Distributed Multi-GPU Ab Initio Density Matrix Renormalization Group Algorithm with Applications to the P-Cluster of Nitrogenase.

The presence of many degenerate d/f orbitals makes polynuclear transition-metal compounds, such as iron-sulfur clusters in nitrogenase, challenging for state-of-the-art quantum chemistry methods. To address this challenge, we present the first distributed multi-graphics processing unit (GPU) ab initio density matrix renormalization group (DMRG) algorithm suitable for modern high-performance computing (HPC) infrastructures. The central idea is to parallelize the most computationally intensive part─the multiplication of O(K2) operators with a trial wave function, where K is the number of spatial orbitals, by combining operator parallelism for distributing the workload with a batched algorithm for performing contractions on GPU. With this new implementation, we are able to reach an unprecedentedly large bond dimension D = 14,000 on 48 GPUs (NVIDIA A100 80 GB SXM) for an active space model (114 electrons in 73 active orbitals) of the P-cluster, which is nearly 3 times larger than the bond dimensions reported in previous DMRG calculations for the same system using only central processing units (CPUs).

[Heredity analysis of main characters of nitrogen use efficiency in maize.].

With P1, P2, F1, F2, B1 and B2 generations of two combinations of maize with high nitrogen use efficiency, hereditary capacity and genetic progress of seventeen characters were studied. The random block design was used in the experiment. The results showed that the heritability of each traits was different at different N levels. Broad heritability was between 0.78 and 0.46, and narrow heritability between 0.68 and 0.23 at low N level treatment. Broad heritability was between 0.76 and 0.49, narrow heritability between 0.67 and 0.25 at high N level treatment. The heritability of the chlorophyll content of ear leaf at heading stage period, NUE, ear weight and area of ear leaf were higher than other major characters at low N, the hereditary capacity of the biomass at heading stage period, ear weight, chlorophyll content of ear leaf at heading stage period and biomass at maturity were higher than other major characters at high N. These characters could be selected at early generation at low and high N, respectively.