Nonadiabatic Tunneling in Photodissociation of Phenol

Geometric Phase Effects in Nonadiabatic Dynamics near Conical Intersections

Dynamical consideration that goes beyond the common Born-Oppenheimer approximation (BOA) becomes necessary when energy differences between electronic potential energy surfaces become small or vanish. One of the typical scenarios of the BOA breakdown in molecules beyond diatomics is a conical intersection (CI) of electronic potential energy surfaces. CIs provide an efficient mechanism for radiationless electronic transitions: acting as "funnels" for the nuclear wave function, they enable rapid conversion of the excessive electronic energy into the nuclear motion. In addition, CIs introduce nontrivial geometric phases (GPs) for both electronic and nuclear wave functions. These phases manifest themselves in change of the wave function signs if one considers an evolution of the system around the CI. This sign change is independent of the shape of the encircling contour and thus has a topological character. How these extra phases affect nonadiabatic dynamics is the main question that is addressed in this Account. We start by considering the simplest model providing the CI topology: two-dimensional two-state linear vibronic coupling model. Selecting this model instead of a real molecule has the advantage that various dynamical regimes can be easily modeled in the model by varying parameters, whereas any fixed molecule provides the system specific behavior that may not be very illustrative. After demonstrating when GP effects are important and how they modify the dynamics for two sets of initial conditions (starting from the ground and excited electronic states), we give examples of molecular systems where the described GP effects are crucial for adequate description of nonadiabatic dynamics. Interestingly, although the GP has a topological character, the extent to which accounting for GPs affect nuclear dynamics profoundly depends on topography of potential energy surfaces. Understanding an extent of changes introduced by the GP in chemical dynamics poses a problem of capturing GP effects by approximate methods of simulating nonadiabatic dynamics that can go beyond simple models. We assess the performance of both fully quantum (wave packet dynamics) and quantum-classical (surface-hopping, Ehrenfest, and quantum-classical Liouville equation) approaches in various cases where GP effects are important. It has been identified that the key to success in approximate methods is a method organization that prevents the quantum nuclear kinetic energy operator to act directly on adiabatic electronic wave functions.

Molecular Photofragmentation Dynamics in the Gas and Condensed Phases

Exciting a molecule with an ultraviolet photon often leads to bond fission, but the final outcome of the bond cleavage is typically both molecule and phase dependent. The photodissociation of an isolated gas-phase molecule can be viewed as a closed system: Energy and momentum are conserved, and the fragmentation is irreversible. The same is not true in a solution-phase photodissociation process. Solvent interactions may dissipate some of the photoexcitation energy prior to bond fission and will dissipate any excess energy partitioned into the dissociation products. Products that have no analog in the corresponding gas-phase study may arise by, for example, geminate recombination. Here, we illustrate the extent to which dynamical insights from gas-phase studies can inform our understanding of the corresponding solution-phase photochemistry and how, in the specific case of photoinduced ring-opening reactions, solution-phase studies can in some cases reveal dynamical insights more clearly than the corresponding gas-phase study.

Quantum Nonadiabatic Cloning of Entangled Coherent States

We propose a systematic approach to the basis set extension for nonadiabatic dynamics of entangled combination of nuclear coherent states (CSs) evolving according to the time-dependent variational principle (TDVP). The TDVP provides a rigorous framework for fully quantum nonadiabatic dynamics of closed systems; however, the quality of results strongly depends on available basis functions. Starting with a single nuclear CS replicated vertically on all electronic states, our approach clones this function when replicas of the CS on different electronic states experience increasingly different forces. Created clones move away from each other (decohere), extending the basis set. To determine a moment for cloning, we introduce generalized forces based on derivatives that maximally contribute to a variation of the total quantum action and thus account for entanglement of all basis functions.

Topologically Correct Quantum Nonadiabatic Formalism for On-the-Fly Dynamics

On-the-fly quantum nonadiabatic dynamics for large systems greatly benefits from the adiabatic representation readily available from electronic structure programs. However, conical intersections frequently occurring in this representation introduce nontrivial geometric or Berry phases which require a special treatment for adequate modeling of the nuclear dynamics. We analyze two approaches for nonadiabatic dynamics using the time-dependent variational principle and the adiabatic representation. The first approach employs adiabatic electronic functions with global parametric dependence on the nuclear coordinates. The second approach uses adiabatic electronic functions obtained only at the centers of moving localized nuclear basis functions (e.g., frozen-width Gaussians). Unless a gauge transformation is used to enforce single-valued boundary conditions, the first approach fails to capture the geometric phase. In contrast, the second approach accounts for the geometric phase naturally because of the absence of the global nuclear coordinate dependence in the electronic functions.

Fano resonances in the photoinduced H-atom elimination dynamics in the πσ* states of pyrrole

The interference is supported by two distinct dynamical scenarios controlled by two exit channel conical intersections between the πσ* states and the ground electronic state.

Molecular “topological insulators”: a case study of electron transfer in the bis(methylene) adamantyl carbocation

A topological or geometric phase blockade can be introduced in molecular electron transfer processes if a conical intersection occurs between two charge configurations.

Accurate nonadiabatic dynamics

This Perspective addresses the use of coupled diabatic potential energy surfaces (PESs) together with rigorous quantum dynamics in full or reduced dimensional coordinate spaces to obtain accurate solutions to problems in nonadiabatic dynamics.