Many-body Polarization Interactions Research Articles

Predictive models of gas sorption in a metal-organic framework with open-metal sites and small pore sizes.

Simulations of CO2 and H2 sorption were performed in UTSA-20, a metal-organic framework (MOF) having zyg topology and composed of Cu2+ ions coordinated to 3,3',3'',5,5',5''-benzene-1,3,5-triyl-hexabenzoate (BHB) linkers. Previous experimental studies have shown that this MOF displays remarkable CO2 sorption properties and exhibits one of the highest gravimetric H2 uptakes at 77 K/1.0 atm (2.9 wt%) [Z. Guo, et al. Angew. Chem., Int. Ed., 2011, 50, 3178-3181]. For both sorbates, the simulations were executed with the inclusion of explicit many-body polarization interactions, which was necessary to reproduce sorption onto the open-metal sites. Non-polarizable potentials were also utilized for simulations of CO2 sorption as a control. The simulated excess sorption isotherms for both CO2 and H2 are in very good agreement with the corresponding experimental data over a wide range of temperatures and pressures, thus demonstrating the accuracy and predictive power of the polarizable potentials used herein. The theoretical isosteric heat of adsorption (Qst) values are also in good agreement with the newly reported experimental Qst values for the respective sorbates in UTSA-20. Sorption onto the more positively charged Cu2+ ion of the [Cu2(O2CR)4] cluster was observed for both CO2 and H2. However, a binding site with energetics comparable to that for an open-metal site was also discovered for both sorbates. A radial distribution function (g(r)) analysis about the preferential Cu2+ ions for CO2 and H2 revealed that both sorbates display different trends for the relative occupancy about such sites upon increasing/decreasing the pressure in the MOF. Overall, this study provides insights into the CO2 and H2 sorption mechanisms in this MOF containing open-metal sites and small pore sizes for the first time through a classical polarizable force field.

Understanding Hydrogen Sorption in In-soc-MOF: A Charged Metal-Organic Framework with Open-Metal Sites, Narrow Channels, and Counterions

Grand canonical Monte Carlo (GCMC) simulations of hydrogen sorption were performed in In-soc-MOF, a charged metal–organic framework (MOF) that contains In3O trimers coordinated to 5,5′-azobis(1,3-benzenedicarboxylate) linkers. The MOF contains nitrate counterions that are located in carcerand-like capsules of the framework. This MOF was shown to have a high hydrogen uptake at 77 K and 1.0 atm. The simulations were performed with a potential that includes explicit many-body polarization interactions, which were important for modeling gas sorption in a charged/polar MOF such as In-soc-MOF. The simulated hydrogen sorption isotherms were in good agreement with experiment in this challenging platform for modeling. The simulations predict a high initial isosteric heat of adsorption, Qst, value of about 8.5 kJ mol–1, which is in contrast to the experimental value of 6.5 kJ mol–1 for all loadings. The difference in the Qst behavior between experiment and simulation is attributed to the fact that, in experimental measurements, the sorbate molecules cannot access the isolated cages containing the nitrate ions, the most energetically favorable site in the MOF, at low pressures due to an observed diffusion barrier. In contrast, the simulations were able to capture the sorption of hydrogen onto the nitrate ions at low loading due to the equilibrium nature of GCMC simulations. The experimental Qst values were reproduced in simulation by blocking access to all of the nitrate ions in the MOF. Furthermore, at 77 K, the sorbed hydrogen molecules were reminiscent of a dense fluid in In-soc-MOF starting at approximately 5.0 atm, and this was verified by monitoring the isothermal compressibility, βT, values. The favorable sites for hydrogen sorption were identified from the polarization distribution as the nitrate ions, the In3O trimers, and the azobenzene nitrogen atoms. Lastly, the two-dimensional quantum rotational levels for a hydrogen molecule sorbed about the aforementioned sites were calculated and the transitions were in good agreement with those that were observed in the experimental inelastic neutron scattering spectra.

Accurate and efficient quantum chemistry calculations for noncovalent interactions in many-body systems: the XSAPT family of methods.

We present an overview of "XSAPT", a family of quantum chemistry methods for noncovalent interactions. These methods combine an efficient, iterative, monomer-based approach to computing many-body polarization interactions with a two-body version of symmetry-adapted perturbation theory (SAPT). The result is an efficient method for computing accurate intermolecular interaction energies in large noncovalent assemblies such as molecular and ionic clusters, molecular crystals, clathrates, or protein-ligand complexes. As in traditional SAPT, the XSAPT energy is decomposable into physically meaningful components. Dispersion interactions are problematic in traditional low-order SAPT, and two new approaches are introduced here in an attempt to improve this situation: (1) third-generation empirical atom-atom dispersion potentials, and (2) an empirically scaled version of second-order SAPT dispersion. Comparison to high-level ab initio benchmarks for dimers, water clusters, halide-water clusters, a methane clathrate hydrate, and a DNA intercalation complex illustrate both the accuracy of XSAPT-based methods as well as their limitations. The computational cost of XSAPT scales as O(N(3))-O(N(5)) with respect to monomer size, N, depending upon the particular version that is employed, but the accuracy is typically superior to alternative ab initio methods with similar scaling. Moreover, the monomer-based nature of XSAPT calculations makes them trivially parallelizable, such that wall times scale linearly with respect to the number of monomer units. XSAPT-based methods thus open the door to both qualitative and quantitative studies of noncovalent interactions in clusters, biomolecules, and condensed-phase systems.

