Nested wreath groups and their applications to phylogeny in biology and Cayley trees in chemistry and physics

Nested wreath product groups arise from looped or recursive structures that contain repeated copies of the same structure one within the other. Phylogeny trees in biology, Cayley trees, Bethe lattices, NMR graphs of non-rigid molecules, ammoniated ammonium ions are all examples of structures that exhibit such nested wreath product automorphism groups. We show that the conjugacy classes, irreducible representations and character tables of these nested group structures can be generated using multinomial generating functions cast in terms of matrix types that can be simplified into generalized cycle type polynomials. The nested wreath product groups rapidly increase in orders, for example, a simple wreath product group \(\hbox {S}_{7}[\hbox {S}_{7}]\) consists of \((7!)^{8}\) or \(4.1633\times 10^{23}\) operations, 481,890 conjugacy classes, spanning a 481,891 \(\times \) 481,891 character table that would occupy 232,217,972 pages. We have obtained powerful recursive relations for the conjugacy classes, character tables and the orders of various conjugacy cases of any nested wreath product \(\{[\hbox {S}_{\mathrm{n}}]\}^{\mathrm{m}}\) or \(\hbox {S}_{\mathrm{n}}[\hbox {S}_{\mathrm{n}}[\hbox {S}_{\mathrm{n}}{\ldots }.[\hbox {S}_{\mathrm{n}}]]{\ldots }.]\) with order \(\left( {n!}\right) ^{a_m},\,\hbox {a}_{\mathrm{m}}=(\hbox {n}^{\mathrm{m}}-1)/(\hbox {n}-1)\). We have obtained the character tables of phylogenetic trees of any order, character tables of Cayley trees of degrees 3 and 4 and for Cayley trees of larger degrees, we have derived exact analytical expressions for the conjugacy classes and IRs for up to \(\{[\hbox {S}_{7}]\}^{\mathrm{m}}\) with order \((7!)^{137257}\) for \(\hbox {m}=7\). Applications to colorings of phylogenic trees in biology are considered.     

Surface Oxidation of Supported,Size-Selected Silver Clusters

We use surface second harmonic generation spectroscopy to study the oxidation of supported, size-selected silver clusters under ultra-high vacuum conditions. The oxidation reaction of small silver clusters between \(Ag_{9}\) and \(Ag_{55}\) is monitored by means of their localized surface plasmon resonance. We observe a rapid decline of the SH-intensity, as soon as cluster samples are exposed to an oxygen partial pressure of \(5 \cdot 10^{-6}\) mbar, which is attributed to the formation of silver–oxygen-bonds. The evolution of the SH-intensity under exposure to oxygen shows a double-exponential character for all investigated cluster sizes. Since the oxidation of single crystalline silver surfaces follow single-exponential Langmuir-kinetics, the two independent pathways of SH-intensity loss are attributed to a surface- and an interface-oxidation of supported clusters, respectiveley. For small cluster sizes, a complete loss of the SH intensity is obtained, which suggests the complete oxidation of the clusters. For larger clusters a plasmonic resonance is still observed after oxidation, indicating a residual free-electron density.     

Single carbon dioxide molecules on surfaces studied by low-temperature scanning tunneling microscopy

The chemical conversion of carbon dioxide (\(\hbox {CO}_2\)) has been intensively studied because the molecule is responsible for global warming. Rational design of catalysts plays an important role in converting \(\hbox {CO}_2\) into value-added compounds. Understanding the interaction between \(\hbox {CO}_2\) and surfaces of catalysts is a prerequisite to preparing high-performance catalysts. This review focuses on the investigations of \(\hbox {CO}_2\) molecules on single crystalline surfaces studied by low-temperature scanning tunneling microscopy. Molecular adsorption, diffusion, and conversion on metal surfaces, metal oxide surfaces, and surfaces decorated by metal-organic frameworks are summarized.     

