Critical evaluation of approximate quantum decoherence rates for an electronic transition in methanol solution

We present a quantum molecular dynamics calculation of a semiclassical decoherence function to evaluate the accuracy of alternative short-time approximations for coherence loss in the dynamics of condensed phase electronically non-adiabatic processes. The semiclassical function from mixed quantum-classical molecular dynamics simulations and frozen Gaussian wave packets is computed for the electronic transition of an excited state excess electron to the ground state in liquid methanol. The decoherence function decays on a 10 fs timescale qualitatively similar to the aqueous case. We demonstrate that it is the motion of the hydrogen atom, and in particular, the hydrogen rotation around the oxygen-methyl bond which is predominantly responsible for destroying the quantum correlations between alternative states. Multiple timescales due to the slower diffusive nuclear modes, which dominate the solvation response of methanol, do not contribute to the coherence loss. The choice of the coordinate representation is investigated in detail and concluded to be irrelevant to the decay. Changes in both nuclear momenta and positions on the two alternative potential surfaces are found to contribute to decoherence, the former dominating at short times (t < 5 fs), the latter controlling the decay at longer times. Various short-time approximations to the full dynamics for the decoherence function are tested for the first time. The present treatment rigorously develops the short-time description and establishes its range of validity. Whereas the lowest-order short-time approximation proves to be a very good approximation up to about 5 fs, we also find that it bounds the decay of the decoherence function. After 5 fs, the coherence decay in fact becomes faster than the single Gaussian predicted in the lowest-order short-time limit. This decay is well reflected by an enhanced low-order approximation, which is also easily computed from equilibrium classical forces

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

A new electron–methanol molecule pseudopotential is developed and tested in the present paper. The formal development of the potential is based on quantum mechanical calculations on the electron-methanol molecule model in the static exchange approximation. The computational model includes a steep confining potential that keeps the otherwise unbound excess electron in the vicinity of the methanol molecule. Using the Phillips-Kleinman theorem we introduce a smooth pseudo-wave function of the excess electron with the exact eigenenergy and correct asymptotic behavior. The non-local potential energy operator of the model Hamiltonian is then replaced to a local potential that reproduces the ground-state properties of the excess electron satisfactorily. The pseudopotential is then optimized in an analytically simple functional form to fit this approximate local potential in conjunction with the point charges and the geometry of a classical, all-site methanol-methanol interaction potential. Of the adjustable parameters, the parameters for the carbon and the methyl hydrogen atoms are optimized, while those for the oxygen and the hydroxyl hydrogen are taken from a previous electron-water molecule pseudopotential. A polarization term is added to the potential a posteriori. The polarization parameters are chosen to reproduce the experimental position of the optical absorption spectrum of an excess electron in mixed quantum-classical molecular dynamics simulations. The energetic, structural and spectroscopic properties of the solvated electron in a methanol bath are simulated at 300 K, and compared to previous solvated electron simulations and available experimental data

Analysis Of Localization Sites for An Excess Electron In Neutral Methanol Clusters Using Approximate Pseudopotential Quantum-Mechanical Calculations

We have used a recently developed electron–methanol molecule pseudopotential in approximate quantum mechanical calculations to evaluate and statistically analyze the physical properties of an excess electron in the field of equilibrated neutral methanol clusters ((CH3OH)n , n = 50 – 500). The methanol clusters were generated in classical molecular dynamics simulations at nominal 100 K and 200 K temperatures. Topological analysis of the neutral clusters indicates that methyl groups cover the surface of the clusters almost exclusively, while the associated hydroxyl groups point inside. Since the initial neutral clusters are lacking polarity on the surface and compact inside, the excess electron can barely attach to these structures. Nevertheless, most of the investigated cluster configurations do support weakly stabilized cluster anion states. We find that similarly to water clusters, the pre-existing instantaneous dipole moment of the neutral clusters binds the electron. The localizing electrons occupy diffuse, weakly bound surface states that largely engulf the cluster although their centers are located outside the cluster molecular frame. The initial localization of the excess electron is reflected in its larger radius compared to water due to the lack of free OH hydrogens on the cluster surface. The stabilization of the excess electron increases, while the radius decreases monotonically as the clusters grow in size. Stable, interior bound states of the excess electron are not observed to form neither in finite size methanol clusters nor in the equilibrium bulk

Quantum-Classical Simulation of Electron Localization in Negatively Charged Methanol Clusters

