Exploration of Entropy Pair Functional Theory.

Evaluation of the entropy from molecular dynamics (MD) simulation remains an outstanding challenge. The standard approach requires thermodynamic integration across a series of simulations. Recent work Nicholson et al. demonstrated the ability to construct a functional that returns excess entropy, based on the pair correlation function (PCF); it was capable of providing, with acceptable accuracy, the absolute excess entropy of iron simulated with a pair potential in both fluid and crystalline states. In this work, the general applicability of the Entropy Pair Functional Theory (EPFT) approach is explored by applying it to three many-body interaction potentials. These potentials are state of the art for large scale models for the three materials in this study: Fe modelled with a modified embedded atom method (MEAM) potential, Cu modelled with an MEAM and Si modelled with a Tersoff potential. We demonstrate the robust nature of EPFT in determining excess entropy for diverse systems with many-body interactions. These are steps toward a universal Entropy Pair Functional, EPF, that can be applied with confidence to determine the entropy associated with sophisticated optimized potentials and first principles simulations of liquids, crystals, engineered structures, and defects.

Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions.

We prove that, within the class of pair potential Hamiltonians, the excess entropy is a universal, temperature-independent functional of the density and pair correlation function. This result extends Henderson's theorem, which states that the free energy is a temperature dependent functional of the density and pair correlation. The stationarity and concavity of the excess entropy functional are discussed and related to the Gibbs-Bugoliubov inequality and to the free energy. We apply the Kirkwood approximation, which is commonly used for fluids, to both fluids and solids. Approximate excess entropy functionals are developed and compared to results from thermodynamic integration. The pair functional approach gives the absolute entropy and free energy based on simulation output at a single temperature without thermodynamic integration. We argue that a functional of the type, which is strictly applicable to pair potentials, is also suitable for first principles calculation of free energies from Born-Oppenheimer molecular dynamics performed at a single temperature. This advancement has the potential to reduce the evaluation the free energy to a simple modification to any procedure that evaluates the energy and the pair correlation function.

Molecular simulations of adsorption of RDX and TATP on IRMOF-1(Be).

The influence of different sorption sites of isoreticular metal-organic frameworks (IRMOFs) on interactions with explosive molecules is investigated. Different connector effects are taken into account by choosing IRMOF-1(Be) (IRMOF-1 with Zn replaced by Be), and two high explosive molecules: 1,3,5-trinitro-s-triazine (RDX) and triacetone triperoxide (TATP). The key interaction features (structural, electronic and energetic) of selected contaminants were analyzed by means of density functional calculations. The interaction of RDX and TATP with different IRMOF-1(Be) fragments is studied. The results show that physisorption is favored and occurs due to hydrogen bonding, which involves the C-H groups of both molecules and the carbonyl oxygen atoms of IRMOF-1(Be). Additional stabilization of RDX and TATP arises from weak electrostatic interactions. Interaction with IRMOF-1(Be) fragments leads to polarization of the target molecules. Of the molecular configurations we have studied, the Be-O-C cluster connected with six benzene linkers (1,4-benzenedicarboxylate, BDC), possesses the highest binding energy for the studied explosives (-16.4 kcal mol(-1) for RDX and -12.9 kcal mol(-1) for TATP). The main difference was discovered to be in the preferable adsorption site for adsorbates (RDX above the small and TATP placed above the big cage). Based on these results, IRMOF-1 can be suggested as an effective material for storage and also for separation of similar explosives. Hydration destabilizes most of the studied adsorption systems by 1-3 kcal mol(-1) but it leads to the same trend in the binding strength as found for the non-hydrated complexes.

A coarse-grained model for polyethylene glycol polymer.

A coarse-grained (CG) model of polyethylene glycol (PEG) was developed and implemented in CG molecular dynamics (MD) simulations of PEG chains with degree of polymerization (DP) 20 and 40. In the model, two repeat units of PEG are grouped as one CG bead. Atomistic MD simulation of PEG chains with DP = 20 was first conducted to obtain the bonded structural probability distribution functions (PDFs) and nonbonded pair correlation function (PCF) of the CG beads. The bonded CG potentials are obtained by simple inversion of the corresponding PDFs. The CG nonbonded potential is parameterized to the PCF using both an inversion procedure based on the Ornstein-Zernike equation with the Percus-Yevick approximation (OZPY(-1)) and a combination of OZPY(-1) with the iterative Boltzmann inversion (IBI) method (OZPY(-1)+IBI). As a simple one step method, the OZPY(-1) method possesses an advantage in computational efficiency. Using the potential from OZPY(-1) as an initial guess, the IBI method shows fast convergence. The coarse-grained molecular dynamics (CGMD) simulations of PEG chains with DP = 20 using potentials from both methods satisfactorily reproduce the structural properties from atomistic MD simulation of the same systems. The OZPY(-1)+IBI method yields better agreement than the OZPY(-1) method alone. The new CG model and CG potentials from OZPY(-1)+IBI method was further tested through CGMD simulation of PEG with DP = 40 system. No significant changes are observed in the comparison of PCFs from CGMD simulations of PEG with DP = 20 and 40 systems indicating that the potential is independent of chain length.

