Quantum propagation of electronic excitations in macromolecules: A computationally efficient multiscale approach

We introduce a theoretical approach to study the quantum-dissipative dynamics of electronic excitations in macromolecules, which enables to perform calculations in large systems and cover long-time intervals. All the parameters of the underlying microscopic Hamiltonian are obtained from ab initio electronic structure calculations, ensuring chemical detail. In the short-time regime, the theory is solvable using a diagrammatic perturbation theory, enabling analytic insight. To compute the time evolution of the density matrix at intermediate times, typically ps, we develop a Monte Carlo algorithm free from any sign or phase problem, hence computationally efficient. Finally, the dynamics in the long-time and large-distance limit can be studied combining the microscopic calculations with renormalization group techniques to define a rigorous low-resolution effective theory. We benchmark our Monte Carlo algorithm against the results obtained in perturbation theory and using a semiclassical nonperturbative scheme. Then, we apply it to compute the intrachain charge mobility in a realistic conjugated polymer.