Vibratio nal assig nme nts,co nformatio nal a nalysis,a nd molecular structures of $$\left[ {\text{C}_{\text{ n}} \text{mim}} \right]\left[ {\text{NTF}_{\text{2}} } \right]$$C nmimNTF2 ( n = 2, 4, 6, a nd 8) imidazolium-based io nic liquids: a combi ned experime ntal a nd qua ntum chemical approach

This work is aimed at providing physical insights about the interactions of cations, anion, and ion pairs of four imidazolium-based ionic liquids of \(\left[ {{\text{C}}_{\text{n}} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\) with varying alkyl chain lengths (n = 2, 4, 6, and 8) using both DFT calculations and vibrational spectroscopic measurements (IR absorption and Raman scattering) in the mid- and far regions. The calculated Mulliken charge distributions of \(\left[ {{\text{C}}_{\text{n}} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\) ion pairs indicate that hydrogen-bonding interactions between oxygen and nitrogen atoms (more negative charge) on \(\left[ {{\text{NTF}}_{2} } \right]^{ - }\) anion and the hydrogen atoms (more positive charge) on the imidazolium ring play a dominating role in the formation of ion pair. Thirteen stable conformers of \(\left[ {{\text{C}}_{2} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\) were optimized. According to our results, the strongest and weakest hydrogen bonds were existing in \(\left[ {{\text{C}}_{2} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\) and \(\left[ {{\text{C}}_{8} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\), respectively. A redshift of 290, 262, 258, and 257 cm^?1 has been observed for cations involving \(\left[ {{\text{C}}_{2} {\text{mim}}} \right]^{ + }\), \(\left[ {{\text{C}}_{4} {\text{mim}}} \right]^{ + }\),\(\left[ {{\text{C}}_{6} {\text{mim}}} \right]^{ + }\), and stretching vibrations of \({\text{C}}12{-}{\text{H}}3\), respectively. By increasing the chain length, the strength of hydrogen bonds decreases as a result of \({\text{C}}12{-}{\text{H}}3\) bond elongation and less changes are observed in stretching vibrations of \({\text{C}}12{-}{\text{H}}3\) compared to the free cations. To the best of our knowledge, this research is the first work which reports the far-IR of \(\left[ {{\text{C}}_{4} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\), \(\left[ {{\text{C}}_{6} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\), and \(\left[ {{\text{C}}_{8} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\) and the mid-IR of \(\left[ {{\text{C}}_{8} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\).     

Determination of the Distribution of Cobalt-Chloro Complexes in Hydrochloric Acid Solutions at 298 K

Knowledge of the distribution of metal-chloro complexes in hydrochloric acid solutions is fundamental for understanding the anion-exchange reaction. Anion-exchange separation allows ultrahigh purification during hydrometallurgical processes. However, at present the exchange reactions are not understood in detail. A more sophisticated purification needs improvement of the anion-exchange separation process. The process is based upon anion-exchange reactions and the distribution of metal-chloro complexes. The present work deals with cobalt-chloro complexes which exhibit a beautiful deep blue color in a concentrated hydrochloric acid solution. The intensity of the absorption attributed to the deep blue color is so strong that it is hard to obtain meaningful results by factor analysis. Another absorption band was chosen to be used in factor analysis and the attempt was successful. The number of cobalt-chloro complexes in hydrochloric acid solutions was determined to be three, and the cumulative formation constants were fitted to absorption spectra decomposed by factor analysis. During the optimization of the cumulative formation constants, a modified Debye–Hückel model for estimation of the activity coefficients of \(\hbox {Cl}^{-}\) was used. It was found that there are three cobalt complexes \([\hbox {Co}^{\mathrm{II}}(\hbox {H}_{2}\hbox {O})_{6}]^{2+}\), \([\hbox {Co}^{\mathrm{II}}\hbox {Cl}(\hbox {H}_{2}\hbox {O})_{5}]^{+}\), and \([\hbox {Co}^{\mathrm{II}}\hbox {Cl}_{4}]^{2-}\), and the two cumulative formation constants were optimized such that \(\log _{10}\beta _{1} = -\,0.861\) and \(\log _{10}\beta _{4} = -\,7.40\). The geometries of the complexes are proposed by assignment of absorption bands using ligand field theory. A qualitative assessment of the relationship between the acquired distribution of cobalt-chloro complexes and the adsorption function of cobalt species from hydrochloric acid solutions to anion-exchange resin was made.     

