Thermodynamic and Kinetic Origins of Lithiation ... - ACS Publications

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Thermodynamic and Kinetic Origins of Lithiation-Induced Amorphous-to-Crystalline Phase Transition of Phosphorus Sung Chul Jung and Young-Kyu Han* Department of Energy and Materials Engineering and Advanced Energy and Electronic Materials Research Center, Dongguk UniversitySeoul, Seoul 100-715, Republic of Korea S Supporting Information *

ABSTRACT: Despite its fundamental importance, real-time observation of atomic motions during phase transition is challenging because the transition processes usually occur on ultrafast time scales. Herein, we directly monitored a fleeting and spontaneous crystallization of Li3P from amorphous LixP phases with x ∼ 3 at room temperature via first-principles molecular dynamics simulations. The crystallization is a collective atomic ordering process continued for 0.4 ps and it is driven by the following key impetuses: (1) the crystalline Li3P phase is more stable than its amorphous counterpart, (2) the amorphous LixP phase corresponds thermodynamically to the local minimum energy state at x ∼ 3, which enables its crystallization under an electrochemical equilibrium condition without net flux of lithium ions in the host material, (3) the crystalline and amorphous structures of Li3P are so similar that the average displacement of the mobile Li atoms during crystallization is only 0.56 Å, and (4) highly lithiated materials with all isolated host elements, such as the amorphous Li3P phase, are advantageous for crystallization because the isolation induces a kinetically favorable low-barrier transition without complicated multistep P−P bond breaking/ forming processes.

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INTRODUCTION Identification of lithiation products during the electrochemical operation of lithium ion batteries is essential because their characteristic structural and electronic properties could be linked to battery performance. In this sense, the structural change of the host electrode materials with charge−discharge cycles is one of the significant subjects of elaborate in situ experimental studies.1−6 In particular, the distinct structural changes of the crystalline-to-amorphous phase transition, and vice versa, have been reported for high-capacity alloy-type anode materials such as silicon7−13 and germanium.14,15 These phase transitions may significantly alter the important electrochemical properties of an electrode material such as carrier ion transport, and thus, they have been thoroughly explored to elucidate the underlying mechanisms.9−11,15 Real-time observation is critical for a microscopic understanding of the phase transition process. This technique has been widely employed to clarify the structural, chemical, and mechanical changes of anode materials, especially silicon.4−11,16−25 For example, amorphous LixSi phases, trans© 2015 American Chemical Society

formed from diamond silicon during lithiation via electrochemically driven solid-state amorphization, suddenly crystallize into Li15Si4 upon full lithiation.7,13 A fascinating in situ transmission electron microscopy study on silicon nanowires conducted by Wang’s group9,10 suggested that the crystallization of Li15Si4 is a spontaneous and congruent phase transition process without phase separation or large-scale atomic motion, which is drastically different from what is expected from a classic nucleation and growth process. The observed fast propagation of a crystallized region along the lithium diffusion direction is significant for understanding the amorphous-to-crystalline phase transitions in alloy-type anode materials, although the local atomic rearrangement process during the crystallization was not captured in their studies. Phosphorus is one of the promising anode materials for lithium ion batteries because of its specific capacity of 2596 mA Received: March 4, 2015 Revised: May 11, 2015 Published: May 13, 2015 12130

