Person: Parkhill, John Anthony
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Parkhill
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John Anthony
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Parkhill, John Anthony
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Publication A Correlated-Polaron Electronic Propagator: Open Electronic Dynamics beyond the Born-Oppenheimer Approximation(American Institute of Physics, 2012) Parkhill, John Anthony; Markovich, Thomas Lee; Tempel, David; Aspuru-Guzik, AlanIn this work, we develop an approach to treat correlated many-electron dynamics, dressed by the presence of a finite-temperature harmonic bath. Our theory combines a small polaron transformation with the second-order time-convolutionless master equation and includes both electronic and system-bath correlations on equal footing. Our theory is based on the ab initio Hamiltonian, and is thus well-defined apart from any phenomenological choice of basis states or electronic system-bath coupling model. The equation-of-motion for the density matrix we derive includes non-Markovian and non-perturbative bath effects and can be used to simulate environmentally broadened electronic spectra and dissipative dynamics, which are subjects of recent interest. The theory also goes beyond the adiabatic Born-Oppenheimer approximation, but with computational cost scaling such as the Born-Oppenheimer approach. Example propagations with a developmental code are performed, demonstrating the treatment of electron-correlation in absorption spectra, vibronic structure, and decay in an open system. An untransformed version of the theory is also presented to treat more general baths and larger systems.Publication More Accurate and Efficient Bath Spectral Densities from Super-Resolution(2013) Markovich, Thomas Lee; Blau, Sam Meltzer; Parkhill, John Anthony; Kreisbeck, Christoph; Sanders, Jacob; Andrade, Xavier; Aspuru-Guzik, AlanQuantum transport and other phenomena are typically modeled by coupling the system of interest to an environment, or bath, held at thermal equilibrium. Realistic bath models are at least as challenging to construct as models for the quantum systems themselves, since they must incorporate many degrees of freedom that interact with the system on a wide range of timescales. Owing to computational limitations, the environment is often modeled with simple functional forms, with a few parameters fit to experiment to yield semi-quantitative results. Growing computational resources have enabled the construction of more realistic bath models from molecular dynamics (MD) simulations. In this paper, we develop a numerical technique to construct these atomistic bath models with better accuracy and decreased cost. We apply a novel signal processing technique, known as super-resolution, combined with a dictionary of physically-motivated bath modes to derive spectral densities from MD simulations. Our approach reduces the required simulation time and provides a more accurate spectral density than can be obtained via standard Fourier transform methods. Moreover, the spectral density is provided as a convenient closed-form expression which yields an analytic time-dependent bath kernel. Exciton dynamics of the Fenna-Matthews-Olsen light-harvesting complex are simulated with a second order time-convolutionless master equation, and spectral densities constructed via super-resolution are shown to reproduce the dynamics using only a quarter of the amount of MD data.Publication Measurement of the Third-Order Nonlinear Optical Susceptibility \(\chi^{(3)}\) for the \(1002-cm^{-1}\) Mode of Benzenethiol Using Coherent Anti-Stokes Raman Scattering with Continuous-Wave Diode Lasers(Wiley-Blackwell, 2012) Aggarwal, R. L.; Farrar, L. W.; Parkhill, John Anthony; Aspuru-Guzik, Alan; Polla, D. L.The components of the third-order nonlinear optical susceptibility \(\chi^{(3)}\) for the \(1002-cm^{–1}\) mode of neat benzenethiol have been measured using coherent anti-Stokes Raman scattering with continuous-wave diode pump and Stokes lasers at 785.0 and 852.0 nm, respectively. Values of \(2.8 ± 0.3 × 10^{–12}\), \(2.0 ± 0.2 × 10^{–12}\), and \(0.8 ± 0.1 × 10^{–12} cm g^{–1} s^2\) were measured for the xxxx, xxyy, and xyyx components of \(|3\chi^{(3)}|\), respectively. We have calculated these quantities using a microscopic model, reproducing the