, Marjan Bele, Goran Drazič, Iztok Arcon, Samo Hocevar, Anton Kokalj, Nejc Hodnik, and Miran Gabersčeǩ, ACS Catal. 6, 5530–5534 (2016) DOI : 10.1021/acscatal.6b00557

[9] James G. Speight. Lange's handbook of chemistry 16th ed. McGraw-Hill. (2005)

[10] Sang-Ho Oh, Jin-Soo Kim, Chang Seo Park and Byeong-Joo Lee, Compu. Mater. Sci. (2021)

[11] Jaemin Wang and Byeong-Joo Lee, Compu. Mater. Sci. 188, 110177 (2021)

[12] Sang-Ho Oh, Donghyuk Seol and Byeong-Joo Lee, CALPHAD 70, 101791 (2020)

[13] Jaemin Wang, Sang-Ho Oh and Byeong-Joo Lee, Compu. Mater. Sci. 178, 109627 (2020)

[14] Ga-Un Jeong, Chang Seo Park, Hyeon-Seok Do, Seul-Mi Park and Byeong-Joo Lee, CALPHAD 62, 172-186 (2018)

[15] Jin-Soo Kim, Donghyuk Seol, Joonho Ji, Hyo-Sun Jang, Yongmin Kim, Byeong-Joo Lee, CALPHAD 59, 131-141 (2017)

[16] Jaesong Kim, Yangmo Koo and Byeong-Joo Lee, J. Materials Research 21, 199-208 (2006)

In this page, we will simulate oxide reduction reaction of Pt (111) slab with Modeling, Sample Ananlysis and Activity Lab.

How to use?

- Build and save the sample in Modeling Lab.
- In Sample Analysis Lab, run Structure Stabilizer with proper calculation option. This step takes several hours or days.
- Load Electronic structure data in Sample Analysis Lab.
- With optimized structure, generate moleculars' sites for Pt (111) surface and calculate the lowest energy and the orientation of total system, the catalysis with a molecule.
- Draw reaction diagram with several systems.

In this page, we will simulate oxide reduction reaction of Pt_{3}Ni (111) slab with Modeling, Sample Ananlysis and Activity Lab. Most of the process is similar with Example 1 so check Example 1; Pt (111) surface.

How to use?

1. Build and save the sample in Modeling Lab. 2. In Sample Analysis Lab, run Structure Stabilizer with proper calculation option. This step takes several hours or days.

3. Load Electronic structure data in Sample Analysis Lab.

4. With optimized structure, generate moleculars' sites for Pt (111) surface and calculate the lowest energy and the orientation of total system, the catalysis with a molecule.

5. Draw reaction diagram with several systems.

In this page, we will simulate Pt3Co 1nm particle with Modeling and Stability Lab.

How to use?

1. Build and save the sample in Modeling Lab. 2. In Stability Lab, run Thermal Stabilizer with proper calculation option. This step takes several hours or days.

Everything is repeated infinitely.

Except molecules and sub-nm particles, materials consists of vast amount of atoms, so it is not able to take every individual atom into account to the calculations. To solve this problem in atomistic modelling, people conventionally assumes that a group of atoms repeats periodically to form a large object, similar to single crystal in crystallography, and this is called the periodic boundary condition (PBC). In PBC, there is a unit cell which is defined by three cell vectors and atoms in it, and the unit cell is repeated in all three directions, just like a single crystal. However, even things that are not actually repetitive are repeated in PBC, such as atomic defect in solids or adsorbed chemicals on solid surfaces. The PBC is a mathematical tools that allows computation of large size of materials, comparing to atomic size, with limited computational resources.

**Be careful! You have to consider whether your ‘periodic’ model structure is suitable to describe real material. **

How large vacuum?

At least 10 Angstrom of vacuum between neighbor unit cell is neccessary, 15-20 Angstrom is recommended.

Suppose you are simulating surface of a solid, and the z-axis is the surface normal direction in your atomistic model, you may want to make half-infinite surface model that infinitely thick material and vacuum are facing with each other. However, such structure is impossible because every thing, including empty space, is periodic. Therefore, there is no choice but to make space between atoms in the neighbor unit cells so that interaction between them to be ignorable.

How to set "Periodic Boundary" at the Modeling Lab.

