# Previous Research

# Stanford University

Stanford University

## Constructing chemically intuitive states

Constructing chemically intuitive states

**Why it's interesting:**Diabats - or chemically intuitive charge-localized states whose chemical character does not change along the course of a chemical reaction - form the basis of numerous and highly successful descriptions of chemical processes such Marcus theory of electron transfer. However, constructing these states and calculating their electronic coupling poses a difficult theoretical problem.

**What we achieved:**We introduced two DFT-based approaches to achieve this goal. One of these approaches, ALMO(MSDFT2), provides a number of advantageous qualities, including:

1. Accurate diabatic couplings across a wide array of molecules supporting electron and hole transfer, including conjugated organic molecules, such as thiophene and pentacene, and DNA base pairs.2. Variationally optimized wavefunctions that give easy access to forces, enabling the calculation of on-the-fly nonadiabatic dynamics.3. Great performance, even when using the lowest tiers of the DFT hierarchy (see results in figure corresponding to PBE, a low-tier GGA functional), rendering it affordable to elucidate processes in the condensed phase.

**Relevant paper:**Mao, AMC & Markland. J. Chem. Phys.

**151**, 164114. (2019)

## Capturing vibronic effects & broadening in the optical spectra of condensed systems

Capturing vibronic effects & broadening in the optical spectra of condensed systems

**Why it's interesting:**Optical spectroscopy is an essential tool for identifying and characterizing molecules and materials as well as their energy relaxation processes. However, predicting spectra in the condensed phase presents an enduring challenge due to the need to capture spectral signatures arising from anharmonicity and dynamical effects, such as vibronic progressions and asymmetry.

**What we achieved:**In collaboration with Christine Isborn's group at UC Merced, we demonstrated how different statics- and dynamics-based approaches fare in reproducing optical spectra of solvated organic chromophores in the condensed phase using both models and atomistic ab initio simulations and determined that fully dynamical methods (bottom panel of the figure containing results for the second and third order cumulant methods) provide the best candidate to capture both anharmonic effects and vibronic progressions.

**Relevant paper:**Zuehlsdorff*, AMC*, Napoli, Markland, & Isborn. J. Chem. Phys.

**151**, 074111. (2019)

## Accurate & efficient dynamics of many-level systems through approximate memory kernels

Accurate & efficient dynamics of many-level systems through approximate memory kernels

**Why it's interesting:**The accurate simulation of the quantum dynamics of systems containing many electronic energy levels, such as photosynthetic complexes, molecular aggregates, and nanoparticle arrays, is central to understanding spectroscopy and mechanisms of energy and charge transfer in such systems. However, this remains a difficult challenge.

**What we achieved:**We demonstrated how one can efficiently extend the combination of quantum-classical theory and generalized quantum master equations (GQMEs) to obtain the accurate quantum dynamics of such systems, including the the Light Harvesting Complex II (population dynamics of the chromophores in the figure). To increase the efficiency our quantum-classical GQME, we developed a

*selective sampling algorithm*to dramatically accelerate the calculation of the memory kernel at the heart of the GQME. This algorithm has permitted speedups of up to 100x over the direct quantum-classical simulation.

**Relevant paper:**Pfalzgraff, AMC, Kelly, & Markland. J. Chem. Phys.

**150**, 244109. (2019)

## Exact Cartesian map for fermionic creation & annihilation operators

Exact Cartesian map for fermionic creation & annihilation operators

**Why it's interesting:**Encoding the antisymmetry of fermions, such as electrons, into a simple Cartesian map would offer the opportunity to develop path integral and semiclassical approaches to address the structure and dynamics of problems involving many fermions, especially those where the fermions are coupled to complex nuclear motions and spins, enabling the efficient and accurate study of processes such as electrochemical charge transfer and transport through molecular junctions.

**What we achieved:**We derived an exact quantum mechanical map connecting second quantized fermionic operators to continuous Cartesian variables. Focusing on two celebrated models, the Anderson impurity and Hubbard models, we demonstrated how to construct efficient mappings of these Hamiltonians by using a judicious choice of index ordering of the fermions (see ordering suggested at the bottom of the figure). Besides allowing the development of path integral and semiclassical approaches, this map also opens the door to the development of algorithms to solve problems involving many fermions on continuous-variable quantum computers.