DOI: 10.1021/acs.jpcc.5b02095 J. Phys. Chem. C 2015, 119, 12130−12137

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The Journal of Physical Chemistry C h g−1 corresponding to Li3P, which is 7 times larger than the 372 mA h g−1 capacity for graphite presently used as the anode material. Phosphorus also has higher operating potentials than graphite, which thereby reduces the safety problem. Many experimental studies have examined the performance of black phosphorus,26−30 red phosphorus,31−35 amorphous phosphorus,36,37 and their composites with carbon,26−28,31−37 tin,38−40 copper,30,41 iron,42 and nickel43 for utilization as optimal anode materials. As is the case with silicon, using phosphorus results in a disorder−order phase transition issue during lithiation. Xray diffraction and nuclear magnetic resonance studies reported that only the Li3P phase was clearly observed26−29,32,33 among all known crystalline Li−P phases44LiP7, LiP5, Li3P7, LiP, and Li3P (see Supporting Information, Figure S1 and Table S1). These reports indicate that amorphous LixP phases are the major lithiation products and they can transform into the crystalline Li3P phase at the final lithiation stage. However, an atomic-level understanding of the lithiation-induced structural evolutions of phosphorus, including the crystallization of Li3P, is lacking, although several experimental studies have pursued the characterizations of the phases and phase transformations of the Li−P systems.26,28,32,33,36 In this study, we directly observed the crystallization process of Li3P from amorphous LixP phases with x ∼ 3 via an ab initio molecular dynamics (AIMD) simulation at room temperature. The calculated formation energies, the analyzed atomic and electronic structures, and the observed quantitative atomic-scale information during crystallization provide the thermodynamic and kinetic mechanisms behind the phase transition. The lithiation of phosphorus produces amorphous LixP phases where rings, chains, and isolated atoms appear sequentially during lithiation as the representative local structures of phosphorus. The fully lithiated amorphous LixP phases with x ∼ 3 fleetingly and spontaneously evolve into the crystalline Li3P phase at room temperature. This crystallization is a favorable process in terms of both thermodynamics and kinetics. The crystalline Li3P phase is thermodynamically more stable than its amorphous counterpart. In particular, the amorphous Li3P state with local minimum energy gives an electrochemical equilibrium condition without a large fluctuation of the lithium concentration and thus facilitates the crystallization of Li3P. Furthermore, the isolation of all the phosphorus atoms in the amorphous Li3P phase makes the crystallization kinetically more feasible since it permits low local activation barriers for the mutual transformations between the crystalline and amorphous Li3P phases. Although the crystalline LiP7, LiP5, Li3P, and LiP phases are also thermodynamically more stable than the corresponding amorphous LixP phases, they are unlikely to be formed during lithiation because of the thermodynamic and kinetic disadvantages involved with electrochemical nonequilibrium conditions and the complex multistep P−P bond breaking/forming processes, respectively.

crystalline and amorphous Li−P bulk structures by a periodic supercell. The cell parameters, numbers of used atoms, and kpoint meshes for the Brillouin zone integrations are listed in Tables S2 and S3 in the Supporting Information for the crystalline and amorphous phases, respectively. The simulated X-ray diffraction spectra of black phosphorus and crystalline Li3P are in good agreement with the experimental data (see Supporting Information, Figure S2). The calculated mass density of black phosphorus is 2.42 g cm−3, which compares well with the experimental value of 2.69 g cm−3. We employed the AIMD simulations in the course of (1) preparing the amorphous structures and (2) observing the amorphous-tocrystalline phase transition: The equations of motion were integrated with the Verlet algorithm using a time step of 1 fs, and the temperature was controlled by velocity rescaling during heating or cooling and a canonical ensemble (NVT) using a Nosé−Hoover thermostat during equilibration. (1) The amorphous structures were constructed using a liquid-quench method in which heating, equilibration, and cooling were done in series by the AIMD simulations. Detailed procedures concerning the AIMD simulations are described in the Supporting Information. Similar calculation schemes were successfully used in our previous studies for the structural evolutions of crystalline and amorphous phases during lithiation.48,49 (2) For observing amorphous-to-crystallization phase transition, the AIMD simulations were carried out at room temperature (300 K) for 5 ps.

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RESULTS AND DISCUSSION Figure 1 shows the calculated formation energies of the crystalline LiP7, LiP5, Li3P7, LiP, and Li3P phases and the

Figure 1. Formation energies of LixP, defined as Ef(x) = Etot(LixP) − xEtot(Li) − Etot(P), where Etot(LixP) is the total energy per LixP unit, Etot(Li) is the total energy per atom of bcc Li bulk, and Etot(P) is the total energy per atom of black P.

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amorphous LixP phases, including Li0.14P, Li0.2P, Li0.43P, LiP, and Li3P, which are counterparts to the crystalline phases. All the crystalline Li−P phases are more stable than the amorphous counterparts by 0.13−0.24 eV per LixP formula unit (see Table 1). The most energetically stable amorphous phase is Li3.3P, where x = 3.3 is determined by a least-squares fit to the energies around x = 3.0, with a specific capacity of 2855 mA h g−1. The obtained capacity compares well with the largest experimental value of 2786 mA h g−1, reported by Cui’s group,27 for the first lithiation. This good agreement suggests that the lithiation of phosphorus proceeds until an energetically favorable composition is reached in the electrode.

