Session R03: Challenges for Excited States and Dynamics I

Challenges for excited states and dynamics in the presence of environment

The accurate description of excited states and its dynamics of molecules in the presence of an environment is a very challenging task because it requires, at least i) an appropriate description of the interactions between the chromophore and the environment, and ii) the calculation of the vibrational motion of the whole system. For the former, it is common to describe the environment either by quantum mechanics/continuum or quantum mechanics/molecular mechanics models. For the second, vibrational sampling can be described with Wigner sampling or with molecular dynamics. Several examples will be first shown to illustrate how different models can dramatically affect the excited states energies and other properties of the molecule. In the case of flexible molecules and in order to perform non-adiabatic dynamics, the situation is even more complex, as Wigner distributions cannot be used as initial conditions and molecular dynamics is not suitable to describe large amplitude motions correctly. Surface-hopping simulations using our local code SHARC for non-adiabatic dynamics including spin-orbit couplings will be shown on a transition metal complex in solution.
  

Dual-Functional Tamm-Dancoff Approximation: A Convenient Density Functional Method that Correctly Describes S1/S0 Conical Intersections.

Accurate non-adiabatic dynamics simulations require sophisticated electronic structure theories that can describe the complex wavefunctionsin different regions of the potential energy surfaces (PESs). Conical intersections (CIs), facilitating the population transfer from one state to the other, play an important role in the non-adiabatic processes. Hence, efficient and accurate electronic structure theories should correctly describe the double cone topology of the PESs near CI. The current theories that can correctly describe the CI regions of the PESs are mostly based on the multi-reference methods. However, the computational cost of the multi-reference methods grows exponentially when the active space increases. On the other hand, LR-TDDFT is both efficient and accurate but unable to describe the CIs between ground and excited states. Hence the applications of LR-TDDFT in the non-adiabatic processes are limited. In this presentation, we introduce a novel theoretical method based on LR-TDDFT, named dual functional Tamm-Dancoff approximation that can describe the correct topology of the PESs near CI and can be accurate as LR-TDDFT.   

Quasi Diabatic Representation for Nonadiabatic Quantum Dynamics Propagations

We develop a non-adiabatic quantum dynamics propagation scheme that allows interfacing diabatic quantum dynamics approaches with routine adiabatic electronic structure calculations. This new scheme is based a quasi-diabatic (QD) representation that uses adiabatic states as diabatic states during a short-time quantum dynamics propagation. Between two consecutive short-time propagations, the electronic state basis is transformed from the old to the new QD representation. This scheme allows using diabatic quantum dynamics method with any adiabatic electronic structure methods, resolving the incompatibility challenge between the two methods due to their different representations. In addition, with the QD scheme one avoids explicitly computing the derivative coupling vectors and thus alleviate the numerical instability for quantum propagations in the cases where these vectors change rapidly in time. Using a recently developed diabatic quantum dynamics approach, Partial Linearized Density Matrix (PLDM) path-integral method as a specific exampel, we have demonstrated the accuracy of this QD scheme with a wide range of model non-adiabatic problems as well as the on-the-fly propagations with Density Functional Tight-Binding (DFTB) calculations.   

Spin-Forbidden Channels in the Reactions of Unsaturated Hydrocarbons and O(3P)

A number of theoretical and experimental studies indicate that the role of spin-forbidden channels in the reaction of unsaturated hydrocarbons and O(³P) can be important. Branching ratios of the products are sensitive to the chemical structures of the reactants. In our study we use equation-of-motion coupled-cluster methods to investigate electronic structure and to predict the difference in branching ratios for ethylene, propylene, and acetylene. To evaluate one- and two-electron spin-orbit matrix elements we use perturbative approach. All matrix elements are obtained by rotation of the molecules and applying the corresponding Wigner matrices.   

