Accelerating Real-Time Coupled Cluster Methods with Single-Precision Arithmetic and Adaptive Numerical Integration

Abstract

We explore the framework of a real-time coupled cluster method with a focus on improving its computational efficiency. Propagation of the wave function via the time-dependent Schrödinger equation places high demands on computing resources, particularly for high level theories such as coupled cluster with polynomial scaling. Similar to earlier investigations of coupled cluster properties, we demonstrate that the use of single-precision arithmetic reduces both the storage and multiplicative costs of the real-time simulation by approximately a factor of 2 with no significant impact on the resulting UV/vis absorption spectrum computed via the Fourier transform of the time-dependent dipole moment. Additional speedupsof up to a factor of 14 in test simulations of water clustersare obtained via a straightforward GPU-based implementation as compared to conventional CPU calculations. We also find that further performance optimization is accessible through sagacious selection of numerical integration algorithms, and the adaptive methods, such as the Cash–Karp integrator, provide an effective balance between computing costs and numerical stability. Finally, we demonstrate that a simple mixed-step integrator based on the conventional fourth-order Runge–Kutta approach is capable of stable propagations even for strong external fields, provided the time step is appropriately adapted to the duration of the laser pulse with only minimal computational overhead.

Time‐dependent coupled‐cluster theory

“…More recently, Wang, Peyton, and Crawford 92 investigated modified Runge–Kutta integrators with adaptive time step, which increases stability when the parameters oscillate rapidly and allows larger time steps when they do not. Remarkably, stability and accuracy is maintained also in conjunction with single‐precision arithmetic, which allows highly efficient calculations on graphical processing units.…”

Dynamic Precision Approach for Accelerating Large-Scale Eigenvalue Solvers in Electronic Structure Calculations on Graphics Processing Units

“…A mixed precision (MP) method has been extensively studied to accelerate various scientific computations, including electronic structure calculations. ,,,,− In this method, some part of DP operations is replaced by SP to achieve acceleration. The MP approach has been studied a lot, especially in linear algebra algorithms, − ,, which have also been applied to electronic structure calculations. ,, A detailed explanation can be found in recent review papers. − Many methods using MP have also been proposed to accelerate two-electron integrals in the Hartree–Fock theory and perturbation theory. ,,, …”

Reduced Scaling Real-Time Coupled Cluster Theory

“…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.…”