The Electronic Structure of Dopamine. An ab initio Electrostatic Potential Study of the Catechol Moiety

Electronic properties of dopamine were studied by the ab initio STO-3G MO method. The molecular electrostatic potential (MEP) around the aromatic ring and the catechol group remains practically the same in 3,4-dihydroxytoluene (a model compound) and in neutral dopamine examined in its two extended conformations, namely that found in the crystal (side-chain and aromatic ring almost perpendicular) and the one corresponding to 2-amino-6,7-dihydroxytetralin (6,7-ADTN) (side-chain and aromatic ring almost coplanar). In protonated dopamine and in dopamine hydrochloride, the electrostatic potential of the catechol moiety is overshadowed by the positive charge, but the main features remain discernible. The catechol moiety was examined in its two coplanar conformations containing a ‘flip-flop H-bond’. The electrostatic potential around the catechol moiety is quite complex, with alternating positive and negative maxima. At increasing distances above and away from the catechol moiety, only two peripheral maxima, one negative and one positive, remain perceptible. The ‘flip-flop’ mechanism results in an approximate interchange of these two potential maxima, a fact which tends to level out the structural differences between the α- and β-rotamer of dopamine. Based on these results and on the structure of rigid agonists, some pharmacophoric features of dopamine agonists are proposed.     

Development of an Electrochemical Sensor for Selective Determination of Dopamine Based on Molecularly Imprinted Poly(p-aminothiophenol) Polymeric Film

In this study, a molecularly imprinted electrochemical sensor (MIP/DA) was investigated for selective and sensitive determination of dopamine (DA) by electrochemical polymerization of p-aminothiophenol in the presence of DA on gold electrode. According to electrochemical behaviour of the sensor, gained through cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS), MIP/DA sensor showed distinctive electron transfer characteristics in comparison to the non-imprinted (NIP/DA) sensor. Besides the MIP/DA sensor showed high selectivity for dopamine through its analyte specific cavities. The sensor had a broad working range of 5.0×10⁻⁸–2.0×10⁻⁷ M with a limit of detection (LOD) of 1.8×10⁻⁸ M and the developed sensor was successfully applied for determination of dopamine in pharmaceutical samples.     

Organic Stereochemistry. Part 5

This review continues a general presentation of the principles of stereochemistry with special reference to the medicinal sciences. Here, we discuss and illustrate molecular and clinical phenomena of stereoselectivity in pharmacological effects, namely activity differences between stereoisomers, principally enantiomers. The review begins with didactic models of chiral recognition, with a main focus on the early model of Easson and Stedman. There follows a Molecular Modeling (MM) and Molecular Dynamics (MD) depiction of the differential interaction of the enantiomers of hyoscyamine with cholinergic muscarinic receptors. The next section is devoted to various rationalizations in stereoselective pharmacological activity, e.g., the influence of optical purity on enantioselectivity, Pfeiffer's rule, and eudismic analysis. The review ends with selected examples taken from various fields of preclinical and clinical pharmacology, of differences between stereoisomers in terms of drug absorption, distribution, and excretion. The influence of conformational factor in molecular pharmacology will be discussed in Part 6, while stereoselective aspects of xenobiotic metabolism will be reviewed in Parts 7 and 8.     

A central partition of molecular conformational space. IV. Extracting information from the graph of cells

In previous works (Gabarro-Arpa, J. Math. Chem. 42 (2006) 691–706) a procedure was described for dividing the 3 × N-dimensional conformational space of a molecular system into a number of discrete cells, this partition allowed the building of a combinatorial structure from data sampled in molecular dynamics trajectories: the graph of cells or G, that encodes the set of cells in conformational space that are visited by the system in its thermal wandering. Here we outline a set of procedures for extracting useful information from this structure: (1st) interesting regions in the volume occupied by the system in conformational space can be bounded by a polyhedral cone, whose faces are determined empirically from a set of relations between the coordinates of the molecule, (2nd) it is also shown that this cone can be decomposed into a set of smaller cones, (3rd) the set of cells in a cone can be encoded by a simple combinatorial sequence.     

