Nonadiabatic dynamics: The SHARC approach

Abstract

We review the Surface Hopping including ARbitrary Couplings (SHARC) approach for excited-state nonadiabatic dynamics simulations. As a generalization of the popular surface hopping method, SHARC allows simulating the full-dimensional dynamics of molecules including any type of coupling terms beyond nonadiabatic couplings. Examples of these arbitrary couplings include spin-orbit couplings or dipole moment-laser field couplings, such that SHARC can describe ultrafast internal conversion, intersystem crossing, and radiative processes. The key step of the SHARC approach consists of a diagonalization of the Hamiltonian including these couplings, such that the nuclear dynamics is carried out on potential energy surfaces including the effects of the couplings-this is critical in any applications considering, for example, transition metal complexes or strong laser fields. We also give an overview over the new SHARC2.0 dynamics software package, released under the GNU General Public License, which implements the SHARC approach and several analysis tools. The review closes with a brief survey of applications where SHARC was employed to study the nonadiabatic dynamics of a wide range of molecular systems. This article is categorized under: Theoretical and Physical Chemistry > Reaction Dynamics and KineticsSoftware > Simulation MethodsSoftware > Quantum Chemistry.

Keywords: Ab initio molecular dynamics; SHARC; excited states; nonadiabatic dynamics; surface hopping.

Figure 1

Schematic examples of potential energy surfaces (PESs) and coupling matrix elements in the three different representations discussed in the text (molecular Coulomb Hamiltonian [MCH], diagonal, and spectroscopic). The listed items below the figures summarize the advantages (+) and disadvantages (−) of these representations for SH simulations

Figure 2

Energies and populations of a dynamics simulation with a model system showing the necessity of doing phase corrections to the matrix U. The left panel shows the energies of the six involved states, ordered by energy as is done in Surface Hopping including ARbitrary Couplings (SHARC). Note that in the panel, the energy differences between the multiplet components are arbitrarily increased for clarity; in the computations, they were degenerate. The middle panel shows the evolution of the populations when phase tracking is performed with the old tracking algorithm in SHARC. The right panel shows the populations with the new tracking algorithm of SHARC2.0, delivering the expected result that at the crossing points complete population transfer occurs between the crossing state pairs, whereas the other states are not affected

Figure 3

Work flow of SHARC2.0 dynamics simulations. The left column shows the work flow on the ensemble level, including the preparation (initial conditions), dynamics, and analysis steps, each with applicable options. The labels on the left give the names of the SHARC2.0 subprogram, which performs the respective task. Subprograms which are new with respect to the original implementation of SHARC are marked in orange. The middle column shows the work flow inside the dynamics driver, on a trajectory level. The right column shows, on the time step level, the work flow of the quantum chemistry (QC) interface

Figure 4

Overview over results obtained from SHARC simulations for 2‐thiouracil using the MS‐CASPT2(12,9)/cc‐pVDZ method (Mai, Marquetand, & González, 2016). In (a), the time‐dependent populations (thin lines) and kinetic model fits (thick lines). In (b), the assumed kinetic model with the obtained fit parameters and errors. In (c) and (d), the temporal evolution of two key geometric parameters (C=C bond length and thiocarbonyl pyramidalization angle). (Reprinted with permission from Mai, Marquetand, and González (2016). Copyright 2016 ACS, published under CC‐BY license)

Figure 5

Time‐dependent wave function composition of an exemplary trajectory of [Re(CO)₃(Im)(Phen)]⁺ in water. The different colors indicate the contributions of different charge transfer classes to the electronic wave function. Initially, the trajectory is predominantly in a Re(CO)₃→ Phen (MLCT) state, but around 60 fs it converts to a very pure Im→Phen (LLCT) state