Capturing the H2–Metal Interaction in Mg-MOF-74 Using Classical Polarization

Grand canonical Monte Carlo (GCMC) simulations of H2 sorption were performed in Mg-MOF-74, a metal–organic framework (MOF) that displays very high H2 sorption affinity. Experimental H2 sorption isotherms and isosteric heats of adsorption (Qst) values were reproduced using a general purpose materials sorption potential that includes many-body polarization interactions. In contrast, using two models that include only charge–quadrupole interactions failed to reproduce such experimental measurements even though they are the type normally employed in such classical force field calculations. Utilizing the present explicit polarizable model in GCMC simulation resulted in a Mg2+–H2 distance of 2.60 Å, which is close to a previously reported value that was obtained using electronic structure methods and comparable to similar experimental measurements. The induced dipole distribution obtained from simulation assisted in the characterization of two previously identified sorption sites in the MOF: the Mg2+ ions and the oxido group of the linkers. The calculated two-dimensional quantum rotational levels for a H2 molecule sorbed onto the Mg2+ ion were in good agreement with experimental inelastic neutron scattering (INS) data. Although the H2–metal interaction in MOFs may be thought of as a quantum mechanical effect, this study demonstrates how the interaction between the sorbate molecules and the open-metal sites in a particular highly sorbing MOF can be captured using classical simulation techniques that involve a polarizable potential.

Simulation of the Mechanism of Gas Sorption in a Metal–Organic Framework with Open Metal Sites: Molecular Hydrogen in PCN-61

Grand canonical Monte Carlo (GCMC) simulations were performed to investigate hydrogen sorption in an rht-type metal–organic framework (MOF), PCN-61. The MOF was shown to have a large hydrogen uptake, and this was studied using three different hydrogen potentials, effective for bulk hydrogen, but of varying sophistication: a model that includes only repulsion/dispersion parameters, one augmented with charge-quadrupole interactions, and one supplemented with many-body polarization interactions. Calculated hydrogen uptake isotherms and isosteric heats of adsorption, Qst, were in quantitative agreement with experiment only for the model with explicit polarization. This success in reproducing empirical measurements suggests that modeling MOFs that have open metal sites is feasible, though it is often not considered to be well described via a classical potential function; here it is shown that such systems may be accurately described by explicitly including polarization effects in an otherwise traditional empir...

Field-Induced Self-Assembly of Suspended Colloidal Membranes

We report experiments that probe the self-assembly of micrometer-size colloids into one-particle-thick, robust, and self-healing membranes. In a magic-angle precessing magnetic field, superparamagnetic spheres experience isotropic pair attraction similar to the van der Waals force between atoms. But the many-body polarization interactions among them steer an ordered aggregation pathway consisting of growth of short chains, cross-linking and network formation, network coarsening, and consolidation of membrane patches. This generic aggregation scenario can be induced in any particles of large enough susceptibility.

Are many-body electronic polarization effects important in liquid water?

Many-body electronic polarization effects may be important for an accurate description of aqueous environments. As a result, numerous polarizable water models have been developed to include explicit polarization effects in intermolecular potential functions. In this paper, it is shown for liquid water at ambient conditions that such many-body polarization interactions can be decomposed into effective pairwise contributions using the force-matching (FM) method [Izvekov et al., J. Chem. Phys. 120, 10896 (2004)]. It is found that an effective pairwise water model obtained by the FM method can accurately reproduce various bulk structural and thermodynamic properties obtained from an accurate fully polarizable water model. In addition, the effective pairwise water model also provides a reasonable description of the water liquid-vapor interface, thus exhibiting a degree of transferability to heterogeneous environments. These results suggest that the role and importance of many-body electronic polarization effects in aqueous systems might be fruitfully explored relative to the best possible pairwise decomposable bulk phase model as the reference state.

