From Surface Hopping to Quantum Dynamics and Back. Finding Essential Electronic and Nuclear Degrees of Freedom and Optimal Surface Hopping Parameters

Abstract

We report an efficient iterative procedure that exploits surface-hopping trajectory methods and quantum dynamics to achieve two complementary purposes: to identify the minimum dimensionality of a molecular Hamiltonian in terms of electronic and nuclear degrees of freedom to study radiationless relaxation mechanisms as well as to provide a reference quantum dynamical calculation that allows assessing of the validity of surface-hopping parameters. This double goal is achieved by a feedback loop between surface hopping and MCTDH calculations based on potential energy surfaces parametrized with a linear vibronic coupling method. Initially, a surface hopping calculation in full dimensionality with a chosen set of parameters is performed, and it is repeated, gradually reducing its dimensionality until divergence with the initial calculation is observed or the system is small enough to be treated quantum dynamically. A comparison between the quantum dynamics and surface hopping simulations dictates the validity of the surface hopping parameters. Using these new parameters, the reduction loop is started again, until convergence. As an example, this strategy is applied to simulate the ultrafast intersystem crossing dynamics of [PtBr 6 ] 2− in solution. The 15-dimensional space initially including 200 electronic states is reduced to a 9-dimensional problem with 76 electronic states, without a considerable loss of accuracy.

The quantum-Ehrenfest method with the inclusion of an IR pulse: Application to electron dynamics of the allene radical cation

“…We use this representation for the gwp because of the orthogonality of this representation and the ability to easily identify the relevant degrees of freedom compared to the cartesian representation where the degrees of freedom are strongly coupled together. 38 We first discuss the electron dynamics, which we visualize with the spin density on the terminal carbon atom 2 (C2) (averaged using the weights of the gwp). The complementary data for carbon atom 3 (C3) can be found in Figure S4 in SI.…”

Machine Learning for Electronically Excited States of Molecules

“…Nonetheless, the computations are computationally costly, and the nuclear degrees of freedom are often reduced to only a few important key coordinates, 239 , 406 where classical simulations can help identify the latter. 407 Whether quantum dynamics of such reduced-dimensionality models are better than using classical dynamics of a full-dimensional system is still under debate and probably depends on the system. In the case of quantum dynamics, the potentials need to be presented to the algorithm in the diabatic basis, mostly due to numerical stability (e.g., smooth couplings are easier to integrate than singular ones).…”

“…Because of the aforementioned problems, a description of medium-sized to large molecules with diabatic potentials is often done with more crude approximations. 142 , 407 An example is the LVC model, 239 with its one-shot variant, 240 or the exciton model. 182 , 654 For more details on this topic, the reader is referred to refs ( 64 , 239 , 331 , and 655 − 657 ).…”

The Quest to Simulate Excited-State Dynamics of Transition Metal Complexes

“…In this way, a minimum set of degrees of freedom can be identified, as illustrated in a small platinum(IV) complex that could be reduced from its 15-dimensional space initially considering 200 electronic states to a nine-dimensional problem with 76 electronic states without loss of accuracy. 195 …”