We explore quantum + classical theories of molecules, materials, and their interaction with light
Research
Quantum mechanics reigns at the atomic scale, yet classical mechanics successfully predicts large-scale phenomena. As such, we have two complementary theories with each their own realm of applicability. But what defines the quantum–classical boundary? Developments in quantum materials and quantum information science are increasingly pushing quantum behaviors into scales formerly attributed to the classical realm. Conversely, one may wonder how far we can extend the success of classical mechanics into the quantum realm.
These are questions driving the research in The Tempelaar Team. By exploring the interface of quantum and classical theories, we seek to better understand the foundations of both quantum and classical behaviors, to replace computationally-expensive quantum models by inexpensive classical models, and to construct new hybrid models invoking both classical and quantum mechanics. In doing so, we seek to optimally contribute to breakthroughs in chemistry, physics, and materials science by targeting well-defined scientific problems and by closely collaborating with experimental scientists.
Quantum materials
In some materials, quantum behaviors emanating from the constituent electrons survive at macroscopic scales, giving rise to unusual material properties with far-reaching technological implications. How do electronic quantum effects survive in an environment of vibrating nuclei? We seek to address this question by developing new mixed quantum–classical models that go beyond the Born–Oppenheimer approximation in realistically capturing electron–nuclear interactions within a material.
Spin & chirality
Electrons, nuclei, and photons each carry a spin degree of freedom which can be used to store and process quantum information. Quantum information applications oftentimes rely on coupling photonic spin states to chiral excitations in matter, which relies in chiroptical interactions. We seek to amplify and control such interactions by using optical resonators. This poses the need for novel chiroptical materials, some of which we have helped develop.
Polaritonics
Strong coupling of quantum excitations in matter to confined optical fields gives rise to a new hybrid light–matter state called polariton. Polariton formation radically changes the properties of the host materials, with tunability afforded by the applied optical field, opening a new realm for chemical control and materials engineering. We study the behavior of polaritons through the development of full quantum models as well as models that represent optical fields classically through Maxwell's equations.
In collaboration with Science in Society, and under National Science Foundation funding, we are developing an introductory course in Python programming. By means of a series of "escape room"-like challenges driven by a narrative, we aim to present an engaging and playful course that fosters excitement about coding among early high-schoolers. The course infrastructure will be web-based and tailored to smartphones, intended to increase the likelihood of student engagement "beyond the classroom" among a demographic that has easier access to smartphones than to computers. Through the course's use of Python, the students will gain familiarity with a highly capable and abundant programming language, acquiring experience and skills that are increasingly relevant to employment.
A prototype of our coding course is currently available, consisting of a single sequence with narrative-driven challenges. We have run a pilot based on this prototype at Lake View High School in Chicago, and based on student feedback we are currently designing the actual programming course. Stay tuned for updates...
Our research covers mixed quantum-classical dynamics, chiral polaritons, and more. Below are a few representative examples.
Mixed quantum-classical modeling of band-like materials
Mixed quantum-classical dynamics arises when nuclei are approximated as classical while their interactions with the quantum-mechanical electrons is treated self-consistently. This approach has seen great success in describing a wide variety of molecular phenomena involving localized excited states. However, its application to crystalline materials, where excitations instead are organized in delocalized bands, remains quite limited. We are rethinking the significance of classical nuclear coordinates, allowing them to represent delocalized vibrations called phonons, through which band-like phenomena can be accurately modeled. We have obtained promising proof-of-concept results, in particular for the popular surface hopping method (figure).
Derivative couplings, which govern nonadiabatic transitions, attain a gauge freedom in the presence of geometric phase effects. This prohibits the application of surface hopping to topological materials, as surface hopping techniques require gauge-invariant derivative couplings for momentum rescalings. We have formulated a theory that eliminates this gauge freedom. When applied to surface hopping calculations, this theory produces results in good agreement with exact quantum modeling for a series of topologically-nontrivial avoided crossings (figure).