Simultaneous Determination of Epinephrine and Dopamine by Using Candida tropicalis Yeast Cells Immobilized in a Carbon Paste Electrode Modified with Single Wall Carbon Nanotube

A new electrochemical microbial biosensor system based on Candida tropicalis was developed for the fast detecting of dopamine and epinephrine. Candida tropicalis was immobilized in a carbon paste electrode (CPE) with single wall carbon nanotube (SWCNT). Immobilized cells were used as a origin of the polyphenol oxidase (PPO) to develop voltammetric epinephrine and dopamine biosensor. Voltammetric determination of phenolic compounds such as epinephrine and dopamine a simple technique which is available. Direct oxidation of phenols can be used, but the oxidation potentials of this compounds are similar and they can not be detected distinctively. Another possibility is the use of biosensors based on the polyphenol oxidase (tyrosinase) enzyme that oxidizes the phenolic compounds into their related quinones. By this way, phenolic compounds are epinephrine and dopamine which were used in this study as well detected at different potentials. In this study differential pulse voltammetry and amperometry techniques were used for the determination of dopamine and epinephrine. The effect of varying the amounts of SWCNT and the response of microorganism to epinephrine was investigated to find the optimum composition of the sensor. The effects of pH and temperature were also examined. Increases in biosensor responses obtained by amperometric measurements were linearly related to dopamine concentrations between 0.025 and 0.25 mM and epinephrine concentrations between 0.01 and 0.1 mM. Limits of detection of the biosensor for dopamine and epinephrine were calculated to be 0.008 and 0.0023 mM, respectively. Finally, proposed system was applied to epinephrine and dopamine analysis in pharmaceutical drugs and synthetic serum and the results were compared with LC MS MS method.     

Low nM Detection Limits at Porous 1–3 nm Thick Membrane‐Coated Nanostructured Microdisk Electrodes

Low (15 nM) limits of detection (LOD) of dopamine were obtained at porous 1–3 nm‐thick overoxidized polypyrrole (OPPY) membrane‐coated microdisk carbon fiber electrodes of small size (r=3.5 µm). The excellent mass transport through the porous OPPY membrane (efficiency as good as solution transport) contributes to the low LOD, together with dopamine preconcentration in the membrane. Structural characterization of the membrane coated electrodes confirms the contribution of membrane nanostructure to the high sensitivity and the low LOD.     

Theoretical studies of the mechanism of the action of the neurohypophyseal hormones. I. Molecular electrostatic potential (MEP) and molecular electrostatic field (MEF) maps of some vasopressin analogues

Summary Continuing our theoretical studies of the oxytocin and vasopressin analogues, we have analysed the molecular electrostatic potential (MEP) and the norm of the molecular electrostatic field (MEF) of [1--mercaptopropionic acid]-arginine-vasopressin ([Mpa¹]-AVP), [1-(-mercapto-,-cyclopentamethylene)propionic acid]-arginine-vasopressin ([Cpp]-AVP), and [1-thiosalicylic acid]-arginine-vasopressin ([Ths]-AVP) whose low-energy conformations were calculated in our previous work. These compounds are known from experiment to exhibit different biological activity. The scalar fields mentioned determine the energy of interaction with either charged (MEP) or polar (MEF) species, the energy being in the second case either optimal or Boltzmann-averaged over all the possible orientations of the dipole moment versus the electrostatic field. The electrostatic interactions slowly vanish with distance and can therefore be considered to be the factor determining the molecular shape at greater distances, which can help in both predicting the interactions with the receptor at the stage of remote recognition and in finding the preferred directions of solvation by a polar solvent. In the analysis of the fields three techniques have been used: (i) the construction of maps in certain planes; (ii) the construction of maps on spheres centered in the charge center of the molecule under study and of poles chosen according to the main axes of the quadrupole moment; and (iii) the construction of surfaces corresponding to a given value of potential. The results obtained show that the shapes of both MEP and MEF are similar in the case of [Mpa¹]-AVP and [Cpp¹-AVP (biologically active), while some differences emerge when comparing these compounds with [Ths¹]-AVP (inactive). It has also been found that both MEP and MEF depend even more strongly on conformation.     