Transition-metal dichalcogenide heterostructure solar cells: a numerical study

We evaluate the tunneling short-circuit current density \(J_{TU}\) in a p–i–n solar cell in which the transition metal dichalcogenide heterostructure (\(\hbox {MoS}_2/\hbox {WS}_2\) superlattice) is embedded in the intrinsic i region. The effects of varying well and barrier widths, Fermi energy levels and number of quantum wells in the i region on \(J_{TU}\) are examined. A similar analysis is performed for the thermionic current \(J_{TH}\) that arises due to the escape and recapture of charge carriers between adjacent potential wells in the i-region. The interplay between \(J_{TU}\) and \(J_{TH}\) in the temperature range (300–330 K) is examined. The thermionic current is seen to exceed the tunneling current considerably at temperatures beyond 310 K, a desirable attribute in heterostructure solar cells. This work demonstrates the versatility of monolayer transition metal dichalcogenides when utilized as fabrication materials for van der Waals heterostructure solar cells.     

Structural,Energetic, and Magnetic Properties of Ag$$_{}$$Rh$$_{m}$$m and Ag$$_{m}$$mRh$$_{}$$ Clusters with $$n \le 20$$n≤20 and $$m=0,1$$m=0,1

At first, a genetic algorithm in combination with either the parametrized density-functional tight-binding method or a Gupta-potential is used to determine the putative global minimum energy structures of mixed Ag\(_{n-m}\)Rh\(_{m}\) and Ag\(_{m}\)Rh\(_{n-m}\) clusters with \(n\le 20\) and \(m=0,1\). Subsequently, the resulting structures are re-optimized with a first-principles method. The results demonstrate that the exchange of a single silver atom by rhodium leads to compact core-shell-like structures with structural motifs well known from the Lennard-Jones system. For the systems of the present study, AgRh\(_{n-1}\) clusters retain their cube-based structural motif and the silver atoms typically avoid the corner positions within a cube if possible. Population analysis of both cluster systems shows that the total magnetic moment is mainly due to unpaired electrons on the rhodium atoms with a small ferro-magnetic contribution of the silver host in Ag\(_{n-1}\)Rh and virtually no contribution to the total magnetic moment from the single silver atom in AgRh\(_{n-1}\) clusters.     

Exact solutions and coherent states for a generalized potential

Exact solutions of the vibrational Schrödinger equation for a generalized potential energy function \(\hbox {V(R)}=\hbox {C}_{0}(\mathrm{{R}-\mathrm {R}}_{\mathrm{e}})^{2}/[\hbox {aR}\,+\,(\mathrm{{b}-\mathrm {a}})\hbox {R}_{\mathrm{e}}]^{2}\) are obtained. It includes those of Dunham, Ogilvie and Simons–Parr–Finlan potentials as special cases corresponding to b \(=\) 1, a \(=\) 0, 1/2, 1, respectively. The analytical wave functions derived are useful to test the quality of numerical methods or to perform perturbative or variational calculations for the problems that cannot be solved exactly. Coherent states for generalized potential, which minimize the position–momentum uncertainty relation are also constructed.     

Solubility Thermodynamics of CyMe$$_{}$$-BTBP in Various Diluents Mixed with TBP

The two organic ligands 6,6′-bis(5,5,8,8-tetramethyl-5,6,7,8-tetrahydrobenzo[1,2,4]triazin-3-yl)[2,2′]bipyridine (CyMe\(_{4}\)-BTBP) and tri-butyl phosphate (TBP) have previously been investigated in different diluents for use within recycling of used nuclear fuel through solvent extraction. The thermodynamic parameters, \(K_{\mathrm{S}}\), \(\Delta C_{p}\), \(\Delta H^{0}\) and \(\Delta S^{0}\), of the CyMe\(_{4}\)-BTBP solubility in three diluents (cyclohexanone, octanol and phenyl trifluoromethyl sulfone) mixed with TBP have been studied at 288, 298 and 308 K, both as pristine solutions and pre-equilibrated with 4 mol\(\cdot \)L\(^{-1}\) nitric acid. In addition, the amount of acid in the organic phase and density change after pre-equilibration have been measured. The solubility of CyMe\(_{4}\)-BTBP increases with an increased temperature in all systems, especially after acid pre-equilibration. This increased CyMe\(_{4}\)-BTBP solubility after pre-equilibration could be explained by acid dissolution into the solvent. Comparing the \(\Delta H^{0}\) and \(\Delta S^{0}\) calculated using \(\Delta C_{p}\) with the same parameters derived from a linear fit indicates temperature independence of all three thermodynamic systems. The change in enthalpy is positive in all solutions.     

