Molecular multipole moments

Supercritical CO2-induced anti-nanoconfinement effect to obtain novel 2D structures

Space confined reactions have emerged as a viable strategy for achieving important and fascinating properties in functional materials. Various scaffolds have been reported so far for confinement and it gives rise to the phenomenon of nanoconfinement, where the energetics and kinetics of catalytic reactions can be modulated upon confining the catalysts in a particular site. Although various systems have been reported so far for confinement, emphasis has been placed on the concept of space confinement, and the changes in the confined space itself are neglected. Strikingly, this critical issue would be touched on and revealed by supercritical CO₂ (SC CO₂) that is used in confined geometries. Herein, we define the structural changes of confined spaces induced by SC CO₂ as an anti-nanoconfinement effect, which can bring about a series of variations together with electronic band and structural transformation. Moreover, progress in the design and applications of the anti-nanoconfinement effect is traced, and there is a discussion of emerging issues that have yet to be explored to achieve a future direction to develop more novel two-dimensional (2D) structures.

On the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model. II. Evaluation of the properties in an infinite crystal

The previously reported exact potential and multipole moment (EP/MM) method for fast and precise evaluation of the intermolecular electrostatic interaction energies in molecular crystals using the pseudoatom representation of the electron density [Nguyen, Macchi & Volkov (2020), Acta Cryst. A76, 630-651] has been extended to the calculation of the electrostatic potential (ESP), electric field (EF) and electric field gradient (EFG) in an infinite crystal. The presented approach combines an efficient Ewald-type summation (ES) of atomic multipoles up to the hexadecapolar level in direct and reciprocal spaces with corrections for (i) the net polarization of the sample (the `surface term') due to a net dipole moment of the crystallographic unit cell (if present) and (ii) the short-range electron-density penetration effects. The rederived and reported closed-form expressions for all terms in the ES algorithm have been augmented by the expressions for the surface term available in the literature [Stenhammar, Trulsson & Linse (2011), J. Chem. Phys. 134, 224104] and the exact potential expressions reported in a previous study [Volkov, King, Coppens & Farrugia (2006), Acta Cryst. A62, 400-408]. The resulting algorithm, coded using Fortran in the XDPROP module of the software package XD, was tested on several small molecular crystal systems (formamide, benzene, L-dopa, paracetamol, amino acids etc.) and compared with a series of EP/MM-based direct-space summations (DS) performed within a certain number of unit cells generated along both the positive and negative crystallographic directions. The EP/MM-based ES technique allows for a noticeably more precise determination of the EF and EFG and significantly better precision of the evaluated ESP when compared with the DS calculations, even when the latter include contributions from an array of symmetry-equivalent atoms generated within four additional unit cells along each crystallographic direction. In terms of computational performance, the ES/EP/MM method is significantly faster than the DS calculations performed within the extended unit-cell limits but trails the DS calculations within the reduced summation ranges. Nonetheless, the described EP/MM-based ES algorithm is superior to the direct-space summations as it does not require the user to monitor continuously the convergence of the evaluated properties as a function of the summation limits and offers a better precision-performance balance.

Fast analytical evaluation of intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density. III. Application to crystal structures via the Ewald and direct summation methods

The previously reported exact potential and multipole moment (EP/MM) method for fast and accurate evaluation of the intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density [Volkov, Koritsanszky & Coppens (2004). Chem. Phys. Lett. 391, 170-175; Nguyen, Kisiel & Volkov (2018). Acta Cryst. A74, 524-536; Nguyen & Volkov (2019). Acta Cryst. A75, 448-464] is extended to the calculation of electrostatic interaction energies in molecular crystals using two newly developed implementations: (i) the Ewald summation (ES), which includes interactions up to the hexadecapolar level and the EP correction to account for short-range electron-density penetration effects, and (ii) the enhanced EP/MM-based direct summation (DS), which at sufficiently large intermolecular separations replaces the atomic multipole moment approximation to the electrostatic energy with that based on the molecular multipole moments. As in the previous study [Nguyen, Kisiel & Volkov (2018). Acta Cryst. A74, 524-536], the EP electron repulsion integral is evaluated analytically using the Löwdin α-function approach. The resulting techniques, incorporated in the XDPROP module of the software package XD2016, have been tested on several small-molecule crystal systems (benzene, L-dopa, paracetamol, amino acids etc.) and the crystal structure of a 181-atom decapeptide molecule (Z = 4) using electron densities constructed via the University at Buffalo Aspherical Pseudoatom Databank [Volkov, Li, Koritsanszky & Coppens (2004). J. Phys. Chem. A, 108, 4283-4300]. Using a 2015 2.8 GHz Intel Xeon E3-1505M v5 computer processor, a 64-bit implementation of the Löwdin α-function and one of the higher optimization levels in the GNU Fortran compiler, the ES method evaluates the electrostatic interaction energy with a numerical precision of at least 10^-5 kJ mol^-1 in under 6 s for any of the tested small-molecule crystal structures, and in 48.5 s for the decapeptide structure. The DS approach is competitive in terms of precision and speed with the ES technique only for crystal structures of small molecules that do not carry a large molecular dipole moment. The electron-density penetration effects, correctly accounted for by the two described methods, contribute 28-64% to the total electrostatic interaction energy in the examined systems, and thus cannot be neglected.

