Quantum Master Equations for Simulating Chemical Dynamics

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

Professor Eitan Geva of the University of Michigan is supported by an award from the Chemical Theory, Models and Computational Methods (CTMC) program in the Division of Chemistry to develop a new general purpose cost-effective and efficient methodology that will enable computer simulations of the chemical dynamics underlying technologically and biologically important processes, such as photosynthesis, photovoltaics and nanoelectronics. The new methodology aims at closing the gap between theory and experiment, by focusing on measurable quantities and reducing the inputs to the minimum required in order to understand how those measurable quantities change over time. In addition, Eitan Geva will also advance a novel Compute-to-Learn (C2L) pedagogy, which is based on a peer-led honors studio where undergraduate students work collaboratively to create public-domain interactive computer demos that demonstrate physical chemistry concepts. With above 50% female enrollment, the C2L pedagogy is a model for how to make teaching programming inclusive. Eitan Geva and his group will develop and benchmark new types of generalized quantum master equations that allow for much greater flexibility than is currently available with respect to the electronic observables of interest and their dimensionality, thereby giving rise to more streamlined, cost-effective and efficient implementations. Each generalized quantum master equation corresponds to the exact equation of motion for the electronic observable it is derived for. Within those equations, the effect of projected-out degrees of freedom is given in terms of compact memory kernels and inhomogeneous terms, which can be obtained from projection-free inputs by solving Volterra equations. Computational protocols are developed for calculating the projection-free inputs for all-atom models of chemical condensed-phase systems via either mapping onto harmonic models and using quantum-mechanically exact methods or using quasiclassical methods based on combining the linearized semiclassical approximation with the mapping Hamiltonian framework. In addition, multiple new perturbative quantum master equations that mirror the multitude of non-perturbative generalized quantum master equations are developed, as well as protocols for calculating the corresponding perturbative memory kernels via the same methods used for calculating the projection-free inputs. The quantum master equations developed will be applied to and tested on new benchmark models, all-atom models and polaritonic chemistry models. The potential of using initial state entanglement to achieve quantum control of chemical dynamics is also investigated. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.