Research And Implementation Of Hartree-Fock And DFT Algorithm Based On CPU/GPU Heterogeneous Architecture

Graphical Processing Units(GPUs)are emerging as a promising architecture to tackle many computational bottlenecks in quantum chemistry calculations.Herein,we present the details of our GPU-accelerated Hartree-Fock(HF)and Density functional theory(DFT)algorithms in Beijing Density Functional(BDF)Package,and the large scale parallel DFT algorithm on CPU + GPU heterogeneous computing platform.All time-consuming steps,such as calculation of electron repulsion integrals(ERIs),the formation of Fock matrix,the exchange-correlation terms,and the calculation of gradient of exchange-correlation energy in HF and DFT are implemented on the GPU.In the algorithm,the Coulomb-and Exchange-matrix are evaluated directly on GPU by contracting the primitive ERIs with density matrix.The 1T1PI(One Thread-One Primitive Integral)algorithm is used to calculate the ERIs on GPU.After the full Coulomband Exchange-matrix are computed on the GPU,the resulting matrices are copy back to the CPU and accumulated with the one-electron terms to obtain the final Fock matrix.The exchange-correlation terms and the gradient of exchange-correlation energy are calculated on GPU through a numerical integration procedure due to the complex form of the exchange-correlation functionals.For the heterogeneous computing platform of CPU and GPU,two parallel DFT algorithms of OpenMP+OpenCL and MPI+OpenMP+OpenCL are implemented.The program utilizes the OpenCL platform and thus can execute on a variety of computing devices from different companies.Benchmark calculations carried out on several different GPUs from NVIDIA and AMD indicates that the algorithm implemented on the GPU can achieve up to 148-fold speedup over a serial CPU implementation.Because all operations on GPU are carried out in double-precision accuracy,the energy and gradient calculated on the GPU is as accurate as the resulting calculated on the CPU.The parallel tests on multiple compute nodes shows that both parallel DFT algorithms of OpenMP+OpenCL and MPI+OpenMP+OpenCL achieve good acceleration.The BDF program supports the Time-Dependent Density Functional Theory(TDDFT)calculation of excited state.Finally,the TDDFT calculation of glyceraldehyde molecule are completed using BDF program,and write a python program to draw its Ultraviolet–visible Spectroscopy.According to the output file of TDDFT calculation,we get the UV-Vis Spectrum of theoretical calculation,which is of great significance to predict the experimental results and explain the experimental phenomena.