Quantum effects from classical molecular dynamics via a quantum thermostat

Thema:
Quantum effects from classical molecular dynamics via a quantum thermostat

Einordnung:
Analyzing the dynamics of many-body systems ranging from small gas phase molecules to large proteins in solution is one of the main goals in modern molecular physics. In many cases, a purely classical molecular dynamics (MD) treatment is possible as, for instance, for the low-frequency collective motion of heavy atom groups from torsion or bending motions within a single molecule to folding of huge proteins. In contrast, high-frequency vibrations of lighter atoms, like the stretching modes of hydrogen in water, often require a correct quantum treatment. In particular, the absence of zero-point energy can lead to dramatically wrong results in cases when it exceeds the thermal energy.

Beschreibung:
One way to account for zero-point energy is to supplement the system with a so-called Quantum Thermostat. Here, the classical vibrational motion is perturbed by a frequency-dependent stochastic noise term, which is designed to mimic the quantum-fluctuations. Although this might sound like an ad hoc procedure, one can show that for harmonic systems the correct quantum distribution of positions and momenta is guaranteed. It thus seems physically plausible to apply this procedure to anharmonic vibrations as well.
The method of Quantum Thermostats is particularly useful for the so-called semiclassical initial value representation methods. Here, the basic idea is to perform classical MD starting from a quantum-mechanically correct distribution of initial positions and momenta including zero-point energy (see also a related topic Semiclassics). Due to the equipartition theorem, the zero-point energy of high-frequency modes would leak out into the low-frequency modes if mere classical dynamics were used. The Quantum Thermostat can be thus employed to restore correct quantum fluctuations during the dynamics.
The goal of the bachelor project is to implement the quantum thermostat and to test its performance reaching from test one-dimensional systems to realistic molecules. Within the scope of this project the student is introduced to the theory of molecular spectroscopy, the art of classical MD simulations and the method of Quantum Thermostats. It is foreseen to include the method into a semiclassical initial value representation procedure as described above. More technical education like scientific writing, programming, using Linux, scripting, etc. is provided as well.

Betreuer: Fabian Gottwald