Electrochemical Determination of Dopamine Using a Poly(3,4-Ethylenedioxythiophene)-Reduced Graphene Oxide-Modified Glassy Carbon Electrode

Poly(3,4-ethylenedioxythiophene) was deposited on a reduced graphene oxide-decorated glassy carbon electrode through an electrochemical polymerization. The resulting glassy carbon electrode-reduced graphene oxide-poly(3,4-ethylenedioxythiophene) electrode was applied as an electrochemical biosensor for the determination of dopamine in the presence of ascorbic acid and uric acid. The material deposited on glassy carbon electrode was investigated in terms of morphology and structural analysis. The comparison of electrochemical behavior of the glassy carbon electrode-reduced graphene oxide-poly(3,4-ethylenedioxythiophene) electrode with the glassy carbon electrode-graphene oxide, glassy carbon electrode-reduced graphene oxide, and glassy carbon electrode-poly(3,4-ethylenedioxythiophene) electrodes exhibited high electrocatalytic activity for dopamine detection. Electrochemical kinetic parameters of glassy carbon electrode-reduced graphene oxide-poly(3,4-ethylenedioxythiophene), including the charge transfer coefficient α (0.49) and electron transfer rate constant k_s (1.04), were determined and discussed. The glassy carbon electrode-reduced graphene oxide-poly(3,4-ethylenedioxythiophene) electrode was studied for the determination of dopamine by differential pulse voltammetry and exhibited a linear range from 19.6 to 122.8?µM with a sensitivity of 3.27?µA?µM^?1?cm^?2 and a detection limit of 1.92?µM. The developed biosensor exhibited good selectivity toward dopamine with high reproducibility and stability.     

The effect of N‐acetylcysteine on amphetamine‐mediated dopamine release in rat brain striatal slices by ion‐pair reversed‐phase high performance liquid chromatography

The amphetamine (AMPH)‐induced alteration in rat brain dopamine levels modified by N‐acetylcysteine (NAC) administration has been examined using isocratic ion‐pair reversed‐phase high‐performance liquid chromatography with electrochemical detection. The aim of the development of a novel validated evaluation scheme implying a double AMPH challenge was to enhance the efficiency of AMPH‐triggered dopamine release measurements in rat brain striatal slices by improving the reproducibility of the results. The proposed experimental protocol was tested in vivo and proved to be capable of fast and reliable drug screening for tracing the effect of NAC as a model compound in AMPH‐mediated dopaminergic response. The subcellular localization of the dopamine mobilizing effect of NAC has been established indirectly by the use of an irreversible dopamine vesicular depletor, reserpine. The antioxidant NAC at 10 mm plays an important role in the complete suppression of acute AMPH‐elicited dopamine release. The possible role of this quenching effect is discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Inside Back Cover: Electronic Control of the Scholl Reaction: Selective Synthesis of Spiro vs Helical Nanographenes (Angew. Chem. Int. Ed. 7/2023)

Scholl oxidation has become an essential reaction in the bottom-up synthesis of molecular nanographenes. Herein, we describe a Scholl reaction controlled by the electronic effects on the starting substrate ( 1 a , b ). Anthracene-based polyphenylenes lead to spironanographenes under Scholl conditions. In contrast, an electron-deficient anthracene substrate affords a helically arranged molecular nanographene formed by two orthogonal dibenzo[fg,ij]phenanthro-[9,10,1,2,3-pqrst]pentaphene (DBPP) moieties linked through an octafluoroanthracene core. Density Functional Theory (DFT) calculations predict that electronic effects control either the first formation of spirocycles and subsequent Scholl reaction to form spironanographene 2 , or the expected dehydrogenation reaction leading solely to the helical nanographene 3 . The crystal structures of four of the new spiro compounds (syn 2 , syn 9 , anti 9 and syn 10 ) were solved by single crystal X-ray diffraction. The photophysical properties of the new molecular nanographene 3 reveal a remarkable dual fluorescent emission.     

左苯丙胺在多巴胺第三受体分子通道中传输分子动力学模拟

左旋苯丙胺(又称左苯丙胺, RAT)在临床上被用于治疗多种病症,作用在中枢神经细胞多巴胺受体上,同时它具有依赖性和成瘾性。为了探讨RAT被用作药物的药理和成瘾机制,本文用分子模拟获得RAT与多巴胺第三受体(D₃R)复合蛋白优化结构,并且采用伞形样本平均力势(PMF)方法和卵磷脂脂质分子模拟生物膜,采用分子动力学模拟获得RAT在D₃R结构中分子通道运动轨迹和自由能变化。RAT通过D₃R结构中的功能分子通道,朝细胞外方向传输运动的自由能变化为91.4 kJ·mol^-1。RAT通过D₃R结构中的保护分子通道,朝细胞双层膜方向传输运动的自由能变化为117.7 kJ·mol^-1。自由能数值表明RAT分子更容易通过D₃R结构中的功能分子通道,发挥其功能作用,增大功能多巴胺分子的释放,导致包括依赖性和成瘾性多种功能效果。研究结果证明RAT被用作药物的药理和成瘾机制与它在多巴胺受体中的分子通道上传输动力学和机制有密切关联。     