Experimental Research of OH and N<Stack><Subscript>2</Subscript><Superscript>+</Superscript></Stack> Spatially Resolved Spectra in a Needle-Plate Pulsed Streamer Discharge

In this study, the spatial distributions of the emission intensity of OH (\(\hbox{A}^{2}\Upsigma {\rightarrow}\hbox{X}^{2}\Uppi,\) 0-0) and \(\hbox{N}_{2}^{+} (\hbox{B}^{2}\Upsigma_{\rm u}^{+}\rightarrow \hbox{X}^{2}\Upsigma_{\rm g}^{+},\) 0-0, 391.4 nm) are investigated in the atmospheric pressure pulsed streamer discharge of H₂O and N₂ mixture in a needle-plate reactor configuration. The effects of pulsed peak voltage, pulsed repetition rate, input power, and O₂ flow rate on the spatial distributions of the emission intensity of OH (\(\hbox{A}^{2}\Upsigma {\rightarrow}\hbox{X}^{2}\Uppi,\) 0-0), \(\hbox{N}_{2}^{+} (\hbox{B}^{2}\Upsigma _{\rm u}^{+} \rightarrow \hbox{X}^{2}\Upsigma _{\rm g}^{+},\) 0-0, 391.4 nm), and the vibrational temperature of N₂ (C) in the lengthwise direction from needle to plate are attained. It is found that the emission intensities of OH (\(\hbox{A}^{2}\Upsigma {\rightarrow}\hbox{X}^{2}\Uppi,\) 0-0) and \(\hbox{N}_{2}^{+} (\hbox{B}^{2}\Upsigma_{\rm u}^{+} \rightarrow \hbox{X}^{2}\Upsigma_{\rm g}^{+},\) 0-0, 391.4 nm) rise with increasing the pulsed peak voltage, the pulsed repetition rate and the input power, and decrease with increasing O₂ flow rate. In the direction from needle to plate, the emission intensity of OH (\(\hbox{A}^{2}\Upsigma {\rightarrow}\hbox{X}^{2}\Uppi,\) 0-0) decreases firstly, and rises near the plate electrode, while the emission intensity of \(\hbox{N}_{2}^{+}(\hbox{B}^{2}\Upsigma_{\rm u}^{+} \rightarrow \hbox{X}^{2}\Upsigma_{\rm g}^{+},\) 0-0, 391.4 nm) is nearly constant along the needle to plate direction firstly, and rises sharply near the plate electrode. The vibrational temperature of N₂ (C) is almost independent of the pulsed peak voltage and the pulsed repetition rate, but rises with increasing the O₂ flow rate and keeps nearly constant in the lengthwise direction. The main physicochemical processes involved are discussed.     

Special function representations of the Poisson kernel on hyperbolic spaces

In this paper we compute explicit formulae for the Poisson kernels on the hyperbolic upper half-space \(\mathbf {H}^{n}\) and the Poincaré unit ball \(\mathbf {D}^{n}\). We first construct an associated Legendre function expression for eigenfunctions of the Laplacian and use superposition principle to get a solution for the Laplace equation on \(\mathbf {H}^{n}\). The Poisson kernel on \(\mathbf {D}^{n}\) is obtained from that on \(\mathbf {H}^{n}\) by letting the hyperbolic distance \(\rho =d(w,w')\) \((w,w'\in \mathbf {H}^{n})\) tend to infinity. These Poisson kernels, apart from being interesting in their own right lead to various identities that seem to be novel in the context of special functions.     

