Distributed Memory, GPU Accelerated Fock Construction for Hybrid, Gaussian Basis Density Functional Theory

With the growing reliance of modern supercomputers on accelerator-based architectures such a GPUs, the development and optimization of electronic structure methods to exploit these massively parallel resources has become a recent priority. While significant strides have been made in the development of GPU accelerated, distributed memory algorithms for many-body (e.g. coupled-cluster) and spectral single-body (e.g. planewave, real-space and finite-element density functional theory [DFT]), the vast majority of GPU-accelerated Gaussian atomic orbital methods have focused on shared memory systems with only a handful of examples pursuing massive parallelism on distributed memory GPU architectures. In the present work, we present a set of distributed memory algorithms for the evaluation of the Coulomb and exact-exchange matrices for hybrid Kohn-Sham DFT with Gaussian basis sets via direct density-fitted (DF-J-Engine) and seminumerical (sn-K) methods, respectively. The absolute performance and strong scalability of the developed methods are demonstrated on systems ranging from a few hundred to over one thousand atoms using up to 128 NVIDIA A100 GPUs on the Perlmutter supercomputer.Comment: 45 pages, 9 figure

Evaluation of Left Ventricular Endocardial Volumes and Ejection Fractions Computed from Gated Perfusion SPECT with MR: Comparision of Two Methods

Background. Two methods of computing left ventricular volumes and ejection fraction (EF) from 8-frame gated perfusion single photon emission computed tomography (SPECT) were compared with each other and with magnetic resonance (MR) imaging. Methods and Results. Thirty-five subjects underwent 8-frame gated dual-isotope SPECT imaging and 12- to 16-frame gated MR imaging. Endocardial boundaries on short-axis MR images were hand traced by experts blinded to any SPECT results. Volumes and EF were computed with the use of Simpson\u27s rule. SPECT images were analyzed for the same functional variables with the use of 2 automatic programs, Quantitative Gated SPECT (QGS) and the Emory Cardiac Toolbox (ECTb). The mean difference between MR and SPECT EF was 0.008 for ECTb and 0.08 for QGS. QGS showed a slight trend toward higher correlation for EF (r = 0.72, SE of the ESTIMATE = 0.08) than ECTb (r = 0.70, SE of the ESTIMATE = 0.09). For both SPECT methods, left ventricular volumes were similarly correlated with MR, although SPECT volumes were higher than MR values by approximately 30%. Conclusions. QGS and ECTb values of cardiac function computed from 8-frame gated perfusion SPECT correlate very well with each other and correlate well with MR. Averaged over all subjects, ECTb measurements of EF are not significantly different from MR values but QGS significantly underestimates the MR values