Article Cite This: Chem. Mater. 2018, 30, 6242−6248
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Material Genome Explorations and New Phases of Two-Dimensional MoS2, WS2, and ReS2 Monolayers Zhanghui Chen and Lin-Wang Wang* Materials Sciences Division, Lawrence Berkeley National Laboratory, One Cyclotron Road, Mail Stop 50F, Berkeley, California 94720, United States
Chem. Mater. 2018.30:6242-6248. Downloaded from pubs.acs.org by KAOHSIUNG MEDICAL UNIV on 11/10/18. For personal use only.
S Supporting Information *
ABSTRACT: Two-dimensional transition metal dichalcogenides have attracted intense interests in recent years. Existing studies have fully explored the properties of their ground-state structures, but their global energy landscapes are still not well understood. The global energy landscape is important for understanding the experimental synthesis and thermal dynamic properties as well as for discovering new phases. This work uses material genome techniques (huge global search and data mining) to explore the global energy landscapes and new phases of two-dimensional MoS2, WS2, and ReS2 monolayers at ab initio level. Our results show that their energy landscapes have two or three major funnels, each of which consists of a few local minima with hexagonal, octahedral, quadrilateral, nanoribbon structures as well as their distorted and hybrid structures. The global-minimum structures are confined in deep funnels while the higher-energy minima stay in flat funnels and can transform to other minima at high temperatures. A few new phases with high geometry symmetry are found, e.g., quadrilateral phase, nanoribbon phase, distorted hexagonal phase, 4-2-coordination phase, and Pmm2 space group phase. These new phases exhibit novel phonon and electron properties (e.g., direct Γ point band gap and distorted Dirac cone), and could be the new candidates for devices applications. We further demonstrate that these phases could have better stability with charge doping and thus could be fabricated in experiments.
T
funnel and deep energy valley will certainly correlate with the easiness of synthesizing the structure, while shallow-valley phases might become unstable at high temperature. Such new phases and global landscapes are still not well-known for 2D MoS2, WS2, and ReS2. There have been a few material genome studies on the new phases and global energy landscapes of other materials.19−21 For example, Pulido et al. used energy−structure maps to discover functional materials.22 Goedecker et al. studied the energy landscapes of a few atomic clusters using a minima hopping method and determined their glassy landscape features.23 Du et al. used particle swarm optimization to study graphene-like 2D ionic boron24 and to discover new phases with lower energies. Organov et al. used their ab initio evolutionary algorithm USPEX to study the graphene allotrope with novel properties.25 Chen et al. also studied the energy landscapes of SiO2 crystals and Pt clusters at the ab initio level.26,27 A general understanding of soft glassy materials has been obtained by Crocker et al. using an energy landscape approach.28 Schön and co-workers have explored the energy
wo dimensional (2D) transition metal dichalcogenides XS2 (X = Mo, W, and Re)1−5 materials have been studied extensively in recent years, due to their excellent properties and potential applications in nanoelectronics,6 photonics,7 valleytronics,8 and battery.9 MoS2 and WS2 have a ground-state structure of hexagonal (H) phase,10 and ReS2 has a distorted octahedral (T′) phase.5 These three systems are semiconductors with direct band gaps. Numerous theoretical studies have been performed to understand their mechanical, electronic, magnetic, and optical properties, and have provided physical insights to the experimental findings on these systems.11−18 These studies focus on several well-known structures (e.g., H, T, and distorted T′ phases) as well as their local energy landscapes.11,12 To fully understand a system, it will also be very important to study its global energy landscape. Such nonequilibrium landscape describes other possible local minimum structures (new phases) and the energy funnels of all phases as well as their energy/structural connections. The new phases could have different properties and could become stable under the conditions like substrate, pressure, and electron doping. This thus provides a basis for experiment exploration and device design. The picture of energy funnels and barriers can provide the insights to the synthesis process and the thermodynamic properties including structure stabilities and phase transitions. For example, a large © 2018 American Chemical Society
Received: February 4, 2018 Revised: August 15, 2018 Published: August 16, 2018 6242
DOI: 10.1021/acs.chemmater.8b00525 Chem. Mater. 2018, 30, 6242−6248
Article
