Telephone: (617) XXX-XXXX
E-mail: john.parkhill [at] gmail.com
Address: 12 Oxford Street, Mailbox 157, Cambridge, MA 02138
B.S. Chemistry (Honors), University of Chicago, Thesis Advisor: Viresh Rawal (2005)
B.S. Mathematics, University of Chicago (2005)
- Quantum Many-Body Problem
- “Electronic Structure” expanded beyond electrons
- Energy Transport and Dynamics
The number of degrees of freedom in the dynamics of a quantum many-body system grows exponentially with the number of physical particles. For quantum computation this is seen as a resource for information processing, and for simulation in classical computers it is seen as a severe problem. However for any physical system the amount of information really needed to characterize the quantum state is limited by spatial locality, and the flow of information to the surroundings. I develop new models which exploit these two limitations on quantum correlations to treat new physical phenomena.
“Electronic Structure” is a discipline which usually solves the many-electron, Born-Oppenheimer Schrodinger equation for static, and linear-response molecular properties at zero-temperature. Many clever and useful approaches for treating quantum systems have been developed in this context, and pushed to the limits of efficiency. I’m interested in applying the tools of electronic structure to new problems, for example tackling the dynamics system-bath correlation using techniques inspired by electronic correlation approaches.
It is virtually impossible to answer the following basic physical questions without phenomenological information with current formalism in a satisfying way. (ie: including relaxation, dephasing effects from nuclear motion, and electron-correlation):
How large is an exciton in a given organic semiconductor?
How large is an charge carrier in a given organic semiconductor?
What is an equation of motion for the density matrix of an exciton as it dissociates into charge carriers?
How does the shape, size and motion of an exciton vary with temperature?
All these questions must be answered phenomenologically (although in-principle the non-equilibrium Green’s function approach can answer them all), since we have no computable formalism for including the effects of nuclear relaxation and dephasing into a tractable electronic dynamics. Using the new formalism I’m developing for including vibronic effects into an electronic EOM, I’m studying transport dynamics and associated phenomena.
- Keith V. Lawler, John A. Parkhill, and Martin Head-Gordon. Penalty functions for combining coupled-cluster and perturbation amplitudes in local correlation methods with optimized orbitals. Molecular Physics, 106(19):2309–2324, 2008.
- Keith V. Lawler, John A. Parkhill, and Martin Head-Gordon. The numerical condition of electron correlation theories when only active pairs of electrons are spin-unrestricted. The Journal of Chemical Physics, 130(18):184113, 2009.
- Narbe Mardirossian, John A. Parkhill, and Martin Head-Gordon. Benchmark results for empirical post-gga functionals: Difficult exchange problems and independent tests. Phys. Chem. Chem. Phys., 13(43):19325–19337, 2011.
- Andrew L. Mattioda, Lindsay Rutter, John Parkhill, Martin Head-Gordon, Timothy J. Lee, , and Louis J. Allamandola. Near-infrared spectroscopy of nitrogenated polycyclic aromatic hydrocarbon cations from 0.7 to 2.5 μm. The Astrophysical Journal, 680(2):1243–1255, 2008.
- John A. Parkhill, Julian Azar, and Martin Head-Gordon. The formulation and performance of a perturbative correction to the perfect quadruples model. The Journal of Chemical Physics, 134(15):154112, 2011.
- John A. Parkhill, Jeng-Da Chai, and Martin Head-Gordon. The exchange energy of a uniform electron gas experiencing a new, flexible range separation. Chemical Physics Letters, 478:283– 286, 2009.
- John A Parkhill and Martin Head-Gordon. A sparse framework for the derivation and implementation of fermion algebra. Molecular Physics, 108(3):513, 2010.
- John A. Parkhill and Martin Head-Gordon. A tractable and accurate electronic structure method for static correlations: The perfect hextuples model. The Journal of Chemical Physics, 133(2):024103, 2010.
- John A. Parkhill and Martin Head-Gordon. A truncation hierarchy of coupled cluster models of strongly correlated systems based on perfect-pairing references: The singles + doubles models. The Journal of Chemical Physics, 133(12):124102, 2010.
- John A. Parkhill, Keith Lawler, and Martin Head-Gordon. The perfect quadruples model for electron correlation in a valence active space. The Journal of Chemical Physics, 130(8):084101, 2009.
- John A. Parkhill, Dmitrij Rappoport, and Alán Aspuru-Guzik. Modeling coherent anti- stokes raman scattering with time-dependent density functional theory: Vacuum and surface enhancement. The Journal of Physical Chemistry Letters, 2(15):1849–1854, 2011.
- John A. Parkhill, David G. Tempel, and Alan Aspuru-Guzik. Exciton coherence lifetimes from electronic structure. The Journal of Chemical Physics, 136(10):104510, 2012.