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Time-Dependent Relativistic Two-Component Equation-of-Motion Coupled-Cluster for Open-Shell Systems: TD-EA/IP-EOMCC

P. D. Varuna S. Pathirage, Stephen H. Yuwono, A. Eugene DePrince

TL;DR

The authors develop a real-time, time-dependent EA/IP-EOMCCSD method within an exact two-component relativistic framework to compute linear absorption spectra of open-shell species. By propagating imaginary-time Koopman determinants, they generate suitable initial states for real-time evolution, enabling momentum- and energy-resolved spectra via the dipole autocorrelation. The approach yields spectra in good agreement with frequency-domain EA/IP-EOMCCSD results, with absolute peak positions converging as the initial state improves and relative peak positions remaining robust. This TD-EA/IP-EOMCC framework reduces memory requirements and extends accurate spectroscopic capabilities to open-shell systems with spin-orbit coupling, validated on group I alkali metals and group VII halogens. Peak-intensity trends and zero-field splitting features further demonstrate the practical reliability of the imaginary-time initialization in shaping spectral intensities.

Abstract

We present a combined imaginary-time/real-time time-dependent (TD) approach for evaluating linear absorption spectra of open-shell systems at the electron attachment (EA) and ionization potential (IP) equation-of-motion coupled-cluster (EOMCC) levels of theory and within the exact two-component relativistic framework. The absorption lineshape is given by the Fourier transform of the electric dipole autocorrelation function, which is obtained from a real-time simulation. Approximations of the lowest-energy EA- and IP-EOMCC eigenstates, which are required as initial states for the real-time simulation, are generated by propagating a Koopman EA/IP state in imaginary time. TD-EA/IP-EOMCC linear absorption spectra of open-shell atomic systems (Na, K, Rb, F, Cl, and Br) closely reproduce those obtained from standard TD-EA/IP procedures carried out in the frequency domain. We find that the existence of low-lying states with non-negligible overlap with the Koopman determinant impacts the length of the imaginary-time propagation required to obtain an initial state that produces correct absolute energies and peak height intensities in spectra extracted from the subsequent real-time TD-EA/IP-EOMCC calculations.

Time-Dependent Relativistic Two-Component Equation-of-Motion Coupled-Cluster for Open-Shell Systems: TD-EA/IP-EOMCC

TL;DR

The authors develop a real-time, time-dependent EA/IP-EOMCCSD method within an exact two-component relativistic framework to compute linear absorption spectra of open-shell species. By propagating imaginary-time Koopman determinants, they generate suitable initial states for real-time evolution, enabling momentum- and energy-resolved spectra via the dipole autocorrelation. The approach yields spectra in good agreement with frequency-domain EA/IP-EOMCCSD results, with absolute peak positions converging as the initial state improves and relative peak positions remaining robust. This TD-EA/IP-EOMCC framework reduces memory requirements and extends accurate spectroscopic capabilities to open-shell systems with spin-orbit coupling, validated on group I alkali metals and group VII halogens. Peak-intensity trends and zero-field splitting features further demonstrate the practical reliability of the imaginary-time initialization in shaping spectral intensities.

Abstract

We present a combined imaginary-time/real-time time-dependent (TD) approach for evaluating linear absorption spectra of open-shell systems at the electron attachment (EA) and ionization potential (IP) equation-of-motion coupled-cluster (EOMCC) levels of theory and within the exact two-component relativistic framework. The absorption lineshape is given by the Fourier transform of the electric dipole autocorrelation function, which is obtained from a real-time simulation. Approximations of the lowest-energy EA- and IP-EOMCC eigenstates, which are required as initial states for the real-time simulation, are generated by propagating a Koopman EA/IP state in imaginary time. TD-EA/IP-EOMCC linear absorption spectra of open-shell atomic systems (Na, K, Rb, F, Cl, and Br) closely reproduce those obtained from standard TD-EA/IP procedures carried out in the frequency domain. We find that the existence of low-lying states with non-negligible overlap with the Koopman determinant impacts the length of the imaginary-time propagation required to obtain an initial state that produces correct absolute energies and peak height intensities in spectra extracted from the subsequent real-time TD-EA/IP-EOMCC calculations.
Paper Structure (7 sections, 25 equations, 2 figures, 2 tables)

This paper contains 7 sections, 25 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Theory
  3. The EA/IP-EOMCCSD formalism
  4. Extension of EA/IP-EOMCCSD to the time-domain
  5. Computational Details
  6. Results and Discussion
  7. Conclusions

Figures (2)

  • Figure 1: Energy convergence for group I atoms with EA-EOMCCSD (top) and group VII atoms with IP-EOMCCSD (bottom).
  • Figure 2: Real-time spectrum obtained from Koopman state ($\tau = 0.0$, in blue), imaginary propagated states at $\tau = 2.5, 5.0, 7.5$ and $10.0$ (in orange, green, red and purple respectively) and the frequency domain spectrum (in brown) for alkali metals and halogens. The peak heights are normalized to the highest intensity peak within the range 0 -- 50 eV. For all the atoms except for F, the peak with the highest intensity is situated within the range from 0 -- 50 eV. The peak with the highest intensity for F is situated $\approx 107.5$ eV (see Fig. S2 in Supporting Information).