Hydrogen adsorption mechanism of MOF-74 metal–organic frameworks: an insight from first principles calculations

The microscopic mechanism of the H₂ adsorption of two Mg-MOF-74 isoreticular frameworks, one with a benzenedicarboxylate (BDC) linker and the other with a dihydroxyfumarate (DHF) linker, were studied on the basis of density functional theory (DFT) method. Possible adsorption sites on the internal surface of the two MOFs were detected using ab initio molecular dynamics (AIMD) annealing simulations. The simulations were able to reproduce all adsorption sites which have been experimentally observed for the BDC-based M-MOF-74 frameworks with M = Ni and Zn. In descending order of binding strengths, they are the adsorption sites primarily induced by the open metal sites P₁, the oxygen atoms of the oxido groups P₂ and the aromatic rings P₃. The H₂–framework binding strengths were properly evaluated by taking into account the vibrational zero-point energy (ZPE) contribution. An additional type of adsorption sites induced by the oxygen atoms of the carboxyl groups P₄ is predicted for the Mg-MOF-74 framework. Two types of adsorption sites primarily induced by the open metal sites P₁ and oxygen atoms of the carboxyl groups P₂ were predicted for the DHF-based Mg-MOF-74 framework. Detailed analysis of the electron density showed that the electrostatic interaction of the H₂ molecule with the charge distribution of the local framework environment within a radius of ∼3.5 Å is a key factor to define adsorption positions and binding strength. The absence of the P₄ sites in the BDC-based Zn-MOF-74 framework is caused by the lower charge density at the oxygen atoms induced by less electro-positive metal. The substitution of the nonaromatic DHF linker for the aromatic BDC linker reduces the binding strength at the metal induced adsorption sites by 1.45 kJ mol⁻¹ due to the absence of the aromatic ring.

The microscopic mechanism of the H₂ adsorption of two Mg-MOF-74 isoreticular frameworks, one with a benzenedicarboxylate linker and the other with a dihydroxyfumarate linker, were studied on the basis of density functional theory (DFT) method.

Dependence of the multipole moments, static polarizabilities, and static hyperpolarizabilities of the hydrogen molecule on the H-H separation in the ground singlet state

In this work, we provide values for the quadrupole moment Θ, the hexadecapole moment Φ, the dipole polarizability α, the quadrupole polarizability C, the dipole-octopole polarizability E, the second dipole hyperpolarizability γ, and the dipole-dipole-quadrupole hyperpolarizability B for the hydrogen molecule in the ground singlet state, evaluated by finite-field configuration interaction singles and doubles (CISD) and coupled-cluster singles and doubles (CCSD) methods for 26 different H-H separations r, ranging from 0.567 a.u. to 10.0 a.u. Results obtained with various large correlation-consistent basis sets are compared at the vibrationally averaged bond length r₀ in the ground state. Results over the full range of r values are presented at the CISD/d-aug-cc-pV6Z level for all of the independent components of the property tensors. In general, our values agree well with previous ab initio results of high accuracy for the ranges of H-H distances that have been treated in common. To our knowledge, for H₂ in the ground state, our results are the first to be reported in the literature for Φ for r > 7.0 a.u., γ and B for r > 6.0 a.u., and C and E for any H-H separation outside a narrow range around the potential minimum. Quantum Monte Carlo values of Θ have been given previously for H-H distances out to 10.0 a.u., but the statistical error is relatively large for r > 7.0 a.u. At the larger r values in this work, α_xx and α_zz show the expected functional forms, to leading order in r^-1. As r increases further, Θ and Φ vanish, while α, γ, and the components of B converge to twice the isolated-atom values. Components of C and E diverge as r increases. Vibrationally averaged values of the properties are reported for all of the bound states (vibrational quantum numbers υ = 0-14) with rotational quantum numbers J = 0-3.

