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In developing coarse-grained (CG) polymer models it is important to reproduce both local and molecule-scale structure. We develop a procedure for fast calculation of the bond-orientation correlation and the internal squared distance 〈R²(M)〉 through evaluation of the probability distribution functions that represent a CG model. Different CG models inherently contain or omit correlations between CG variables. Here, we construct CG models that contain specific correlations between CG variables. The importance of different correlations is tested on CG models of polyethylene, polytetrafluoroethylene, and poly-L-lactic acid. The chain stiffness and 〈R²(M)〉 are calculated using both analytic evaluation and Monte Carlo sampling, and approximate model results are compared with exact results from all-atom simulations. For polymers with an exponential correlation decay, the bond-orientation correlation and 〈R²(M)〉 indicate which CG variable correlations are most important to reproduce molecule-scale structure. Analysis of the bond-orientation correlation and internal-squared distance indicates that for poly-L-lactic acid the bond-orientation correlation requires qualitatively different additional terms in CG models and quantifies the error in neglecting this important behavior. [ABSTRACT FROM AUTHOR]

The nested sampling algorithm has been shown to be a general method for calculating the pressure-temperature-composition phase diagrams of materials. While the previous implementation used single-particle Monte Carlo moves, these are inefficient for condensed systems with general interactions where single-particle moves cannot be evaluated faster than the energy of the whole system. Here we enhance the method by using all-particle moves: either Galilean Monte Carlo or the total enthalpy Hamiltonian Monte Carlo algorithm, introduced in this paper. We show that these algorithms enable the determination of phase transition temperatures with equivalent accuracy to the previous method at 1/N of the cost for an N-particle system with general interactions, or at equal cost when single-particle moves can be done in 1/N of the cost of a full N-particle energy evaluation. We demonstrate this speed-up for the freezing and condensation transitions of the Lennard-Jones system and show the utility of the algorithms by calculating the order-disorder phase transition of a binary Lennard-Jones model alloy, the eutectic of copper-gold, the density anomaly of water, and the condensation and solidification of bead-spring polymers. The nested sampling method with all three algorithms is implemented in the pymatnest software. [ABSTRACT FROM AUTHOR]