Monte Carlo study of complex biological and materials systems

This thesis addresses several complex biological and material systems by Monte Carlo methods. Both new methods and new physical results are presented.; A new, biased Monte Carlo scheme for simulating complex, cyclic peptides is presented. Backbone atoms are equilibrated with a biased rebridging scheme, and side-chain atoms are equilibrated with a look-ahead configurational bias Monte Carlo. Parallel tempering is shown to be an important ingredient in the construction of an efficient approach.; The analytical rebridging scheme for Monte Carlo simulation of proline-containing, cyclic peptides is presented. The cis/trans isomerization is accommodated by allowing for two states of the amide bond. The method is applied to five peptides that have previously been characterized by NMR methods. The simulations achieve effective equilibration and agree well with experimental data in all cases. The importance of effective equilibration as well as the role of bond flexibility and solvent effects in the prediction of equilibrium properties is discussed.; An atomic-scale model for silicate solutions is introduced for investigation of the nucleation process during zeolite synthesis. Monte Carlo schemes are developed to determine the equilibrium distribution of silicate cluster sizes within the context of this model. How the nucleation barrier and critical cluster size change with Si monomer concentration is discussed. Distance and angle histograms as well as ring size distributions are calculated and compared with known zeolite structures. The free energies of critical clusters are compared with those for small clusters of quartz.; The synthesis, structure solution, and characterization of the high-silica zeolite SSZ-55 is described. SSZ-55 is synthesized at hydrothermal conditions using [(1-(3-fluorophenyl)cyclopentyl)methyl]trimethyl ammonium cation as the structuring directing agent. The framework topology and symmetry of SSZ-55 are determined by Monte Carlo methods. Rietveld refinement of the X-ray powder diffraction data confirms the structure and the space group assignment of Cmc2₁ for the structure. Transmission electron microscopy confirms the unit cell and the topology of the structure. SSZ-55 contains one-dimensional pores circumscribed by 12 T atoms.; The r−n interaction energy, 1 ≤ n < 3, for a infinitely periodic system with explicit charges and a neutralizing, uniform background charge density is derived. The Ewald-based expression for this energy has an extra term proportional to the square of the total explicit charge of the system. This expression may be useful for simulations in which explicit charge neutrality does not hold or for which the total explicit charge is a fluctuating quantity.