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We report the first-ever formulation of the molecular dynamics problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem and demonstrate its successful solution on a D-Wave quantum annealer. This methodology, named a Quantum Differential Equation (QDE) solver, is applied to propagate trajectories for the vibrational motion of hydrogen molecule, H2, in three different energy regimes: nearly harmonic, highly anharmonic, and above dissociation threshold. The results obtained using the D-Wave 2000Q quantum annealer are mutually consistent and quickly converge to the exact solution. Several alternative strategies for such calculations are explored and it is shown that the most accurate result and the best efficiency are obtained by combining quantum annealer with classical post-processing (known as “greedy” algorithm). Importantly, the QDE framework developed here is entirely general and can be applied to solve any system of first-order ordinary nonlinear differential equations using a quantum annealer. 

Photoexcitation of multichromophoric light harvesting molecules induces a number of intramolecular electronic energy relaxation and redistribution pathways that can ultimately lead to ultrafast exciton self-trapping on a single chromophore unit. We investigate the photoinduced processes that take place on a phenylene-ethynylene dendrimer, consisting of nine equivalent linear chromophore units or branches. meta -Substituted links between branches break the conjugation giving rise to weak couplings between them and to localized excitations. Our nonadiabatic excited-state molecular dynamics simulations reveal that the ultrafast internal conversion process to the lowest excited state is accompanied by an inner → outer inter-branch migration of the exciton due to the entropic bias associated with energetically equivalent conjugated segments. The electronic energy redistribution among chromophore units occurs through several possible pathways in which through-bond transport and through-space exciton hopping mechanisms can be distinguished. Besides, triple bond excitations coincide with the localization of the electronic transition densities, suggesting that the intramolecular energy redistribution is a concerted electronic and vibrational energy transfer process.