Gaussian-based techniques for quantum propagation from the time-dependent variational principle: Formulation in terms of trajectories of coupled classical and quantum variables

In this article, two coherent-state based methods of quantum propagation, namely, coupled coherent states (CCS) and Gaussian-based multiconfiguration time-dependent Hartree (G-MCTDH), are put on the same formal footing, using a derivation from a variational principle in Lagrangian form. By this approach, oscillations of the classical-like Gaussian parameters and oscillations of the quantum amplitudes are formally treated in an identical fashion. We also suggest a new approach denoted here as coupled coherent states trajectories (CCST), which completes the family of Gaussian-based methods. Using the same formalism for all related techniques allows their systematization and a straightforward comparison of their mathematical structure and cost

Exciton dissociation at donor-acceptor polymer heterojunctions: quantum nonadiabatic dynamics and effective-mode analysis

The quantum-dynamical mechanism of photoinduced subpicosecond exciton dissociation and the concomitant formation of a charge-separated state at a TFB:F8BT polymer heterojunction is elucidated. The analysis is based upon a two-state vibronic coupling Hamiltonian including an explicit 24-mode representation of a phonon bath comprising high-frequency (C$=$C stretch) and low-frequency (torsional) modes. The initial relaxation behavior is characterized by coherent oscillations, along with the decay through an extended nonadiabatic coupling region. This region is located in the vicinity of a conical intersection hypersurface. A central ingredient of the analysis is a novel effective mode representation, which highlights the role of the low-frequency modes in the nonadiabatic dynamics. Quantum dynamical simulations were carried out using the multiconfiguration time-dependent Hartree (MCTDH) method

Carbon Dioxide Reduction Systems

The Methoxy system for regenerating oxygen from carbon dioxide was studied. Experiments indicate that the reaction between carbon dioxide and hydrogen can be carried out with ease in an efficient manner and with excellent heat conservation. A small reactor capable of handling the C02 expired by three men has been built and operated. The decomposition of methane by therma1,arc and catalytic processes was studied. Both the arc and catalytic processes gave encouraging results with over 90 percent of the methane being decomposed to carbon and hydrogen in some of the catalytic processes. Control of the carbon deposition in both the catalytic and arc processes is of great importance to prevent catalyst deactivation and short circuiting of electrical equipment. Sensitive analytical techniques have been developed for all of the components present in the reactor effluent streams

Universal Markovian reduction of Brownian particle dynamics

Non-Markovian processes can often be turned Markovian by enlarging the set of variables. Here we show, by an explicit construction, how this can be done for the dynamics of a Brownian particle obeying the generalized Langevin equation. Given an arbitrary bath spectral density $J_{0}$, we introduce an orthogonal transformation of the bath variables into effective modes, leading stepwise to a semi-infinite chain with nearest-neighbor interactions. The transformation is uniquely determined by $J_{0}$ and defines a sequence $\{J_{n}\}_{n\in\mathbb{N}}$ of residual spectral densities describing the interaction of the terminal chain mode, at each step, with the remaining bath. We derive a simple, one-term recurrence relation for this sequence, and show that its limit is the quasi-Ohmic expression provided by the Rubin model of dissipation. Numerical calculations show that, irrespective of the details of $J_{0}$, convergence is fast enough to be useful in practice for an effective Markovian reduction of quantum dissipative dynamics

Local-in-Time Error in Variational Quantum Dynamics

The McLachlan "minimum-distance" principle for optimizing approximate solutions of the time-dependent Schrodinger equation is revisited, with a focus on the local-in-time error accompanying the variational solutions. Simple, exact expressions are provided for this error, which are then evaluated in illustrative cases, notably the widely used mean-field approach and the adiabatic quantum molecular dynamics. Based on these findings, we demonstrate the rigorous formulation of an adaptive scheme that resizes on the fly the underlying variational manifold and, hence, optimizes the overall computational cost of a quantum dynamical simulation. Such adaptive schemes are a crucial requirement for devising and applying direct quantum dynamical methods to molecular and condensed-phase problems