Localized Orbitals vs. Pseudopotential-Plane Waves Basis Sets: Performances and Accuracy for Molecular Magnetic Systems

 Density functional theory, in combination with a) a careful choice of the exchange-correlation part of the total energy and b) localized basis sets for the electronic orbitals, has become the method of choice for calculating the exchange-couplings in magnetic molecular complexes. Orbital expansion on plane waves can be seen as an alternative basis set especially suited to allow optimization of newly synthesized materials of unknown geometries. However, little is known on the predictive power of this scheme to yield quantitative values for exchange coupling constants J as small as a few hundredths of eV (50–300 cm⁻¹). We have used density functional theory and a plane waves basis set to calculate the exchange couplings J of three homodinuclear Cu-based molecular complexes with experimental values ranging from +40 cm⁻¹ to −300 cm⁻¹. The plane waves basis set proves as accurate as the localized basis set, thereby suggesting that this approach can be reliably employed to predict and rationalize the magnetic properties of molecular-based materials. Corresponding author. E-mail: Carlo.Massobrio@ipcms.u-strasbg.fr Received August 5, 2002; accepted August 9, 2002     

Study of a fluorescence quenching mechanism of enoxacin and its determination in human serum and urine samples

The maximum emission wavelength of dopamine is 317 nm with excitation at 290 nm. The relative fluorescence intensity of dopamine decreased in the presence of enoxacin, which showed that fluorescence quenching occurred. The Stern-Volmer (S-V) plot showed a nonlinear relationship between the relative fluorescence intensity of dopamine and the concentration of enoxain. The quenching mechanism was studied and the results suggested that both dynamic and static quenching processes were responsible for the observed positive deviation in the S-V plot. When the S-V plot was modified by logarithm, the linear relationship was obtained between logF ₀/F and C in the range of 0.10 to 13.0 μg/mL (where F ₀ is the relative fluorescence intensity of dopamine, F is the relative fluorescence intensity of dopamine in the presence of enoxacin, and C is the concentration of enoxacin). The fluorescence quenching method for the determination of enoxacin was developed. The linear regression equation of the calibration graph of enoxacin was C = 13.70 (logF ₀/F) − 0.5836, with the correlation coefficient 0.9984. The detection limit was 2.0 ng/mL and the relative standard deviation was 2.52%. The effects of pH, the stability of dopamine in the presence of enoxacin, and foreign ions on the determination of enoxacin have been examined. The recovery of enoxacin was from 94.9 to 103.0% in a human serum sample and from 94.9 to 108.0% in a urine sample. The method is simple, rapid, and can be used for the determination of enoxacin in human serum and urine samples with satisfactory results. The text was submitted by the authors in English.     

The Role of Binary and Many-centre Molecular Interactions in Spin Crossover in the Solid State. Part II. Non-ideality Parameters Defined via Binary Molecular Potentials

Summary. Parameters of the formalism [1–6] describing spin crossover in the solid state have been defined via molecular potentials in model systems of neutral and ionic complexes. In the first instance Lennard-Jones and electric dipole–dipole potentials have been used whereas in ionic systems Lennard-Jones and electric point-charge potentials have been used. Electric dipole–dipole interaction of neutral complexes brings about a positive excess energy controlled by the difference of electric dipole moments of HS and LS molecules. Differences of the order of Δμ = 1–2 D cause an abrupt spin crossover in systems with T_1/2 = 100–150 K. Magnetic coupling contributes both to the excess energy and excess entropy, however the overall effect is equivalent to a modest positive excess energy. Ionic systems in the absence of specific interactions are characterised by very small excess energies corresponding to practically linear van’t Hoff plots. Detectable positive and negative excess energies in these systems may arise from interactions of ligands belonging to neighbouring complexes. The HOMO–LUMO overlap in HS–LS pairs can bring about a nontrivial variation of the shape of transition curves. Examples of regression analysis of experimental transition curves in terms of molecular potentials are given.     

