Short Iterative Lanczos Integration in Time-Dependent Equation-of-Motion Coupled-Cluster Theory

Abstract

A time-dependent (TD) formulation of equation-of-motion coupled-cluster (EOM-CC) theory can provide excited-state information over an arbitrarily wide energy window with a reduced memory footprint relative to conventional, frequency-domain EOM-CC theory. However, the floating-point costs of the time-integration required by TD-EOM-CC are generally far larger than those of the frequency-domain form of the approach. This work considers the potential of the short iterative Lanczos (SIL) integration scheme [J. Chem. Phys. 1986, 85, 5870–5876] to reduce the floating-point costs of TD-EOM-CC simulations. Low-energy and K-edge absorption features for small molecules are evaluated using TD-EOM-CC with single and double excitations, with the time-integrations carried out via SIL and fourth-order Runge–Kutta (RK4) schemes. Spectra derived from SIL- and RK4-driven simulations are nearly indistinguishable, and with an appropriately chosen subspace dimension, the SIL requires far fewer floating-point operations than are required by RK4. For K-edge spectra, SIL is the more efficient scheme by an average factor of 7.2.

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

“…Real-time coupled cluster (RT-CC) methods, in particular, can achieve exceptionally high accuracy in many cases , and have been explored in the context of real-time simulations for some years. − ,− However, RT-CC approaches also suffer from the same affliction as that of their time-independent counterparts, namely, high-degree polynomial scaling with the size of the molecular system. For ground-state coupled cluster theory, techniques, such as local correlation, − fragmentation, − tensor decomposition, − and others, have been developed to permit applications to larger molecular systems than conventional implementations allow.…”

“…For the application to core excitation spectra, Bartlett and co-workers , compared time-independent (TI) EOM-CC and time-dependent (TD) EOM-CCas well as contributions beyond the dipole approximationand concluded that TD-EOM-CC can provide accurate spectra for both core and valence spectra. In addition, in 2021, Li, DePrince, and co-workers applied the short iterative Lanczos integration to the time-dependent (TD) EOM-CC method for a more efficient calculation of K-edge spectra.…”

Real-time equation-of-motion CC cumulant and CC Green's function simulations of photoemission spectra of water and water dimer

“…Time-dependent CC formulations, which provide an alternative way of describing excited-state processes, have attracted significant attention in the last decade. [50][51][52][53][54][55][56] In this context, we have recently developed a real-time equation-of-motion CC (RT-EOM-CC) method [57][58][59][60] to compute the one-electron GF based on a CCSD cumulant approach, which provides several advantages compared to other excited-state formulations. For example, the approach leads to an explicit exponential cumulant representation of the Green's function [61] and, at the same time, allows one to formulate a non-perturbative expression for the cumulant in terms of the solutions to a set of coupled, first-order nonlinear differential equations for the CC amplitudes.…”

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

“…Real-time coupled cluster (RT-CC) methods, in particular, can achieve exceptionally high accuracy in many cases 17,18 and have been explored in the context of real-time simulations for some years. [9][10][11][19][20][21][22][23][24][25][26][27] However, RT-CC approaches also suffer from the same affliction as that of their time-independent counterparts, viz., high-degree polynomial scaling with the size of the molecular system. For ground-state coupled cluster theory, techniques such as local correlation, [28][29][30][31][32][33][34][35] fragmentation, [36][37][38][39] tensor decomposition, [40][41][42][43][44][45] and others have been developed to permit applications to larger molecular systems than conventional implementations allow.…”

“…For the application to core excitation spectra, Bartlett and coworkers 25,26 compared timeindependent (TI) EOM-CC and time-dependent (TD) EOM-CC -as well as contributions beyond the dipole approximation -and concluded that TD-EOM-CC can provide accurate spectra for both core and valance spectra. In addition, in 2021, Li, DePrince, and co-workers 27 applied the short iterative Lanczos integration to the time-dependent (TD) EOM-CC method for a more efficient calculation of K-edge spectra.…”