Optimized Ensemble Time-Dependent Density Functional Theory

The recent discovery of unphysical divergences in approximate
single-state response theories has underscored the need for more robust
excited-state electronic structure methods. I will present an optimized
ensemble (oe) extension of time-dependent density functional (TDDFT)
theory which produces excited state properties free of artificial
divergences while retaining desirable features of single-state TDDFT
such as orthogonality and computational efficiency. I will explain how
oe-TDDFT reduces self-interaction error in charge-transfer excited
states and can yield conical intersections with the ground state with
correct topology.   

Non-adiabatic molecular dynamics of carbon dioxide at metal surfaces

We investigate theoretically the collisions of carbon dioxide with gold surfaces at hyperthermal kinetic energies. We parameterize an accurate and computationally efficient system-specific tight-binding model to propagate molecular dynamics trajectories and sample over initial conditions, and incorporate the electron-hole pair excitations in the metal by an electronic friction model. We observe that the molecular electronic states interact along the trajectories of atomic motion and describe the non-adiabatic coupling at the state-averaged complete active space self-consistent field level. The theoretical model allows us to gain insight into the non-adiabatic molecular dynamics of carbon dioxide at metal surfaces.   

On the exact factorization equations and quantum-classical approximations

A time-dependent molecular wavefunction may be written exactly as a single product of the nuclear and electronic wavefunctions, with a pair of corresponding equations of motion [1]. Although the nuclear equation is a time-dependent Schrödinger equation, the electronic equation is not and has a structure with as yet unknown stability and convergence properties. We present preliminary studies of this, with a view to investigating approximations to the non-adiabatic terms.

This exact factorization provides a starting point for rigorous and practical approximations. One approximate scheme is the coupled trajectory mixed quantum classical approach [2] which captures non-adiabatic effects such as wavepacket splitting and decoherence remarkably well, and recently successfully simulated ring-opening in oxirane [3]. We study the roles of the coupling terms in this algorithm and show that nuclear wavepacket splitting can occur even if the nuclear forces are Ehrenfest-like, provided the quantum momentum term remains in the electronic equation.

[1] A. Abedi, et al, J. Chem. Phys 137, (2012)
[2] F. Agostini, et al, J. Chem. Theory Comput.12 , 2127, (2016)
[3] S. K. Min et al, J. Phys. Chem. Lett 8, 3048, (2017)   

Photodissociation dynamics of organic iodides studied via ultrafast photoelectron spectroscopy

Photodissociation reactions are prototypical systems for ultrafast dynamics studies. While direct excitation to a repulsive excited state followed by direct dissociation is the fastest dissociation mechanism, bond breaking can occur via a variety of pathways. In the present study, we use ultrafast photoelectron spectroscopy with resonant ionization via molecular Rydberg states to investigate C-I bond cleavage in the molecule 1,4-diiodobenzene excited by 4.6 eV photons. The photoelectron spectrum suggests that the first step of the dissociation is an ultrafast curve crossing from the initially excited bound state. Subsequent probing via resonant ionization reveals a detailed picture of the ensuing wavepacket dynamics.
  

Non-Adabatic Chemiluminescent Dynamics of the Methyl-Substituted 1,2-Dioxetanes

That the origin of chemi- and bioluminescence is a non-adiabatic process originating from the breakage of a peroxide bond is well understood. However, some details in the mechanisms of chemi- and bioluminescence are not well understood. In this lecture we will unravel one of these lesser understood experimental observations. That is, the intriguing and dramatic increase - 0.003 to 0.35 - of the quantum yield of the phosphorescence for the series of 1,2-dioxetane molecules substituted going from none up to four methyl groups. This changes of quantum yield, more than two orders of magnitude, is studied in a series of non-adiabatic surface hopping dynamics simulations using multi-configurational electron structure theory. The dynamics reveal how the seemingly innocent methyl groups retards the dynamic of the fragmentation process - 1,2-dioxetane thermally fragments to two formaldehyde - in a so-called entropic trap, there by enhancing the interstate crossing efficiency. The lecture will initially give a brief background to the field of chemi- and bioluminescence, followed by the details for the problem and simulations listed above.