Efficient calculation of many-body induced electrostatics in molecular systems

PHAHST Potential: Modeling Sorption in a Dispersion-Dominated Environment

PHAHST (potentials with high accuracy, high speed, and transferability) is a recently developed force field that utilizes exponential repulsion, multiple dispersion terms, explicit many-body polarization, and many-body van der Waals interactions. The result is a systematic approach to force field development that is computationally practical. Here, PHAHST is employed in the simulation for rare gas uptake of krypton and xenon in the metal-organic material, HKUST-1. This material has shown promise in use as an adsorptive separating agent and presents a challenge to model due to the presence of heterogeneous interaction sorption surfaces, which include pores with readily accessible, open-metal sites that compete with dispersion-dominated pores. Such environments are difficult to simulate with commonly used empirical force fields, such as the Lennard-Jones (LJ) potential, which perform better when electrostatics are dominant in determining the nature of sorption and alone are incapable of modeling interactions with open-metal sites. The effectiveness of PHAHST is compared to the LJ potential in a series of mixed Kr-Xe gas simulations. It has been demonstrated that PHAHST compares favorably with experimental results, and the LJ potential is inadequate. Overall, we establish that force fields with physically grounded repulsion/dispersion terms are required in order to accurately model sorption, as these interactions are an important component of the energy. Furthermore, it is shown that the simple mixing rules work nearly quantitatively for the true pair potentials, while they are not transferable for effective potentials like LJ.

Non-Ewald methods for evaluating the electrostatic interactions of charge systems: similarity and difference

In molecular simulations, it is essential to properly calculate the electrostatic interactions of particles in the physical system of interest. Here we consider a method called the non-Ewald method, which does not rely on the standard Ewald method with periodic boundary conditions, but instead relies on the cutoff-based techniques. We focus on the physicochemical and mathematical conceptual aspects of the method in order to gain a deeper understanding of the simulation methodology. In particular, we take into account the reaction field (RF) method, the isotropic periodic sum (IPS) method, and the zero-multipole summation method (ZMM). These cutoff-based methods are based on different physical ideas and are completely distinguishable in their underlying concepts. The RF and IPS methods are "additive" methods that incorporate information outside the cutoff region, via dielectric medium and isotropic boundary condition, respectively. In contrast, the ZMM is a "subtraction" method that tries to remove the artificial effects, generated near the boundary, from the cutoff sphere. Nonetheless, we find physical and/or mathematical similarities between these methods. In particular, the modified RF method can be derived by the principle of neutralization utilized in the ZMM, and we also found a direct relationship between IPS and ZMM.

Investigating H2 Adsorption in Isostructural Metal-Organic Frameworks M-CUK-1 (M = Co and Mg) through Experimental and Theoretical Studies

A combined experimental and theoretical study of H₂ adsorption was carried out in Co-CUK-1 and Mg-CUK-1, two isostructural metal-organic frameworks (MOFs) that consist of M²⁺ ions (M = Co and Mg) coordinated to pyridine-2,4-dicarboxylate (pdc^2-) and OH^- ligands. These MOFs possess saturated metal centers in distorted octahedral environments and narrow pore sizes and display high chemical and thermal stability. Previous experimental studies revealed that Co-CUK-1 exhibits a H₂ uptake of 183 cm³ g^-1 at 77 K/1.0 atm [ Angew. Chem., Int. Ed. 2007, 46, 272-275, DOI: 10.1002/anie.200601627], while that for Mg-CUK-1 under the same conditions is 240 cm³ g^-1 on the basis of the experimental measurements carried out herein. The theoretical H₂ adsorption isotherms are in close agreement with the corresponding experimental measurements for simulations using electrostatic and polarizable potentials of the adsorbate. Through simulated annealing calculations, it was found that the primary binding site for H₂ in both isostructural analogues is localized proximal to the center of the aromatic rings belonging to the pdc^2- linkers. Inelastic neutron scattering (INS) spectroscopic studies of H₂ adsorbed in both MOFs revealed a rotational tunnelling transition occurring at around 8 meV in the corresponding spectra; this peak represents H₂ adsorbed at the primary binding site. Two-dimensional quantum rotation calculations for H₂ localized at the primary and secondary binding sites in both MOFs yielded rotational energy levels that are in agreement with the transitions observed in the INS spectra. Even though both M-CUK-1 analogues possess different metal ions, they exhibit similar electrostatic environments, modeled structures at H₂ saturation, and rotational potentials for H₂ adsorbed at the most favorable adsorption site. Overall, this study demonstrates how important molecular-level details of the H₂ adsorption mechanism inside MOF micropores can be derived from a combination of experimental measurements and theoretical calculations using two stable and isostructural MOFs with saturated metal centers and small pore windows as model systems.

