Layered transition-metal oxides have attracted intensive interest for cathode materials of sodium-ion batteries. However, they are hindered by the limited capacity and inferior phase transition due to the gliding of transition-metal layers upon Na⁺ extraction and insertion in the cathode materials. Here, we report that the large-sized K⁺ is riveted in the prismatic Na⁺ sites of P2-Na_0.612K_0.056MnO₂ to enable more thermodynamically favorable Na⁺ vacancies. The Mn-O bonds are reinforced to reduce phase transition during charge and discharge. 0.901 Na⁺ per formula are reversibly extracted and inserted, in which only the two-phase transition of P2 ↔ P'2 occurs at low voltages. It exhibits the highest specific capacity of 240.5 mAh g^-1 and energy density of 654 Wh kg^-1 based on the redox of Mn³⁺/Mn⁴⁺, and a capacity retention of 98.2% after 100 cycles. This investigation will shed lights on the tuneable chemical environments of transition-metal oxides for advanced cathode materials and promote the development of sodium-ion batteries.

QMCPACK is an open source quantum Monte Carlo package for ab initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wavefunctions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary-field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit and graphical processing unit systems. We detail the program's capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://qmcpack.org.