Role of Ionic Liquid [EMIM]+[SCN]- in the Adsorption and Diffusion of Gases in Metal-Organic Frameworks

We study the adsorption performance of metal-organic frameworks (MOFs) impregnated of ionic liquids (ILs). To this aim we calculated adsorption and diffusion of light gases (CO₂, CH₄, N₂) and their mixtures in hybrid composites using molecular simulations. The hybrid composites consist of 1-ethyl-3-methylimidazolium thiocyanate impregnated in IRMOF-1, HMOF-1, MIL-47, and MOF-1. We found that the increase of the amount of IL enhances the adsorption selectivity in favor of carbon dioxide for the mixtures CO₂/CH₄ and CO₂/N₂ and in favor of methane in the mixture CH₄/N₂. We also provide detailed analysis of the microscopic organization of ILs and adsorbates via radial distribution functions and average occupation profiles and study the impact of the ILs in the diffusion of the adsorbates inside the pores of the MOFs. Based on our findings, we discuss the advantages of using IL/MOF composites for gas adsorption to increase the adsorption of gases and to control the pore sizes of the structures to foster selective adsorption.

Structure-Property Relationships in CO2-philic (Co)polymers: Phase Behavior, Self-Assembly, and Stabilization of Water/CO2 Emulsions

This Review provides comprehensive guidelines for the design of CO2-philic copolymers through an exhaustive and precise coverage of factors governing the solubility of different classes of polymers. Starting from computational calculations describing the interactions of CO2 with various functionalities, we describe the phase behavior in sc-CO2 of the main families of polymers reported in literature. The self-assembly of amphiphilic copolymers of controlled architecture in supercritical carbon dioxide and their use as stabilizers for water/carbon dioxide emulsions then are covered. The relationships between the structure of such materials and their behavior in solutions and at interfaces are systematically underlined throughout these sections.

Comparing gas separation performance between all known zeolites and their zeolitic imidazolate framework counterparts

Candidate structures for environmental and industrial gas separations. No correlation between zeolites and their respective Zeolitic Imidazolate framework counterparts.

On the performance of FAU and MFI zeolites for the adsorptive removal of a series of volatile organic compounds from air using molecular simulation

Volatile organic compound (VOC) emissions can cause serious risk to human health and the environment. In this work, we used Monte Carlo simulations to assess the performance of industrially important zeolites for the adsorption-based removal of a number of common air pollutants, particularly small saturated and unsaturated hydrocarbons: propane, butane, propene, and 1-butene. We focused on the cage-like FAU and channel-like MFI zeolites. The adsorption isotherms of the multicomponent N2/O2/Ar/VOC mixtures at real concentrations and room temperature reveal a considerable influence of the host topology and pore dimensions. While the adsorption of the VOCs from the mixture in FAU is almost negligible, it is remarkable in MFI. The adsorption selectivity of each VOC over the air compounds exhibits a maximum at about 10(6)-10(7) Pa, and then decreases to virtually zero due to entropic effects. This behaviour for selectivity is maintained regardless of the chain length and the presence of double bonds in the VOC, but the values are indeed affected. Also, we examined the selectivity at 10(7) Pa for a number of other widely used zeolites, with pore features ensuring the diffusion of the adsorbates. Apart from MFI, we also found the channel-like MEL and MTW zeolite candidates for the targeted air decontamination.

Explicit expressions for totally symmetric spherical functions and symmetry-dependent properties of multipoles

Closed expressions for matrix elements 〈 lm' | A (G)| lm 〉, where | lm 〉 are spherical functions and A (G) is the average of all symmetry operators of point group G, are derived for all point groups (PGs) and then used to obtain linear combinations of spherical functions that are totally symmetric under all symmetry operations of G. In the derivation, we exploit the product structure of the groups. The obtained expressions are used to explore properties of multipoles of symmetric charge distributions. We produce complete lists of selection rules for multipoles Q l and their moments Q lm , as well as of numbers of independent moments in a multipole, for any l and m and for all PGs. Periodicities and other trends in these properties are revealed.

