An important group of chemical reactions are those that involve the transfer of energy within or between molecules. These types of reactions include vibrational and electronic relaxation, oxidation-reduction reactions, charge transfer, and optical response and are pertinent to many technologically- and biologically-relevant processes, such as in photovoltaics and photosynthetic systems. Quantum dynamical effects play a central role in these important processes that take place in molecular condensed phase systems. As a result, the simulation of quantum dynamics in such systems remains one of the most important challenges facing computational chemistry. Theoretically, Schrödinger's equation can simulate quantum dynamics for these systems. However, the exponential scaling of the computational cost with system dimensionality makes the numerically exact simulation of quantum dynamics in complex molecular systems non-feasible, with the important exception of a subclass of Hamiltonians whose form makes such an exact simulation possible. Because of this, many methods involving approximations have been proposed to simulate quantum dynamics in the condensed phase.

The generalized quantum master equation (GQME) is arguably the most general framework for simulating electronically nonadiabatic reduced dynamics, as it requires no approximations in its derivation and has the ability to capture the full electronic density matrix. The GQME-based methodology fills a gap which is not addressed by currently available methods for simulating electronically nonadiabatic dynamics. Methods based on Marcus theory, Fermi's golden rule, or the Redfield equation require assuming weak electronic coupling between donor and acceptor states while direct application of quasiclassical methods that can handle strong coupling, such as Ehrenfest, linearized semiclassical, or the mixed quantum-classical Liouville methods, often have decreasing reliability and/or computational feasibility with increasing simulation time. The GQME-based methodology allows one to restrict the dynamical input to short times via the memory kernel while providing a unified framework that can describe a wide range of electronic coupling strengths. As such, it capitalizes on the advantages of both alternative approaches without suffering from the corresponding disadvantages.

For a short video about my research, you can view my **Lightning Talk** from the 2020 Virtual Conference in Theoretical Chemistry.

**E. Mulvihill**, E. Geva,.__Simulating the Dynamics of Electronic Observables via Reduced-Dimensionality Generalized Quantum Master Equations__*J. Chem. Phys.***156**, 044119 (2022)**E. Mulvihill**, E. Geva,.__A Road Map to Various Pathways for Calculating the Memory Kernel of the Generalized Quantum Master Equation__*J. Phys. Chem. B*2021, 125, 34, 9834–9852- H. P. Hendrickson, K. M. Lenn, F. X. Vazquez, K. L. Williams, B. A. Winograd,
**E. A. Mulvihill**, E. Geva,in__The Compute-to-Learn Pedagogy and Its Implementation in the Chemistry Curriculum__*Teaching Programming across the Chemistry Curriculum*edited by A. Ringer McDonald and J. A. Nash (ACS Publications, 2021), pp. 69-87 **E. Mulvihill**, K. M. Lenn, X. Gao, A. Schubert, B. D. Dunietz, E. Geva,.__Simulating energy transfer dynamics in the Fenna–Matthews–Olson complex via the modified generalized quantum master equation__*J. Chem. Phys.***154**, 204109 (2021)- Y. Liu, X. Gao, Y. Lai,
**E. Mulvihill**, E. Geva,.__Electronic Dynamics through Conical Intersections via Quasiclassical Mapping Hamiltonian Methods__*J. Chem. Theory Comput.*2020, 16, 7, 4479–4488 **E. Mulvihill**, X. Gao, Y. Liu, A. Schubert, B. D. Dunietz, E. Geva,.__Combining the Mapping Hamiltonian Linearized Semiclassical Approach with the Generalized Quantum Master Equation to Simulate Electronically Nonadiabatic Molecular Dynamics__*J. Chem. Phys.***151**, 074103 (2019)**E. Mulvihill**, A. Schubert, X. Sun, B. D. Dunietz, E. Geva,.__A modified approach for simulating electronically nonadiabatic dynamics via the generalized quantum master equation__*J. Chem. Phys.***150**, 034101 (2019)- Jafari, M.; Welden, A.R.; Williams, K.L.; Winograd, B.;
**Mulvihill, E.**; Hendrickson, H.P.; Lenard, M.; Gottfried, A.; and Geva, E..__Compute-to-Learn: Authentic Learning via Development of Interactive Computer Demonstrations within a Peer-Led Studio Environment__*J. Chem. Educ.***2017**,*94*(12), pp. 1896-1903.