Chemistry of Materials landscapes of various chemical systems.29−31 These activities support the importance of the material genome studies and global energy landscapes in these emerging materials. In this paper, we have used material genome techniques (global search and data mining) to uncover the global energy landscapes and new phases of 2D MoS2, WS2, and ReS2 monolayer at ab initio level. After comprehensive atomic structure searches (over 5000 ab initio local relaxation for each system), we have found several hundreds of different local minima. Data mining of their energies and geometries shows the whole energy landscape has two or three major funnels, each consisting of a few local funnels with either ordered highsymmetry structures or disordered structures. The global minima (H-phase) of MoS2 and WS2 are separated far away from other minima in both the energy space and geometry configuration space. They are confined in deep and steep funnels. The stability of ReS2 ground state (T1′-phase) is relatively worse than H-MoS2 and H-WS2. For all the three systems, their high-energy local minima are usually far from the ground state and are contained in flat funnels. We have also discovered many new stable structures, which exhibit novel phonon and electron properties (e.g., direct Γ point band gap and distorted Dirac cone), and could be the new candidates for electronic devices. We further demonstrate that these new phases could be fabricated by either electron or hole doping. The exploration of the energy landscape was performed by our Structure Global Optimization (SGO) engine.26 SGO uses a parallel differential evolutional (DE) algorithm, which belongs to the family of evolutionary algorithms (EAs) and employs a population of trial structures (i.e., individuals) cooperating with each other in the global search. Random initialization, differential mutation, cut-and-splice crossover, ab initio local relaxation, and greedy selection operators are employed to evolve the population. In detail, atoms are randomly placed within a slab to generate the initial structure Xi,G, where i ∈ [1, Np] is the structure index, Np is the population size, and G is the generation index. Bonding distance constraint and structure similarity check are used to improve the structure quality. These initial structures are then permutated by a differential mutation operator to produce a permutated individual V i,G. A conventional differential mutation uses a linear combination of a randomly selected base individual (Xr3,G) and a scaled difference of two other donor individuals (Xr1,G, Xr2,G): Vi,G = Xr3,G + F·(Xr1,G − Xr2,G) (F ∈ [0, 1] is a user-input scaling factor). The Vi,G is then passed to the crossover step. Here we use a classical cut-andsplice crossover operator to assemble two subsystems into a new structure Ui,G. The Ui,G is relaxed to its local minimum, which competes to survive to the next generation via greedy selection operator. This evolution procedure (mutation, crossover, relaxation, and selection) is repeated until the SGO program converges to the global minimum. A more detailed description of this procedure can be found in ref 26. In the search of the MoS2, WS2, and ReS2 systems, we set Np to 8 and use a 12-atom supercell in each individual. To compensate the stochastic feature of the search algorithm and to fully explore the energy landscape, we have performed a few independent runs of the whole SGO procedure with different initial structures. In total, over 5000 structures have been searched for each XS2 system. For each structure, we used ab initio calculations to relax its atomic positions and in-plane cell parameters. The out-of-plane cell parameters were set with over 15 Å vacuum thickness. The exchange and correlation
potentials were treated in the framework of generalized gradient approximation (GGA) of Perdew−Burke−Ernzerhof (PBE).32 To accelerate the search, a 3 × 3 × 1 K-point mesh was adopted in the atomic relaxation and the force precision was set to 0.02 eV/Å. Symmetry operation was switched off to remove any artificial constraints in order to search all the possible configurations. In order to study the structure stability of each local minimum and to fully explore its local energy landscape, we have also performed phonon dissipation calculations33 and high-temperature molecular dynamics (MD) simulations for a few selected structures (see the Supporting Information (SI)). The hybrid functional method (HSE06) has been employed to calculate the electronic band structures.34 After this thorough ab initio global search, we have obtained several hundreds of different minima for these 2D systems. Their energy spectra and a few selected phases are presented in Figure 1 and Figures S1−S3 (SI). We can see that the global minimum of MoS2 is the wellknown H-phase monolayer with a hexagonal close-packed structure. It is separated far away from all the other minima. This indicates that H-phase is very stable, and even high temperature cannot not destroy it. This high stability makes it possible to peel the MoS2 monolayer off the subtract to fabricate a large-scale array.35,36 