Inclusion complexes of $$\hbox{cholesteryl-(}\varepsilon\hbox{-caprolactone})_{\overline{10}}$$ functionalized polymer with γ-cyclodextrin

An inclusion complex (IC) of γ-cyclodextrin with biodegradable \(\hbox{cholesteryl-(}\varepsilon\hbox{-caprolactone})_{\overline{10}}\) \(\hbox{(Chol-(CL)}_{\overline{10}})\) functionalized polymer was prepared by using a general method of mixing solution. The formation of \(\gamma \hbox{-CD-Chol-(CL)}_{\overline{10}}\) IC was determined by Fourier transform infrared (FTIR),¹H-NMR, differential scanning calorimetry (DSC), and wide angle X-ray diffraction (WAXD), respectively. The results indicated that the \(\hbox{oligo}(\varepsilon\hbox{-CL})_{\overline{10}}\) blocks as well as the end cholesteryl moiety of the functionalized polymer were included and covered by γ-CD in a single-stranded mode in the \(\gamma \hbox{-CD-Chol-(CL)}_{\overline{10}}\) ICs. Moreover, the \(\gamma \hbox{-CD-Chol-(CL)}_{\overline{10}}\) ICs had a channel-type crystalline structure similar to that formed between the poly(propylene glycol) (PPG) and γ-CD. Finally, TGA revealed that the ICs had better thermal stability than their free components due to the inclusion complexation.     

Quasi-classical trajectory insight into stereodynamics for reaction $$\hbox {He}+\hbox {D}_{2}^{+}\rightarrow \hbox {HeD}^{+}+\hbox {D}$$ with the improved potential energy surface

In this work, a theoretical study on the detailed vector correlation for the reaction \(\hbox {He}+\hbox {D}_{2}^{+}\rightarrow \hbox {HeD}^{+}+\hbox {D}~(\hbox {v}, \hbox {j})\) has been carried out at the collision energy of 23.06 kcal/mol with different rotational states of j \(=\) 0–5 and vibrational states v \(=\) 1–5 by use of the quasi-classical trajectory calculation on an improved potential energy surface. The features of \({{\varvec{P}}}\mathbf{(}{\varvec{\theta }}_{{\varvec{r}}}{} \mathbf{)}\) distributions describing k and \(\mathbf{j}^\prime \) correlations were discussed. In addition, in order to get full knowledge of stereodynamics of the system, the distributions of dihedral angle \({{\varvec{P}}}\mathbf{(}{\varvec{\varphi }}_{{\varvec{r}}}{} \mathbf{)}\) and the polarization-dependent differential cross-sections (PDDCSs) were also reported. It has been demonstrated that both product alignment and polarization are sensitive to the reagent vibrational and rotational number. Furthermore, the dynamics behavior of the reaction is independently changed with respect to j under a certain v except for the product alignment effect \(({\varvec{P}}({\varvec{\theta }}_{{\varvec{r}}}))\), while it exhibits a generally regular trend concerning v when j is invariable.     

The Radial Distribution of Ions and Electrons in RF Inductively Coupled H<Subscript>2</Subscript>/T<Subscript>2</Subscript>B Plasmas

A glow discharge polymer (GDP) was fabricated using trans-2-butene (T₂B) and hydrogen (H₂) via a plasma-enhanced chemical vapor deposition (PECVD) system. The uniformity of the GDP films was significantly affected by the radial distribution of the H₂/T₂B plasma parameters. The plasma properties while discharging by a multi-carbon gas source of mixed H₂/T₂B were investigated during the GDP deposition process. The main positive ions and ion energy distributions in inductively coupled H₂/T₂B plasmas were analyzed by energy-resolved mass spectrometer (MS), and the electron density and the effective electron temperature were mainly analyzed using a Langmuir probe. The MS results show that the main positive ions in the plasmas are \({\text{C}}_{ 2} {\text{H}}_{ 4}^{ + }\), \({\text{C}}_{ 2} {\text{H}}_{ 6}^{ + }\), \({\text{C}}_{ 3} {\text{H}}_{ 3}^{ + }\), \({\text{C}}_{ 3} {\text{H}}_{ 6}^{ + }\), \({\text{C}}_{ 3} {\text{H}}_{ 8}^{ + }\), \({\text{C}}_{ 4} {\text{H}}_{ 5}^{ + }\), \({\text{C}}_{ 4} {\text{H}}_{ 1 0}^{ + }\), \({\text{C}}_{ 5} {\text{H}}_{ 5}^{ + }\), and \({\text{C}}_{ 5} {\text{H}}_{ 7}^{ + }\) with mass-to-charge ratios (m/e) of 28, 30, 39, 42, 44, 53, 58, 65, and 67, respectively. For a normalized ion intensity, the relative intensities of saturated CH ions increase with increasing radial distance, while the unsaturated CH ions decrease with increasing radial distance. The ion energy distribution of \({\text{C}}_{ 2} {\text{H}}_{ 6}^{ + }\) (m/e = 30) presents a bimodal structure. Additionally, both the electron density and the effective electron temperature decrease with increasing radial distance.     