**2020 Karle Symposium**,*Poster Session:*"Generalized Quantum Master Equation: a reduced dynamics approach for electronically nonadiabatic dynamics."**Mulvihill, E.**; Gao, X.; Liu, Y.; Schubert, A.; Sun, X; Dunietz, B. D.; Geva, E.*July 29th, 2020.***Won Best Physical Chemistry Poster Award.****2020 Virtual Conference in Theoretical Chemistry**,"Simulating Electronically Nonadiabatic Dynamics via the Generalized Quantum Master Equation."__Lightning Talk__and Poster Session:**Mulvihill, E.**; Gao, X.; Liu, Y.; Schubert, A.; Sun, X; Dunietz, B. D.; Geva, E.*July 29th, 2020.***Won Outstanding Lightning Talk Graduate Student Award.****2019 Penn Conference in Theoretical Chemistry**,*Poster Session:*"Simulating Electronically Nonadiabatic Dynamics via a Modified Approach to the Generalized Quantum Master Equation."**Mulvihill, E.**; Gao, X.; Liu, Y.; Schubert, A.; Sun, X; Dunietz, B. D.; Geva, E.*August 14th, 2019.***2019 Karle Symposium**,*Poster Session:*"Simulating Electronically Nonadiabatic Dynamics via a Modified Generalized Quantum Master Equation."**Mulvihill, E.**; Gao, X.; Liu, Y.; Schubert, A.; Sun, X; Dunietz, B. D.; Geva, E.*August 2nd, 2019.***2019 Midwest Theoretical Chemistry Conference**,*Oral Presentation:*"Generalized Quantum Master Equation-based Approaches to Electronically Nonadiabatic Dynamics: Mapping Hamiltonian + LSC."**Mulvihill, E.**; Gao, X.; Liu, Y.; Schubert, A.; Sun, X.; Dunietz, B. D.; Geva, E.*June 8th, 2019.***Quantum Science and Technology Workshop at University of Michigan, Ann Arbor, MI**,*Poster Session:*"A Modified Generalized Quantum Master Equation for Simulating Electronically Nonadiabatic Dynamics."**Mulvihill, E.**; Schubert, A.; Gao, X.; Liu, Y.; Sun, X.; Lai, Y.; Dunietz, B. D.; Geva, E.*April 12th, 2019.***Invited Research Presentation at Lafayette College, Easton, PA**,*Oral Presentation:*"A Modified Generalized Quantum Master Equation for Simulating Electronically Nonadiabatic Dynamics."**Mulvihill, E.**; Lai, Y.; Schubert, A.; Sun, X.; Dunietz, B. D.; Geva, E.*November 1st, 2018.***2018 Midwest Theoretical Chemistry Conference**,*Oral Presentation:*"A Modified Generalized Quantum Master Equation for Simulating Electronically Nonadiabatic Dynamics."**Mulvihill, E.**; Lai, Y.; Schubert, A.; Sun, X.; Dunietz, B. D.; Geva, E.*June 22nd, 2018.***ACS National Meeting, New Orleans, LA**,*Physical Chemistry Poster Session:*"A Modified Generalized Quantum Master Equation for Simulating Electronically Nonadiabatic Dynamics."**Mulvihill, E.**; Schubert, A.; Sun, X.; Lai, Y.; Dunietz, B. D.; Geva, E.*March 21st, 2018.**Won Outstanding Student Poster Award.***ACS National Meeting, New Orleans, LA**,*Physical Chemistry Poster Session:*"Compute-to-Learn: Authentic learning via development of interactive computer demonstrations within a peer-led studio environment." Jafari, M.; Welden, A.R.; Williams, K.L.; Winograd, B.;**Mulvihill, E.**; Hendrickson, H.P.; Lenard, M.; Gottfried, A.; Geva, E.*March 18th, 2018.***2017 Midwest Theoretical Chemistry Conference**,*Poster Session:*"Post-Marcus Electronic Transition Dynamics via the Generalized Quantum Master Equation."**Mulvihill, E.**; Schubert, A.; Sun, X.; Dunietz, B. D.; Geva, E.*June 1st, 2017.***2017 MICDE Annual Symposium**,*Poster Session:*"Post-Marcus Electronic Transition Dynamics via the Generalized Quantum Master Equation."**Mulvihill, E.**; Schubert, A.; Sun, X.; Dunietz, B. D.; Geva, E.*April 18th, 2017.***ACS National Meeting, San Francisco, CA**,*Physical Chemistry Poster Session:*"Post-Marcus Electronic Transition Dynamics via the Generalized Quantum Master Equation."**Mulvihill, E.**; Schubert, A.; Sun, X.; Dunietz, B. D.; Geva, E.*April 5th, 2017.*

*ellen.mulvihill@yale.edu*