Doubly Modified Electrodes for the Selective Determination of Dopamine in the Presence of Interfering Species

In this paper, we describe the double modification of the glassy carbon electrode surface with two polymer layers for the selective determination of dopamine. The first layer was the electropolymerized macrocyclic nickel complex acting as an electrocatalyst for the dopamine oxidation and the second layer the polyurethane benzyl L ‐glutamate (PUBLG) for screening interfering species. Hydrolyzed PUBLG (PU‐C) showed a better screening effect. Thus prepared GC/Ni(II) complex film/PU‐C electrodes exhibited improved selectivity and better performance than unmodified counterparts, with minimum passivation even in the presence of large excess of interferents. Under optimal conditions, these electrodes showed a linear response over a dopamine concentration range of 2.5×10^?7 and 3.0×10^?5 M with a correlation coefficient of 0.999 and detection limit (at S/N=3) of 8.0×10^?8 M. The recoveries of dopamine in the 5‐fold diluted human urine sample were 96.9% for 4 measurements. The rate constant for the dopamine oxidation measured by the rotating disk electrode was found to be 1.1×10^?3 cm s^?1.     

Thiol–Yne Click Reactions on Alkynyl–Dopamine‐Modified Reduced Graphene Oxide

The large‐scale preparation of graphene is of great importance due to its potential applications in various fields. We report herein a simple method for the simultaneous exfoliation and reduction of graphene oxide (GO) to reduced GO (rGO) by using alkynyl‐terminated dopamine as the reducing agent. The reaction was performed under mild conditions to yield rGO functionalized with the dopamine derivative. The chemical reactivity of the alkynyl function was demonstrated by post‐functionalization with two thiolated precursors, namely 6‐(ferrocenyl)hexanethiol and 1H,1H,2H,2H‐perfluorodecanethiol. X‐ray photoelectron spectroscopy, UV/Vis spectrophotometry, Raman spectroscopy, conductivity measurements, and cyclic voltammetry were used to characterize the resulting surfaces.     

Molecular mechanical and quantum chemical study of the species involved in the hydrolysis ofcis-diamminedichloroplatinum(II) and substitutedbis(ethylenediamine)-dichloroplatinum(II) complexes II. Simulated transition states

Summary cis-Diamminedichloroplatinum(II) (cisplatin) and its substituted ethylenediamine derivativescis-PtCl₂(R ₂ en) (en=ethylenediamine,R=H,Ph,2-,3-, and 4-PhOH) have been investigated with respect to the possible structures of the hypothetical Transition State Complexes (TSC) of the hydrolytic S_N2 reaction in which one Cl is replaced by H₂O.TSCs withtrigonal bipyramid (TBP) andsquare pyramid (SP) geometry (coordination number 5), have been studied by Molecular Mechanics (MM) and ExtendedHückel (EH) methods. TheEH andMM energies as well as the number of occurrence (entropy factor) for the cisplatinum compound point to a preferredTBP TSC geometry with NH₃ and Cl in axial positions. However, foren and substituteden compounds,TSCs withSP geometries (Cl in apical position) are preferred. The calculatedEH andMM energies of theTBP andSP structures do not differ significantly andTBP SP interconversions may play an essential role inTSC formation. To improve the discrimination, theMM-optimized geometries were treated in terms of displacement coordinates for D_3h (TBP) and C_4v (SP) by calculating the total distortion vectors (DV).DV identified once again theTBP with NH₃ and Cl in axial position as the least-distorted conformer, but it also revealed the combinations of displacement coordinates which shape theTSC geometry.

