Eric R. Bittner

Quantum decoherence in mixed quantum‐classical systems: Nonadiabatic processes

We address the issue of quantum decoherence in mixed quantum‐classical simulations. We demonstrate that restricting the classical paths to a single path among all the quantum paths affects a coarse graining of the quantum paths. Such coarse graining causes the quantum paths to lose coherence as the various possible classical paths associated with each quantum state diverge. This defines a reduction mapping of the quantum density matrix, and we derive a quantum master equation suitable for mixed quantum‐classical systems. The equation includes two terms: first, the ordinary quantum Liouvillian which is parametrized by a single classical path, and second, a quantum decoherence term that includes both a coherence time and length scale which are determined by the dynamics of the classical paths. Model calculations for electronic coherence loss in nonadiabatic mixed quantum‐classical dynamics are presented as examples. For a model charge transfer chemical reaction with nonadiabatic transitions, application of ...

Quantum decoherence and the isotope effect in condensed phase nonadiabatic molecular dynamics simulations

In this paper, we explore in detail the way in which quantum decoherence is treated in different mixed quantum‐classical molecular dynamics algorithms. The quantum decoherence time proves to be a key ingredient in the production of accurate nonadiabatic dynamics from computer simulations. Based on a short time expansion to a semiclassical golden rule expression due to Neria and Nitzan [J. Chem. Phys. 99, 1109 (1993)], we develop a new computationally efficient method for estimating the decay of quantum coherence in condensed phase molecular simulations. Using the hydrated electron as an example, application of this method finds that quantum decoherence times are on the order of a few femtoseconds for condensed phase chemical systems and that they play a direct role in determining nonadiabatic transition rates. The decay of quantum coherence for the solvated electron is found to take ≊50% longer in D2O than in H2O, providing a rationalization for a long standing puzzle concerning the lack of experimentally...

Quantum wave packet dynamics with trajectories: Implementation with adaptive Lagrangian grids

The quantum trajectory method was recently developed to solve the hydrodynamic equations of motion in the Lagrangian, moving-with-the-fluid, picture. In this approach, trajectories are integrated for fluid elements (“particles”) moving under the influence of the combined force from the potential surface and the quantum potential. To accurately compute the quantum potential and the quantum force, it is necessary to obtain the derivatives of a function given only the values on the unstructured mesh defined by the particle locations. However, in some regions of space–time, the particle mesh shows compression and inflation associated with regions of large and small density, respectively. Inflation is especially severe near nodes in the wave function. In order to circumvent problems associated with highly nonuniform grids defined by the particle locations, adaptation of moving grids is introduced in this study. By changing the representation of the wave function in these local regions (which can be identified ...

Spin-dependent electron-hole capture kinetics in luminescent conjugated polymers

The recombination of electron-hole pairs injected in extended conjugated systems is modeled as a multistep interconversion relaxation in monoexcited electronic state space, mediated by electron-phonon coupling. The computed ratio of triplet-to-singlet exciton formation times r=tau(T)/tau(S) increases from 0.9 for a model dimer to 2.5 for a 32-unit chain, in good agreement with recent experiments. We rationalize the conjugation-length dependence of r in terms of spin-specific energetics and mutual vibronic coupling of the excited states.

Quantum tunneling dynamics using hydrodynamic trajectories

In this paper we compute quantum trajectories arising from Bohm’s causal description of quantum mechanics. Our computational methodology is based upon a finite-element moving least-squares method (MWLS) presented recently by Wyatt and co-workers [Lopreore and Wyatt, Phys. Rev. Lett. 82, 5190 (1999)]. This method treats the “particles” in the quantum Hamilton–Jacobi equation as Lagrangian fluid elements that carry the phase, S, and density, ρ, required to reconstruct the quantum wave function. Here, we compare results obtained via the MWLS procedure to exact results obtained either analytically or by numerical solution of the time-dependent Schrodinger equation. Two systems are considered: first, dynamics in a harmonic well and second, tunneling dynamics in a double well potential. In the case of tunneling in the double well potential, the quantum potential acts to lower the barrier, separating the right- and left-hand sides of the well, permitting trajectories to pass from one side to another. However, as...