Applications of a general random-walk theory for confined diffusion.

A general random walk theory for diffusion in the presence of nanoscale confinement is developed and applied. The random-walk theory contains two parameters describing confinement: a cage size and a cage-to-cage hopping probability. The theory captures the correct nonlinear dependence of the mean square displacement (MSD) on observation time for intermediate times. Because of its simplicity, the theory also requires modest computational requirements and is thus able to simulate systems with very low diffusivities for sufficiently long time to reach the infinite-time-limit regime where the Einstein relation can be used to extract the self-diffusivity. The theory is applied to three practical cases in which the degree of order in confinement varies. The three systems include diffusion of (i) polyatomic molecules in metal organic frameworks, (ii) water in proton exchange membranes, and (iii) liquid and glassy iron. For all three cases, the comparison between theory and the results of molecular dynamics (MD) simulations indicates that the theory can describe the observed diffusion behavior with a small fraction of the computational expense. The confined-random-walk theory fit to the MSDs of very short MD simulations is capable of accurately reproducing the MSDs of much longer MD simulations. Furthermore, the values of the parameter for cage size correspond to the physical dimensions of the systems and the cage-to-cage hopping probability corresponds to the activation barrier for diffusion, indicating that the two parameters in the theory are not simply fitted values but correspond to real properties of the physical system.

Use of the Ornstein-Zernike Percus-Yevick equation to extract interaction potentials from pair correlation functions.

In this work, we test the ability of the Ornstein-Zernike equation in the Percus-Yevick approximation (OZPY) to generate interaction potentials from pair correlation functions (PCFs) of monatomic and diatomic Lennard-Jones fluids. The PCFs are generated by solving OZPY equation (monatomic fluid) and molecular-dynamics (MD) simulations (diatomic fluid). Since the interaction potentials are inputs in the OZPY method and the MD simulation, the extraction of the potential from the PCFs using OZPY is a test of self-consistency. This test is necessary if the procedure is to be used to generate coarse-grained (CG) potentials from PCFs. We find that the procedure is completely self-consistent for the monatomic fluid in the whole range of densities studied (reduced density up to 0.55, under reduced temperature of 2.0). In the diatomic case, we find that the procedure is generally self-consistent under both low and high densities, although there is a systematic deviation at high densities. The method is able to reproduce the two parameters (ε and σ) of the input Lennard-Jones potential model to within about 1%. This CG potential generating procedure can be straightforwardly extended to more complicated molecules.

Effect of charge distribution on RDX adsorption in IRMOF-10.

Quantum mechanical (QM) calculations, classical grand canonical Monte Carlo (GCMC) simulations, and classical molecular dynamics (MD) simulations are performed to test the effect of charge distribution on hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) adsorption and diffusion in IRMOF-10. Several different methods for mapping QM electron distributions onto atomic point charges are explored, including the electrostatic potential (ESP) method, Mulliken population analysis, Lowdin population analysis, and natural bond orbital analysis. Classical GCMC and MD simulations of RDX in IRMOF-10 are performed using 15 combinations of charge sources of RDX and IRMOF-10. As the charge distributions vary, interaction potential energies, the adsorption loading, and the self-diffusivities are significantly different. None of the 15 combinations are able to quantitatively capture the dependence of the energy of adsorption on local configuration of RDX as observed in the QM calculations. We observe changes in the charge distributions of RDX and IRMOF-10 with the introduction of an RDX molecule into the cage. We also observe a large dispersion contribution to the interaction energy from QM calculations that is not reproduced in the classical simulations, indicating that the source of discrepancy may not lie exclusively with the assignment of charges.

Electronic structure and properties of isoreticular metal-organic frameworks: the case of M-IRMOF1 (M = Zn, Cd, Be, Mg, and Ca).

We investigate the possibility of tailoring the electronic properties of isoreticular metal-organic materials by replacing the metal atom in the metal-organic cluster and by doping. The electronic structure of M-IRMOF1, where IRMOF1 stands for isoreticular metal-organic framework 1 and M = Be, Mg, Ca, Zn, and Cd, was examined using density-functional theory. The results show that these materials have similar band gaps (ca. 3.5 eV) and a conduction band that is split into two bands, the lower of which has a width that varies with metal substitution. This variation prompted us to investigate whether doping with Al or Li could be used to tailor the electronic properties of the Zn-IRMOF1 and Be-IRMOF1 materials. It is shown that replacing one metal atom with Al can effectively be used to create IRMOFs with different metallic properties. On the other hand, adding Li produces structural changes that render this approach less suitable.