Atomistic systems containing light atoms at low temperatures can be described with Path integral molecular dynamics (PIMD). In the present work, new, highly accurate simulation techniques in this field were developed. Thereby, the required interatomic potential is calculated with coupled cluster theory (CC), which is the current state of the science. As an highly accurate theory is usually accompanied with significant computational demands, the aim of the present work was furthermore to reduce the computational cost of both techniques the CC calculation and the PIMD simulation. The calculation of the interatomic potential in the molecular dynamics simulation is accelerated by providing initial guesses to several iterative equations in CC theory that approximate their final solution. New methods to reduce the computational demands of the PIMD simulation are presented that exploit further properties of the interatomic potential. These techniques are applied to the CC-based PIMD simulations, but can also be used with general analytic interatomic potentials. They are especially beneficial for systems with light particles and low temperatures and therefore performed with hydrogen-bonded systems. As a result of these investigations, the slightest perturbations to the molecular electronic structure is investigated by inspecting the highly sensitive nuclear magnetic resonance parameters. This simulation technique can now be used for small molecules at finite temperature on a routine basis.