Decoherent histories and nonadiabatic quantum molecular dynamics simulations

The role of quantum coherence loss in mixed quantum-classical dynamical systems is explored in the context of the theory of quantum decoherence introduced recently by Bittner and Rossky [J. Chem. Phys. 103, 8130 (1995)]. This theory, which is based upon the consistent histories interpretation of quantum mechanics, introduces decoherence in the quantum subsystem by carefully considering the relevant time and length scales over which one must consider the effects of phase interference between alternative histories of the classical subsystem. Such alternative histories are an integral part of any quantum-classical computational scheme which employs transitions between discrete quantum states; consequently, the coherences between alternative histories have a profound effect on the transition probability between quantum states. In this paper, we review the Bittner–Rossky theory and detail a computational algorithm suitable for large-scale quantum molecular dynamics simulations which implements this theory. App...

Noise-induced quantum coherence drives photo-carrier generation dynamics at polymeric semiconductor heterojunctions

Here we report on an exciton/lattice model of the electronic dynamics of primary photo excitations in a polymeric semiconductor heterojunction that includes both polymer π-stacking, energetic disorder and phonon relaxation. Our model indicates that that in polymer/fulerene heterojunction systems, resonant tunnelling processes brought about by environmental fluctuations couple photo excitations directly to photocurrent producing charge-transfer states on <100 fs time scales. Moreover, we find this process to be independent of the location of energetic disorder in the system, and hence we expect exciton fission via resonant tunnelling to polarons to be a ubiquitous feature of these systems.

Phonon-Driven Ultrafast Exciton Dissociation at Donor-Acceptor Polymer Heterojunctions

A quantum-dynamical analysis of exciton dissociation at polymer heterojunctions is presented, using a hierarchical electron-phonon model parametrized for three electronic states and 28 vibrational modes. Two representative interfacial configurations are considered, both of which exhibit an ultrafast exciton decay. The efficiency of the process depends critically on the presence of intermediate bridge states, and on the dynamical interplay of high- vs low-frequency phonon modes. The ultrafast, highly nonequilibrium dynamics is consistent with time-resolved spectroscopic observations.

Franck–Condon spectra and electron-libration coupling in para-polyphenyls

Proceeding from quantum-chemical potential energy surfaces, we compute the absorption and fluorescence spectra of conventional and ladder-type para-phenylene oligomers (OPP and OLPP) with up to 7 benzene rings. Electronically excited states are addressed by means of extended configuration interaction within a standard molecular all-valence-electron semiempirical Hamiltonian. Adiabatic excitation energies, interstate distortions and normal modes are used to compute Franck–Condon band shapes with rigorous consideration of vibrational structure. Theoretical spectra agree with the experiment and rationalize the striking disparities in the linear optical response of OPP and OLPP. Whereas electron–phonon coupling in OLPP is essentially restricted to the carbon–carbon bond-stretching modes, photoexcitation, and emission processes in OPP are followed by significant relaxations in ring-torsional degrees of freedom. The broadening of spectra of OPP, especially pronounced in absorption, and the large Stokes shift be...

Rigorous Franck-Condon Absorption and Emission Spectra of Conjugated Oligomers from Quantum Chemistry

A harmonic Condon approach is used to calculate excitation and emission band shapes for the lowest dipole-allowed electronic transitions in conjugated oligomers: polyenes, oligorylenes, and para-phenylenevinylenes. Ground- and excited-state adiabatic energies, equilibrium structures, and vibrational modes are obtained within standard all-valence-electron molecular Hamiltonian incorporating extended configuration interaction. The interstate distortion is cast in normal coordinates and used to calculate transition probabilities from the zero-phonon initial state to the vibrational manifold of the final state. Spectral profiles are obtained as a superposition of Lorentzian line shapes. Theoretical band shapes reproduce prominent features in the absorption and fluorescence spectra of the oligomers in question. The strength of the bond-stretching vibronic progression increases with oligomeric length in polyenes, but decreases in para-phenylenevinylenes. In line with experiment, absorption and emission band sha...