We have proposed a route towards designing "2D chiral polaritons", which are half-light-half-matter quantum states with angular momentum-like polarizations. Such states are relevant for the transduction of quantum information, and may open new technologies such as chiral lasing. Our proposed design relies on an emergent phenomenon called apparent circular dichroism, which manifests in certain organic thin films. In collaboration with the Goldsmith group at UW–Madison, we have embedded such thin films inside Fabry–Pérot cavities, and experimentally shown a breaking of the 2D chirality of cavity resonances.
Bridging classical electrodynamics with quantum chemistry
Classical electrodynamics has seen great success in describing complex multimodal optical fields, even under strong light–matter coupling. However, combining this theory with quantum models of molecules and materials has proven nontrivial. We have proposed a modification to Ehrenfest's theorem for the self-consistent coupling between quantum and classical systems wherein vacuum fluctuations are decoupled from the quantum ground state, preventing a spurious zero-point leakage out of the optical field. This yields remarkable accuracy improvements for the modeling of cavity-embedded quantum emitters (figure).
Representative publication:
Hsieh, Krotz, & Tempelaar, J. Phys. Chem. Lett. (2023) (Link)
High chiral selectivity through apparent circular dichroism
It has been long known that strong chiroptical signals may arise from an interference between linear dichroism and linear birefringence in assemblies of oriented molecules (figure). However, much remains to be learned about how such apparent circular dichroism can be harnessed in order to engineer high chiral selectivities for technological purposes. By combining Mueller calculus from classical optics with a quantum oscillator model, we have constructed the first fully-microscopic theory of apparent circular dichroism, allowing this effect to be understood and designed based on electronic structure theory. Favorable agreement with experimental measurements of organic thin films indicates this theory reaches the desired predictiveness.
Representative publication:
Salij, Goldsmith, & Tempelaar, J. Am. Chem. Soc. (2022) (Link)
Roel Tempelaar
Principal investigator
Roel (pronounced "Rule") was born in the Netherlands. He received his Ph.D. in 2015 from the University of Groningen, where he was advised by Jasper Knoester and Thomas La Cour Jansen. During his graduate years the Dutch government awarded him the Huygens Fellowship to conduct research at Temple University under guidance of Frank Spano. For his postdoctoral studies at Columbia University in the group of David Reichman he received the Rubicon Grant from the Dutch Research Council. He started as an assistant professor of chemistry at Northwestern University in January 2020. He was a recipient of the NSF CAREER award in 2022 as well as the 2024 Cadence/OpenEye Outstanding Junior Faculty Award by the ACS COMP Division.
Anna Bondarenko
Postdoctoral researcher
Ph.D. University of Groningen, the Netherlands (2019)
M.S. University of Porto, Portugal (2014)
B.S. & M.S. Karazin University, Ukraine (2009)
Anna completed her B.S. and M.S. at the V.N. Karazin Kharkiv National University in Ukraine, after which the Erasmus Mundus program took her to the University of Porto and the University of Groningen. After completing her Ph.D. in Groningen, she joined the Team as a postdoctoral researcher in the Fall of 2020.
Representative publication:
Bondarenko & Tempelaar, J. Chem. Phys. (2023) (Link)
Ethan Byrd
Undergraduate student
Ethan joined the Tempelaar Team in June 2024. He is studying the impact of coherent corrections to surface hopping on the method's ability to describe the Tully problems.
Antonio Garzón Ramírez
Postdoctoral researcher
Ph.D. University of Rochester (2021)
B.S. Universidad del Valle, Colombia (2013)
Upon completing his B.S. at the Universidad del Valle in Colombia, Antonio performed his graduate studies with Ignacio Franco at Rochester University, followed by a postdoctoral position with Lena Simine at McGill University. He joined the Team as a postdoctoral researcher in January 2023.
Ming-Hsiu Hsieh
Graduate student (since Fall 2021)
2023 Ryan Fellow
B.S. National Chiao Tung University, Taiwan (2021)
As a student at the National Chiao Tung University in Taiwan, Ming-Hsiu experienced the pitfalls of the Born-Oppenheimer approximation first-hand. This instilled in him a hunger for improving over existing quantum-computational methods, driving him to the Team where he started his graduate studies in Fall 2021.