The second-lowest-energy minimum is a distorted T′-phase (T′1) with an octahedral coordination.11 Above it, there are several other distorted T′phases with very close energies and geometries, e.g., T2′ and T3′ (see SI). This indicates that they might coexist in fabrication.10,11 On the top of these T′ structures (0.81 eV), it is a new phase which has never been reported. Each Mo atom in this structure connects with four S atoms at one side but with two S atoms at the other side. This structure is recorded as 42′-phase, and a similar one (see SI) with a higher energy (0.86 eV) and higher symmetry is recorded as 42-phase. Above them (1.07 eV), there is a new phase with the space group Pmm2. It has two types of S atoms. One is located at the center of two nearest Mo atoms, while the other is located at the center of a square formed by four Mo atoms. As a result, each Mo atom connects with four S atoms at the upper side while connects with three S atoms at the lower side. Its coordinate number in total is seven; thus, we can expect a ptype-like doping state during the band gap. At the energy of 1.12 eV, it is a nanoribbon structure. The coordinate number of the Mo atom in each ribbon is five, which could result in an n-type-like doping state. Besides these structures, there are a few other new phases (Figure S1), including hybrid structures of H-phase and T-phase (noted as Hybrid-phase and Hybrid2phase), quadrilateral structure, etc. It should be noted that the well-known octahedral T-phase is not stable and its energy is 0.83 eV, close to these new phases. The energy landscape of WS2 is similar to that of MoS2 in the low-energy region. The ground-state H-phase is far away from a few close-energies distorted T′-phase. But the highenergy region is different. The 42′-phase mentioned earlier is not stable in WS2, while the 42-phase (Figure 1(e2)) is stable. The nanoribbon phase (1.18 eV) here has a lower energy than the high-symmetry Pmm2-phase (1.24 eV). Above them, there are a few other new phases (Figure S2) such as a quadrilateral structure. ReS2 is very different from MoS2 and WS2. Both of its Hphase and T-phase are not stable. Its global minimum is a distorted T1′ -phase (Figure 1(b3)),5 which is about 0.05 eV 6243
DOI: 10.1021/acs.chemmater.8b00525 Chem. Mater. 2018, 30, 6242−6248
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Figure 1. Energy landscapes of 2D (left) MoS2, (middle) WS2, and (right) ReS2. (a1, a2, a3): Configurational energy spectra. Each line represents one local minimum. The y coordinate indicates the corresponding total energy per formula unit, and the energy of the global-minimum configuration is set to the referenced zero value. (b1−g1, b2−g2, b3−g3): Atomic structures of several selected phases at two different views.
lower than the next T2′ -phase. The higher T3′ -phase (Figure S3) is at 0.20 eV and T′4-phase is at 0.40 eV. These distorted T′phases have relatively close energies and could coexist in experiment samples. This is observed in recent experiments37,38 where multiple orientations of Re-atom chains coexist. Above them, we find a very interesting hexagonal structure, distorted H′-phase (0.68 eV). This phase cannot exist in MoS2 and WS2 due to nonzero forces and has not been reported elsewhere for ReS2. We could expect its potential applications in electronic devices as H-MoS2. Unlike MoS2 and WS2, the nanoribbon phase (0.71 eV) here is lower than the 42-phase (0.74 eV). Above them, there is a new Quad-phase (0.93 eV), which, at the top view, has a quadrilateral structure formed by two Re atoms and two S atoms. In order to verify the stability of these phases, we have performed phonon spectrum calculations for them (Figures S4 and S5). We have the following observations: (1) T′-phase (T1′, T2′, T3′ , etc.), 42-phase, Ribbon-phase, and Quad-phase are stable at all the three systems. (2) H-phase is stable at MoS2 and WS2, while ReS2 has a stable H′-phase. (3) 42′-phase is stable at MoS2, but it has imaginary frequency at WS2 and does not exist at ReS2 due to nonzero force. In contrast, Hybrid2phase is stable at ReS2, but has imaginary frequency at MoS2 and does not exist at WS2. (4) Pmm2-phase is stable at both MoS2 and WS2, but has imaginary frequency at ReS2. The Hybird-phase is completely opposite, with imaginary frequency at MoS2 and WS2 but stable at ReS2. The Quad2-phase is stable only at MoS2. (5) The three lowest acoustic modes (inplane longitudinal acoustic, in-plane transverse acoustic, and out-of-plane acoustic mode)16 are kept in all the stable structures. However, the gap between the high-frequency optical modes and the low-frequency modes is missing in most
