Simulating Photo-Excited Processes using Grids and Gaussian Wavepackets
Professor Graham Worth (UCL)
Simulating the time-evolution of molecular systems after photo-excitation is complicated by the need to include a manifold of excited electronic states. These states are coupled by so-called non-adiabatic coupling due to the interaction of the electronic and nuclear motion which makes the system highly quantum mechanical. As a result it is necessary to solve the time-dependent Schroedinger Equation (TDSE) for reliable results. To solve the TDSE, however, is a hard computational problem due to the exponential scaling of required resources with system size. The multi-configuration time-dependent Hartree (MCTDH) method provides a suitable algorithm that efficiently contracts the wavefunction to make it manageable for many degrees of freedom [1]. Such simulations can provide a full description of the evolving system, and it is possible to include the excitation by light pulses to obtain a spectroscopic signal that can be directly compared to experiments, such as REMPI spectra [2]. It is also possible to study the coherences induced in a system by a set of pulses [3]. These simulations, however, are constrained by the need for an analytic Hamiltonian, which is usually unable to describe long-range motions. For this, methods such as the direct dynamics variational multi-configuration Gaussian (DD-vMCG) method are required that calculate the potential surfaces on-the-fly and so allow a flexible description of the longe-time molecular response [4].
[1] Beck et al Phys. Rep. (00) 324: 1
[2] Dey et al PCCP (24) 26: 3451
[3] Dey et al PRL (22) 129: 173203
[4] Spinlove et al Farad. Discuss. (18) 212: 191
Simulating the time-evolution of molecular systems after photo-excitation is complicated by the need to include a manifold of excited electronic states. These states are coupled by so-called non-adiabatic coupling due to the interaction of the electronic and nuclear motion which makes the system highly quantum mechanical. As a result it is necessary to solve the time-dependent Schroedinger Equation (TDSE) for reliable results. To solve the TDSE, however, is a hard computational problem due to the exponential scaling of required resources with system size. The multi-configuration time-dependent Hartree (MCTDH) method provides a suitable algorithm that efficiently contracts the wavefunction to make it manageable for many degrees of freedom [1]. Such simulations can provide a full description of the evolving system, and it is possible to include the excitation by light pulses to obtain a spectroscopic signal that can be directly compared to experiments, such as REMPI spectra [2]. It is also possible to study the coherences induced in a system by a set of pulses [3]. These simulations, however, are constrained by the need for an analytic Hamiltonian, which is usually unable to describe long-range motions. For this, methods such as the direct dynamics variational multi-configuration Gaussian (DD-vMCG) method are required that calculate the potential surfaces on-the-fly and so allow a flexible description of the longe-time molecular response [4].
[1] Beck et al Phys. Rep. (00) 324: 1
[2] Dey et al PCCP (24) 26: 3451
[3] Dey et al PRL (22) 129: 173203
[4] Spinlove et al Farad. Discuss. (18) 212: 191
