  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 \emph{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 $\lesssim$~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
semi-classical non-perturbative scheme. Then we apply it to compute the
intra-chain charge mobility in a realistic conjugate polymer.
