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arxiv: 2602.00985 · v2 · submitted 2026-02-01 · ⚛️ physics.chem-ph

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 , Xiaosong Li , A. Eugene DePrince III This is my paper

Pith reviewed 2026-05-16 08:57 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords time-dependent EOMCCrelativistic two-componentopen-shell systemselectron attachmentionization potentialabsorption spectraimaginary-time propagationreal-time dynamics
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The pith

A combined imaginary-time and real-time propagation scheme at the relativistic EA/IP-EOMCC level produces linear absorption spectra that match frequency-domain results for open-shell atoms and molecules.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a time-dependent approach to linear absorption spectra within the electron-attachment and ionization-potential equation-of-motion coupled-cluster framework under an exact two-component relativistic treatment. Initial states are prepared by propagating a simple Koopmans determinant in imaginary time; the subsequent real-time evolution supplies the electric-dipole autocorrelation function whose Fourier transform yields the spectrum. For a test set of open-shell atoms (Na, K, Rb, F, Cl, Br) and diatomics (SiH, ClO) the resulting lineshapes reproduce the absolute energies and intensities obtained from conventional frequency-domain EA/IP-EOMCC calculations. The work therefore offers an alternative route to spectra that avoids explicit solution of the full eigenvalue problem while remaining inside the same coupled-cluster hierarchy.

Core claim

The TD-EA/IP-EOMCC method obtains the absorption lineshape as the Fourier transform of the real-time electric-dipole autocorrelation function; the required initial EA or IP eigenstates are approximated by imaginary-time propagation of a Koopmans reference determinant, and these spectra closely reproduce the positions and intensities of peaks computed by standard frequency-domain EA/IP-EOMCC for the open-shell atomic and diatomic systems examined.

What carries the argument

Imaginary-time propagation of a Koopmans EA/IP determinant to approximate the lowest eigenstates, followed by real-time evolution that furnishes the dipole autocorrelation function whose Fourier transform gives the spectrum, all inside the exact two-component relativistic EOMCC framework.

If this is right

  • Absorption spectra of open-shell species can be extracted without solving the full frequency-domain eigenvalue problem.
  • The same real-time propagation infrastructure can in principle be reused for time-dependent properties beyond linear absorption.
  • Longer imaginary-time propagations are required whenever low-lying states have non-negligible overlap with the Koopmans reference.
  • The method remains formally exact within the chosen EOMCC truncation once the imaginary-time step is taken to convergence.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach may extend naturally to real-time simulations of laser-driven dynamics or nonlinear spectroscopies once the initial-state preparation is validated.
  • Because the propagation steps are independent of the final frequency grid, the method could offer computational savings for dense spectra or broad energy windows.
  • Similar imaginary-time preparation might be combined with other real-time propagators (TD-DFT, TD-HF) to test transferability beyond coupled-cluster.

Load-bearing premise

Imaginary-time evolution starting from a Koopmans determinant yields a sufficiently accurate approximation to the lowest-energy eigenstates even when other low-lying states overlap with that initial determinant.

What would settle it

A direct comparison on any of the tested open-shell systems in which the imaginary-time-prepared initial state produces peak positions or relative intensities that deviate from the converged frequency-domain EA/IP-EOMCC spectrum would falsify the central claim.

read the original 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 Koopmans EA/IP state in imaginary time. TD-EA/IP-EOMCC linear absorption spectra of open-shell atomic (Na, K, Rb, F, Cl, and Br) and diatomic (SiH and ClO) systems 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 Koopmans 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper presents a combined imaginary-time and real-time time-dependent relativistic two-component EA/IP-EOMCC method for computing linear absorption spectra of open-shell systems. Initial states are approximated by imaginary-time propagation of Koopmans EA/IP determinants; real-time propagation then yields the electric dipole autocorrelation function whose Fourier transform produces the absorption lineshape. The approach is demonstrated on open-shell atoms (Na, K, Rb, F, Cl, Br) and diatomics (SiH, ClO), with the resulting spectra reported to closely reproduce those from standard frequency-domain TD-EA/IP-EOMCC calculations. The abstract notes that low-lying states with non-negligible overlap with the Koopmans determinant increase the imaginary-time propagation length needed for correct absolute energies and intensities.

