Real-Time Equation-of-Motion Coupled-Cluster Cumulant Green’s Function Method: Heterogeneous Parallel Implementation Based on the Tensor Algebra for Many-Body Methods Infrastructure

Abstract

We report the implementation of the real-time equation-of-motion coupled-cluster (RT-EOM-CC) cumulant Green's function method [J. Chem. Phys. 2020, 152, 174113] within the Tensor Algebra for Many-body Methods (TAMM) infrastructure. TAMM is a massively parallel heterogeneous tensor library designed for utilizing forthcoming exascale computing resources. The two-body electron repulsion matrix elements are Cholesky-decomposed, and we imposed spin-explicit forms of the various operators when evaluating the tensor contractions. Unlike our previous real algebra Tensor Contraction Engine (TCE) implementation, the TAMM implementation supports fully complex algebra. The RT-EOM-CC singles (S) and doubles (D) time-dependent amplitudes are propagated using a first-order Adams−Moulton method. This new implementation shows excellent scalability tested up to 500 GPUs using the Zn-porphyrin molecule with 655 basis functions, with parallel efficiencies above 90% up to 400 GPUs. The TAMM RT-EOM-CCSD was used to study core photoemission spectra in the formaldehyde and ethyl trifluoroacetate (ESCA) molecules. Simulations of the latter involve as many as 71 occupied and 649 virtual orbitals. The relative quasiparticle ionization energies and overall spectral functions agree well with available experimental results.

Reduced Scaling Real-Time Coupled Cluster Theory

“…The alternative of real-time CC (RTCC) methods has been discussed nearly as far back as the origins of CC itself in the realm of nuclear physics. − More recently, a renewed interest in RTCC has developed for the reasons discussed above, and in the past 10 years several implementations have been reported, − with new insights into the aspects of numerical integration , and interpretation , as well as applications for a number of spectral properties. ,,− Orbital-adaptive and orbital-optimized variants have also explored the limitations of unrelaxed canonical Hartree–Fock orbitals as well as the effects of alternative reference orbitals on the propagation of unphysical imaginary components to energetics and electric dipole moments. Notably absent, however, are studies of the ability to reduce the cost of RTCC methods.…”

“…Borrowing from the vast literature of reduced-scaling ground-state or frequency-domain CC, there are numerous potential candidates for reducing the cost of RTCC beyond the successful approaches implemented for RT-TDDFT described above. First, the standard nonperturbative truncated approaches used for properties such as CC2 and CC3 are immediately possible, as are property-optimized basis sets. − Further, details of implementation such as the choice of intermediate tensors, the effects of single or mixed precision, or the use of graphical processing units have only just begun to be explored. , An alternative formulation developed separately by the DePrince and Bartlett groups, dubbed the time-dependent equation-of-motion CC (TD-EOM-CC) method, ,,− reduces the cost by targeting the difficulty of numerical integration of multiple “stiff” coupled differential equations. By selection of a given moment function to propagate in time, the coupled right- and left-hand wave function amplitudes of CC theory do not have to be propagated separately, reducing both the number and difficulty of numerical integrations required.…”

“…64−72 Further, details of implementation such as the choice of intermediate tensors, the effects of single or mixed precision, or the use of graphical processing units have only just begun to be explored. 55,73 An alternative formulation developed separately by the DePrince and Bartlett groups, dubbed the timedependent equation-of-motion CC (TD-EOM-CC) method, 52,54,58−60 reduces the cost by targeting the difficulty of numerical integration of multiple "stiff" coupled differential equations. By selection of a given moment function to propagate in time, the coupled right-and left-hand wave function amplitudes of CC theory do not have to be propagated separately, reducing both the number and difficulty of numerical integrations required.…”

Approximate Exponential Integrators for Time-Dependent Equation-of-Motion Coupled Cluster Theory

“…Due to its simplicity and low memory requirement, RK4 has generally been the integrator of choice for time-domain CC methods in the recent past . Symplectic, − multistep, and adaptive integrators for time-domain CC methods have been developed and have yielded significant efficiency improvements over their nonsymplectic counterparts. Exponential Runge–Kutta integrators have been explored in the context of nonlinear time-dependent CC theory (TD-CC) but have yet to see wider adoption.…”

RT-EOM-CCSD Calculations of Inner and Outer Valence Ionization Energies and Spectral Functions

“…Given the similarity between the static and real-time forms of the amplitude equations, the performance per time step of the RT-EOM-CCSD is identical to that of the static method. For instance, in our TAMM implementation of the method we find nearly ideal scaling up to 400 GPUs for a large system with 655 basis functions . The TCE implementation used here has a much more modest performance, scaling only up to a few dozen processors for the systems used here.…”