Explicit Polarization Research Articles

Potential of polarizable force fields for predicting the separation performance of small hydrocarbons in M-MOF-74.

The separation of light olefins from paraffins via cryogenic distillation is a very energy intensive process. Solid adsorbents and especially metal-organic frameworks with open metal sites have the potential to significantly lower the required energy. Specifically, M-MOF-74 has drawn considerable attention for application in olefin/paraffin separation. To investigate how the separation proceeds on a molecular level and to design better materials, molecular simulation can be a useful tool. Unfortunately, it is still a challenge to model the adsorption behavior of many adsorbates in metal-organic frameworks with open metal sites. Previously, the inclusion of explicit polarization has been suggested to improve the quality of classical force fields for such systems. Here, the potential of polarizable force fields for the description of olefins and paraffins in metal-organic frameworks with open metal sites is investigated. In particular, heats of adsorption, binding geometries, and adsorption isotherms are calculated for C2H4, C2H6, C3H6, and C3H8 in M-MOF-74 (with M = Co, Mn, Fe, and Ni). In this study, no force field parameters are adjusted to improve the model. The results show that including explicit polarization significantly improves the description of the adsorption in comparison to non-polarizable generic force fields which do not consider explicit polarization. The study also reveals that simulation predictions are sensitive to the assigned repulsive potential and framework charges. A fully re-parametrized polarizable force field may have the capability to improve the predictions even further.

Simulating Osmotic Equilibria: A New Tool for Calculating Activity Coefficients in Concentrated Aqueous Salt Solutions.

Herein, a new theoretical method is presented for predicting osmotic equilibria and activities, where a bulk liquid and its corresponding vapor phase are simulated by means of molecular dynamics using explicit polarization. Calculated time-averaged number density profiles provide the amount of evaporated molecules present in the vapor phase and consequently the vapor-phase density. The activity of the solvent and the corresponding osmotic coefficient are determined by the vapor density at different solute concentrations with respect to the reference vapor density of the pure solvent. With the extended Debye-Hückel equation for the activity coefficient along with the corresponding Gibbs-Duhem relation, the activity coefficients of the solutes are calculated by fitting the osmotic coefficients. A simple model based on the combination of Poisson processes and Maxwell-Boltzmann velocity distributions is introduced to interpret statistical phenomena observed during the simulations, which are related to evaporation and recondensation. This method is applied to aqueous dysprosium nitrate [Dy(NO3)3] solutions at different concentrations. The obtained densities of the liquid bulk and the osmotic and activity coefficients are in good agreement with the experimental results for concentrated and saturated solutions. Density profiles of the liquid-vapor interface at different concentrations provide detailed insight into the spatial distributions of all compounds.

Resolving dispersion and induction components for polarisable molecular simulations of ionic liquids.

One important development in interaction potential models, or atomistic force fields, for molecular simulation is the inclusion of explicit polarisation, which represents the induction effects of charged or polar molecules on polarisable electron clouds. Polarisation can be included through fluctuating charges, induced multipoles, or Drude dipoles. This work uses Drude dipoles and is focused on room-temperature ionic liquids, for which fixed-charge models predict too slow dynamics. The aim of this study is to devise a strategy to adapt existing non-polarisable force fields upon addition of polarisation, because induction was already contained to an extent, implicitly, due to parametrisation against empirical data. Therefore, a fraction of the van der Waals interaction energy should be subtracted so that the Lennard-Jones terms only account for dispersion and the Drude dipoles for induction. Symmetry-adapted perturbation theory is used to resolve the dispersion and induction terms in dimers and to calculate scaling factors to reduce the Lennard-Jones terms from the non-polarisable model. Simply adding Drude dipoles to an existing fixed-charge model already improves the prediction of transport properties, increasing diffusion coefficients, and lowering the viscosity. Scaling down the Lennard-Jones terms leads to still faster dynamics and densities that match experiment extremely well. The concept developed here improves the overall prediction of density and transport properties and can be adapted to other models and systems. In terms of microscopic structure of the ionic liquids, the inclusion of polarisation and the down-scaling of Lennard-Jones terms affect only slightly the ordering of the first shell of counterions, leading to small decreases in coordination numbers. Remarkably, the effect of polarisation is major beyond first neighbours, significantly weakening spatial correlations, a structural effect that is certainly related to the faster dynamics of polarisable models.