Check all three (x, y and z). It is 3-D structures, and there is no vacuum in any direction.

Un-check the surface normal direction in "Periodic Boundary" It is for surfaces of solids and 2-D materials, such as Pt (111), graphene and MoS

1D structure needs vacuum in two directions. If the wire axis is parallel to the z-axis, uncheck x and y, and check z. Insert vacuum in x and y directions.

Uncheck all directions (x, y and z) and insert vacuum.

What happens if "Periodic Boundary" is improperly set?

Regardless of checking x, y and z in "Periodic Boundary" in the Modeling Lab, the atomic structure is periodic. But, "Periodic Boundary" affects speed and accuracy of the calculations. If 'z' is un-checked, number of k-point in 'z' direction for structure stabilizer, DOS and optical calculation set to be 1. If it is checked for the direction having vacuum, the calculation results are accurate but it may takes longer time than it should be. If it is un-checked for the direction having no vacum, the results may not be accurate.

How to check atomic structure outside the unitcell?

Use the "Ghosts" in VLAtoms. Click the right button in the VLAtoms (atomic structure visulaizer) and check "Ghosts". Atoms in the neighbor unit cells will be shown. Computational detail

- Theory : Kohn-Sham Density functional theory (DFT)
- Software : Quantum ESPRESSO V.6.6 [11]
- Functional : RPBE [12]
- Pseudopotential: PBE potential from GBRV v1.5 [13, 14] and SSSP efficient [15, 16]
- k-point: k spacing = 0.041 reciprocal lattice (i.e. one kpt in 30 Ang cell)
- Kinetic energy cutoff for wavefunctions : 40 Ry
- Kinetic energy cutoff for electron density: 320 Ry
- Gaussian smearing = 2 mRy
- Spin : spin-polarized calculation (colinear spin without spin-orbit coupling (SOC) interaction)
- SCF converence thershold : 1.0e-8 Ry
- Force thershold for relaxation : 0.025 eV/Ang

- cell_dofree = '2Dxy' : only x and y components are allowed to change
- Pressure tolerance : 0.3 kbar

Sample Analysis Lab: no geometric constraint for "variable unit cell" calculation, cell vectors are fixed for "fixed unit cell".

Activity Lab: Cell vectors are fixed, and bottom three layers are fixed as well. (See the example below.)

** An example** of 2x2 of Pt (111) surface relaxation (in the **Sample Analysis Lab**)

&CONTROL prefix = 'qCat' restart_mode = 'from_scratch' calculation = 'vc-relax' pseudo_dir = './' outdir = './output/' nstep = 1000 forc_conv_thr = 0.001 verbosity='high' tprnfor = .TRUE. disk_io = 'default' wf_collect = .TRUE. / &SYSTEM ecutwfc = 40, ecutrho = 320 ntyp = 1, nat = 20 ibrav = 0 occupations = 'smearing', smearing='gaussian', degauss = 0.002, nspin=2 nosym = .TRUE. input_dft = 'RPBE' starting_magnetization(1)=0.2 / &ELECTRONS mixing_mode = 'plain' mixing_beta = 0.10 conv_thr = 1.0e-6 electron_maxstep = 300 startingwfc = 'random' diagonalization = 'david' / &IONS ion_dynamics = 'bfgs' upscale = 100 / &CELL cell_dynamics = 'bfgs' cell_dofree = '2Dxy' / ATOMIC_SPECIES Pt 195.078 pt_pbe_v1.4.uspp.F.UPF CELL_PARAMETERS (Angstrom) 5.63156844 0 0 -2.81578398 4.87708092 0 0 0 22 K_POINTS (automatic) 5 5 1 0 0 0 ATOMIC_POSITIONS (angstrom) Pt 1.40789199 0.81284678 10.3615808 Pt 0 0 8.22386742 Pt 0 1.62569368 6.0671711 ...

** An example** of O adsorption on 2x2 Pt (111) surface (in the **Activity Lab**)

Note that, three layers from the bottom are fixed during the adsorption calculation, while no one is fixed during relaxation in the Sample Analysis Lab.

