slices of the trajectories obtained for water (top) and for methanol (bottom). In each frame, the top curve reports the time-dependent energy gap and, for clarity, the bottom one gives the absolute value of the coupling, with a minus sign to avoid overlaps.
Normalized energy gap correlation function for an equilibrated solvated -electron in water (top) and in methanol (bottom).
Spectral density (in arbitrary units) of the nonadiabatic coupling in water (top) and in methanol (bottom).
Classical reactive flux correlation function for water (top) and methanol (bottom). The circles indicate the direct numerical integration of Eqs. (12) and (17), whereas the solid line involves the Gaussian approximation for the dephasing function with neglect of the cross-correlation terms, as in Eq. (24).
Quantum reactive flux for water (top) and methanol (bottom). The solid line is for the direct integration of Eq. (22), including all terms, and the dashed line involves a Gaussian approximation for the dephasing function and the neglect of the cross-correlation terms, Eq. (25). The dot-dashed line recalls the classical results of Fig. 4.
Frequency dependent rate for water (top) and methanol (bottom). The solid curve indicates the quantized result using the harmonic quantization scheme, and the dashed-dotted curves denote the standard quantization procedure [Eqs. (20)–(23)]. The Gaussian-type dashed curve on top is the “window” function of Eq. (34) (renormalized to fit in the figure).
The probability distribution of the energy gap, , and its approximation by a Gaussian distribution (dashed, upper frame). The average value of sampled at each particular energy value (lower frame).
The lifetime of the excited state electron for alternative approximations as a function of the mean energy gap (see text). Classical case (solid), standard (dashed), and harmonic quantization schemes (dotted). The harmonic quantization with the very high frequency coupling contributions removed is also shown (dash-dot).
Averaged classical quantities collected along the MD runs and the corresponding quantized quantities (denoted by the subscript) computed using the harmonic quantization scheme. All quantities are in .
Classical and quantized nonadiabatic transition times, and dephasing times for electronic relaxation of an equilibrated excited state solvated electron in water and methanol (see text). The quantized rates are computed using either the harmonic or the standard quantization scheme. The classical dephasing times and the quantum decoherence times using the harmonic quantization are also shown. All quantities are in fs.
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