Hierarchical enumeration of Kekulé’s benzenes,Ladenburg’s benzenes,Dewar’s benzenes,and benzvalenes by using combined-permutation representations

The group hierarchy for each skeleton of ligancy 6 is formulated to be: point group (PG \({\varvec{G}}_{\sigma }\)) \(\subseteq \) RS-stereoisomeric group (RS-SIG \({\varvec{G}}_{\sigma \widetilde{\sigma }\widehat{I}}\)) \(\subseteq \) stereoisomeric group (SIG \(\widetilde{{\varvec{G}}}_{\sigma \widetilde{\sigma }\widehat{I}}\)) \(\subseteq \) isoskeletomeric group (ISG \(\widetilde{\widetilde{{\varvec{G}}}}_{\sigma \widetilde{\sigma }\widehat{I}}\) = \({\varvec{S}}^{[6]}_{\sigma \widehat{I}}\)), where we start from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{D}}_{6h}\) for the Kekulé benzene skeleton, from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{D}}_{3h}\) for the Ladenburg benzene skeleton, from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{C}}_{2v}\) for the Dewar benzene skeleton, or from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{C}}_{2v}\) for the benzvalene skeleton. After these groups are constructed as combined-permutation representations, the calculation of the respective cycle indices with chirality fittingness (CI-CFs) and the introduction of ligand-inventory functions are conducted to give generation functions for 3D-based enumerations (for PGs and RS-SIGs) and 2D-based enumerations (for SIGs and ISGs). The enumeration results are discussed by means of isomer-classification diagrams, in which equivalence classes under enantiomerism (for PGs), RS-stereoisomerism (for RS-SIGs), stereoisomerism (for SIGs), and isoskeletomerism (for ISGs) are illustrated schematically. The implicit connotations of the conventional terms “skeletal isomerism”, “positional isomerism”, and “constitutional isomerism” are discussed, where the effects of the concept of isoskeletomerism are emphasized.     

Volumetric Investigations on Molecular Interactions of Glycine/<Emphasis Type="SmallCaps">l</Emphasis>-alanine in Aqueous Citric Acid Solutions at Different Temperatures

Apparent molar volumes \((\phi_{V})\) of glycine/l-alanine in water and in aqueous citric acid (CA) solutions of varying concentrations, i.e. (0.05, 0.10, 0.20, 0.30, 0.40 and 0.50) mol·kg^?1 were determined from density measurements at temperatures T?=?(288.15, 298.15, 308.15, 310.15 and 318.15) K and at atmospheric pressure. Limiting partial molar volumes \((\phi_V^{\text{o}})\) and their corresponding partial molar volumes of transfer \((\Delta_{\text{tr}} \phi_{V} )\) have been calculated from the \(\phi_{V}\) data. The negative \(\Delta_{\text{tr}} \phi_{V}\) values obtained for glycine/l-alanine from water to aqueous CA solutions indicate the dominance of hydrophilic–hydrophobic/hydrophobic–hydrophilic and hydrophobic–hydrophobic interactions over ion/hydrophilic–dipolar interactions. Further, pair and triplet interaction coefficients, i.e. \((V_{\text{AB}} )\;{\text{and}}\; (V_{\text{ABB}} )\) along with hydration number \((n_{\text{H}} )\) have also been calculated. The effect of temperature on the volumetric properties of glycine/l-alanine in water and in aqueous CA solutions has been determined from the limiting partial molar expansibilities \((\partial \phi_{V}^{\text{o}} /\partial T)_{p}\) and their second-order derivative \((\partial^{2} \phi_{V}^{\text{o}} /\partial T^{2} )_{{P}}\). The apparent specific volumes \((\nu_{\phi} )\) for glycine and l-alanine tend to approach sweet taste behavior both in the presence of water and in aqueous CA solutions. The \(\nu_{\phi}\) values for glycine/l-alanine increase with increase in concentration of CA at all temperatures studied. This reveals that CA helps in enhancing the sweet taste behavior of glycine/l-alanine which also supports the dominance of hydrophobic–hydrophobic interactions.     