COMPUTATIONAL DETAILS The density functional theory (DFT) calculations were performed using the Vienna ab initio simulation package (VASP).45 The electron−electron interaction was treated by the Perdew−Burke−Ernzerhof (PBE) exchange and correlation functionals,46 and the ion−electron interaction was treated by the projector augmented wave (PAW) method.47 The electronic wave functions were expanded on a plane wave basis of 271.6 eV. The Li 1s22s1 and P 3s23p3 orbitals were treated as the valence electron configurations. We simulated the 12131


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The Journal of Physical Chemistry C

phosphorus, the most stable allotrope of elemental phosphorus,26 the crystalline Li3P and amorphous Li3.3P phases exhibit volume expansions of 176 and 206%, respectively, which are much smaller than the volume expansion of 298% for the fully lithiated Li3.8Si phase.50 Thus, the pulverization by volume expansion would be alleviated to a greater degree in phosphorus than in silicon. Figure 2b shows the calculated average voltages for the amorphous LixP phases. The voltage curve, overall, lies in between the experimental charge− discharge profiles,27,36 verifying that our formation energy calculations describe the Li−P alloying reactions reasonably well. Interestingly, we succeeded in directly observing the crystallization of Li3P during an AIMD simulation of the amorphous Li3.3P phase at room temperature. The total energy curve for the simulation reveals the existence of an abrupt energy drop at 1.6 ps, implying a clear structural change (see Figure 3a). The characteristics before and after this energy drop are very similar to the characteristics of the amorphous and crystalline Li3P phases, respectively, as evidenced by the radial distribution functions (RDFs) for the Li−P and P−P pairs and the angle distribution functions (ADFs) for the Li−P−Li bond shown in Figure 3b,c. Thus, it is obvious that the amorphousto-crystalline phase transition of Li3P occurs during the energy drop from 1.6 to 2.0 ps. The snapshots during the AIMD simulation of Li3.3P shown in Figure 4 clearly unveil the atomic ordering process that is occurring over the energy drop, which reveals a transformation to the crystalline Li3P phase with a hexagonal symmetry (see also the crystallization process in Supporting Information, movie S1). We note for the crystalline phase (at 2.4 ps) that an extra 0.3 Li atom per P occupies the interstitial sites of the Li3P crystal, but they scarcely perturb the crystal structure. The crystallization takes only 0.4 ps, which may only be captured by experimental techniques with ultrafast temporal resolutions, indicating that the phase transition is a very “fleeting” process. The energy curve shown in Figure 3a also demonstrates that the phase transition is a “spontaneous” process with a very low barrier that can be sufficiently overcome at room temperature. The activation barrier seems to be low enough to allow the phase transition even at T = 70 K. The simulations for the temperature dependence of the phase transition show that the occurring time of crystallization increases as the temperature decreases from T = 500 K to T = 70 K, and ultimately, at T = 20 K, the crystallization does not

Table 1. Formation Energies of Crystalline and Amorphous Li−P Phasesa Ef (eV) crystalline

amorphous ΔEf (eV)

black P LiP7 LiP5 Li3P7 LiP Li3P

0 −0.22 −0.27 −0.55 −1.09 −2.76

P Li0.14P Li0.2P Li0.43P LiP Li3P

+0.16 −0.02 −0.14 −0.38 −0.91 −2.52

0.16 0.20 0.13 0.17 0.18 0.24

Ef and ΔEf represent the formation energy and the formation-energy difference between the crystalline and amorphous Li−P phases, respectively. a

The volume of lithiated phosphorus increases almost linearly with increasing lithium (see Figure 2a). Compared to black

Figure 2. (a) Volume expansion ratios of LixP. V and V0 are the volumes of LixP and black P, respectively. (b) Average voltages of amorphous LixP, defined as V(x) = −[Etot(Lix+ΔxP) − Etot(LixP)]/Δx + Etot(Li). The experimental charge−discharge profile 1 and profile 2 were measured at the first cycle for the amorphous P/C composite36 and black P/graphite composite,27 respectively.

Figure 3. (a) Total energies of the amorphous Li3.3P phase during an AIMD simulation at T = 300 K. (b) RDFs for the Li−P and P−P pairs and (c) ADFs for the Li−P−Li bond in the crystalline and amorphous Li3P phases. 12132


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Figure 4. Snapshots during the AIMD simulation of Li3.3P shown in Figure 3a. Yellow and purple balls represent the Li and P atoms, respectively. In the crystalline phase, an extra 0.3 Li atom per P occupies the interstitial sites of the Li3P crystal, such as a Li atom enclosed with a black circle.

