Quantum perturbation theory is pivotal in determining the critical physical properties of materials. The first-principles computations of these properties have yielded profound and quantitative insights in diverse domains of chemistry and physics. In this work, we propose a portable and scalable OpenCL implementation for quantum perturbation theory, which can be generalized across various high-performance computing (HPC) systems. Optimal portability is realized through the utilization of a cross-platform unified interface and a collection of performance-portable heterogeneous optimizations. Exceptional scalability is attained by addressing major constraints on memory and communication, employing a locality-enhancing task mapping strategy and a packed hierarchical collective communication scheme. Experiments on two advanced supercomputers demonstrate that our implementation exhibits remarkably performance on various material systems, scaling the system to 200,000 atoms with all-electron precision. This research enables all-electron quantum perturbation simulations on substantially larger molecular scales, with a potentially significant impact on progress in material sciences.

The first-principles approach based on density-functional theory (DFT)/density-functional perturbation theory (DFPT) is widely used in calculations of the systems’ ground state energy, response properties (e.g., polarizability, phonon dispersions) and is playing an increasingly important role in chemistry, physics and materials science. For the large-scale calculations, the computation of the density matrix/response density matrix in DFT/DFPT has become the main performance bottleneck. One of the solutions is using the linear scaling method to get the density matrix and response density matrix. Here a massively parallel medium sparse matrix-matrix multiplication algorithm is designed for first-principle calculations and implemented on the new-generation Sunway supercomputer. Experiments show that the proposed method has obvious performance advantages compared to the original parallel version under moderate sparsity. The computing cores scale to 3,900,000 with strong scalability of 77.3$\%$.

Raman spectroscopy provides chemical and compositional information that can serve as a structural fingerprint for various materials. Therefore, simulations of Raman spectra, including both quantum perturbation analyses and ground-state calculations are of significant interest. However, highly accurate full quantum mechanical (QM) simulations of Raman spectra have previously been confined to small systems. For large systems such as biological materials, the computational cost of full QM simulations is extremely high, and their extension to such systems remains challenging. In the work described here, by employing robust new algorithms and advances in implementation for the many-core architectures, we are able to perform fast, accurate, and massively parallel full ab initio simulations of the Raman spectra of biological systems with excellent strong and weak scaling, thereby providing a starting point for applying QM approaches to structural studies of such systems.

Raman spectroscopy provides chemical and compositional information that can serve as a structural fingerprint for various materials. Therefore, simulations of Raman spectra, including both quantum perturbation analyses and ground-state calculations, are of significant interest. However, highly accurate full quantum mechanical (QM) simulations of Raman spectra have previously been confined to small systems. For large systems such as biological materials, full QM simulations have an extremely high computational cost and remain challenging. In this work, robust new algorithms and advanced implementations on many-core architectures are employed to enable fast, accurate, and massively parallel full ab initio simulations of the Raman spectra of realistic biological systems containing up to 3006 atoms, with excellent strong and weak scaling. Up to a performance of 468.5 PFLOP/s in double-precision and 813.7 PLOPS/s in mixed-half precision is achieved on the new-generation Sunway high-performance computing system, suggesting the potential for new applications of the QM approach to biological systems.