The NonEquilibrium Phase Search method is designed to help elucidate the hysteresis and nonequilibrium reaction pathways associated with these conversion materials. We apply this methodology to investigate a variety of lithiation reaction pathways of Co_{3}O_{4}, NiO, MoS_{2}, CuS, (Cu,Co)_{3}O_{4} by systematically exploring the energetics of a large number of equilibrium and nonequilibrium structural configurations using firstprinciple calculations. (See Zhenpeng's Research Website for more details.) The NEPS computational method involves, the following five steps, described below: i) Starting with the host compound (which may or may not contain Li), identify all possible insertion sites. The method is initiated by searching for interstitial sites in the original transition metal oxide structures. An inhouse code MINT (openly available on GitHub) was used which automates the search for insertion sites. The algorithm works by placing an analytic, exponential decaying function (Exp[r/a]) at each atomic site and searching for geometric minima in the resulting function. ii) Generate all symmetrically distinct configurations for Li insertion. We worked with the Enum code to generate all symmetricallydistinct configurations of Li on the unoccupied sites. All configurations were classified according to their composition Li_{x}▢_{1}_{x}MO. iii) Compute total energies of all configurations generated in step ii). To enable a fast energy sampling, simple pointcharge electrostatic calculations were usually conducted, using nominal charge states for the ions in the system. Alternatively, coarse DFT calculation can be performed to fulfill the energy sampling. iv) Select the structures with lowest electrostatic energies to be computed more accurately and atomicallyrelaxed in DFT. For each composition, the structures were ranked by the electrostatic energies, and the three lowest energy structures were further relaxed using DFT. The formation energies for these selected structures were evaluated according to the following reaction: MO + xLi^{+} → Li_{x}MO. v) Using all of these nonequilibrium structures derived from insertion of Li into the initial TM oxide, build the “nonequilibrium convex hull” and determine phases. For each specific system (LiMO), we build the corresponding nonequilibrium convex hulls with the calculated formation energies at all compositions. The compositions, structures, energies located on the convex hull correspond to the identified nonequilibrium phases. Here is an illustration of the NEPS method: Electrochemical lithiation process of Co_{3}O_{4} Figure 6. Convex hulls generated with all the calculated nonequilibrium phases for Co_{3}O_{4} and the corresponding voltage profiles of the Li insertion into Co_{3}O_{4}. Predicted nonequilibrium reaction voltage profiles fall into the experimental lithiation voltage intervals. [Ref. 1]Representative Publications

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