Figure 5. Crystalline LiP7, LiP5, Li3P7, LiP, and Li3P phases and amorphous Li0.14P, Li0.2P, Li0.43P, LiP, and Li3P phases. Only the P atoms are displayed for clarity. The P−P bonds are connected when the bond distance is within 2.5 Å.

We observed that the average displacements of the Li and P atoms during the energy drop from 1.6 to 2.0 ps, shown in Figure 3a, are only 0.56 and 0.39 Å, respectively (see Supporting Information, Figure S4). The observed displacements are much smaller than the Li−P and Li−Li bond lengths in Li3P, which are about 2.5 and 2.7 Å, respectively. This is highly responsible for the very short duration (0.4 ps) for the crystallization. The volume change upon the phase transition is also small. The volume of the crystalline Li3P phase is smaller than the volume of the amorphous Li3P phase by only 2%, as shown in Figure 2a. In terms of the coordination number, the average number of Li atoms around P slightly increases from 9.8 in amorphous Li3P to 10.6 in crystalline Li3P (see Supporting Information, Table S4), which is consistent with the marginal volume contraction of Li3P upon phase transition. We think that the crystallization of Li3P is a kinetically favorable process because all the observed small structural changes can be associated with low local activation barriers for the crystallization. We emphasize that the isolation of phosphorus atoms in the amorphous Li3P phase is crucial for its kinetically favorable crystallization. Figure 5 shows the phosphorus structures in the crystalline LiP7, LiP5, Li3P7, LiP, and Li3P phases and their amorphous counterparts. The crystalline and amorphous Li3P structures are commonly featured by all of the isolated phosphorus atoms (see also the Li−P and P−P distances of 2.4−2.8 and 4.0−4.8 Å, respectively, in the RDF peaks shown in Figure 3b). The isolation of the phosphorus atoms in the two Li3P phases can lead to low barriers for the mutual transformations, thereby making the crystallization of Li3P kinetically feasible at room temperature. In contrast, the

occur for 5 ps (see Supporting Information, Figure S3). Our discovery provides conclusive proof of the amorphous-tocrystalline phase transition of Li3P, which is consistent with the clear observations of the crystalline Li3P phase during electrochemical lithiation.26−29,32,33 Our formation energy calculations provide insights into the thermodynamic aspects of the crystallization of Li3P. All the crystalline Li−P phases are more stable than their amorphous counterparts by 0.13−0.24 eV (see Table 1), which are basic requirements for the amorphous-to-crystalline phase transitions. We note, in particular, that only the crystalline Li3P phase is very close in composition to the amorphous Li3.3P phase that corresponds to the minimum energy point (see Figure 1). This implies that the crystalline Li3P phase can easily sustain its crystallinity against the attack of lithium ions because the flow of lithium ions into the host material rapidly diminishes around x ∼ 3. In this regard, even if the crystalline LiP7, LiP5, Li3P7, and LiP phases are formed during lithiation because their formation energies are lower than those of their amorphous counterparts, it is difficult to maintain crystallinity under nonequilibrium conditions where the lithium concentration varies continuously. Moreover, the crystalline LiP7, LiP5, Li3P7, and LiP phases are not stable enough to prohibit their return to the amorphous phase during lithiation (see Table 1). Consequently, whether an amorphous LixP phase corresponds to the local minimum energy point is important in terms of its crystallization since the minimum energy state provides an electrochemical equilibrium condition with no net flux of carrier ions. We conclude that among all the crystalline Li−P phases the Li3P phase is the one that is thermodynamically most likely to be formed during lithiation. 12133