A series of quantum molecular dynamics simulations have been performed to investigate the energetic, structural, dynamic and spectroscopic properties of methanol cluster anions, [(CH3OH)n]– , (n = 50 – 500). Consistent with the inference from photo-electron imaging experiments, we find two main localization modes of the excess electron in equilibrated methanol clusters at ~200 K. The two different localization patterns have strikingly different physical properties, consistent with experimental observations, and are manifest in comparable cluster sizes to those observed. Smaller clusters (n≤128) tend to localize the electron in very weakly bound, diffuse electronic states on the surface of the cluster, while in larger ones the electron is stabilized in solvent cavities, in compact interior-bound states. The interior states exhibit properties that largely resemble and smoothly extrapolate to those simulated for a solvated electron in bulk methanol. The surface electronic states of methanol cluster anions are significantly more weakly bound than the surface states of the anionic water clusters. The key source of the difference is the lack of stabilizing free hydroxyl groups on a relaxed methanol cluster surface. We also provide a mechanistic picture that illustrates the essential role of the interactions of the excess electron with the hydroxyl groups in the dynamic process of excess electron transition from surface-bound states to interior-bound states

Nuclear quantum effects on the non-adiabatic decay mechanism of an excited hydrated electron

We present a kinetic analysis of the non-adiabatic decay mechanism of an excited state hydrated electron to the ground state. The theoretical treatment is based on a quantized, gap dependent golden rule rate constant formula which describes the non-adiabatic transition rate between two quantum states. The rate formula is expressed in terms of quantum time correlation functions of the energy gap, and of the non-adiabatic coupling. These gap dependent quantities are evaluated from three different sets of mixed quantum-classical molecular dynamics simulations of a hydrated electron equilibrated a) in its ground state, b) in its first excited state, and c) on a hypothetical mixed potential energy surface which is the average of the ground and the first excited electronic states. The quantized, gap-dependent rate results are applied in a phenomenological kinetic equation which provides the survival probability function of the excited state electron. Although the lifetime of the equilibrated excited state electron is computed to be very short (well under 100 fs), the survival probability function for the non-equilibrium process in pump-probe experiments yields an effective excited state lifetime of around 300 fs, a value consistent with the findings of several experimental groups and previous theoretical estimates

Response to Comment on “Characterization of Excess Electrons in Water-Cluster Anions by Quantum Simulations”

In response to the Comment by Neumark and co-workers, we reiterate that the conclusions of the title Report are based on identifiable characteristic trends in several observables with cluster size. The numerical comparison between simulated and experimental vertical detachment energies emphasized in the Comment reflect quantitative limitations of our atomistic model, but, in our opinion, do not undermine these conclusions

Comment on “Does the Hydrated Electron Occupy a Cavity?” [Science 329, 65, (2010)]

Exact quantum mechanical calculations examining a recently implemented pseudopotential show that the results reported by Larsen et al. are based on a model that contains inaccuracies. We illustrate that, in contrast to the model used, the true electron-water interaction is repulsive in the region relevant to the reported extended electron distribution, consistent with the cavity model. The reported simulated properties of the hydrated electron are shown to be very sensitive to this problem

On the applicability of one- and many-electron quantum chemistry models for hydrated electron clusters.

We evaluate the applicability of a hierarchy of quantum models in characterizing the binding energy of excess electrons to water clusters. In particular, we calculate the vertical detachment energy of an excess electron from water cluster anions with methods that include one-electron pseudopotential calculations, density functional theory (DFT) based calculations, and ab initio quantum chemistry using MP2 and eom-EA-CCSD levels of theory. The examined clusters range from the smallest cluster size (n = 2) up to nearly nanosize clusters with n = 1000 molecules. The examined cluster configurations are extracted from mixed quantum-classical molecular dynamics trajectories of cluster anions with n = 1000 water molecules using two different one-electron pseudopotenial models. We find that while MP2 calculations with large diffuse basis set provide a reasonable description for the hydrated electron system, DFT methods should be used with precaution and only after careful benchmarking. Strictly tested one-electron psudopotentials can still be considered as reasonable alternatives to DFT methods, especially in large systems. The results of quantum chemistry calculations performed on configurations that represent possible excess electron binding motifs in the clusters appear to be consistent with the results using a cavity structure preferring one-electron pseudopotential for the hydrated electron, while they are in sharp disagreement with the structural predictions of a non-cavity model