new phases, while T3′ -WS2, 42-WS2, T3′-ReS2, 42-ReS2, and Ribbon-ReS2 exhibit a novel direct gap at the Γ point. Compared to H-MoS2 and H-WS2, their Raman active modes and infrared active modes have an obvious red shift. These phonon dispersion features should contribute to the measurement during the synthesis. Having these minima, we further analyze the relationship between structures and energies using data mining techniques (unstable structures are not considered here). We first define the fingerprint of each structure as the vector of the eigenvalue set of the Natom × Natom Gaussian overlap distance matrix.23 The Gaussian matrix element is defined as exp(dR2ij/σ2), where dRij is the distance between the atom i and atom j at the periodic image; σ is the bond parameter, taken as the average length of the first nearest neighbor bond for all the minima of one system. This definition is invariant to the translational and rotational symmetry. The distance between two structures is then defined as the root-mean-square distance between their fingerprint vectors. On the basis of this structure−structure distance, we have identified the energy as a function of the distance for all the local minimum configurations relative to the global minimum, and performed a hierarchical clustering analysis39 for these minima. The results are shown in Figure 2. It can be seen from the energy−distance map that the ground states of MoS2 and WS2 are isolated and separated far away from other minima (Figure 2a,c). This is an indicator that H-phase is confined in a deep funnel and is very stable.23 In comparison, the ground-state T1′-phase of ReS2 is separated from other minima, but with relatively smaller distances. This indicates its stability should be worse than that of H-MoS2 and H-WS2. In addition, although the energies have no linear correlation with the distances, overall, the minima with far 6244
DOI: 10.1021/acs.chemmater.8b00525 Chem. Mater. 2018, 30, 6242−6248
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Figure 2. Data mining of energy landscapes of 2D (left) MoS2, (middle) WS2, and (right) ReS2. (a, c, e): Relationship between energy difference and fingerprint distance to the global-minimum configuration. Each colored circle represents one configuration. The origin point is the globalminimum one. (b, d, f): Hierarchical clustering based on fingerprint. The x coordinates of leaf nodes represent different configurations; the branch height (y axis) in the top panel indicates the average fingerprint distance between different configuration groups, while the y axis in the bottom panel is the configuration energy difference to the global minimum. The order of configurations in the x axis is arranged to avoid crossing branches. The labeled colors represent different groups.
steep. In detail, the evolution of the energy, pair distribution function, and atomic moving function (Figure S6) show that the structure fluctuates at its own funnel during the simulation process. This is confirmed by further relaxations of a few structures during the MD process and all of them fall back to H-phase. At the initial stage, the energy can rise to as high as 4 eV, indicating the barrier height is larger than 4 eV in some directions. At the equilibrium stage, the energy fluctuates around a narrow region from 0.5 to 1.0 eV, and the pair distribution function and atomic moving function only have slight changes. This indicates the funnel is very steep and restricts the structure fluctuation. In comparison, T1′-MoS2 transforms to H-phase during the 2000 K simulation (Figure S7). The structure first rises to about 2.0 eV and passes through the barrier, then entering into the funnel of H-phase. Its energy in the later stage is lower than the initial T1′-phase, and the further relaxation confirms it falls to H-phase. At a lower temperature, T′1-phase transforms to another distorted T′ structure at 1000 K while keeps stable at its own funnel at 300 K (Figure S7). The simulations for T′2-MoS2 also show it can hop into and out of neighboring T′ phases at 2000 K, with a wide energy fluctuation from 0.4 to 1.5 eV, but it is stable at a lower temperature (Figure S8). All of these demonstrate the flat funnel feature of the high-energy region. Having understood the energy landscapes and discovering a few new phases, we further study their electronic properties and see if they qualify for device applications. We have used the hybrid HSE06 functional to calculate the band structures of the 18 configurations in Figure 1. All of them are stable without imaginary frequency. The results are shown in Figure 3. For MoS2, H-phase is a semiconductor with a direct gap at the K point. Its calculated band gap is 1.90 eV, the same as the
