Compact MCTDH Wave Functions for High-Dimensional System-Bath Quantum Dynamics

Criteria for the Classification of System and Bath Variables in Nonadiabatic Dynamics: Application to Pyrazine

The present work deals with the system-bath separation of the vibrational modes involved in a nonadiabatic system. System modes are the strongly interacting modes which dominate the overall dynamics and, hence, need a near-exact treatment. Bath modes have relatively weaker couplings and can be approximately treated. Thus, the exponential bottleneck involved in computations is controlled by the size of the system-subspace. The aim of this work is to put forward a set of criteria that provides clear guidelines for choosing the system degrees of freedom. The extent of wave packet dephasing caused by repeated crossings across the surface of curve-crossing is the basis for distinction between system and bath modes. The mechanisms of the wave packet dephasing and the criteria are discussed in detail. Numerically converged results presented for the 24-mode pyrazine and 3-mode spin-boson model validate the efficiency of these criteria.

On simulating the dynamics of electronic populations and coherences via quantum master equations based on treating off-diagonal electronic coupling terms as a small perturbation

Quantum master equations provide a general framework for describing the dynamics of electronic observables within a complex molecular system. One particular family of such equations is based on treating the off-diagonal coupling terms between electronic states as a small perturbation within the framework of second-order perturbation theory. In this paper, we show how different choices of projection operators, as well as whether one starts out with the time-convolution or the time-convolutionless forms of the generalized quantum master equation, give rise to four different types of such off-diagonal quantum master equations (OD-QMEs), namely, time-convolution and time-convolutionless versions of a Pauli-type OD-QME for only the electronic populations and an OD-QME for the full electronic density matrix (including both electronic populations and coherences). The fact that those OD-QMEs are given in terms of the interaction picture makes it non-trivial to obtain Schrödinger picture electronic coherences from them. To address this, we also extend a procedure for extracting Schrödinger picture electronic coherences from interaction picture populations recently introduced by Trushechkin in the context of time-convolutionless Pauli-type OD-QME to the other three types of OD-QMEs. The performance of the aforementioned four types of OD-QMEs is explored in the context of the Garg-Onuchic-Ambegaokar benchmark model for charge transfer in the condensed phase across a relatively wide parameter range. The results show that time-convolution OD-QMEs can be significantly more accurate than their time-convolutionless counterparts, particularly in the case of Pauli-type OD-QMEs, and that rather accurate Schrödinger picture coherences can be obtained from interaction picture electronic inputs.

A hierarchical effective mode approach to phonon-driven multilevel vibrational relaxation dynamics at surfaces

We discuss an efficient Hierarchical Effective Mode (HEM) representation of a high-dimensional harmonic oscillator bath, which describes phonon-driven vibrational relaxation of an adsorbate-surface system, namely, deuterium adsorbed on Si(100). Starting from the original Hamiltonian of the adsorbate-surface system, the HEM representation is constructed via iterative orthogonal transformations, which are efficiently implemented with Householder matrices. The detailed description of the HEM representation and its construction are given in the second quantization representation. The hierarchical nature of this representation allows access to the exact quantum dynamics of the adsorbate-surface system over finite time intervals, controllable via the truncation order of the hierarchy. To study the convergence properties of the effective mode representation, we solve the time-dependent Schrödinger equation of the truncated system-bath HEM Hamiltonian, with the help of the multilayer extension of the Multiconfigurational Time-Dependent Hartree (ML-MCTDH) method. The results of the HEM representation are compared with those obtained with a quantum-mechanical tier-model. The convergence of the HEM representation with respect to the truncation order of the hierarchy is discussed for different initial conditions of the adsorbate-surface system. The combination of the HEM representation with the ML-MCTDH method provides information on the time evolution of the system (adsorbate) and multiple effective modes of the bath (surface). This permits insight into mechanisms of vibration-phonon coupling of the adsorbate-surface system, as well as inter-mode couplings of the effective bath.

Exact vs. asymptotic spectral densities in the Garg-Onuchic-Ambegaokar charge transfer model and its effect on Fermi's golden rule rate constants

The Garg-Onuchic-Ambegaokar model [J. Chem. Phys. 83, 4491 (1985)] has been used extensively for benchmarking methods aimed at calculating charge transfer rates. Within this model, the donor and acceptor diabats are described as shifted parabolas along a single primary mode, which is bilinearly coupled to a harmonic bath consisting of secondary modes, characterized by an Ohmic spectral density with exponential cutoff. Rate calculations for this model are often performed in the normal mode representation, with the corresponding effective spectral density given by an asymptotic expression derived at the limit where the Ohmic bath cutoff frequency is much larger than the primary mode frequency. We compare Fermi's golden rule rate constants obtained with the asymptotic and exact effective spectral densities. We find significant deviations between rate constants obtained from the asymptotic spectral density and those obtained from the exact one in the deep inverted region. Within the range of primary mode frequencies commonly employed, we find that the discrepancies increase with decreasing temperature and with decreasing primary mode frequency.