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The Journal of Physical Chemistry C phosphorus atoms are connected to each other in both the crystalline LiP7, LiP5, Li3P7, and LiP structures and their amorphous counterparts. The transformations from amorphous phases to these crystalline phases during lithiation must involve complicated multistep P−P bond breaking/forming processes to create peculiar phosphorus networks, namely, one-dimensional helicoidal cluster chains consisting of two- or threecoordinated atoms, three-dimensional layers resulting from edge-shared six-membered rings, isolated seven-membered clusters, and one-dimensional helicoidal single-atom chains in the crystalline LiP7, LiP5, Li3P7, and LiP phases, respectively. Such drastic reconstructions would require high energy barriers, which can be overcome at elevated temperatures. In fact, we observed no P−P bond breaking/forming processes during a room-temperature AIMD simulation of the amorphous LiP phase for 5 ps, the same as the simulation time for the amorphous Li3.3P phase shown in Figure 3a. Instead, we merely observed vibrational motions of phosphorus atoms. The isolation of phosphorus atoms allows very short transition paths, which leads to a fast transition process. As shown in Figure 6, the local structures of the crystalline and

Figure 7. Amorphous P, LiP, Li1.5P, Li2P, Li2.5P, and Li3P phases. Only the P atoms are displayed for clarity. The ring, chain, and isolated atom depicted in green are representative local structures of phosphorus during lithiation. The P−P bonds are connected when the bond distance is within 2.5 Å.

The isolated phosphorus atoms in the amorphous Li3P phase have highly uniform charge states, as evidenced by a single sharp peak centered at −2.4 in the phosphorus charge distributions (see Figure 8), because they are in a homogeneous environment surrounded by only about 9.8 Li atoms. This peak is nearly identical to the peak arising from a regular local structure in the crystalline Li3P phase. The strong electronic similarity between the two Li3P phases suggests that the amorphous LixP phases with x ∼ 3 can transform into the crystalline Li3P phase without significant charge redistributions. In contrast, the phosphorus atoms in the amorphous Li0.14P, Li0.2P, Li0.43P, and LiP phases, which are in heterogeneous environments surrounded by both the Li and P atoms, have relatively diverse charge states depending on the ratio and configuration of the neighboring Li and P atoms. For instance, the phosphorus charge distributions in the amorphous LiP phase consist of three broad peaks centered at −1.4, −0.8, and −0.3, which stem from different P atoms with one, two, and three nearest-neighbor P atoms, respectively (see Figure 5). The broad and continuous peaks in the amorphous LixP phases, except Li3P, fairly differ from the relatively sharp and discrete peaks resulting from the regular local structures in their crystalline counterparts. It is worth noting that the thermodynamic and kinetic origins of the crystallization of Li3P are also valid for the crystallization of Li15Si4, which is an important structural change occurring at the end of the lithiation of silicon. First, the formation energies of all the crystalline Li−Si phases, including Li15Si4, are lower by 0.27−0.67 eV per LixSi formula unit than those of the amorphous counterparts.9 Second, the composition of x = 3.75

Figure 6. Crystalline and amorphous Li3P phases and their representative local structures. Yellow and purple balls represent the Li and P atoms, respectively. In the local structures, central P atoms are surrounded by the first-nearest-neighbor Li and the secondnearest-neighbor P atoms, displaying their isolations. The Li−P bonds are connected when the bond distance is within 3.0 Å.

amorphous Li3P phases exhibiting the isolation of the central phosphorus atoms suggest that the crystallization of Li3P can occur through a small-scale collective alignment process of interatomic distances and bond angles, not diffusion events such as atomic hopping or exchange. This alignment process is also confirmed by the structural snapshots shown in Figure 4. The isolation of all of the phosphorus atoms is achieved above x = 2.5 in the amorphous LixP phases. This is proven by the structural evolution of the phosphorus network, which demonstrates that the intricately interlinked polygonal rings evolve sequentially into smaller rings, chains, and isolated atoms as lithiation proceeds (see Figure 7). Our finding implies that the number of lithium ions that can be accommodated by a host material should be large enough to isolate all of the host elements. Therefore, the isolation-induced crystallization can be observed only in high-capacity electrode materials. From a kinetic point of view, we conclude that the isolation of all phosphorus atoms can be a very advantageous condition for the crystallization of Li3P. 12134


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Figure 8. Distribution histograms of the Bader populations of phosphorus in the crystalline LiP7, LiP5, Li3P7, LiP, and Li3P phases and the amorphous Li0.14P, Li0.2P, Li0.43P, LiP, and Li3P phases.

