Session V03: Challenges for excited states and dynamics II

Non-adiabatic couplings in the EOM-CC framework

This talk will describe theory of non-adiabatic coupling (NAC) forces within the EOM-CCSD framework and present a recent implementation. Using illustrative examples, I will compare NAC forces computed using EOM-CC and multi-reference (MR) wave functions (for selected cases, we also consider configuration interaction singles). In addition to the magnitude of the NAC forces, I will also analyze their direction, which is important for the calculations of the rate of nonadiabatic transitions. The numeric results confirm that the accuracy of NAC forces depends critically on the quality of the underlying wave functions. Within their domain of applicability, EOM-CC provides a viable alternative to MR methods.   

Partial Hydrodynamic Representation of Quantum Molecular Dynamics

A hybrid method is proposed to propagate system-bath quantum dynamics that uses both basis functions and coupled quantum trajectories. In it, the bath is represented with an ensemble of Bohmian trajectories while the system degrees of freedom are accounted through reduced density matrices. By retaining the Hilbert space structure for the system, the method is able to capture interference processes that are challenging to describe in Bohmian dynamics due to singularities that these processes introduce in the quantum potential. By adopting quantum trajectories to represent the bath, the method beats the exponential scaling of computational cost with bath size. This combination makes the method suitable for large-scale ground and excited state fully quantum molecular dynamics simulations.

B. Gu and I. Franco, J. Chem. Phys. 146, 194104 (2017)   

Machine Learning Optimal Effective Hamiltonians for Excited State Molecular Systems

Excited state molecular dynamics calculations require many expensive excited state calculations, severely limiting the length and time scales of examinable phenomena. Effective Hamiltonian models (such as tight-binding, the Hubbard, Hückel theory and semi-empirical methods), which retain the quantum complexity of the original problem albeit in a reduced parameter subspace, provide an opportunity to sidestep this bottleneck. These methods can be very accurate when properly tuned to the system at hand.

In recent years, Machine Learning algorithms have accurately reproduced both energies and properties derived from quantum chemistry without the need to solve the Schrödinger equation. Here, databases of optimized effective Hamiltonians for molecular systems are used to train a deep neural network, which can then produce optimized effective Hamiltonians for new systems on the fly. This methodology is applied to various semi-empirical forms, including Hückel and Modified Neglect of Diatomic Overlap (MNDO) type Hamiltonians. The accuracy of these optimized Hamiltonians is quantified by comparing orbital energies, excited state energies, and various molecular properties to higher level ab initio calculations.   

Electronic Delocalization, Vibrational Dynamics, and Energy Transfer in Organic Chromophores

The efficiency of materials developed for solar energy and technological applications depends on the interplay between molecular architecture and light-induced electronic energy redistribution. The spatial localization of electronic excitations is very sensitive to molecular distortions. Vibrational nuclear motions can couple to electronic dynamics driving changes in localization. The electronic energy transfer among multiple chromophores arises from several distinct mechanisms that can give rise to experimentally measured signals. Atomistic simulations of coupled electron-vibrational dynamics can help uncover the nuclear motions directing energy fl ow. Through careful analysis of excited state wave function evolution and a useful fragmenting of multichromophore systems, through-bond transport and exciton hopping (through-space) mechanisms can be distinguished. Such insights are crucial in the interpretation of fl uorescence anisotropy measurements and can aid materials design. This Perspective highlights the interconnected vibrational and electronic motions at the foundation of nonadiabatic dynamics where nuclear motions, including torsional rotations and bond vibrations, drive electronic transitions.
  

Open challenges in nonadiabatic dynamics: photons and electron-hole pairs

The theory of nonadiabatic dynamics is the story of "following the energy." A photon's energy flows into an electronic excitation, the electronic excitation leaks into nuclear motion, etc. Unfortunately, describing this flow quantitatively can be very problematic in practice: electronic structure is expensive, dynamics are non-standard with multiple surfaces, and some processes are very slow. As if this weren't difficult enough, the situation becomes yet more complicated when molecules are under light and/or near metal surfaces. In this talk, I will highlight our recent investigations of nonadiabatic dynamics in these many different environments and I will highlight open questions for the community.   

Quantum Mechanical Photochemistry

We are working on several aspects of the general problem of quantum mechanical calculations of photochemistry. This includes more accurate methods for calculating electronic excitation energies by Kohn-Sham density functional theory and by multi-configuration pair-density functional theory, new ways to treat conical intersections, new methods for diabatization, and simulations of molecular photodissociation processes by coherent switches with decay of mixing and army ants tunneling. Selected highlights of recent progress will be presented in the lecture. I am grateful to several collaborators who will be acknowledged in the lecture.   

Quinonile Photobasicity is Mediated by Hole Injection

Photoacids and photobases drive acid-base reactions by photon energy. Although known since 1940, the large-scale development of photoacids and photobases into efficient molecular light harvesting devices has been confounded by a lack of mechanistic understanding. A new mechanism explaining the photobasicity of quinolines is proposed based on nonadiabatic molecular dynamics simulations using time-dependent density functional theory (TDDFT). Rather than changing the basicity of the quinoline, photoexcitation is found to induce oxidation of adjacent water molecules. We develop a mechanistic understanding of the process in the molecular orbital theory framework, and discuss the limitations of our methods arising from using TDDFT to simulate excited state. Further support for the proposed mechanism is provided by comparison to experimental time-resolved fluorescence spectroscopy and correlated wavefunction calculations. These results suggest that the conventional picture of excited acid-base equilibrium may need to be revisited.   

Splitting a system into small fragments: Electron dynamics from real-time density matrix embedding theory

The simulation of non-equilibrium electron dynamics in real systems provides a challenge for theoretical methods due to the need to treat both large system sizes and electron correlation. Towards this goal, we present an extension of the density matrix embedding theory (DMET) for the simulation of real-time electron dynamics in strongly correlated systems. As in the previously developed static DMET, real-time DMET partitions the system into an impurity corresponding the region of interest coupled to the surrounding environment, which is efficiently represented by a quantum bath of the same size as the impurity. The dynamics of the coupled impurity and bath embedding problem are obtained through use of the time-dependent variational principle. The methodology allows for the efficient and accurate simulation of non-equilibrium electron dynamics in the presence of strong correlation, reaching total system sizes unobtainable by conventional methodology.
  

Quantifying Early Time Quantum Decoherence Dynamics through Fluctuations

We introduce a general but simple relation between the timescale for quantum coherence loss and the initial fluctuations of operators that couple a quantum system with a surrounding bath. The relation allows the prediction and measurement of early time decoherence dynamics for open quantum systems, through purity, without reconstructing the system’s many-body density matrix. It is applied to predict the decoherence time for the Holstein chain, spin-boson and Caldeira-Legget models. Such development also offers a practical platform to test the ability of approximate quantum dynamics methods to capture decoherence. In particular, a class of mixed quantum-classical schemes for molecular dynamics where the bath is treated classically, such as Ehrenfest dynamics, are shown to correctly capture short-time decoherence when the initial conditions are sampled from the Wigner distribution. Further, this relation is used to develop a general theory of electronic decoherence in molecules, a basic molecular process that is essential to the development of approximation schemes to excited states and non-adiabatic dynamics. These advances provide a useful platform to develop decoherence times for molecular processes and to test approximate molecular dynamics methods.