Nuclear quantum effects in electronically adiabatic quantum time correlation functions: Application to the absorption spectrum of a hydrated electron

Abstract

A general formalism for introducing nuclear quantum effects in the expression of the quantum time correlation function of an operator in a multi-level electronic system is presented in the adiabatic limit. The final formula includes the nuclear quantum time correlation functions of the operator matrix elements, of the energy gap, and their cross terms.These quantities can be inferred and evaluated from their classical analogs obtained by mixed quantum-classical molecular dynamics simulations. The formalism is applied to the absorption spectrum of a hydrated electron, expressed in terms of the time correlation function of the dipole operator in the ground electronic state. We find that both static and dynamic nuclear quantum effects distinctly influence the shape of the absorption spectrum, especially its high-energy tail related to transitions to delocalized electron states. Their inclusion does improve significantly the agreement between theory and experiment for both the low and high frequency edges of the spectrum. It does not appear sufficient, however, to d

A new electron-methanol molecule pseudopotential and its application for the solvated electron in methanol

“…3 We also note that the absorption peak in methanol is ~0.1 eV blue-shifted compared to the hydrated electron. 32,62 The integrated oscillator strength from the simulation (0.89) is also in reasonable agreement with the experimental value (0.69). 3 These observations indicate good overall agreement with experiment.…”

“…It is suspected that relatively asymmetric excited states may contribute to the large-energy part of the absorption band. 62 …”

“…It is also noteworthy that, although the spectrum is asymmetric, the large energy tail of the spectrum is hardly developed in the simulations (~0.9 eV calculated vs. ~1.4 eV experimental half width 4 ) similarly to the hydrated electron case. It has been pointed out recently 62 that inclusion of higher transitions, and inclusion of nuclear quantum effects are necessary to significantly improve this part of the spectrum. Nevertheless, it has become apparent that, even with such improvements, the quantized spectrum is still distinctly lacking in intensity at around 2.5 eV.…”

Does the Hydrated Electron Occupy a Cavity?

“…Moreover, shifting the experimental spectrum 0.15 eV lower in energy (dashed black curve) shows that the shape of the low-energy edge of the calculated spectrum is correct. We do not expect to reproduce the high-energy tail of the spectrum in these calculations, both because of the small number of excited states we have included (calculations with 20 states on a few configurations show that the tail does begin to fill in) and because we have not accounted for quantum effects in the solvent (22). Fig.…”

Theoretical Studies of Spectroscopy and Dynamics of Hydrated Electrons

“…The Kubo formula, as we discussed in Section 3, opens a possibility to an a posteriori quantization of the calculated absorption spectrum. 181 The quantized spectrum can be written in the following form:…”