Quantized time correlation function approach to nonadiabatic decay rates in condensed phase: Application to solvated electrons in water and methanol

Abstract

Abstract:A new, alternative form of the golden rule formula defining the non-adiabatic transition rate between two quantum states in condensed phase is presented. The formula involves the quantum time correlation function of the energy gap, of the non-adiabatic coupling, and their cross terms. Those quantities can be inferred from their classical counterparts, determined via MD simulations. The formalism is applied to the problem of the non-adiabatic s p → relaxation of an equilibrated pelectron in water and methanol. We find that, in both solvent, the relaxation is induced by the coupling to the vibrational modes and the quantum effects modify the rate by a factor of 2-10 depending on the quantization procedure applied. The resulting p-state lifetime for a hypothetical equilibrium excited state appears extremely short, in the sub-100 fs regime. Although this result is in contrast with all previous theoretical predictions, we also illustrate that the lifetimes computed here are very sensitive to the simulated electronic quantum gap and to the strongly correlated non-adiabatic coupling.d

Excess electrons in methanol clusters: Beyond the one-electron picture

“…26 The improved potential was then successfully applied in QCMD simulations of excess electrons in bulk methanol and in methanol clusters. 26,27,28,15 The emerging molecular picture provided semiquantitative agreement between experiment and theory, and in particular, was consistent with the presence of two isomers in cluster experiments. 11,15 Nevertheless, despite the relatively clear picture of the mechanistic details of the interactions and the dynamics, it is surprising that no effort has been made to perform high level quantum chemistry and many-electron quantum dynamics calculations on methanol cluster anions.…”

Isotopic effect and temperature dependent intramolecular excitation energy transfer in a model donor–acceptor dyad

“…In this case, ultrafast pump-probe experiments by Barbara's group indicate a k (H) /k (D) = 1.4 in comparing the ground-state recovery of an excess electron in water versus heavy water 22 . The effect was largely attributed to the quantum mechanical librational modes of the surrounding solvent cavity [23][24][25][26][27] .…”

Nuclear quantum effects on the nonadiabatic decay mechanism of an excited hydrated electron

“…We verified that for the specific problem of the solvated electron, the cross terms are negligible, and the gap fluctuations fulfill the so-called slow modulation limit in which only the initial value determines the correlation function. 23 Thus, the preceding equation reduces to…”

“…16 Neria and Nitzan predicted ~220 fs with a similar approach but with a different flexible water model and incorporation of nuclear semi-classical (high-temperature) In a previous paper, we have introduced a quantum time correlation formula for the NA decay rate between two adiabatic quantum states based on the Fermi golden rule. 23 The lifetime of the equilibrium excited state electron has been predicted with the expression to be extremely short, ~10 fs. Although this result is in contrast with all previous simulations, we have also pointed out that the lifetime depends very strongly on the equilibrium energy gap, larger gaps resulting in significantly longer lifetimes.…”

“…23 The formula involves the quantum correlation function of the coupling, the energy gap fluctuation, and their cross-terms. We verified that for the specific problem of the solvated electron, the cross terms are negligible, and the gap fluctuations fulfill the so-called slow modulation limit in which only the initial value determines the correlation function.…”