Path integral Langevin dynamics of complex molecular systems: from low-temperature quantum clusters to biomolecules
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This thesis presents an implementation of path integral molecular dynamics (PIMD) for sampling equilibrium and dynamical properties within the molecular modelling toolkit (MMTK) [J. Comp. Chem. 21, 79 (2000)], an open source Python package. Rigorous simulation using this code serves to benchmark this implementation as well as the robust- ness of the path integral Langevin equation as a thermostat [J. Chem. Phys. 133, 124104 (2010)]. PIMD is used to calculate equilibrium properties for clusters of HeN-CO2 at low- temperatures, with comparison to experimental and exact results. We characterize the convergence of structural and energetic properties as a function of path-integral discretiza- tion error. The radial and angular distribution of these clusters is studied as a function of size in the absence of rotation and bosonic exchange. These distributions are subsequently used to calculate vibrational shifts of CO2. This result is compared to high-accuracy path integral Monte Carlo simulations which include rotational and exchange effects. These sim- ulations indicate that the neglect of rotational degrees of freedom leads to an unphysical localization of helium atoms and incorrect vibrational shifts when compared to experiment. Approximate real-time quantum dynamics is presented for doped helium clusters using the ring-polymer molecular dynamics (RPMD) method. The accuracy of RPMD is tested iii for low-temperature simulations and compared to exact results. Preliminary calculation of the dynamics of the helium solvated CO2 dopant with respect to the center of mass of the cluster is presented. The effect of a cartesian integrator versus a normal-mode integrator for quantum dynamics is addressed. The path integral ground-state method is applied in order to calculate T = 0 properties. A convergence study of the ground-state energy of the quantum harmonic oscillator with respect to sampling time and path discretization is shown. As a final application of this implementation, a sugar in a periodic water box is simulated at T = 300K. The calculation of rotamer populations and a dipole autocorrelation indicate negligible change with the inclusion of quantum effects. This work offers a comprehensive foundation from which to base future PIMD centered research.