&CONTROL prefix = 'qCat' restart_mode = 'from_scratch' calculation = 'relax' pseudo_dir = './' outdir = './output/' nstep = 1000 forc_conv_thr = 0.001 verbosity='high' tprnfor = .TRUE. wf_collect = .TRUE. / &SYSTEM ecutwfc = 40 , ecutrho = 320 ntyp = 2, nat = 21 ibrav = 0 occupations = 'smearing', smearing='gaussian', degauss = 0.002, nspin=2 nosym = .TRUE. input_dft = 'RPBE' starting_magnetization(1)=0.2 starting_magnetization(2)=0.2 / &ELECTRONS mixing_mode = 'plain' mixing_beta = 0.10 conv_thr = 1.0e-6 electron_maxstep = 300 startingwfc = 'random' diagonalization = 'david' / &IONS ion_dynamics = 'bfgs' upscale = 100 / !! CELL will be ignored for "calculation = 'relax'". &CELL cell_dynamics = 'bfgs', cell_dofree = '2Dxy', press_conv_thr = 0.3, / ATOMIC_SPECIES Pt 195.078 pt_pbe_v1.4.uspp.F.UPF O 15.9994 O.pbe-n-kjpaw_psl.0.1.UPF CELL_PARAMETERS (Angstrom) 5.6315700000000000 0.0000000000000000 0.0000000000000000 -2.8157800000000002 4.8770800000000003 0.0000000000000000 0.0000000000000000 0.0000000000000000 22.0000000000000000 K_POINTS (automatic) 5 5 1 0 0 0 ATOMIC_POSITIONS (angstrom) O -1.3579322175969248 4.114258669925789 12.048499999873801 1 1 1 Pt 2.815760175499999 3.2514029236 10.692 1 1 1 Pt 4.223650175499999 0.8128629236000001 10.692 1 1 1 Pt -2.48244999999e-05 3.2514029236 10.692 1 1 1 Pt 1.4078651755 0.8128629236000001 10.692 1 1 1 Pt 1.407895 2.43854 8.35274 1 1 1 Pt 2.815785 0.0 8.35274 1 1 1 Pt -1.4078899999999999 2.43854 8.35274 1 1 1 Pt 0.0 0.0 8.35274 1 1 1 Pt 1.4079248244999998 4.0642170764 6.06716 0 0 0 Pt 2.8158148245 1.6256770764000001 6.06716 0 0 0 Pt -1.4078601755000002 4.0642170764 6.06716 0 0 0 Pt 2.98245e-05 1.6256770764000001 6.06716 0 0 0 Pt 2.815760175499999 3.2514029236 3.7815800000000004 0 0 0 Pt 4.223650175499999 0.8128629236000001 3.7815800000000004 0 0 0 Pt -2.48244999999e-05 3.2514029236 3.7815800000000004 0 0 0 Pt 1.4078651755 0.8128629236000001 3.7815800000000004 0 0 0 Pt 1.407895 2.43854 1.4423199999999998 0 0 0 Pt 2.815785 0.0 1.4423199999999998 0 0 0 Pt -1.4078899999999999 2.43854 1.4423199999999998 0 0 0 Pt 0.0 0.0 1.4423199999999998 0 0 0

References

[1]Wang, Xiaoqian, et al. "Review of metal catalysts for oxygen reduction reaction: from nanoscale engineering to atomic design." Chem 5.6 (2019): 1486-1511.

[2]Kusada, Kohei, and Hiroshi Kitagawa. "A route for phase control in metal nanoparticles: a potential strategy to create advanced materials." Advanced Materials 28.6 (2016): 1129-1142.

[3]Kittel, C. "Introduction to Solid State Physics . John Wiley& Sons." Inc., New York (2004).

[4]Hoffmann, R. "Solids and Surfaces: A Chemist's View of Bonding in Extended Structures. VCH Publ." Inc., New York (1988).

[5]Kusada, Kohei, et al. "Emergence of high ORR activity through controlling local density-of-states by alloying immiscible Au and Ir." Chemical science 10.3 (2019): 652-656.

[6]Toyoshima, I., and G. A. Somorjai. "Heat of hydrogen and oxygen adsorption." Catal Rev Sci Eng 19 (1979): 105.