Introducing the mean field approximation to CDFT/MMpol method: Statistically converged equilibrium and nonequilibrium free energy calculation for electron transfer reactions in condensed phases

A new theoretical method to study electron transfer reactions in condensed phases is proposed by introducing the mean-field approximation into the constrained density functional theory/molecular mechanical method with a polarizable force field (CDFT/MMpol). The method enables us to efficiently calculate the statistically converged equilibrium and nonequilibrium free energies for diabatic states in an electron transfer reaction by virtue of the mean field approximation that drastically reduces the number of CDFT calculations. We apply the method to the system of a formanilide-anthraquinone dyad in dimethylsulfoxide, in which charge recombination and cis-trans isomerization reactions can take place, previously studied by the CDFT/MMpol method. Quantitative agreement of the driving force and the reorganization energy between our results and those from the CDFT/MMpol calculation and the experimental estimates supports the utility of our method. The calculated nonequilibrium free energy is analyzed by its decomposition into several contributions such as those from the averaged solute-solvent electrostatic interactions and the explicit solvent electronic polarization. The former contribution is qualitatively well described by a model composed of a coarse-grained dyad in a solution in the linear response regime. The latter contribution reduces the reorganization energy by more than 10 kcal/mol.

An averaged polarizable potential for multiscale modeling in phospholipid membranes

A set of average atom-centered charges and polarizabilities has been developed for three types of phospholipids for use in polarizable embedding calculations. The lipids investigated are 1,2-dimyristoyl-sn-glycero-3-phosphocholine, 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine, and 1-palmitoyl-2-oleoyl-sn-glycerol-3-phospho-L-serine given their common use both in experimental and computational studies. The charges, and to a lesser extent the polarizabilities, are found to depend strongly on the molecular conformation of the lipids. Furthermore, the importance of explicit polarization is underlined for the description of larger assemblies of lipids, that is, membranes. In conclusion, we find that specially developed polarizable parameters are needed for embedding calculations in membranes, while common non-polarizable point-charge force fields usually perform well enough for structural and dynamical studies. © 2017 Wiley Periodicals, Inc.

Improved CHARMM Additive Force Field Parameters to Accurately Model Tyrosine-Choline Cation-π Interactions

Cation-π interactions between methylated ammonium groups and tyrosine amino acids have been shown to be important for epigenetic recognition motifs, choline-binding proteins, and for protein-lipid interactions. Accurately modeling cation-π interactions in biomolecular simulations remains a challenge due to the lack of explicit polarization or charge transfer effects. In this work, we investigate the nature of tyrosine-choline cation-π interactions by performing high-level Quantum Mechanical (QM) calculations and building Potential Energy Surfaces (PES). We benchmark QM levels of theory and find that SAPT2+/aug-cc-pVDZ level of theory performs well compared to large basis set CCSD(T). Further, we compared QM PES (using SAPT2+/aug-cc-pVDZ) to both additive CHARMM36 and Drude polarizable force field. With CHARMM36, the equilibrium distances are well captured while the interaction energies are underestimated for various approach angles of TMA with respect to phenol. While using the Drude polarizable force field, the interaction energies deviate less compared to target QM data. However, the obtained equilibrium geometries are slightly underestimated. The best agreement between force field and QM PES is obtained by modifying the Lennard-Jones potentials for selected atom pairs involved in phenol-TMA cation-π interactions. We performed MD simulations of a bilayer-bound bacterial phospholipase and calculate the occupancies of tyrosine-choline cation-π interactions. The cation-π occupancies obtained with the modified set correlate better with experimental data than those obtained with the CHARMM force field.

Full field of view polarization effect measurement and error analysis of non-polarized channels of spaceborne directional polarimetric camera

The optical system of spaceborne directional polarimetric camera that employs an ultra wide-angle lens for its multiangle, a filter wheel for its multispectral and also its multipolarization capability, a CCD itself for its imaging has a certain polarization effect, which can affect the radiometric accuracy of the non-polarized channels of the instrument. The transmittance of the oblique light rays that are incident on the optical element surfaces is sensitive to the orientation of the electric field, contributing to the linear polarization effect of optical system. The precise polarization measurement and calibration of the passive imaging polarimetry are in urgent need to eliminate the instrumental polarization effect and to improve its radiometric accuracy for observation scenes. The non-polarized channel radiometric model considering the linear polarization effect is deduced in detail by analyzing the instrumental principle and optical structures. Moreover, the reasonably simplified model is established based on the actual lens characteristics. A calibration method in which completely linearly polarized light with different kinds of polarization angles irradiates sparsely the instrument within full field of view and subsequently fits the response in the least square sense, is proposed and simulated. In addition, the measured relative errors of the intensity of incident light with different kinds of polarization states caused by the calibration deviations of instrumental principal physical parameters are analyzed and calculated, such as the azimuthal angle of single pixels, explicit optic polarization rate and low frequency spatial relative transmittance. The actual instrumental parameter values and their calibration deviation amounts are acquired by carrying out the laboratory calibration experiment for instrument and combining the least square fitting. Furthermore, the maximum radiometric calibration relative error caused by the deviation of the physical parameter called explicit optic polarization rate is calculated to be 0.4%, fulfilling completely the requirement of radiometric relative accuracy 5% and retaining abundant tolerance. The study provides a theoretical basis and an experimental guidance in high accurately measuring radiation, calibrating and processing data for the instrumental non-polarized channels with full field of view.