**Relevant paper:**AMC & Markland. Sci. Rep.

**8**, 12929. (2018)

# Columbia University

Columbia University

## Unlocking the secrets of memory kernels

Unlocking the secrets of memory kernels

**Why it's interesting:**As several groups have demonstrated, combining the generalized quantum master equation (GQME) formalism with quantum-classical theories by approximating the memory kernels at the heart of GQMEs

*can significantly improve both the accuracy and efficiency of quantum-classical methods*(see the figure to the left). However, the origin of these improvements and how to extend them systematically to other methods remained unknown.

**What we achieved:**To answer this and other fundamental questions about the applicability of this approach, we:

1. Provided a detailed analysis that pointed to the source of these improvements [A].2. Showed different but quantum mechanically equivalent ways of expressing the memory kernels whose approximation could lead to distinct levels of accuracy [A & B].3. Produced analytical proofs that determine when approximating the memory kernel dynamics could and could not lead to different levels of accuracy [B].4. Extended the method beyond nonequilibirum dynamics of two-level systems to equilibrium time correlation functions [C] by developing an exact path integral approach [D] to generate the Wigner-transformed equilibrium density.

**Relevant papers:**[A] AMC & Reichman. J. Chem. Phys.

**144**, 184104. (2016)[B] Kelly*, AMC*, Wang & Markland. J. Chem. Phys.

**144**, 184105. (2016)[C] AMC & Reichman. J. Chem. Phys.

**146**, 084110. (2017)[D] AMC & Reichman. J. Chem. Phys.

**146**, 024107. (2017)

## Energy transfer trends in low-dimensions

Energy transfer trends in low-dimensions

**Why it's interesting:**Understanding and predicting energy transfer trends in low-dimensional heterostructures is essential to engineer devices with advantageous energy conversion and transport properties.

**What we achieved:**In collaboration with the experimental work of Archana Raja, Louis Brus, Tony Heinz and coworkers, we employed classical electromagnetic theory to show that contrasting trends of nonradiative energy transfer from quantum dots to two-dimensional (2D) stacks of graphene and MoS2 of different thicknesses (see figure) arise from the competition between screening and absorption of the electric field of the quantum dot dipole inside the 2D materials. We also employed our analysis to predict NRET behavior for the near-field coupling of a chromophore to a range of semiconducting and metallic thin film materials.

**Relevant paper:**Raja, AMC*, Zultak*, Zhang, Ye, Roquelet, Chenet, van der Zande, Huang, Jockusch, Hone, Reichman, Brus, & Heinz. Nano Lett.

**16**, 2328. (2016)

## Getting more juice out of Redfield Theory

Getting more juice out of Redfield Theory

**Why it's interesting:**Redfield theory - a major workhorse for the investigation of spin dynamics and the linear and nonlinear spectroscopy of molecular aggregates and photosynthetic complexes - is known to suffer from severe problems when the electronic-nuclear coupling is not weak and the timescale of the nuclear motions is slow.

**What we achieved:**Employing the simple insight that, to a fast moving particle, a slow one appears to not be moving, i.e., extreme timescale separation, we showed how one can dramatically extend the applicability of this celebrated theory to physical scenarios with slow nuclear dynamics and intermediate to strong electronic-nuclear coupling. The figure shows bare Redfield and our timescale-separated (Frozen modes) Redfield dynamics (solid lines) in comparison to the exact results (circles, squares, & diamonds) for the Fenna-Matthews-Olson photosynthetic complex. Several research groups have since adopted and adapted our approach to study diverse processes ranging from the nonlinear spectroscopy of model photosynthetic complexes, to singlet fission, polaron dynamics, and photoisomerization dynamics through conical intersections.

**Relevant paper:**AMC, Berkelbach, & Reichman. J. Chem. Phys.

**143**, 194108. (2015)