Green-function thimbles for internal conversion
- 1Department of Chemistry, Faculty of Science
- 2University of Helsinki
Abstract
Oscillatory real-time integrals and the complete quadratic transformation between electronic-state normal modes are persistent obstacles in molecular internal-conversion calculations. We develop a finite-temperature Tyablikov–Moskalenko Green-function formulation that retains unequal frequencies, equilibrium displacement, Duschinsky rotation, the anomalous squeezing block, and a general first-order Herzberg–Teller nonadiabatic operator. The closed equations of motion reconstruct the vibronic correlation function by coupling-constant integration, while analytic continuation to complex time permits both a systematic saddle expansion and globally controlled integration on Lefschetz thimbles without numerical damping. For the 102-mode tetraoxa[8]circulene (4B) model at 300 K, the complete rate is 1.656× 10 7 s −1 at 18500 cm −1 . Herzberg–Teller coupling and Duschinsky rotation increase the rate by factors of approximately 2.45 and 2.06, respectively, while the squeezing contribution is about 46% in the mode-mixed calculation. The next-to-leading saddle result differs from the full thimble value by 0.66% at the molecular gap; one contributing thimble and no Stokes transition are found throughout 5000–35000 cm −1 . The same formalism gives aligned electric-and magnetic-field thresholds of 1.06 × 108 V m −1 and 41.6 T. The method therefore provides a fast, damping-free route to complete harmonic vibronic rates together with an explicit global test of the integration contour.
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BibTeX
@misc{valiev2026greenfunction,
title = {{Green-function thimbles for internal conversion}},
author = {Rashid Valiev},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15010092/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010092/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Green-function thimbles for internal conversion
AU - Rashid Valiev
PY - 2026
DA - 2026/10/08
PB - ChemRxiv
DO - 10.26434/chemrxiv.15010092/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010092/v1
AB - Oscillatory real-time integrals and the complete quadratic transformation between electronic-state normal modes are persistent obstacles in molecular internal-conversion calculations. We develop a finite-temperature Tyablikov–Moskalenko Green-function formulation that retains unequal frequencies, equilibrium displacement, Duschinsky rotation, the anomalous squeezing block, and a general first-order Herzberg–Teller nonadiabatic operator. The closed equations of motion reconstruct the vibronic correlation function by coupling-constant integration, while analytic continuation to complex time permits both a systematic saddle expansion and globally controlled integration on Lefschetz thimbles without numerical damping. For the 102-mode tetraoxa[8]circulene (4B) model at 300 K, the complete rate is 1.656× 10 7 s −1 at 18500 cm −1 . Herzberg–Teller coupling and Duschinsky rotation increase the rate by factors of approximately 2.45 and 2.06, respectively, while the squeezing contribution is about 46% in the mode-mixed calculation. The next-to-leading saddle result differs from the full thimble value by 0.66% at the molecular gap; one contributing thimble and no Stokes transition are found throughout 5000–35000 cm −1 . The same formalism gives aligned electric-and magnetic-field thresholds of 1.06 × 108 V m −1 and 41.6 T. The method therefore provides a fast, damping-free route to complete harmonic vibronic rates together with an explicit global test of the integration contour.
ER -