[7]Rossmeisl, Jan, Ashildur Logadottir, and Jens Kehlet Nørskov. "Electrolysis of water on (oxidized) metal surfaces." Chemical physics 319.1-3 (2005): 178-184.

[8]Nørskov, Jens Kehlet, et al. "Origin of the overpotential for oxygen reduction at a fuel-cell cathode." The Journal of Physical Chemistry B 108.46 (2004): 17886-17892.

[9]Hammer, Bjørk, and Jens Kehlet Nørskov. "Theoretical surface science and catalysis—calculations and concepts." Advances in catalysis 45 (2000): 71-129.

[10]Demiroglu, Ilker, et al. "A DFT study of molecular adsorption on Au–Rh nanoalloys." Catalysis Science & Technology 6.18 (2016): 6916-6931.

[11]Quantum ESPRESSO: P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. De Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A.P. Seitsonen, A. Smogunov, P. Umari, R.M. Wentzcovitch, QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials, J. Phys. Condens. Matter. (2009). https://doi.org/10.1088/0953-8984/21/39/395502.

[12] B. Hammer, L. B. Hansen, and J. K. Nørskov, "Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals", Phys. Rev. B 59, 7413 (1999).

https://doi.org/10.1103/PhysRevB.59.7413

[13] Kevin F.Garrity, Joseph W.Bennett, Karin M.Rabe, and DavidVanderbilt, "Pseudopotentials for high-throughput DFT calculations", Computational Materials Science 81, 446 (2014)

[14] https://www.physics.rutgers.edu/gbrv/

[15] psuedo-potential: SSSP efficient.

[16] Elements not in GBRV v1.5 but from SSSP: Ar, Bi, Ce, Dy, Er, Eu, Gd, He, Ho, Kr, Lu, Nd, Ne, Pm, Po, Pr, Rn, Sm, Tb, Tm, Xe, Yb

Single atom calculations

GBRV v1.5 ( https://www.physics.rutgers.edu/gbrv)

SSSP: C, H, O, N, P, Ar, Bi, Ce, Dy, Er, Eu, Gd, He, Ho, Kr, Lu, Nd, Ne, Pm, Po, Pr, Rn, Sm, Tb, Tm, Xe, Y

- Quantum ESPRESSO v 6.6
- Ecutwfc = 40 Ry, Ecutrho = 320 Ry
- Cell = 11 x 12 x 12 Ang
^{3} - spin colinear polarization (SOC is not included.)
- k-point = Γ-point
- conv_th = 5.0E-7 Ry
- assume_isolated = 'mt'
- degauss = 2 mRy (if occupation = 'smearing')
- The minimum energy case was choisen among three calculations; occupation='fixed', starting_magnetization = 0.2 or 1.0 for occupation = 'smearing'

Note: E

Note: Electronic configurations of Tb, Gd, W, V, Ti and Zr are different from the real. Especially, Gd and Tb have partially occupied atomic orbitals. For *occupation = 'fixed'*, two or three different tot_magnetization were tried, beside from *occupation = 'smearing'* calculations, for these six elemetns.

Note:

Symbol | UPF | E_{tot}(Ryd) | E_{tot}(eV) | TS (meV) | mag. (μ_{B}) |
---|---|---|---|---|---|