distances to the ground state have high energies. The hierarchical clustering further casts that the landscape of MoS2 contains two major funnels (Figure 2b). The first one consists of a few ordered structures such as H, T′, Pmm2, and Quad phases. It is located at the left region of the energy− distance map (Figure 2a) and has lower energies. The second one consists of very disordered monolayer structures and distorted nanoribbon structures, and it is at the right region with higher energies. Each major funnel can be further divided into several small groups. For example, in the first funnel, Hphase and several Hybrid-phases are in one group; T′-phases and 42-phase are in one group; ordered ribbon-phases are in another group. For WS2 and ReS2, there are three major funnels (Figure 2d,f) in their landscapes. Overall, these funnels are arranged at the left, middle, and right regions of the energy−distance map (Figure 2c,e), respectively. The first major funnel consists of a few ordered structures (T′, 42, Pmm2 phases, etc.) and it is at the low-energy region. The second and the third funnels are at the high-energy region, and have no remarkable difference in energies between each other. The second one majorly consists of distorted nanoribbon structures, while the third one majorly consists of very disordered structures, e.g., the structures with S atoms peeled off the monolayer. For all the three systems, we also note that most of high-energy minima have several neighboring minima with close structures and close energies. This indicates the landscape at the high-energy region is relatively flat. Thus, these minima could be glassy, and could hop into or out of neighboring funnels at high temperature. This provides an insight into the overall landscape of these 2D systems. To verify the above discussions on funnel features, we have performed MD simulations for some selected phases. The 2000 K simulations for H-MoS2 show its funnel is deep and 6245
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Figure 3. Band structures of several selected phases of 2D (top) MoS2, (middle) WS2, and (bottom) ReS2 using the HSE06 exchange-correlation functionals. In each row, the phases are arranged with the energy from low to high, corresponding to Figure 1. The Fermi level (Ef) is set to the zero energy of the y axis.
Figure 4. Energy of different phases as a function of charge doping. (a) Left panel is for MoS2; (b) middle panel is for WS2; (c) right panel is for ReS2. The y-axis ΔE is defined as the energy (per formula unit) of each phase relative to the original ground state (i.e., H for MoS2 and WS2, and T1′ for ReS2). Negative charge means electron doping, and positive charge means hole doping.
experimental value.3 T1′ and T2′ phases are metal (or semimetal) and have crossing bands (Dirac cone) around the Fermi level.10 The 42′-phase has a 0.36 eV indirect gap. Pmm2-phase is very interesting. It has a partially occupied state close to the Fermi level and valence band maximum (VBM), forming a band structure similar to p-type doping. This is because each Mo atom has seven coordinations in this phase, resulting in a certain percentage of unpaired holes in oxygen atoms. The Ribbon-phase has a 0.75 eV indirect gap. Compared to H-phase, it has a localized conduction state on top of the Fermi level. This is due to that its coordination number of Mo atom is five, resulting in unpaired electrons in Mo and a corresponding band structure similar to n-type doping. The band structures of WS2 are similar to the same phases in MoS2. Compared to MoS2, the states around the Fermi level have slight shift or distortion. Its T′1-phase has no crossing bands near the Fermi level, while T2′-phase has two crossing points. The indirect gap in the Ribbon-phase increases to 0.79 eV. Specially, band structures of 42-phase and Pmm2-phase are
very interesting. The 42-phase is a semiconductor with a 0.27 eV direct gap at the Γ point. This corresponds to 4.6 × 103 nm infrared light and is good for infrared device applications. Its effective mass is estimated about 20% of that of H-WS2, and it should have a better transport property. When it is packed into the bulk (Figure S9), the Γ point direct gap shrinks to 0.005 eV. Pmm2-phase exhibits a clear band crossing near the Fermi level, forming a distorted Dirac cone. Since its lower side (noted as “A” side) and upper side (noted as “B” side) are different, it can have two types of packing, i.e., ABAB and ABBA. We found the crossing bands also exist in both types of bulk and have some minor shifts (Figure S10). In the ABBA bulk, each band splits into two bands and forms some new crossing points, due to the symmetry breaking. ReS2 is very different. Its T′1-phase has a 1.55 eV direct gap at the Γ point, close to the experimental value.5 T′2-phase has a 1.60 eV indirect gap. Both are semiconductors rather than metals or semimetals. The distorted H′-phase has a small indirect gap (0.50 eV), and its valence bands are significantly degenerate and localized. The indirect gap of the Ribbon-phase 6246
DOI: 10.1021/acs.chemmater.8b00525 Chem. Mater. 2018, 30, 6242−6248
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experimental synthesis. We have also discovered a few new phases which exhibit novel phonon and electron properties. They could be promising candidates for future electronic applications and can also be used as motifs for structure searches of other element compounds. These new phases are demonstrated to become stable over the original ground states under the condition of electron or hole dopings.
