Toward Fully Quantum Modelling of Ultrafast Photodissociation Imaging Experiments. Treating Tunnelling in the Ab Initio Multiple Cloning Approach

We present an account of our recent effort to improve simulation of the photodissociation of small heteroaromatic molecules using the Ab Initio Multiple Cloning (AIMC) algorithm. The ultimate goal is to create a quantitative and converged technique for fully quantum simulations which treats both electrons and nuclei on a fully quantum level. We calculate and analyse the total kinetic energy release (TKER) spectra and Velocity Map Images (VMI), and compare the results directly with experimental measurements. In this work, we perform new extensive calculations using an improved AIMC algorithm that now takes into account the tunnelling of hydrogen atoms. This can play an extremely important role in photodissociation dynamics

Dynamics of a one-dimensional Holstein polaron: The multiconfigurational Ehrenfest method

We have extended the multiconfigurational Ehrenfest (MCE) approach to investigate the dynamics of a one-dimensional Holstein molecular crystal model. It has been shown that the extended MCE approach yields results in perfect agreement with benchmark calculations by the hierarchy equations of motion method. The accuracies of the MCE approach in describing the dynamical properties of the Holstein polaron over a wide range of exciton transfer integrals and exciton-phonon couplings are carefully examined by a detailed comparison with the fully variational multiple Davydov D2 ansatz. It is found that while the MCE approach and the multi-D2 ansatz produce almost exactly the same results for a small transfer integral, the results obtained by the multi-D2 ansatz start to deviate from those by the MCE approach at longer times for a large transfer integral. A large number of coherent state basis functions are required to characterize the delocalized features of the phonon wavefunction in the case of large transfer integral, which becomes computationally too demanding for the multi-D2 ansatz. The MCE approach, on the other hand, uses hundreds to thousands of trajectory guided basis functions and converges very well, thus providing an effective tool for accurate and efficient simulations of polaron dynamics

Fully Atomistic Simulations of Protein Unfolding in Low Speed Atomic Force Microscope and Force Clamp Experiments with the Help of Boxed Molecular Dynamics

The results of Boxed Dynamics (BXD) fully atomistic simulations of protein unfolding by Atomic Force Microscope (AFM), in both force clamp (FC) and velocity clamp (VC) modes are reported. In AFM experiments the unfolding occurs on time scale which is too long for standard atomistic Molecular Dynamics (MD) simulations, which are usually performed with the addition of forces which exceed those of experiment by many orders of magnitude. BXD can reach the time scale of slow unfolding and sample the very high free energy unfolding pathway, reproducing the experimental dependence of pulling force against extension and extension against time. Calculations show the presence of the pulling force ‘humps’ previously observed in the Velocity Clamp (VC) AFM experiments and allow the identification of intermediate protein conformations responsible for them. Fully atomistic BXD simulations can estimate the rate of unfolding in the Force Clamp (FC) experiments up to the time scale of seconds

Ultrafast X-ray Scattering from Molecules

We present a theoretical framework for the analysis of ultrafast X-ray scattering experiments using nonadiabatic quantum molecular dynamics simulations of photochemical dynamics. A detailed simulation of a pump-probe experiment in ethylene is used to examine the sensitivity of the scattering signal to simulation parameters. The results are robust with respect to the number of wavepackets included in the total expansion of the molecular wave function. Overall, the calculated scattering signals correlate closely with the dynamics of the molecule

A two-layer approach to the coupled coherent states method

In this paper a two-layer scheme is outlined for the coupled coherent states (CCS) method, dubbed two-layer CCS (2L-CCS). The theoretical framework is motivated by that of the multiconfigurational Ehrenfest (MCE) method, where different dynamical descriptions are used for different subsystems of a quantum mechanical system. This leads to a flexible representation of the wavefunction, making the method particularly suited to the study of composite systems. It was tested on a 20-dimensional asymmetric system-bath tunnelling problem, with results compared to a benchmark calculation, as well as existing CCS, MP/SOFT and CI expansion methods. The two-layer method was found to lead to improved short and long term propagation over standard CCS, alongside improved numerical efficiency and parallel scalability. These promising results provide impetus for future development of the method for on-the-fly direct dynamics calculations

Zombie states for description of structure and dynamics of multi-electron systems

Canonical Coherent States (CSs) of Harmonic Oscillator have been extensively used as a basis in a number of computational methods of quantum dynamics. However, generalising such techniques for fermionic systems is difficult because Fermionic Coherent States (FCSs) require complicated algebra of Grassmann numbers not well suited for numerical calculations. This paper introduces a coherent antisymmetrised superposition of “dead” and “alive” electronic states called here Zombie State (ZS), which can be used in a manner of FCSs but without Grassmann algebra. Instead, for Zombie States, a very simple sign-changing rule is used in the definition of creation and annihilation operators. Then, calculation of electronic structure Hamiltonian matrix elements between two ZSs becomes very simple and a straightforward technique for time propagation of fermionic wave functions can be developed. By analogy with the existing methods based on Canonical Coherent States of Harmonic Oscillator, fermionic wave functions can be propagated using a set of randomly selected Zombie States as a basis. As a proof of principles, the proposed Coupled Zombie States approach is tested on a simple example showing that the technique is exact

Benchmark calculation for tunnelling through a multidimensional asymmetric double well potential

A benchmark calculation is presented for the quantum dynamics of tunnelling through a multidimensional asymmetric double well potential. A model Hamiltonian is used with a 1-dimensional tunnelling mode coupled to an (M − 1)-dimensional harmonic bath, a system-bath problem. The benchmark calculation uses a basis set expansion of the wavefunction, with separate basis functions for the system and bath. Indistinguishability of configurations is exploited to greatly reduce the expense of the calculation, and a fully converged result is achieved. Comparison is offered to existing quantum dynamical methods that have tested this model problem, and further benchmark results not previously studied are presented