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.

Improving the Force Field Description of Tyrosine-Choline Cation-π Interactions: QM Investigation of Phenol-N(Me)4+ Interactions.

Cation-π interactions between tyrosine amino acids and compounds containing N,N,N-trimethylethanolammonium (N(CH3)3) are involved in the recognition of histone tails by chromodomains and in the recognition of phosphatidylcholine (PC) phospholipids by membrane-binding proteins. Yet, the lack of explicit polarization or charge transfer effects in molecular mechanics force fields raises questions about the reliability of the representation of these interactions in biomolecular simulations. Here, we investigate the nature of phenol-tetramethylammonium (TMA) interactions using quantum mechanical (QM) calculations, which we also use to evaluate the accuracy of the additive CHARMM36 and Drude polarizable force fields in modeling tyrosine-choline interactions. We show that the potential energy surface (PES) obtained using SAPT2+/aug-cc-pVDZ compares well with the large basis-set CCSD(T) PES when TMA approaches the phenol ring perpendicularly. Furthermore, the SAPT energy decomposition reveals comparable contributions from electrostatics and dispersion in phenol-TMA interactions. We then compared the SAPT2+/aug-cc-pVDZ PES obtained along various approach directions to the corresponding PES obtained with CHARMM, and we show that the force field accurately reproduces the minimum distances while the interaction energies are underestimated. The use of the Drude polarizable force field significantly improves the interaction energies but decreases the agreement on distances at energy minima. The best agreement between force field and QM PES is obtained by modifying the Lennard-Jones terms for atom pairs involved in the phenol-TMA cation-π interactions. This is further shown to improve the correlation between the occupancy of tyrosine-choline cation-π interactions obtained from molecular dynamics simulations of a bilayer-bound bacterial phospholipase and experimental affinity data of the wild-type protein and selected mutants.

TINKTEP: A fully self-consistent, mutually polarizable QM/MM approach based on the AMOEBA force field.

We present a novel quantum mechanical/molecular mechanics (QM/MM) approach in which a quantum subsystem is coupled to a classical subsystem described by the AMOEBA polarizable force field. Our approach permits mutual polarization between the QM and MM subsystems, effected through multipolar electrostatics. Self-consistency is achieved for both the QM and MM subsystems through a total energy minimization scheme. We provide an expression for the Hamiltonian of the coupled QM/MM system, which we minimize using gradient methods. The QM subsystem is described by the onetep linear-scaling DFT approach, which makes use of strictly localized orbitals expressed in a set of periodic sinc basis functions equivalent to plane waves. The MM subsystem is described by the multipolar, polarizable force field AMOEBA, as implemented in tinker. Distributed multipole analysis is used to obtain, on the fly, a classical representation of the QM subsystem in terms of atom-centered multipoles. This auxiliary representation is used for all polarization interactions between QM and MM, allowing us to treat them on the same footing as in AMOEBA. We validate our method in tests of solute-solvent interaction energies, for neutral and charged molecules, demonstrating the simultaneous optimization of the quantum and classical degrees of freedom. Encouragingly, we find that the inclusion of explicit polarization in the MM part of QM/MM improves the agreement with fully QM calculations.

Accurate H2 Sorption Modeling in the rht-MOF NOTT-112 Using Explicit Polarization

Hydrogen sorption was characterized theoretically in NOTT-112, an rht-metal–organic framework (MOF) that consists of Cu2+ ions coordinated to 1,3,5-tris(3′,5′-dicarboxy[1,1′-biphenyl]-4-yl)benzene ligands. Grand canonical Monte Carlo (GCMC) simulations of H2 sorption were performed using three different sorbate potentials of increasing complexity to elucidate the mechanism of interaction in NOTT-112. Reasonable agreement with the experimental H2 sorption isotherms, isosteric heats of adsorption (Qst), and H2–Cu2+ distances was obtained with the model that includes explicit many-body polarization. This highlights the physical importance of induction in H2 sorption in MOFs with open-metal sites. The two Cu2+ ions within the paddlewheels in NOTT-112 have distinct electrostatic profiles and sorption characteristics. The Cu2+ ions projecting into the cuboctahedral (cub–Oh) cage of the MOF are more electropositive than the Cu2+ ions projecting toward the organic linker, and therefore serve as the initial loadin...