here increases to 0.85 eV. The 42-phase turns to be a metal, with a delocalized state near the Fermi level. The new Quadphase is an indirect-gap (0.67 eV) semiconductor. These novel properties make the discovered phases be promising candidates for device applications. One major concern is how to synthesize them. Very recently, Zhang et al. have achieved the 2H − 1T structural phase transition in monolayer MoTe2 by electron doping.40,41 Following this technique, we have studied the energies of the above 18 structures as a function of charge doping. The results are shown in Figure 4. It is seen that the high-energy MoS2 phases can become more stable than H-phase by either electron doping or hole doping. To be specific, at an electron doping of −0.61 e/MoS2, the T′2-phase becomes the most stable and T′1phase almost coincides with T′2-phase. At a hole doping of 0.68 e/MoS2, Ribbon-phase becomes the new ground state. The stability of 42′-phase can also become over H-phase from a high hole doping of 1.79 e/MoS2. These trends are attributed to their different band structures. Under electron doping, the electrons will fill the conduction bands of H-phase, which are far above the Fermi level. This leads to a significant energy increase. In contrast, the other phases are either metallic, semimetallic, or small band gap semiconductors, in which doped electrons will fill the states near the Fermi level, leading to a smaller energy increase. Similarly, under hole doping, the valence electrons of H-phase, which are far below the Fermi level, will be removed. This leads to a larger energy increase, compared to the other phases where the states close to the Fermi level are involved. It should be noted that these doping concentrations are higher than the ones needed for MoTe2 due to the larger energy differences.40,41 Thus, the corresponding phase transitions are more difficult. But they are still possible by either electrostatic40 or ion doping (e.g., Li ion).42 For WS2, T1′ -phase becomes the most stable from an electron doping of −0.49 e/WS2, while Ribbon-phase becomes the most stable from a hole doping of 0.72 e/WS2. 42-phase can be stable over H-phase from 1.20 e/WS2 hole doping. We can see that the behaviors of T′-WS2 are a little different from T′-MoS2, although their corresponding band structures are very similar in the cases without doping. This is resulted from their minor difference around the Fermi level. Those states are very sensitive to charge doping. The new band structures after doping turn to be more different between T′-MoS2 and T′WS2 (Figure S11). For ReS2, Ribbon-phase can become the new ground state from either an electron doping of −0.81 e/ReS2 or a hole doping of 0.60 e/ReS2. H′, T′2, and 42 phases are also stable over T′1-phase from around 0.81 e/ReS2 hole doping. We see the energy difference between T′1-phase and T′2-phase keeps very small in the whole doping region. This supports the possible coexistence of several T′ phases in some fabrication methods, e.g., chemical vapor deposition and molecular beam epitaxy.37,38,41,43 From the above observations, we thus can expect the possible synthesis of these new phases at charge doping. It should be noted that these phases can also be stable in other 2D materials, e.g., MoSe2, MoTe2, and WTe2, in which the phase transition should be easier.40,41 In summary, we have studied the global energy landscapes and new phases of 2D MoS2, WS2, and ReS2 monolayers by material genome methods. Their whole landscape features and local funnels are explored. These landscape pictures provide a new view to understand their structure stability and
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.8b00525. The supporting results of atomic structures, phonon spectra, molecular dynamic simulations, electronic structures, and vacuum thickness effect are provided in Figures S1−S12 (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Zhanghui Chen: 0000-0003-4972-2103 Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, of the under Contract No. DE-AC02-05-CH11231 within the Non-Equilibrium Magnetic Materials program (MSMAG). This research used the resources of the National Energy Research Scientific Computing Center (NERSC) and Oak Ridge Leadership Computing Facility (OLCF) that are supported by the Office of Science of the U.S. Department of Energy, with the computational time allocated by the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) project NTI009.
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REFERENCES
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DOI: 10.1021/acs.chemmater.8b00525 Chem. Mater. 2018, 30, 6242−6248
Article
Chemistry of Materials
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DOI: 10.1021/acs.chemmater.8b00525 Chem. Mater. 2018, 30, 6242−6248