Molecular Sieving of Acetylene from Ethylene in a Rigid Ultra-microporous Metal Organic Framework

Rigid molecular sieving materials are the ideal candidates for gas separation (e. g., C₂ H₂ /C₂ H₄ ) due to their ultrahigh adsorption selectivity and the absence of gas co-adsorption. However, the absolute molecular sieving effect for C₂ H₂ /C₂ H₄ separation has rarely been realized because of their similar physicochemical properties. Herein, we demonstrate the absolute molecular sieving of C₂ H₂ from C₂ H₄ by a rigid ultra-microporous metal-organic framework (F-PYMO-Cu) with 1D regular channels (pore size of ca. 3.4 Å). F-PYMO-Cu exhibited moderate acetylene uptake (35.5 cm³ /cm³ ), but very low ethylene uptake (0.55 cm³ /cm³ ) at 298 K and 1 bar, yielding the second highest C₂ H₂ /C₂ H₄ uptake ratio of 63.6 up to now. One-step C₂ H₄ production from a binary mixture of C₂ H₂ /C₂ H₄ and a ternary mixture of C₂ H₂ /CO₂ /C₂ H₄ at 298 K was achieved and verified by dynamic breakthrough experiments. Coupled with excellent thermal and water stability, F-PYMO-Cu could be a promising candidate for industrial C₂ separation tasks.

Next-Generation Accurate, Transferable, and Polarizable Potentials for Material Simulations

PHAHST (potentials with high accuracy, high speed, and transferability) intermolecular potential energy functions have been developed from first principles for H₂, N₂, the noble gases, and a metal-organic material, HKUST-1. The potentials are designed from the outset to be transferable to heterogeneous environments including porous materials, interfaces, and material simulations. This is accomplished by theoretically justified choices for all functional forms, parameters, and mixing rules, including explicit polarization in every environment and fitting to high quality electronic structure calculations using methods that are tractable for real systems. The models have been validated in neat systems by comparison to second virial coefficients and bulk pressure-density isotherms. For inhomogeneous applications, our main target, comparisons are presented to previously published experimental studies on the metal-organic material HKUST-1 including adsorption, isosteric heats of adsorption, binding site locations, and binding site energies. A systematic prescription is provided for developing compatible potentials for additional small molecules and materials. The resulting models are recommended for use in complex heterogeneous simulations where existing potentials may be inadequate.

Insights into the Gas Adsorption Mechanisms in Metal-Organic Frameworks from Classical Molecular Simulations

Classical molecular simulations can provide significant insights into the gas adsorption mechanisms and binding sites in various metal-organic frameworks (MOFs). These simulations involve assessing the interactions between the MOF and an adsorbate molecule by calculating the potential energy of the MOF-adsorbate system using a functional form that generally includes nonbonded interaction terms, such as the repulsion/dispersion and permanent electrostatic energies. Grand canonical Monte Carlo (GCMC) is the most widely used classical method that is carried out to simulate gas adsorption and separation in MOFs and identify the favorable adsorbate binding sites. In this review, we provide an overview of the GCMC methods that are normally utilized to perform these simulations. We also describe how a typical force field is developed for the MOF, which is required to compute the classical potential energy of the system. Furthermore, we highlight some of the common analysis techniques that have been used to determine the locations of the preferential binding sites in these materials. We also review some of the early classical molecular simulation studies that have contributed to our working understanding of the gas adsorption mechanisms in MOFs. Finally, we show that the implementation of classical polarization for simulations in MOFs can be necessary for the accurate modeling of an adsorbate in these materials, particularly those that contain open-metal sites. In general, molecular simulations can provide a great complement to experimental studies by helping to rationalize the favorable MOF-adsorbate interactions and the mechanism of gas adsorption.

