  In this paper we present a Path Integral Monte Carlo (PIMC) simulation of the
orthorhombic phase of crystalline polyethylene, using an explicit atom force
field with unconstrained bond lengths and angles. This work represents a
quantum extension of our recent classical simulation (J. Chem. Phys. 106, 8918
(1997)). It is aimed both at exploring the applicability of the PIMC method on
such polymer crystal systems, as well as on a detailed assessment of the
importance of quantum effects on different quantities. We used the $NpT$
ensemble and simulated the system at zero pressure in the temperature range 25
- 300 K, using Trotter numbers between 12 and 144. In order to investigate
finite-size effects, we used chains of two different lengths, C_12 and C_24,
corresponding to the total number of atoms in the super-cell being 432 and 864,
respectively. We show here the results for structural parameters, like the
orthorhombic lattice constants a,b,c, and also fluctuations of internal
parameters of the chains, such as bond lengths and bond and torsional angles.
We have also determined the internal energy and diagonal elastic constants
c_11, c_22 and c_33. We discuss the temperature dependence of the measured
quantities and compare to that obtained from the classical simulation. For some
quantities, we discuss the way they are related to the torsional angle
fluctuation. In case of the lattice parameters we compare our results to those
obtained from other theoretical approaches as well as to some available
experimental data. In order to study isotope effects, we simulated also a
deuterated polyethylene crystal at a low temperature. We also suggest possible
ways of extending this study and present some general considerations concerning
modeling of polymer crystals.