same qualitative trend. The Raman cross-section \(\sigma_{RS}\) for the \(1002-cm^{–1}\) mode of neat benzenethiol has been determined to be \(3.1 ± 0.6 × 10^{–29} cm^2\) per molecule. The polarization of the anti-Stokes Raman scattering was found to be parallel to that of the pump laser, which implies negligible depolarization. The Raman linewidth (full-width at half-maximum) \(\Gamma\) was determined to be \(2.4 ± 0.3 cm^{–1}\) using normal Stokes Raman scattering. The measured values of \(\sigma_{RS}\) and \(\Gamma\) yield a value of \(2.1 ± 0.4 × 10^{–12} cm g^{–1} s^2\) for the resonant component of \(3χ^{(3)}\). A value of \(1.9 ± 0.9 × 10^{–12} cm g^{–1} s^2\) has been deduced for the nonresonant component of \(3\chi^{(3)}\).Publication Feynman’s Clock, a New Variational Principle, and Parallel-in-Time Quantum Dynamics(National Academy of Sciences, 2013) McClean, Jarrod Ryan; Parkhill, John Anthony; Aspuru-Guzik, AlanWe introduce a discrete-time variational principle inspired by the quantum clock originally proposed by Feynman and use it to write down quantum evolution as a ground-state eigenvalue problem. The construction allows one to apply ground-state quantum many-body theory to quantum dynamics, extending the reach of many highly developed tools from this fertile research area. Moreover, this formalism naturally leads to an algorithm to parallelize quantum simulation over time. We draw an explicit connection between previously known time-dependent variational principles and the time-embedded variational principle presented. Sample calculations are presented, applying the idea to a hydrogen molecule and the spin degrees of freedom of a model inorganic compound, demonstrating the parallel speedup of our method as well as its flexibility in applying ground-state methodologies. Finally, we take advantage of the unique perspective of this variational principle to examine the error of basis approximations in quantum dynamics.Publication Modeling Coherent Anti-Stokes Raman Scattering with Time-Dependent Density Functional Theory: Vacuum and Surface Enhancement(American Chemical Society, 2011) Parkhill, John Anthony; Rappoport, Dmitrij; Aspuru-Guzik, AlanWe present the first density functional simulations of coherent anti-Stokes Raman scattering (CARS) and an analysis of the chemical effects upon binding to a metal surface. Spectra are obtained from first-principles electronic structure calculations and are compared with available experiments and previously available theoretical results following from Hartree–Fock polarizability derivatives. A first approximation to the nonresonant portion of the CARS signal is also explored. We examine the silver pyridine cluster models of the surface chemical signal enhancement, previously introduced for surface-enhanced Raman scattering. Chemical resonant intensity enhancements of roughly \(10^2\) are found for several model clusters. The prospects of realizing further enhancement of CARS signal with metal surfaces is discussed in light of the predicted chemical enhancements.Publication Exciton Coherence Lifetimes from Electronic Structure(American Institute of Physics, 2012-04-06) Parkhill, John Anthony; Tempel, David; Aspuru-Guzik, AlanWe model the coherent energy transfer of an electronic excitation within covalently linked aromatic homodimers from first-principles. Our results shed light on whether commonly used models of the bath calculated via detailed electronic structure calculations can reproduce the key dynamics. For the systems we model, the time scales of coherent transport are experimentally known from time-dependent polarization anisotropy measurements, and so we can directly assess whether current techniques are predictive for modeling coherent transport. The coupling of the electronic degrees of freedom to the nuclear degrees of freedom is calculated from first-principles rather than assumed, and the fluorescence anisotropy decay is directly reproduced. Surprisingly, we find that although time-dependent density functional theory absolute energies are routinely in error by orders of magnitude more than the coupling energy between monomers, the coherent transport properties of these dimers can be semi-quantitatively reproduced from these calculations. Future directions which must be pursued to yield predictive and reliable models of coherent transport are suggested.