Non-Markovian Memory Kernels in Condensed-Phase Chemical Dynamics: From Dipole Dephasing and Conical Intersections to Spin Crossover and Radical-Pair Magnetoreception
Abstract
Standard theoretical formulations of ultrafast condensed-phase molecular processes rely heavily on Markovian master equations and time-local Lindblad semigroups that assume memoryless bath relaxation (t ≫ τB). However, in viscous solvents, structured protein binding pockets, and biomolecular matrices, environmental fluctuations exhibit power-law algebraic memory tails K(t) ∝ t−µ (µ ∈ (0, 1)) where Markovian approximations break down. In this work, we develop an analytical and computational framework for non-Markovian chemical dynamics governed by the causal Caputo fractional memory kernel of the Multi-Electron Unified Wave Equation (MEUWE). We apply this framework across five benchmark regimes of contemporary chemical physics. First, in molecular dipole autocorrelation dynamics, fractional dephasing replaces exponential Markovian damping with Mittag-Leffler decay Eµ (−Γ0 τ0µ tµ), extending the 10% electronic coherence lifetime by 13.40× (134.15 fs vs. 10.01 fs in H2), while coupled-channel Volterra equations achieve a benchmark vertical excitation mean absolute error (MAE) of 37.85 meV across pyscf Full Configuration Interaction (FCI) benchmarks with exact zero self-interaction error on one-electron ions (0.00 meV vs. TD-B3LYP 1884.37 meV). Second, at the 2D two-state conical intersection governing ultrafast rhodopsin retinal photoisomerization, viscoelastic solvent memory generates a +24.75 fs delay in non-adiabatic transition onset while suppressing coherent recoil back-transfer by up to 99.7% and preserving an all-trans photoproduct quantum yield of 62.625%. Third, in avian cryptochrome magnetoreception, fractional sub-Ohmic spin-bath relaxation delays singlet-triplet dephasing, producing an anisotropic magnetic compass contrast gain of 11.27× (and up to 266.94× at low fields) relative to standard exponential models. Fourth, in [Fe(bpy)3]2+ spin crossover, exact Stieltjes–Laplace inversion yields an asymmetric Fuoss–Kirkwood distribution of relaxation lifetimes spanning 2.288 decades of full-width at half-maximum (FWHM). Finally, on chemical reaction barriers, fractional Grote–Hynes transmission theory predicts a non-monotonic Kramers turnover with enhanced dynamic barrier transmission κGH = 0.513620 (vs. Markovian Kramers 0.242536). These results establish a unified, non-Markovian foundation for condensed-phase photochemistry, quantum biology, and barrier-crossing kinetics.
Related
- Directional transfer from coherence to longitudinal polarization and algebraic storage in a transmon with Markovian dephasing and a glassy environment: A non-Markovian fractional renewal model
- Correlated memory effect of environment in radical-pair magnetoreception
- Heating dynamics of correlated fermions under dephasing
- Quantum geometry phenomena in condensed matter systems
- Retrieval of the dephasing time in solids from spatial high-harmonic spectroscopy
BibTeX
@misc{singh2026nonmarkovian,
title = {{Non-Markovian Memory Kernels in Condensed-Phase Chemical Dynamics: From Dipole Dephasing and Conical Intersections to Spin Crossover and Radical-Pair Magnetoreception}},
author = {Mehardeep Singh},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15010869/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010869/v1},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - Non-Markovian Memory Kernels in Condensed-Phase Chemical Dynamics: From Dipole Dephasing and Conical Intersections to Spin Crossover and Radical-Pair Magnetoreception
AU - Mehardeep Singh
PY - 2026
DA - 2026/10/22
PB - ChemRxiv
DO - 10.26434/chemrxiv.15010869/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010869/v1
AB - Standard theoretical formulations of ultrafast condensed-phase molecular processes rely heavily on Markovian master equations and time-local Lindblad semigroups that assume memoryless bath relaxation (t ≫ τB). However, in viscous solvents, structured protein binding pockets, and biomolecular matrices, environmental fluctuations exhibit power-law algebraic memory tails K(t) ∝ t−µ (µ ∈ (0, 1)) where Markovian approximations break down. In this work, we develop an analytical and computational framework for non-Markovian chemical dynamics governed by the causal Caputo fractional memory kernel of the Multi-Electron Unified Wave Equation (MEUWE). We apply this framework across five benchmark regimes of contemporary chemical physics. First, in molecular dipole autocorrelation dynamics, fractional dephasing replaces exponential Markovian damping with Mittag-Leffler decay Eµ (−Γ0 τ0µ tµ), extending the 10% electronic coherence lifetime by 13.40× (134.15 fs vs. 10.01 fs in H2), while coupled-channel Volterra equations achieve a benchmark vertical excitation mean absolute error (MAE) of 37.85 meV across pyscf Full Configuration Interaction (FCI) benchmarks with exact zero self-interaction error on one-electron ions (0.00 meV vs. TD-B3LYP 1884.37 meV). Second, at the 2D two-state conical intersection governing ultrafast rhodopsin retinal photoisomerization, viscoelastic solvent memory generates a +24.75 fs delay in non-adiabatic transition onset while suppressing coherent recoil back-transfer by up to 99.7% and preserving an all-trans photoproduct quantum yield of 62.625%. Third, in avian cryptochrome magnetoreception, fractional sub-Ohmic spin-bath relaxation delays singlet-triplet dephasing, producing an anisotropic magnetic compass contrast gain of 11.27× (and up to 266.94× at low fields) relative to standard exponential models. Fourth, in [Fe(bpy)3]2+ spin crossover, exact Stieltjes–Laplace inversion yields an asymmetric Fuoss–Kirkwood distribution of relaxation lifetimes spanning 2.288 decades of full-width at half-maximum (FWHM). Finally, on chemical reaction barriers, fractional Grote–Hynes transmission theory predicts a non-monotonic Kramers turnover with enhanced dynamic barrier transmission κGH = 0.513620 (vs. Markovian Kramers 0.242536). These results establish a unified, non-Markovian foundation for condensed-phase photochemistry, quantum biology, and barrier-crossing kinetics.
ER -