Significance. If the imaginary-time approximation is shown to be systematically convergent, the method supplies a viable real-time route to relativistic open-shell spectra that avoids explicit diagonalization of the EOMCC matrix. The reported numerical agreement with frequency-domain results for the tested systems indicates practical utility, particularly for cases where frequency-domain implementations become costly. The work builds directly on established EOMCC and real-time techniques without introducing fitted parameters or self-referential quantities.

major comments (2)
  1. [Abstract and imaginary-time propagation procedure] The central claim that the TD spectra reproduce frequency-domain results rests on the assumption that imaginary-time propagation of the Koopmans state yields a sufficiently accurate approximation to the lowest eigenstate. The abstract explicitly states that non-negligible overlap with low-lying states affects the required propagation length and the resulting absolute energies and peak intensities, yet no convergence metric (energy stabilization threshold, residual norm, or overlap with the target state) is described. This is load-bearing because any residual contamination propagates directly into the real-time autocorrelation and its Fourier transform.
  2. [Results section on atomic and diatomic spectra] No quantitative error metrics (e.g., mean absolute deviation in peak positions or integrated intensity differences) are supplied for the comparison between TD-EA/IP-EOMCC and frequency-domain spectra. Visual agreement alone is insufficient to establish that absolute energies and intensities are correctly recovered across the full set of atoms and diatomics, especially when propagation lengths are system-dependent.
minor comments (2)
  1. [Computational details] Basis-set details, relativistic Hamiltonian specifics (e.g., exact two-component parameters), and any geometry parameters for the diatomics should be tabulated for reproducibility.
  2. [Method and results] The manuscript should clarify whether the same time-step and propagation parameters are used uniformly or adjusted per system, and how this choice is validated.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address each major point below and will revise the manuscript accordingly to improve clarity and rigor.

read point-by-point responses

  1. Referee: [Abstract and imaginary-time propagation procedure] The central claim that the TD spectra reproduce frequency-domain results rests on the assumption that imaginary-time propagation of the Koopmans state yields a sufficiently accurate approximation to the lowest eigenstate. The abstract explicitly states that non-negligible overlap with low-lying states affects the required propagation length and the resulting absolute energies and peak intensities, yet no convergence metric (energy stabilization threshold, residual norm, or overlap with the target state) is described. This is load-bearing because any residual contamination propagates directly into the real-time autocorrelation and its Fourier transform.

    Authors: We agree that an explicit description of the convergence criterion is necessary for reproducibility and to quantify residual contamination. In the revised manuscript we will add a dedicated paragraph in the Methods section detailing the stopping criterion (energy stabilization to within 10^{-6} hartree together with monitoring of the imaginary-time residual norm) and will tabulate the propagation lengths used for each atom and molecule. We will also note how these lengths correlate with the overlap of the Koopmans determinant with low-lying states, directly addressing the concern raised. revision: yes

  2. Referee: [Results section on atomic and diatomic spectra] No quantitative error metrics (e.g., mean absolute deviation in peak positions or integrated intensity differences) are supplied for the comparison between TD-EA/IP-EOMCC and frequency-domain spectra. Visual agreement alone is insufficient to establish that absolute energies and intensities are correctly recovered across the full set of atoms and diatomics, especially when propagation lengths are system-dependent.

    Authors: We acknowledge that quantitative metrics strengthen the validation. In the revised Results section we will include a table reporting mean absolute deviations (in eV) for the positions of the principal peaks and relative intensity differences (as percentages) between the time-dependent and frequency-domain spectra for all eight systems. These metrics will be computed after aligning the spectra on the lowest-energy feature and will be accompanied by a brief discussion of any system-dependent trends linked to imaginary-time propagation length. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation builds on standard EOMCC and propagation methods without reduction to inputs

full rationale

The paper derives a combined imaginary-time/real-time TD-EA/IP-EOMCC procedure for linear absorption spectra by propagating a Koopmans EA/IP determinant in imaginary time to approximate the lowest eigenstate, then performing real-time evolution to obtain the dipole autocorrelation function whose Fourier transform yields the spectrum. This chain relies on established EOMCC equations and time-propagation numerics; the reported numerical agreement with frequency-domain EOMCC results functions as external validation rather than a definitional or fitted equivalence. No parameter is fitted to the target spectra, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz is smuggled in. The derivation remains self-contained against independent benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard coupled-cluster and EOMCC approximations plus the assumption that imaginary-time propagation converges to the desired eigenstates; no new free parameters, invented particles, or ad-hoc entities are introduced.

axioms (2)
  • domain assumption Standard EOMCC approximations remain valid for the open-shell atomic and diatomic systems studied
    The method inherits accuracy expectations from prior EOMCC work without additional justification in the abstract.
  • domain assumption Imaginary-time propagation of the Koopmans determinant yields a usable approximation to the lowest EA/IP eigenstates
    This is the key premise required for the real-time step to produce correct spectra.

pith-pipeline@v0.9.0 · 5552 in / 1432 out tokens · 21961 ms · 2026-05-16T08:57:40.718450+00:00 · methodology

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