Heterogeneous CPU + GPU Algorithm for Variational Two-Electron Reduced-Density Matrix-Driven Complete Active-Space Self-Consistent Field Theory

We present a heterogeneous central processing unit (CPU) + graphical processing unit (GPU) algorithm for the direct variational optimization of the two-electron reduced-density matrix (2RDM) under two-particle N-representability conditions. This variational 2RDM (v2RDM) approach is the driver for a polynomially scaling approximation to configuration-interaction-driven complete active-space self-consistent field (CASSCF) theory. For v2RDM-based CASSCF computations involving an active space consisting of 50 electrons in 50 orbitals, we observe a speedup of a factor of 3.7 when the code is executed on a combination of an NVIDIA TITAN V GPU and an Intel Core i7-6850k CPU, relative to the case when the code is executed on the CPU alone. We use this GPU-accelerated v2RDM-CASSCF algorithm to explore the electronic structure of the 3,k-circumacene and 3,k-periacene series (k = 2-7) and compare indicators of polyradical character in the lowest-energy singlet states to those observed for oligoacene molecules. The singlet states in larger circumacene and periacene molecules display the same polyradical characteristics observed in oligoacenes, with the onset of this behavior occurring at smallest k for periacenes, followed by the circumacenes and then the oligoacenes. However, the unpaired electron density that accumulates along the zigzag edge of the circumacenes is slightly less than that which accumulates in the oligoacenes, while periacenes clearly exhibit the greatest buildup of unpaired electron density in this region.