Ab Initio Atom-Atom Potentials Using CamCASP: Theory and Application to Many-Body Models for the Pyridine Dimer.

Creating accurate, analytic atom-atom potentials for small organic molecules from first principles can be a time-consuming and computationally intensive task, particularly if we also require them to include explicit polarization terms, which are essential in many systems. We describe how the CamCASP suite of programs can be used to generate such potentials using some of the most accurate electronic structure methods currently applicable. We derive the long-range terms from monomer properties and determine the short-range anisotropy parameters by a novel and robust method based on the iterated stockholder atom approach. Using these techniques, we develop distributed multipole models for the electrostatic, polarization, and dispersion interactions in the pyridine dimer and develop a series of many-body potentials for the pyridine system. Even the simplest of these potentials exhibits root mean square errors of only about 0.6 kJ mol(-1) for the low-energy pyridine dimers, significantly surpassing the best empirical potentials. Our best model is shown to support eight stable minima, four of which have not been reported before in the literature. Further, the functional form can be made systematically more elaborate so as to improve the accuracy without a significant increase in the human-time spent in their generation. We investigate the effects of anisotropy, rank of multipoles, and choice of polarizability and dispersion models.

To Polarize or Not to Polarize? Charge-on-Spring versus KBFF Models for Water and Methanol Bulk and Vapor-Liquid Interfacial Mixtures.

Simulations of water and methanol mixtures using polarizable force fields (FFs) for methanol (COS/M and CPC) and water (COS/G2) were performed and compared to experiment and also to a nonpolarizable methanol (KBFF) model with SPC/E water in an effort to quantify the importance of explicit electronic polarization effects in bulk liquid mixtures and vapor-liquid interfaces. The bulk liquid mixture properties studied included the center of mass radial distribution functions, Kirkwood-Buff integrals (KBIs), volumetric properties, isothermal compressibility, enthalpy of mixing, dielectric constant, and diffusion coefficients. The vapor-liquid interface properties investigated included the relative surface probability distributions, surface tension, excess surface adsorption, preferred surface molecule orientations, and the surface dipole. None of the three FFs tested here was clearly superior for all of the properties examined. All the force fields typically reproduced the correct trends with composition for both the bulk and interfacial system properties; the differences between the force fields were primarily quantitative. The overall results suggest that the polarizable FFs are not, at the present stage of development, inherently better able to reproduce the studied bulk and interfacial properties-despite the added degree of explicit transferability that is, by definition, built into the polarizable models. Indeed, the specific parametrization of the FF appears to be just as important as the class of FF.

Can We Execute Reliable MM-PBSA Free Energy Computations of Relative Stabilities of Different Guanine Quadruplex Folds?

The self-assembly and stability of DNA G-quadruplexes (GQs) are affected by the intrinsic stability of different GpG base steps embedded in their G-quartet stems. We have carried out MD simulations followed by MM-PBSA (molecular mechanics Poisson-Boltzmann surface area) free energy calculations on all the experimentally observed three-quartet intramolecular human telomeric GQ topologies. We also studied antiparallel GQ models with alternative syn-anti patterns of the G-quartets. We tested different ions, dihedral variants of the DNA force field, water models, and simulation lengths. In total, ∼35 μs of simulations have been carried out. The systems studied here are considerably more complete than the previously analyzed two-quartet stems. Among other effects, our computations included the stem-loop coupling and ion-ion interactions inside the stem. The calculations showed a broad agreement with the earlier predictions. However, the increase in the completeness of the system was associated with increased noise of the free energy data which could be related, for example, to the presence of long-lived loop substates and rather complex dynamics for the two bound ions inside the G-stem. As a result, the MM-PBSA data were noisy and we could not improve their quantitative convergence even by expanding the simulations to 2.5 μs long trajectories. We also suggest that the quality of MM-based free energy computations based on MD simulations of complete GQs is more sensitive to the neglect of explicit polarization effects, which, in real systems, are associated with the presence of multiple closely spaced ions inside the GQs. Thus, although the MM-PBSA procedure provides very useful insights that complement the structural-dynamics data from MD trajectories of GQs, the method is far from reaching quantitative accuracy. Our conclusions are in agreement with critical assessments of the MM-PBSA methodology available in contemporary literature for other types of problems.