Ag | ag_pbe_v1.4.uspp.F.UPF | -295.53361367 | -4020.97124087 | 0.00 | 1 |

Al | al_pbe_v1.uspp.F.UPF | -6.49382356 | -88.35366459 | 0.00 | 1 |

Ar | Ar_ONCV_PBE-1.1.oncvpsp.upf | -42.27878046 | -575.23663118 | 0.00 | 0 |

As | as_pbe_v1.uspp.F.UPF | -40.15890283 | -546.39400012 | 0.00 | 3 |

Au | au_pbe_v1.uspp.F.UPF | -114.86798088 | -1562.87077426 | 0.00 | 1 |

Ba | ba_pbe_v1.uspp.F.UPF | -70.21025348 | -955.26666680 | 0.00 | 0 |

Be | be_pbe_v1.4.uspp.F.UPF | -28.05371628 | -381.69325296 | 0.00 | 0 |

Bi | Bi_pbe_v1.uspp.F.UPF | -185.19805147 | -2519.76764869 | 0.00 | 3 |

B | b_pbe_v1.4.uspp.F.UPF | -5.96934221 | -81.21767624 | 0.00 | 1 |

Br | br_pbe_v1.4.uspp.F.UPF | -46.82955604 | -637.15357357 | 0.00 | 1 |

Ca | ca_pbe_v1.uspp.F.UPF | -74.85259631 | -1018.42945487 | 0.00 | 0 |

Cd | cd_pbe_v1.uspp.F.UPF | -114.77238095 | -1561.57006073 | 0.00 | 0 |

Ce | Ce.GGA-PBE-paw-v1.0.UPF | -482.47002064 | -6564.39060682 | 0.00 | 2 |

Cl | cl_pbe_v1.4.uspp.F.UPF | -33.23661669 | -452.21075936 | 0.00 | 1 |

Co | co_pbe_v1.2.uspp.F.UPF | -298.21788418 | -4057.49288858 | 0.00 | 3 |

C | C.pbe-n-kjpaw_psl.1.0.0.UPF | -17.99539901 | -244.84179985 | 0.00 | 2 |

Cr | cr_pbe_v1.5.uspp.F.UPF | -175.28978974 | -2384.95782124 | 0.00 | 6 |

Cs | cs_pbe_v1.uspp.F.UPF | -63.08899970 | -858.37631212 | 0.00 | 1 |

Cu | cu_pbe_v1.2.uspp.F.UPF | -403.63710426 | -5491.80571314 | 0.00 | 1 |

Dy | Dy.GGA-PBE-paw-v1.0.UPF | -777.95297341 | -10584.67256562 | 0.00 | 4 |

Er | Er.GGA-PBE-paw-v1.0.UPF | -886.62607886 | -12063.25710375 | 0.00 | 2 |

Eu | Eu.GGA-PBE-paw-v1.0.UPF | -643.20846821 | -8751.36577677 | 0.00 | 7 |

Fe | fe_pbe_v1.5.uspp.F.UPF | -250.08865173 | -3402.65617771 | 0.00 | 4 |

F | f_pbe_v1.4.uspp.F.UPF | -48.44489768 | -659.13158885 | 0.00 | 1 |

Ga | ga_pbe_v1.4.uspp.F.UPF | -415.28048259 | -5650.22319002 | 0.00 | 1 |

Gd | Gd.GGA-PBE-paw-v1.0.UPF | -684.56365622 | -9314.03619380 | 15.35 | 7.01 (8) |

