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

Abstract

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 parametrized 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 which 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.

Mixed-quantum-classical or fully-quantized dynamics? A unified code to compare methods

“…Returning to the original MCTDH ansatz, instead of replacing the SPFs by GWPs, it is more fruitful to consider the GWPs as a time-dependent primitive basis set and expand the SPFs in terms of these [6]. This leads naturally to a multi-layer version able to treat many degrees of freedom [29,30]. In the present work, however, we will stick to the single layer ansatz equation (2.3) and expand the SPFs…”

“…Returning to the original MCTDH ansatz, instead of replacing the SPFs by GWPs, it is more fruitful to consider the GWPs as a time-dependent primitive basis set and expand the SPFs in terms of these [6]. This leads naturally to a multi-layer version able to treat many degrees of freedom [29,30]. In the present work, however, we will stick to the single layer ansatz equation (2.3) and expand the SPFs φjfalse(κfalse)false(Qκfalse)=∑k=1Nκdakjfalse(κfalse)false(tfalse)gkfalse(κfalse)false(Qκ,tfalse). If the GWPs are frozen and separable, it can be easily shown that this approach still uses a superposition of GWPs for the wave function ansatz right left right left right left right left right left right left3pt0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0emtrueΨ(boldq,t) =∑j1=1n1…∑jp=1npAj1…jf(t)∏κ=1p(∑kκ=1Nκdakκjκfalse(κfalse)false(tfalse)gk…”

“…The equations of motion for the GWPs have the same form as before, but now the Y vector contains mean-field terms coupling the GWPs in different particles. The full form of the terms is given in the literature [29,30]. The Hamiltonian now has to be written in a form that is separable between the particles.…”

Quantum dynamics with ab initio potentials

“…Using the multi-layer variant of MCTDH (ML-MCTDH), they could treat seven excited states and all 49 vibrational degrees of freedom and assess the accuracy of the different models. Di Maiolo et al 41 again use the ML-MCTDH method and study an even larger system. Using a parameterized vibronic coupling model, the photo-initiated charge transfer in a fullerene-oligothiophene complex with up to 300 vibrational modes is studied.…”

Effect of temperature gradient on quantum transport

“…From magnetic materials to molecular aggregates, a vast variety of interesting physical phenomena lend themselves to be modeled as extended one-dimensional quantum systems interacting with open thermal environments. Wave functionbased methods such as density matrix renormalization group [1][2][3][4][5][6] (DMRG) and multi-configuration time-dependent Hartree [7][8][9] (MCTDH and ML-MCTDH) and related methods have proven to be exceptionally useful in simulating the quantum dynamics of extended systems. However, due to their computational complexity, these methods are typically less useful when it comes to simulations of open systems.…”