Simulations of hydrogen, carbon dioxide, and small hydrocarbon sorption in a nitrogen-rich rht-metal–organic framework

Detailed theoretical insights into the gas-sorption mechanism of Cu-TDPAH are presented for the first time.

Investigating gas sorption in an rht-metal-organic framework with 1,2,3-triazole groups

Simulations of CO₂ and H₂ sorption were performed in an rht-metal-organic framework (MOF) that consists of Cu²⁺ ions coordinated to 5,5',5''-(4,4',4''-(benzene-1,3,5-triyl)tris(1H-1,2,3-triazole-4,1-diyl))triisophthalate (BTTI) linkers; it is referred to as Cu-BTTI herein. This MOF was previously synthesized and reported by three different experimental groups [Zhao et al., Sci. Rep., 2013, 3, 1149; Schröder et al., Chem. Sci., 2013, 4, 1731-1736; Hupp et al., Energy Environ. Sci., 2013, 6, 1158-1163]. This MOF is notable for the presence of open-metal sites and nitrogen-rich regions through the copper paddlewheel ([Cu₂(O₂CR)₄]) clusters and 1,2,3-triazole groups, respectively, which allows this material to display remarkable CO₂ and H₂ sorption properties. All three groups report distinct experimental and theoretical gas sorption results for the MOF. In contrast to the force fields utilized in the aforementioned studies, our simulations include explicit many-body polarization interactions, which was important to reproduce sorption onto the open-metal sites. Simulations using polarizable potentials for the MOF and sorbates generated sorption isotherms and isosteric heat of adsorption (Q_st) values that are outstanding agreement with the corresponding experimental data for all three groups; this is in contrast to the theoretical results presented in the respective original references. The simulations carried out in the previous studies often looked reasonable but they missed a key feature of the sorption process that lead to unreliable results. Analysis of the radial distribution function (g(r)) about the open-metal sites and examination of the modeled structure reveal that the CO₂ and H₂ molecules prefer to sorb onto two unique types of Cu²⁺ ions that exhibit the highest partial positive charges. Sorption was also observed within the corners of the truncated tetrahedral (T-T_d) cages and onto the 1,2,3-triazole groups of the linkers for both sorbates. Overall, this study demonstrates how utilizing a classical polarizable force field led to the reproduction of experimental observables and allowed for an accurate description of the sorption mechanism in this MOF that is an important member of the rht-MOF family.

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

Simulations of gas sorption in UTSA-20 using highly accurate polarizable potentials reproduced experimental observables and provided insights into the binding sites in the material.

Theoretical Investigations of CO2 and H2 Sorption in Robust Molecular Porous Materials

Molecular simulations of CO₂ and H₂ sorption were performed in MPM-1-Cl and MPM-1-TIFSIX, two robust molecular porous materials (MPMs) with the empirical formula [Cu₂(adenine)₄Cl₂]Cl₂ and [Cu₂(adenine)₄(TiF₆)₂], respectively. Recent experimental studies have shown that MPM-1-TIFSIX displayed higher CO₂ uptake and isosteric heat of adsorption (Q_st) than MPM-1-Cl [Nugent, P. S.; et al. J. Am. Chem. Soc. 2013, 135, 10950-10953]. This was verified through the simulations executed herein, as the presented simulated CO₂ sorption isotherms and Q_st values are in very good agreement with the corresponding experimental data for both MPMs. We also report experimental H₂ sorption data in both MPMs. Experimental studies revealed that MPM-1-TIFSIX exhibits high H₂ uptake at low loadings and an initial H₂ Q_st value of 9.1 kJ mol^-1. This H₂ Q_st value is greater than that for a number of existing metal-organic frameworks (MOFs) and represents the highest yet reported for a MPM. The remarkable H₂ sorption properties for MPM-1-TIFSIX have been confirmed through our simulations. The modeling studies revealed that only one principal sorption site is present for CO₂ and H₂ in MPM-1-Cl, which is sorption onto the Cl^- counterions within the large channels. In contrast, three different sorption sites were discovered for both CO₂ and H₂ in MPM-1-TIFSIX: (1) between two TIFSIX groups within a small passage connecting the large channels, (2) onto the TIFSIX ions lining the large channels, and (3) within the small channels. This study illustrates the detailed insights that molecular simulations can provide on the CO₂ and H₂ sorption mechanism in MPMs.