Nematic order by thermal disorder in a three-dimensional lattice spin model with dipolarlike interactions

At low temperatures, some lattice spin models with simple ferromagnetic or antiferromagnetic interactions (for example, nearest-neighbor interaction being isotropic in spin space on a bipartite three-dimensional lattice) produce orientationally ordered phases exhibiting nematic (second-rank) order, in addition to the primary first-rank one; on the other hand, in the literature, they have been rather seldom investigated in this respect. Here we study the thermodynamic properties of a three-dimensional model with dipolar-like interaction. Its ground state is found to exhibit full orientational order with respect to a suitably defined staggered magnetization (polarization), but no nematic second-rank order. Extensive Monte Carlo simulations, in conjunction with finite-size scaling analysis, have been used for characterizing its critical behavior; on the other hand, it has been found that nematic order does indeed set in at low temperatures, via a mechanism of order by disorder.

CO₂ Capture and Separation Properties in the Ionic Liquid 1-n-Butyl-3-Methylimidazolium Nonafluorobutylsulfonate

Recently, the use of ionic liquids (ILs) for carbon capture and separation processes has gained great interest by many researchers due to the high solubility of CO₂ in ILs. In the present work, solubility measurements of CO₂ in the novel IL 1-n-butyl-3-methylimidazolium nonafluorobutylsulfonate [C₄mim][CF₃CF₂CF₂CF₂SO₃] were performed with a high-pressure view-cell technique in the temperature range from 293.15 to 343.15 K and pressures up to about 4.2 MPa. For comparison, solubilities of H₂, N₂, and O₂ in the IL were also measured at 323.15 K via the same procedure. The Krichevsky-Kasarnovsky equation was employed to correlate the measured solubility data. Henry’s law constants, enthalpies, and entropies of absorption for CO₂ in the IL were also determined and presented. The CO₂ solubility in this IL was compared with other ILs sharing the same cation. It was shown that the solubility of CO₂ in these ILs follows the sequence: [C₄mim][CF₃CF₂CF₂CF₂SO₃] ≈ [C₄mim][Tf₂N] > [C₄mim][CF₃CF₂CF₂COO] > [C₄mim][BF₄], and the solubility selectivity of CO₂ relative to O₂, N₂, and H₂ in [C₄mim][CF₃CF₂CF₂CF₂SO₃] was 8, 16, and 22, respectively. Furthermore, this IL is regenerable and exhibits good stability. Therefore, the IL reported here would be a promising sorbent for CO₂.

Molecular insights into the promiscuous interaction of human pregnane X receptor (hPXR) with diverse environmental chemicals and drug compounds

The nuclear receptor member human pregnane X receptor (hPXR) regulates enzymes and transporters involved in xenobiotic detoxification as well as maintains homeostatic balance of bile acids, thyroid and steroid hormones. hPXR can be recognized and activated by a structurally diverse array of environmental chemicals and drug compounds to initiate adverse biological effects, such as perturbing normal physiological functions and causing dangerous drug-drug interactions and exhibiting a high promiscuity in its ligand spectrum. Understanding of the molecular mechanism and biological implication underlying the promiscuous interaction of hPXR with its diverse ligands is fundamentally important for toxicological and pharmaceutical researches. In the current study, molecular docking and hybrid quantum mechanics/molecular mechanics (QM/MM) were employed to investigate the binding mode, structural basis and energetic property of hPXR interactions with various activators and non-activators. It was found that, as compared to non-activators, the activators adopt few dominant modes to tightly interact with hPXR, which are specified by few polar spots located on the hydrophobic surface of hPXR active pocket. Based on the findings, a novel method called multiple binding mode-based quantitative structure-activity relationship (MBMB-QSAR) that characterizes the nonbonded interaction profile of hPXR with its ligand in multiple binding modes was proposed to model and predict the activating potency of small-molecule compounds on hPXR. Several partial least square (PLS) predictors derived from the MBMB-QSAR modeling were demonstrated to be effective for quantitative characterization of the biological behavior of experimentally confirmed activators, and for qualitatively differentiating the activators from a large number of non-activators. From the predictor models it is suggested that the hydrophobic force and electrostatic interaction play an important role in hPXR-ligand binding, while steric factor contributes moderately to the binding.