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CONCLUSIONS In conclusion, we demonstrated that the crystallization of Li3P is a fleeting and spontaneous collective atomic ordering process by a direct observation using room-temperature AIMD simulations. The crystallization of Li3P is continued for a very short time (0.4 ps) and is accompanied by small atomic displacements of 0.56 and 0.39 Å per Li and P, respectively. The observed phase transition was successfully explained by both thermodynamic and kinetic considerations. In thermodynamics, an important impetus is not only the energetic preference for the crystalline Li3P phase but also the unique thermodynamic status of the amorphous counterpart, i.e., the minimum energy state, which enables crystallization under an electrochemical equilibrium condition. In kinetics, the observed small structural changes upon phase transition prove that the crystallization of Li3P is a kinetically favorable process with low local activation barriers. The isolation of phosphorus atoms is especially critical for facile crystallization, and thus the residual bonds between the host elements can be a prominent obstacle prohibiting crystallization under ambient conditions. The presented atomic-level explanations for the crystallization of Li3P can be wholly applicable to the case of Li15Si4. This work provides not only quantitative atomic-scale information but also thermodynamic and kinetic mechanisms for the amorphous-tocrystallization phase transitions in high-capacity alloy-type electrode materials for next-generation secondary batteries.

for the crystalline Li15Si4 phase is close to the thermodynamically most stable composition of x = 3.78 for the amorphous LixSi phase.50 This thermodynamic status offers an electrochemical equilibrium condition appropriate for the crystallization of Li15Si4. Third, the crystallization of Li15Si4 from the amorphous LixSi phases is not accompanied by long distance displacement and diffusion of the atoms.9,10 Lastly, the silicon atoms in the crystalline Li15Si4 and amorphous Li3.75Si phases are surrounded by about 12 Li ions.51 Isolation of all of the silicon atoms can play a kinetically important role in the fast crystallization of Li15Si4 by providing low-barrier transition paths. This remarkable coincidence of crystallization characteristics between the Li−Si and Li−P systems suggests that the crystallization mechanisms elucidated in this study can be generalized to other high-capacity alloy-type anode materials. It should be mentioned that the time scales of phase transitions in experiments would be longer than the 0.4 ps observed in our simulation. The crystallization of phosphorus anode would proceed through a propagation of the interface between the crystalline Li3P and the amorphous Li3‑δP regions along the Li diffusion direction, as in the case of silicon anode.9,10 It is apparent that the amorphous-to-crystalline phase transition of Li3P takes place at the moving interface. Thus, the duration of crystallization will be approximately equal to the size of the anode divided by the propagation speed. In a way, the time scales observed in simulations reflect the more intrinsic nature of the phase transition of Li3P than they do in experiments because experimental time scales depend on both the size of the anode and the speed of interface migration. We would like to mention that it is experimentally hardly possible to directly visualize atomic motions during transition processes between two distinct phases. To our knowledge, tracing real-time atomic motions during mutual transformations between the crystalline and amorphous phases in a battery electrode material during the charge (or discharge) process has not been successful. High chemical selectivity, high spatial resolution, and fast temporal resolution are all desirable for such visualizations. In particular, it is difficult to capture a critical moment when the atomic motions triggering the phase transition occur because the barrier-crossing transition processes are usually finished within ultrashort time scales ranging from femtoseconds to nanoseconds. In this context, the present AIMD simulations are an exemplary study for providing a direct real-time view of atomic dynamics and understanding the phase transition process.

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ASSOCIATED CONTENT

* Supporting Information S

Details of AIMD simulations, atomic structures of the crystalline Li−P phases, simulated X-ray diffraction spectra of black P and Li3P, the temperature effect on the crystallization of Li3P, average atomic displacements during the room-temperature AIMD simulation of Li3.3P, structural parameters of the Li−P crystals, DFT calculation details, coordination numbers of Li and P in Li3P, and movie for the crystallization process of Li3P. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ acs.jpcc.5b02095.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 12135


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ACKNOWLEDGMENTS This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science, ICT and Future Planning of Korea (2010-C1AAA001-0029018), and the Energy Efficiency & Resources Core Technology Program of the KETEP granted financial resource from the Ministry of Trade, Industry & Energy (20132020000260). This study was also supported by the Industrial Strategic Technology Development Program (10041589), IT R&D program (10041856) funded by the Ministry of Trade, Industry and Energy, and the Supercomputing Center/Korea Institute of Science and Technology Information with supercomputing resources including technical support (KSC-2014-C2-013). We thank Dr. Chongmin Wang (PNNL) for reading the manuscript and providing valuable comments.

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