Multi-layer Gaussian-based multi-configuration time-dependent Hartree (ML-GMCTDH) simulations of ultrafast charge separation in a donor–acceptor complex

We report on first applications of the Multi-Layer Gaussian-based Multi-Configuration Time-Dependent Hartree (ML-GMCTDH) method [Römer et al., J. Chem. Phys. 138, 064106 (2013)] beyond its basic two-layer variant. The ML-GMCTDH scheme provides an embedding of a variationally evolving Gaussian wavepacket basis into a hierarchical tensor representation of the wavefunction. A first-principles parameterized model Hamiltonian for ultrafast non-adiabatic dynamics in an oligothiophene–fullerene charge transfer complex is employed, relying on a two-state linear vibronic coupling model that combines a distribution of tuning type modes with an intermolecular coordinate that also modulates the electronic coupling. Efficient ML-GMCTDH simulations are carried out for up to 300 vibrational modes using an implementation within the QUANTICS program. Excellent agreement with reference ML-MCTDH calculations is obtained

Non-Markovian reduced dynamics of ultrafast charge transfer at an oligothiophene–fullerene heterojunction

We extend our recent quantum dynamical study of the exciton dissociation and charge transfer at an oligothiophene-fullerene heterojunction interface (Tamura et al., 2012) [6] by investigating the process using the non-perturbative hierarchical equations of motion (HEOM) approach. Based upon an effective mode reconstruction of the spectral density the effect of temperature on the charge transfer is studied using reduced density matrices. It was found that the temperature had little effect on the charge transfer and a coherent dynamics persists over the first few tens of femtoseconds, indicating that the primary charge transfer step proceeds by an activationless pathway

Multi-configurational Ehrenfest simulations of ultrafast nonadiabatic dynamics in a charge-transfer complex

Multi-configurational Ehrenfest (MCE) approaches, which are intended to remedy the lack of correlations in the standard mean-field Ehrenfest method, have been proposed as coherent-state based ansatze for quantum propagation [D. V. Shalashilin, J. Chem. Phys. 130, 244101 (2009)] and also as the classical limit of the variational Gaussian-based multiconfiguration time dependent Hartree (G-MCTDH) method [S. Romer and I. Burghardt, Mol. Phys. 111, 3618 (2013)]. In the present paper, we establish the formal connection between these schemes and assess the performance of MCE for a coherent-state representation of the classical-limit subsystem. As a representative model system, we address the ultrafast, coherent charge transfer dynamics in an oligothiophene-fullerene donor acceptor complex described by a two-state linear vibronic coupling model. MCE calculations are compared with reference calculations performed with the MC IDH method, for 10-40 vibrational modes. Beyond a dimensionality of 10 modes, it is shown that the correct representation of electronic coherence depends crucially on the sampling of initially unoccupied Gaussians

Quantum dynamics of hydrogen atoms on graphene. I. System-bath modeling

An accurate system-bath model to investigate the quantum dynamics of hydrogen atoms chemisorbed on graphene is presented. The system comprises a hydrogen atom and the carbon atom from graphene that forms the covalent bond, and it is described by a previously developed 4D potential energy surface based on density functional theory ab initio data. The bath describes the rest of the carbon lattice and is obtained from an empirical force field through inversion of a classical equilibrium correlation function describing the hydrogen motion. By construction, model building easily accommodates improvements coming from the use of higher level electronic structure theory for the system. Further, it is well suited to a determination of the system-environment coupling by means of ab initio molecular dynamics. This paper details the system-bath modeling and shows its application to the quantum dynamics of vibrational relaxation of a chemisorbed hydrogen atom, which is here investigated at T = 0 K with the help of the multi-configuration time-dependent Hartree method. Paper II deals with the sticking dynamics

Kraus representation in the presence of initial correlations

We examine the validity of the Kraus representation in the presence of initial correlations and show that it is assured only when a joint dynamics is locally unitary.Comment: REVTeX4, 12 page