Reduced and Exact Quantum Dynamics of the Vibrational Relaxation of a Molecular System Interacting with a Finite-Dimensional Bath

Abstract

We investigate the vibrational relaxation of a Morse oscillator, nonlinearly coupled to a finite-dimensional bath of harmonic oscillators at zero temperature, using two different approaches: Reduced dynamics with the help of the Lindblad formalism of reduced density matrix theory in combination with Fermi's Golden Rule, and exact dynamics (within the chosen model) with the multiconfiguration time-dependent Hartree (MCTDH) method. Two different models have been constructed, the situation where the bath spectrum is exactly resonant with the anharmonic oscillator transition frequencies, and the case for which the subsystem is slightly off-resonant with the environment. At short times, reduced dynamics calculations describe the relaxation process qualitatively well but fail to reproduce recurrences observed with MCTDH for longer times. Lifetimes of all the vibrational levels of the Morse oscillator have been calculated, and both Lindblad and MCTDH results show the same dependence of the lifetimes on the initial vibrational state quantum number. A prediction, which should be generic for adsorbate systems is a striking, sharp increase of lifetimes of the subsystem vibrational levels close to the dissociation limit. This is contradictory with harmonic/linear extrapolation laws, which predict a monotonic decrease of the lifetime with initial vibrational quantum number.

The multi-configurational time-dependent Hartree approach in optimized second quantization: Imaginary time propagation and particle number conservation

“…Here the equations of motions in imaginary time, given in Eqs. (14), (15), are derived. To this end, the Dirac-Frenkel variational principle is employed.…”

“…It is used by many research groups to study a variety of systems. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] Benchmark applications studied bimolecular reactions [25][26][27][28][29][30][31][32][33][34][35][36][37][38] , proton transfer [39][40][41][42][43][44] , and large amplitude motion [45][46][47][48][49] for molecular systems including six to nine atoms on accurate ab initio potential energy surfaces. MCTDH simulations based on model Hamiltonians describing non-adiabatic dynamics [50][51][52] or electron and proton transfer processes in condensed matter [53]…”

Non-Markovian Vibrational Relaxation Dynamics at Surfaces

“…More recently, these measures have been applied to multi-dimensional TDSE solutions of vibration-phonon problems with an Ohmic spectral bath 59 , and of a spin-boson model 60 . Also other measures of non-Markovianity have been suggested, based, for example, on entanglement and / or system entropy [61][62][63] and on qualitative changes of long-time behavior in driven dissipative systems 64 .…”

A novel system-bath Hamiltonian for vibration-phonon coupling: Formulation, and application to the relaxation of Si–H and Si–D bending modes of H/D:Si(100)-(2 × 1)

“…In principle, these expansions can be derived from ab initio or well parametrized semi-empirical potentials without further assumptions. However, often additional approximations are made, e.g., harmonic behavior of bath or even system modes, bilinear couplings, or the application of model spectral densities such as Ohmic baths [6,7]. More recently, quantum mechanical, parameter-free approaches (apart from parameters implemented in a forcefield, for example) have been applied to treat vibration-phonon coupling via system-bath Hamiltonians for realistic adsorbate-surface systems such as hydrogen atoms on graphene [8,9] or Ge(100) [10], CO on Si(100) [11], or H on Si(100) [12], to name just a few.…”

“…An alternative route is via open-system theory, by solving a Liouville-von Neumann equation for the system reduced density matrix (RDM) instead [12,21,22]. When memory effects are neglected this results in Markovian variants such as Redfield theory [23], or the Lindblad dynamical semigroup [7,12,25,24]. In contrast to system-bath Schrödinger equations, energy is usually not conserved within the open-system approach due to energy transfer from the system to the bath.…”