Representative publication:
Hsieh, Krotz, & Tempelaar, J. Phys. Chem. Lett. (2023) (Link)
Kyle Kairys
Graduate student (since Fall 2023)
B.S. Emory University (2022)
Hailing from New Jersey, Kyle spent his undergraduate years at Emory and Rice, his research activities ranging from gold cluster synthesis to computing polariton-mediated energy transfer. At Northwestern, Kyle will continue honing his cross theory-experimental skills with a joint appointment with the Wasielewski group.
Alex Krotz
Graduate student (since Fall 2020)
2022 Joseph Lambert Award
B.S. Caltech (2020)
Besides spending his free time building a Raman spectrometer and a receiver of satelite images based on an inexpensive radio, Alex completed a B.S. in chemistry at Caltech. He joined the Northwestern graduate program in chemistry in the Fall of 2020.
Graduate student (since Fall 2022)
2022 Chair's Fellow
B.S. Purdue University (2022)
Hailing from Taiwan, Chientzu attended Purdue University for her B.S. where she studied the structural distortions of chlorophylls. She joined the Team for her graduate studies in the Fall of 2022.
Ken Miyazaki
Mark Ratner Postdoctoral Fellow
Ph.D. Cornell University (2023)
B.S. U. Wisconsin-Madison (2017)
Hailing from Japan, Ken's chemistry education brought him to such places as New Paltz, Madison, and Cornell. He joined the Team in the Summer of 2023, bringing expertise in nonadiabatic dynamics.
Mirjeta Remaley
Program Coordinator
Mirjeta (Jeta) joined Northwestern in October of 2019, just months before The Team was established. She worked for four years as a Financial Assistant for the Department of Chemistry, before transitioning into the role of Program Coordinator.
Andrew Salij
Graduate student (since Fall 2019)
2023 Outstanding Researcher Visionary Award
B.A. St. Olaf College (2019)
During his time at St. Olaf College, Andrew was torn between history and chemistry, ultimately gravitating towards the latter. After obtaining his B.A., he started as a chemistry graduate student at Northwestern in the fall of 2019.
Graduate student (since Fall 2023)
B.S. Universidad del Valle, Colombia (2023)
Originally from Valle, Colombia, Luis's early academic endeavors were aimed at tackling the Born-Oppenheimer approximation head-on. After a stint at the University of Rochester, Luis landed at Northwestern in the Fall of 2023. He gives the local coffee scene a pass.
Connor Terry Weatherly
Graduate student (since Fall 2020)
NSF Graduate Research Fellow
B.S. University of Utah (2020)
An aspiring filmmaker in high school, Connor gravitated towards chemistry in college. He obtained his B.S. at the University of Utah, upon which he joined Northwestern as a graduate student in chemisty in the fall of 2020.
Currently at ASML
Graduate student, 2014-2019 (Columbia)
B.S. Harvard University (2014)
Ian has teamed up with Roel in unraveling the excitonic properties of molecular aggregates. He is particularly interested in how to relate the exciton band dispersion to optical properties as well as exciton-exciton annihilation.
Currently a postdoc at the Flatiron Institute
Graduate student, 2016-2021 (Columbia)
B.S. Universität Frankfurt am Main (2016)
Benedikt and Roel have joined forces to develop a highly efficient representation of large electron-vibrationally coupled systems based on tensor decompositions. This has enabled them to discover anomalous mobilities of strongly-coupled excitations.
Representative publication:
Kloss, Reichman, & Tempelaar, Phys. Rev. Lett. (2019) (Link)
Justin Provazza
Currently at QSimulate
Postdoctoral researcher, 2021-2022
Ph.D. Boston University (2020)
B.S. Plymouth State University (2015)
During this stint in the Team, Justin combined the Truncated Wigner Approximation with perturbation theory, and discovered that this enables inexpensive and flexible modeling of system-bath interactions without losing microscopic detail. He utilized this to study how system-bath entanglement formation drives qubit decoherence.