Ge | ge_pbe_v1.4.uspp.F.UPF | -213.52317842 | -2905.15366095 | 0.00 | 2 |

He | He_ONCV_PBE-1.0.oncvpsp.upf | -5.61078694 | -76.33924495 | 0.00 | 0 |

Hf | hf_pbe_v1.uspp.F.UPF | -158.61574673 | -2158.09412686 | 0.00 | 2 |

Hg | hg_pbe_v1.uspp.F.UPF | -107.85503116 | -1467.45398296 | 0.00 | 0 |

Ho | Ho.GGA-PBE-paw-v1.0.UPF | -830.31652220 | -11297.12053775 | 0.00 | 3 |

H | H.pbe-rrkjus_psl.1.0.0.UPF | -1.01009173 | -13.74310606 | 0.00 | 1 |

In | in_pbe_v1.4.uspp.F.UPF | -133.40606161 | -1815.09619305 | 0.00 | 1 |

I | i_pbe_v1.uspp.F.UPF | -65.65933262 | -893.34774776 | 0.00 | 1 |

Ir | ir_pbe_v1.2.uspp.F.UPF | -181.35126422 | -2467.42903072 | 0.00 | 3 |

K | k_pbe_v1.4.uspp.F.UPF | -56.98833069 | -775.37182970 | 0.00 | 1 |

Kr | Kr_ONCV_PBE-1.0.oncvpsp.upf | -37.22857813 | -506.52458832 | 0.00 | 0 |

La | la_pbe_v1.uspp.F.UPF | -102.35580935 | -1392.63267085 | 0.01 | 1 |

Li | li_pbe_v1.4.uspp.F.UPF | -14.41742709 | -196.16062950 | 0.00 | 1 |

Lu | Lu.GGA-PBE-paw-v1.0.UPF | -1080.79266626 | -14705.04885860 | 0.00 | 1 |

Mg | mg_pbe_v1.4.uspp.F.UPF | -125.32131053 | -1705.09668681 | 0.00 | 0 |

Mn | mn_pbe_v1.5.uspp.F.UPF | -211.02469022 | -2871.15973020 | 0.00 | 5 |

Mo | mo_pbe_v1.uspp.F.UPF | -138.95588131 | -1890.60592993 | 0.00 | 6 |

Na | na_pbe_v1.5.uspp.F.UPF | -95.36164320 | -1297.47144505 | 0.00 | 1 |

Nb | nb_pbe_v1.uspp.F.UPF | -117.49569099 | -1598.62287247 | 0.00 | 5 |

Nd | Nd.GGA-PBE-paw-v1.0.UPF | -537.95423484 | -7319.29772839 | 0.00 | 4 |

Ne | Ne_ONCV_PBE-1.0.oncvpsp.upf | -60.90237818 | -828.62557704 | 0.00 | 0 |

Ni | ni_pbe_v1.4.uspp.F.UPF | -343.03962697 | -4667.32855663 | 0.00 | 2 |

N | N.pbe-n-radius_5.UPF | -19.85687013 | -270.16860361 | 0.00 | 3 |

O | O.pbe-n-kjpaw_psl.0.1.UPF | -41.45437184 | -564.01989238 | 0.00 | 2 |

Os | os_pbe_v1.2.uspp.F.UPF | -198.06198142 | -2694.79170680 | 0.00 | 4 |

Pb | pb_pbe_v1.uspp.F.UPF | -164.04985745 | -2232.02955049 | 0.00 | 2 |

Pd | pd_pbe_v1.4.uspp.F.UPF | -198.52590164 | -2701.10371253 | 0.00 | 0 |

Pm | Pm.GGA-PBE-paw-v1.0.UPF | -569.91097631 | -7754.09476148 | 0.00 | 5 |

Po | Po.pbe-dn-rrkjus_psl.1.0.0.UPF | -195.48706906 | -2659.75796422 | 0.00 | 2 |

P | P.pbe-n-rrkjus_psl.1.0.0.UPF | -13.82319627 | -188.07564381 | 0.00 | 3 |

Pr | Pr.GGA-PBE-paw-v1.0.UPF | -508.85360567 | -6923.36038802 | 0.00 | 3 |

Pt | pt_pbe_v1.4.uspp.F.UPF | -210.39108432 | -2862.53901504 | 0.00 | 2 |

Rb | rb_pbe_v1.uspp.F.UPF | -53.16078066 | -723.29494950 | 0.00 | 1 |

Re | re_pbe_v1.2.uspp.F.UPF | -190.18806122 | -2587.66072335 | 0.00 | 5 |

Rh | rh_pbe_v1.4.uspp.F.UPF | -170.87451893 | -2324.88452966 | 0.00 | 3 |

Rn | Rn.pbe-dn-kjpaw_psl.1.0.0.UPF | -1028.27711111 | -13990.53271834 | 0.00 | 0 |

Ru | ru_pbe_v1.2.uspp.F.UPF | -193.85212190 | -2637.51320015 | 0.00 | 4 |

Sb | sb_pbe_v1.4.uspp.F.UPF | -184.86414117 | -2515.22453193 | 0.00 | 3 |

Sc | sc_pbe_v1.uspp.F.UPF | -94.09682215 | -1280.26254281 | 0.00 | 1 |

Se | se_pbe_v1.uspp.F.UPF | -43.50630718 | -591.93811423 | 0.00 | 2 |

Si | si_pbe_v1.uspp.F.UPF | -9.29690552 | -126.49183712 | 0.00 | 2 |

Sm | Sm.GGA-PBE-paw-v1.0.UPF | -604.94184256 | -8230.71772150 | 0.00 | 6 |

Sn | sn_pbe_v1.4.uspp.F.UPF | -159.11526812 | -2164.89051499 | 0.00 | 2 |

S | s_pbe_v1.4.uspp.F.UPF | -23.92708042 | -325.54707078 | 0.00 | 2 |

Sr | sr_pbe_v1.uspp.F.UPF | -70.09303854 | -953.67186377 | 0.00 | 0 |

Ta | ta_pbe_v1.uspp.F.UPF | -141.38190245 | -1923.61388835 | 0.00 | 3 |

Tb | Tb.GGA-PBE-paw-v1.0.UPF | -729.40281292 | -9924.10879203 | 9.89 | 5.35 (5) |