An unusual H2 sorption mechanism in PCN-14: insights from molecular simulation

Molecular simulations of H₂ sorption in the metal–organic framework PCN-14 revealed an unusual sorption mechanism in the material with an intriguing primary binding site.

Dynamics of H2 adsorbed in porous materials as revealed by computational analysis of inelastic neutron scattering spectra

This perspective article reviews the different types of quantum and classical mechanical methods that have been implemented to interpret the INS spectra for H₂ adsorbed in porous materials.

The zero-multipole summation method for estimating electrostatic interactions in molecular dynamics: analysis of the accuracy and application to liquid systems

In the preceding paper [I. Fukuda, J. Chem. Phys. 139, 174107 (2013)], the zero-multipole (ZM) summation method was proposed for efficiently evaluating the electrostatic Coulombic interactions of a classical point charge system. The summation takes a simple pairwise form, but prevents the electrically non-neutral multipole states that may artificially be generated by a simple cutoff truncation, which often causes large energetic noises and significant artifacts. The purpose of this paper is to judge the ability of the ZM method by investigating the accuracy, parameter dependencies, and stability in applications to liquid systems. To conduct this, first, the energy-functional error was divided into three terms and each term was analyzed by a theoretical error-bound estimation. This estimation gave us a clear basis of the discussions on the numerical investigations. It also gave a new viewpoint between the excess energy error and the damping effect by the damping parameter. Second, with the aid of these analyses, the ZM method was evaluated based on molecular dynamics (MD) simulations of two fundamental liquid systems, a molten sodium-chlorine ion system and a pure water molecule system. In the ion system, the energy accuracy, compared with the Ewald summation, was better for a larger value of multipole moment l currently induced until l ≲ 3 on average. This accuracy improvement with increasing l is due to the enhancement of the excess-energy accuracy. However, this improvement is wholly effective in the total accuracy if the theoretical moment l is smaller than or equal to a system intrinsic moment L. The simulation results thus indicate L ∼ 3 in this system, and we observed less accuracy in l = 4. We demonstrated the origins of parameter dependencies appearing in the crossing behavior and the oscillations of the energy error curves. With raising the moment l we observed, smaller values of the damping parameter provided more accurate results and smoother behaviors with respect to cutoff length were obtained. These features can be explained, on the basis of the theoretical error analyses, such that the excess energy accuracy is improved with increasing l and that the total accuracy improvement within l ⩽ L is facilitated by a small damping parameter. Although the accuracy was fundamentally similar to the ion system, the bulk water system exhibited distinguishable quantitative behaviors. A smaller damping parameter was effective in all the practical cutoff distance, and this fact can be interpreted by the reduction of the excess subset. A lower moment was advantageous in the energy accuracy, where l = 1 was slightly superior to l = 2 in this system. However, the method with l = 2 (viz., the zero-quadrupole sum) gave accurate results for the radial distribution function. We confirmed the stability in the numerical integration for MD simulations employing the ZM scheme. This result is supported by the sufficient smoothness of the energy function. Along with the smoothness, the pairwise feature and the allowance of the atom-based cutoff mode on the energy formula lead to the exact zero total-force, ensuring the total-momentum conservations for typical MD equations of motion.