High-resolution absorption studies of the A(1)A2-X(1)A1 2(0)(2)4(0)(1) band of formaldehyde

Absolute peak absorption cross sections and pressure broadening coefficients have been recorded with sub-Doppler limited instrumental resolution for selected rotational lines in the 2(0)(2)4(0)(1) vibronic band of the formaldehyde A(1)A2-X(1)A1 electronic transition. The measured absorption cross sections range between (0.18 +/- 0.01) and (10.1 +/- 0.08) x 10(-19) cm2 molecule(-1) and are considerably larger than values from the literature recorded using apparatus where instrumental broadening was significant. However, comparisons with spectral simulations with equivalent resolution from Smith et al. (J. Phys. Chem. A 2006, 110, 11645-11653) are in excellent agreement. Pressure broadening was studied for the collision partners CH2O, CO2, N2, O2, Ne, Kr, Ar, and He, and the resulting broadening coefficients were found to be reduced in comparison to equivalent values measured in infrared regions, consistent with the reduced dipole moment of the upper state probed in this work. Cavity-enhanced absorption spectroscopy (CEAS) measurements were undertaken using calibrated low concentration (2.9-4.6 ppmv) samples from a permeation source and demonstrate a noise equivalent absorption of 1.2 x 10(-6) cm(-1) Hz(-1/2). This implies a minimum detectable formaldehyde concentration with the current system in atmospheric air of 172 ppbv Hz(-1/2).

Quadrupole, octopole, and hexadecapole electric moments of Sigma, Pi, Delta, and Phi electronic states: cylindrically asymmetric charge density distributions in linear molecules with nonzero electronic angular momentum

The number of independent components, n, of traceless electric 2(l)-multipole moments is determined for C(infinity v) molecules in Sigma(+/-), Pi, Delta, and Phi electronic states (Lambda=0,1,2,3). Each 2(l) pole is defined by a rank-l irreducible tensor with (2l+1) components P(m)((l)) proportional to the solid spherical harmonic r(l)Y(m)(l)(theta,phi). Here we focus our attention on 2(l) poles with l=2,3,4 (quadrupole Theta, octopole Omega, and hexadecapole Phi). An important conclusion of this study is that n can be 1 or 2 depending on both the multipole rank l and state quantum number Lambda. For Sigma(+/-)(Lambda=0) states, all 2(l) poles have one independent parameter (n=1). For spatially degenerate states--Pi, Delta, and Phi (Lambda=1,2,3)--the general rule reads n=1 for l<2/Lambda/ (when the 2(l)-pole rank lies below 2/Lambda/ but n=2 for higher 2(l) poles with l>or=2/Lambda/. The second nonzero term is the off-diagonal matrix element [formula: see text]. Thus, a Pi(Lambda=1) state has one dipole (mu(z)) but two independent 2(l) poles for l>or=2--starting with the quadrupole [Theta(zz),(Theta(xx)-Theta(yy))]. A Delta(Lambda=2) state has n=1 for 2((1,2,3)) poles (mu(z),Theta(zz),Omega(zzz)) but n=2 for higher 2((l>or=4)) poles--from the hexadecapole Phi up. For Phi(Lambda=3) states, it holds that n=1 for 2(1) to 2(5) poles but n=2 for all 2((l>or=6)) poles. In short, what is usually stated in the literature--that n=1 for all possible 2(l) poles of linear molecules--only applies to Sigma(+/-) states. For degenerate states with n=2, all Cartesian 2(l)-pole components (l>or=2/Lambda/) can be expressed as linear combinations of two irreducible multipoles, P(m=0)((l)) and P/m/=2 Lambda)((l)) [parallel (z axis) and anisotropy (xy plane)]. Our predictions are exemplified by the Theta, Omega, and Phi moments calculated for Lambda=0-3 states of selected diatomics (in parentheses): X (2)Sigma(+)(CN), X (2)Pi(NO), a (3)Pi(u)(C(2)), X (2)Delta(NiH), X (3)Delta(TiO), X (3)Phi(CoF), and X (4)Phi(TiF). States of Pi symmetry are most affected by the deviation from axial symmetry.

On the thermodynamic stability of hydrogen clathrate hydrates

The cage occupancy of hydrogen clathrate hydrate has been examined by grand canonical Monte Carlo (GCMC) simulations for wide ranges of temperature and pressure. The simulations are carried out with a fixed number of water molecules and a fixed chemical potential of the guest species so that hydrogen molecules can be created or annihilated in the clathrate. Two types of the GCMC simulations are performed; in one the volume of the clathrate is fixed and in the other it is allowed to adjust itself under a preset pressure so as to take account of compression by a hydrostatic pressure and expansion due to multiple cage occupancy. It is found that the smaller cage in structure II is practically incapable of accommodating more than a single guest molecule even at pressures as high as 500 MPa, which agrees with the recent experimental investigations. The larger cage is found to encapsulate at most 4 hydrogen molecules, but its occupancy is dependent significantly on the pressure of hydrogen.