Development of Quantum Chemistry-Based Force Fields for Poly(ethylene oxide) with Many-Body Polarization Interactions

A methodology for consistent development of the quantum chemistry-based force fields with and without many-body polarizable terms is described. Adequate levels of theory and basis sets for determination of the relative conformational energetics, repulsion and dispersion nonbonded parameters, dipole moments, and molecular polarizability are established. Good agreement between the quantum chemistry-based repulsion and dispersion parameters and those previously obtained by fitting crystal structures of poly(oxymethylene) is obtained. Hartree−Fock (HF) calculations with augmented correlation consistent basis sets are adequate for the determination of repulsion parameters, whereas a double extrapolation to improved treatments of electron correlations and larger basis sets is needed to obtain dispersion parameters. Partial charges are obtained by fitting to the electrostatic grid of model compounds. Atomic polarizabilities are fitted to reproduce polarization energy around the model compounds. The density funct...

Electron affinity of clusters and liquids of polar molecules: Theory of many-body polarization interactions

We examine the attractive interaction between an excess electron and the dipole moments of polar molecules forming a cluster or a liquid. This interaction determines the size dependence of the electron affinity of these clusters. We use the polarizable electropole model for the molecules and include interactions between the permanent and induced dipole moments. Thus, we obtain that the interaction between the excess electron and the molecules is strongly decreased by the induced polarization of the bound electrons, which is opposed to the permanent dipole moments and makes a dielectric screening. Note that previous calculations of the electron affinity of clusters of polar molecules resulted in much larger vertical detachment energies of the excess electron than observed in the experiment. This error is due to the use of an unphysical pair-potential approximation, which neglects the interaction between the permanent dipole moments and induced dipole moments. Thus the attractive interaction between the excess electron and the molecules and the resulting electronic binding energies have been overestimated. The results of our microscopic theory are identical with macroscopic continuum models and agree very well with experimental results. This theory also might be important for the study of solvent effects on oxidation–reduction reactions and on photosynthesis.

Theory for the solvation of alkali metal atoms in clusters of polar molecules. Many-body polarization interactions

We present a theory for the binding energy of clusters of polar molecules (ammonia or water) and an alkali metal atom (Na, Cs). The metal atom dissociates into a positive ion and a separate valence electron, which has the role of an excess electron. The positive ion and the electron have strong electromagnetic interactions with the molecules of the cluster. It is shown that the resulting polarization energy contains important many-body terms and that it is not possible to use a pair-potential approximation for the electronic potential. We propose a model for the ionization potential, including both-initial and final state effects. Our results for the ionization potential of metal-ammonia clusters agree well with recent experiments, indicating that a size-dependent transition from a single-center structure of small clusters to a fully solvated two-center structure for large clusters occurs. Spherically symmetric model structures do not yield a good agreement with experimental results for Na(H 2O) n clusters. Thus these clusters either have a distinct asymmetric shape because of strong hydrogen bridge bonding or an autoionizing resonance might have been observed in the experiment instead of the true ionization threshold.

Electron solvation in methane and ethane

The solvation of excess electrons in fluid methane and ethane is studied by path integral Monte Carlo computer simulation and by the fast-Fourier-transform–Lanczos diagonalization method using a newly developed electron-alkane pseudopotential. Many-body polarization interactions between solvent molecules are treated using a mean field approximation in the simulation. In methane, it is found that the electron is in an extended state throughout the whole fluid density range studied. In ethane, it is found that the solvated electron gradually becomes localized or ‘‘self-trapped,’’ with cavity formation occurring at a fluid density where experimentally the electron is found to have a very low mobility and the threshold value for electron photoconduction rises above zero. The electronic ground state energies in the unperturbed solvent and in the electron-equilibrated solvent were compared. At the same density these electronic energies are very close to each other in methane and in the low density ethane fluids, but at higher ethane densities, where cavity formation takes place, the ground state energy in the electron solvated fluid is lower than that in the unperturbed fluid.

Density dependence of excess electronic ground-state energies in simple atomic fluids

The ground-state energies of an excess electron E0 as a function of solvent density are computed using model electron–atom pseudopotentials in fluid helium, argon, and xenon. E0 is a lower bound to the experimentally measurable threshold to photoconductivity, V0. The nonuniqueness of the pseudopotential description of electron–molecule interactions is demonstrated. We find that when many-body polarization effects are included, our calculated E0 results are in close agreement with experimental V0 values indicating that the conduction-band energy lies close to the ground-state energy across a broad range of densities in these polarizable fluids. If the many-body nature of the polarization interaction is ignored the ground-state energies deviate significantly from the V0 results highlighting the importance of accurate treatment of many-body polarization interactions. It is shown that a mean-field theory of polarization gives substantial agreement with full many-body calculations. This allows us to introduce a mean-field, density-dependent pair potential which greatly simplifies such many-body calculations. In the more polarizable systems, it is found that the spatial extent of the ground-state wave function as a function of solvent density is correlated with the density dependence of both V0 and the electron mobility, and it becomes uniformly spread throughout our simulation cell as the electron mobility goes through its maximum value at intermediate solvent densities.