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Molekularmechanische und quantenchemische Untersuchung der bei der Hydrolyse voncis-Diammindichlorplatin(II) und substituiertenBis(ethylendiamin)dichlorplatin(II)-Komplexen auftretenden Spezies, 2. Mitt. Simulierte Übergangszustände

Zusammenfassung cis-Diammindichlorplatin(II) (Cisplatin) und seine substituierten Ethylendiaminderivatecis-PtCl₂(R ₂ en) (en=Ethylendiamin,R=H, Ph, 2-, 3- und 4-PhOH) wurden im Hinblick auf mögliche Strukturen der hypothetischen Übergangszustandkomplexe (TSC) der hydrolytische S_N2-Reaktion (Substitution eines Cl-Atoms durch H₂O) untersucht.TSCs mit trigonalbipyramidalen (TBP) und quadratisch-pyramidalen (SP) Geometrien (Koordinationszahl 5) wurden mit molekularmechanischen (MM) und Extended-Hückel-Methoden (EH) behandelt.EH- undMM-Energien sowie entropische Faktoren weisen für Cisplatin auf eine trigonale Bipyramide mit NH₃ und Cl in axialen Positionen als bevorzugteTSC-Geometrie hin, während für Komplexe miten-LigandenSP-Geometrien mit Cl in der apicalen Position energetisch begünstigt sind. Da die berechnetenEH- undMM- Energien fürTBP- undSP-Geometrien sehr ähnlich sind, spielen möglicherweiseTBP-SP-Umwandlungen eine wesentliche Rolle bei der Bildung derTSCs. Zur Verbesserung der Unterscheidung wurden für dieMM-optimierten Geometrien die Verschiebungsvektoren (DV) bezüglich D_3h (TBP) und C_4v (SP) berechnet. Daraus resultierte erneut die trigonale Bipyramide mit NH₃ und Cl in den axialen Positionen als das am wenigsten gespannte Konformere; des weiteren konnten mit dieser Methode die Kombinationen der Verschiebungskoordinaten erhalten werden, die für die Ausbildung derTSC-Geometrie verantwortlich sind.

     

Behavior of ethylene and ethane within single-walled carbon nanotubes. 1-Adsorption and equilibrium properties

Endohedral adsorption properties of ethylene and ethane onto single-walled carbon nanotubes were investigated using a united atom (2CLJQ) and a fully atomistic (AA-OPLS) force fields, by Grand Canonical Monte Carlo and Molecular Dynamics techniques. Pure fluids were studied at room temperature, T=300 K, and in the pressure ranges 4×10⁻⁴<p<47.1 bar (C₂H₄) and 4×10⁻⁴<p<37.9 bar (C₂H₆). In the low pressure region, isotherms differ quantitatively depending on the intermolecular potential used, but show the same qualitative features. Both potentials predict that ethane is preferentially adsorbed at low pressures, and the opposite behavior was observed at high loadings. Isosteric heats of adsorption and estimates of low pressure Henry’s constants, confirmed that ethane adsorption is the thermodynamically favored process at low pressures. Binary mixtures of C₂H₄/C₂H₆ were studied under several (p,T) conditions and the corresponding selectivities towards ethane, S, were evaluated. Small values of S<4 were found in all cases studied. Nanotube geometry plays a minor role on the adsorption properties, which seem to be driven at lower pressures primarily by the larger affinity of the alkane towards the carbon surface and at higher pressures by molecular volume and packing effects. The fact that the selectivity towards ethane is similar to that found earlier on carbon slit pores and larger diameter nanotubes points to the fact that the peculiar 1-D geometry of the nanotubes provides no particular incentive for the adsorption of either species.     

Inclusion of Poly(ethylene glycol)s by Crystalline (R)-(1-Naphthyl)glycyl-(R)-phenylglycine

Abstract

Crystallization of (R)-(1-naphthyl)glycyl-(R)-phenyl-glycine [(R,R)-1] in the presence of oligo(ethylene glycol) dimethyl ethers 2(n) or poly(ethylene glycol)s (PEGs, 3(M_n )) afforded inclusion compounds. The ratio of (R,R)-1/the guest polymer (2 or 3) was proportional to the length of the polymer chain. The crystal structure of a hepta(ethylene glycol) dimethyl ether-included compound was disclosed by X-ray crystallography which showed that (R,R)-1 molecules form a sheet and the guest molecule penetrates the crystal lattice of (R,R)-1 through a one-dimensional channel on the sheet. Powder X-ray analysis revealed that, regardless of the length of the guest polymer, the distance between the neighboring sheets remains unchanged (12.0–12.3 Å) in these inclusion crystals. By thermal analysis, it was shown that the decomposition points of these inclusion compounds became higher with the longer PEG included. The inclusion phenomenon enabled the fractionation of PEGs with various molecular weights, among which longer PEG was preferably included.