The primary goals of this project are:
  1. To develop and implement a new discontinuous approach to quantum mechanical materials calculations to make possible complex, realistic simulations of unprecedented size.
  2. To apply the new methodology to reach for the first time the length and time scales necessary to accurately model solid-electrolyte interfaces in lithium-ion batteries, thus paving the way for breakthroughs in understanding, device performance, and safety.
  3. To make the resulting codes available to the larger research community for application to the gamut of physical systems amenable to such large-scale quantum mechanical calculations.
To accomplish the above goals, we are applying and further developing the massively parallel Qbox planewave quantum molecular dynamics (QMD) code for liquid and small solid-liquid interface calculations within its reach (< ~2000 atoms), while developing new Discontinuous Galerkin (DG) and Pole Expansion and Selected Inversion (PEXSI) methods to reach systems of 10,000 atoms or more to model full liquid-on-anode configurations. Of particular interest in this regard is the solid-electrolyte interphase (SEI) layer, a key factor in battery performance, lifetime, and safety.

The new DG methodology achieves planewave accuracy in both total energy and forces with a basis size on the order of minimal Gaussians. The basis is strictly local, orthonormal, and systematically improvable, thus enabling high accuracy and efficient large-scale parallel implementation. These remarkable properties are made possible by releasing the constraint of continuity through the DG formulation of the Kohn-Sham equations. This permits construction of a highly efficient representation of Kohn-Sham wavefunctions in the computational domain as a straightforward union of Kohn-Sham solutions in any chosen set of subdomains. In practice, a large computational unit cell is partitioned into subdomains ("elements") containing just a few atoms each. The Kohn-Sham equations can then be solved in each of the small subdomains in parallel to form the desired highly efficient basis for the full domain. 

The new PEXSI methodology is a Fermi operator based approach which removes the O(N^3) scaling bottleneck inherent in conventional wavefunction based Kohn-Sham approaches, where N is the number of atoms, by eliminating the need to compute wavefunctions altogether; computing instead needed densities, energies, and forces directly from the Kohn-Sham Hamiltonian without diagonalization, while retaining strict systematic improvability and applicability to metals and insulators alike. In combination with atomic-orbital bases, our initial implementation has accomplished Kohn-Sham calculations on systems of over 45,000 atoms.

By combining the new DG and PEXSI approaches, we seek to reach for the first time the length and time scales necessary to accurately model complex solid-electrolyte Li-ion systems.

Having reached a sufficient level of robustness and efficiency, we have now released a parallel implementation of PEXSI (see Software page). Current work centers on the development and application of the combined DG-PEXSI methodology and code which, when complete, will be released also.