LICHEM: A QM/MM program for simulations with multipolar and polarizable force fields.

We introduce an initial implementation of the LICHEM software package. LICHEM can interface with Gaussian, PSI4, NWChem, TINKER, and TINKER-HP to enable QM/MM calculations using multipolar/polarizable force fields. LICHEM extracts forces and energies from unmodified QM and MM software packages to perform geometry optimizations, single-point energy calculations, or Monte Carlo simulations. When the QM and MM regions are connected by covalent bonds, the pseudo-bond approach is employed to smoothly transition between the QM region and the polarizable force field. A series of water clusters and small peptides have been employed to test our initial implementation. The results obtained from these test systems show the capabilities of the new software and highlight the importance of including explicit polarization. © 2016 Wiley Periodicals, Inc.

Molecular hydrogen solvated in water--A computational study.

The aqueous hydrogen molecule is studied with molecular dynamics simulations at ambient temperature and pressure conditions, using a newly developed flexible and polarizable H2 molecule model. The design and implementation of this model, compatible with an existing flexible and polarizable force field for water, is presented in detail. The structure of the hydration layer suggests that first-shell water molecules accommodate the H2 molecule without major structural distortions and two-dimensional, radial-angular distribution functions indicate that as opposed to strictly tangential, the orientation of these water molecules is such that the solute is solvated with one of the free electron pairs of H2O. The calculated self-diffusion coefficient of H2(aq) agrees very well with experimental results and the time dependence of mean square displacement suggests the presence of caging on a time scale corresponding to hydrogen bond network vibrations in liquid water. Orientational correlation function of H2 experiences an extremely short-scale decay, making the H2-H2O interaction potential essentially isotropic by virtue of rotational averaging. The inclusion of explicit polarizability in the model allows for the calculation of Raman spectra that agree very well with available experimental data on H2(aq) under differing pressure conditions, including accurate reproduction of the experimentally noted trends with solute pressure or concentration.

Theoretical analysis of uranium-doped thorium dioxide: Introduction of a thoria force field with explicit polarization

Thorium dioxide is used industrially in high temperature applications, but more insight is needed into the behavior of the material as part of a mixed-oxide (MOX) nuclear fuel, incorporating uranium. We have developed a new interatomic potential model including polarizability via a shell model, and commensurate with a prominent existing UO2 potential, to conduct configurational analyses and to investigate the thermophysical properties of uranium-doped ThO2. Using the GULP and Site Occupancy Disorder (SOD) computational codes, we have analyzed the distribution of low concentrations of uranium in the bulk material, where we have not observed the formation of uranium clusters or the dominance of a single preferred configuration. We have calculated thermophysical properties of pure thorium dioxide and Th(1−x)UxO2 which generated values in very good agreement with experimental data.

Thermodynamics of Associated Electrolytes in Water: Molecular Dynamics Simulations of Sulfate Solutions

A polarizable force field for the sulfate anion SO4(2–) has been developed and extended from nonpolarizable force fields in order to reproduce its structural and thermodynamics properties in aqueous solution. Two force fields with different atomic partial charges on S and O have been tested and used with molecular dynamics with explicit polarization. The results obtained with our developed force field are in good agreement with the experimental hydration properties of the sulfate anion. In addition to molecular dynamics simulations of the sulfate anion in aqueous solution, potentials of mean force of sulfate electrolytes have been calculated via umbrella-sampling molecular dynamics simulations, i.e., MgSO4, EuSO4(+), and UO2SO4. These potentials allow for calculating pair association constants directly comparable to the experimental ones. In the case of monoatomic cations such as Mg(2+) and Eu(3+), the association constants calculated are in very good agreement with the experimental values, i.e., pKcalc = 2.21 (vs 2.21 experimentally) and 3.86 (vs 3.56–3.78 experimentally) for MgSO4 and EuSO4(+), respectively. In the case of purely molecular electrolyte (UO2SO4), the association constant calculated (pKcalc = 1.58–2.07) is in agreement with the range of values available in the literature (pKexp = 1.17–3.14).

Water exchange dynamics around H3O+ and OH− ions

In this letter, we report the first computer simulation of the dynamics of water exchanging between the first and second solvation shells of H3O+. Employing different rate theories for chemical reactions such as the transition state theory, the Grote–Hynes theory, the reactive flux method, and the Impey–Madden–McDonald method, we calculate the solvent exchange rates from molecular dynamics simulations that account for explicit polarization effects. In addition, we also study water exchanges around OH− and find that the corresponding time scale is much smaller than that for H3O+.

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.