Tc | tc_pbe_v1.uspp.F.UPF | -173.85702486 | -2365.46390884 | 0.00 | 5 |

Te | te_pbe_v1.uspp.F.UPF | -26.37694675 | -358.87946209 | 0.00 | 2 |

Ti | ti_pbe_v1.4.uspp.F.UPF | -118.94617034 | -1618.35780441 | 10.32 | 4 (2) |

Tl | tl_pbe_v1.2.uspp.F.UPF | -144.92409177 | -1971.80820780 | 0.00 | 1 |

Tm | Tm.GGA-PBE-paw-v1.0.UPF | -947.09999589 | -12886.05312408 | 0.00 | 1 |

V | v_pbe_v1.4.uspp.F.UPF | -144.76727061 | -1969.67453047 | 0.14 | 5 (3) |

W | w_pbe_v1.2.uspp.F.UPF | -158.62462470 | -2158.21491874 | 0.00 | 6 (4) |

Xe | Xe_ONCV_PBE-1.1.oncvpsp.upf | -231.88290591 | -3154.95244123 | 0.00 | 0 |

Yb | Yb.GGA-PBE-paw-v1.0.UPF | -1011.88597154 | -13767.51815158 | 0.00 | 0 |

Y | y_pbe_v1.4.uspp.F.UPF | -92.59067605 | -1259.77022020 | 0.00 | 1 |

Zn | zn_pbe_v1.uspp.F.UPF | -461.59002376 | -6280.30154527 | 0.00 | 0 |

Zr | zr_pbe_v1.uspp.F.UPF | -98.76983607 | -1343.84263560 | 0.00 | 4 (2) |

Pseudo-potentials listed below are not used in qCat

Symbol | UPF | E_{tot}(Ryd) | E_{tot}(eV) | TS (meV) | mag. (μ_{B}) |
---|---|---|---|---|---|

C | c_pbe_v1.2.uspp.F.UPF | -10.95134075 | -149.00175198 | 0.00 | 2 |

H | h_pbe_v1.4.uspp.F.UPF | -1.01031765 | -13.74617988 | 0.00 | 1 |

O | o_pbe_v1.2.uspp.F.UPF | -31.98997181 | -435.24915845 | 0.00 | 2 |

N | n_pbe_v1.2.uspp.F.UPF | -19.80575883 | -269.47319349 | 0.00 | 3 |

P | p_pbe_v1.5.uspp.F.UPF | -15.30546938 | -208.24315529 | 0.00 | 3 |

Hf | hf_pbe_plus4_v1.uspp.F.UPF | -158.43114314 | -2155.58244733 | 0.00 | 2 |

H02 | H025_pbr.UPF | -0.03678029 | -0.50042527 | 6.11 | 0.25 |

H03 | H033_pbr.UPF | -0.06885592 | -0.93683988 | 7.00 | 0.33 |

H05 | H050_pbr.UPF | -0.18652686 | -2.53784715 | 7.68 | 0.50 |

H06 | H066_pbr.UPF | -0.39255412 | -5.34101285 | 7.00 | 0.67 |

H07 | H075_pbr.UPF | -0.49248700 | -6.70067962 | 6.11 | 0.75 |

H10 | H100_pbr.UPF | -1.00862611 | -13.72316513 | 0.00 | 1 |

H12 | H125_pbr.UPF | -1.69407674 | -23.04926931 | 6.11 | 0.75 |

H13 | H133_pbr.UPF | -1.99168634 | -27.09848600 | 7.00 | 0.67 |

H15 | H150_pbr.UPF | -2.68155526 | -36.48470456 | 7.68 | 0.50 |

H16 | H166_pbr.UPF | -3.53453341 | -48.09015467 | 7.00 | 0.33 |

H17 | H175_pbr.UPF | -4.01537891 | -54.63244237 | 6.11 | 0.25 |

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The project qCat was supported by Nano·Material Technology Development Program

through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT.

through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT.