Hartree-Fock (HF), density functional theory (DFT) and their parameterized variants such as semi-empirical molecular orbital (SEMO) or tight-binding DFT (DFTB) methods are all based on the self-consistent field (SCF) theory, which generally requires solving an eigenvalue problem many times until a convergence criteria is met. Conventionally, dense linear algebra methods are used to diagonalize the Fock matrix, and this part of the calculation becomes the bottleneck when the matrix size reaches thousands. We have developed and benchmarked a PETSc/SLEPc based sparse eigensolver that makes use of shift-and-invert parallel spectral transformations (SIPs). We demonstrate three main advantages of SIPs compared to dense solvers: 1) SIPs exploits the sparsity of the matrices, hence reduces the memory footprint, and computational complexity 2) SIPs divides the eigenvalue problem into chunks that can be solved independently enabling proven scalability up to hundreds of thousands of cores. 3) SIPs makes use of the eigenvalue distribution at a previous iteration to improve the job balance in the subsequent iteration. We will present benchmark results for the standalone solver for DFTB calculations, SIPs integrated DFT package SIESTA, and a prototype SEMO code that we have developed.

Parameterization is important to reduce the computational cost by eliminating integrals and enhancing sparsity and to obtain useful accuracy for large-scale quantum chemistry calculations. Well-calibrated parameters are required not only for SEMO, or DFTB methods, but also for hybrid functionals of DFT. Hence, high-accuracy quantum chemistry calculations are necessary to train parameters for a wide-range of methods. We will present our benchmark results (coupled-cluster calculations at the basis-set limit) for transition metal oxide clusters and their comparison with different DFT functionals.