Redox behavior of $${\text{VO}}^{2 + } / {\text{VO}}_{2}^{ + }$$ as a simulant of $${\text{NpO}}_{2}^{ + } / {\text{NpO}}_{2}^{2 + }$$NpO2+/NpO22+ in boiling nitric acid solution

To evaluate the redox behavior of \({\text{VO}}^{2 + } / {\text{VO}}_{2}^{ + }\) as a simulant of \({\text{NpO}}_{2}^{ + } / {\text{NpO}}_{2}^{2 + }\) in boiling nitric acid solution, i.e., typical operating conditions for nuclear fuel reprocessing plants, oxidation rate measurements for VO²⁺ in boiling and non-boiling nitric acid solutions, thermodynamic calculations, and kinetic calculations were performed. The results indicated that the apparent oxidation rate of VO²⁺ to \({\text{VO}}_{2}^{ + }\) is accelerated by a decrease in \({\text{NO}}_{2}^{ - }\) and HNO₂ concentrations owing to the boiling phenomena of nitric acid solution.     

Aromaticity of Bare Iridium Trimers and Ir3M0/+ and $$\rm{Ir}_3M_2^{+/3+}$$ (M = Li,Na, K,and Be,Ca) Bimetallic Clusters

The structural stabilities, bonding nature, electronic properties, and aromaticity of bare iridium trimers \(\rm{Ir}_3^{+/-}\) with different geometries and spin multiplicities are studied at the DFT/B3LYP level of theory. The ground state of the \(\rm{Ir}_3^{+}\) cation is found to be the ³A₂ (C_2v) triplet state and the ground state of the \(\rm{Ir}_3^{-}\) anion the ⁵A₂ (C_2v) quintet state. A detailed molecular orbital (MO) analysis indicates that the ground-state \(\rm{Ir}_3^{+}\) ion (C_2v, ³A₂) possesses double (σ and partial δ) aromaticity as well as the ground-state \(\rm{Ir}_3^{-}\) ion (C_2v, ⁵A₂). The multiple d-orbital aromaticity is responsible for the totally delocalized three-center metal-metal bond of the triangular Ir₃ framework. \(\rm{Ir}_3^{-}\) (C_2v, ¹A₁) structure motif is perfectly preserved in pyramidal Ir₃M^0/+ (C_s, ¹A′) and bipyramidal \(\rm{Ir}_3M_2^{+/3+}\) (C_2v, ¹A₁) (M = Li, Na, K and Be, Ca) bimetallic clusters which also possess the corresponding d-orbital aromatic characters.     

Assessing protein–ligand binding modes with computational tools: the case of PDE4B

In a first step in the discovery of novel potent inhibitor structures for the PDE4B family with limited side effects, we present a protocol to rank newly designed molecules through the estimation of their IC\(_{50}\) values. Our protocol is based on reproducing the linear relationship between the logarithm of experimental IC\(_{50}\) values [\(\log\)(IC\(_{50}\))] and their calculated binding free energies (\(\Delta G_\mathrm{binding}\)). From 13 known PDE4B inhibitors, we show here that (1) binding free energies obtained after a docking process by AutoDock are not accurate enough to reproduce this linear relationship; (2) MM-GB/SA post-processing of molecular dynamics (MD) trajectories of the top ranked AutoDock pose improves the linear relationship; (3) by taking into account all representative structures obtained by AutoDock and by averaging MM-GB/SA computations on a series of 40 independent MD trajectories, a linear relationship between \(\log\)(IC\(_{50}\)) and the lowest \(\Delta G_\mathrm{binding}\) is achieved with \(R^2=0.944\).     

Magnetic Silicon Fullerenes: Experimental Exploration and Theoretical Insight

The present article summarizes progress in research on silicon clusters with encapsulated metal atoms, and specifically focuses on the recent identification of magnetic silicon fullerenes. Considering that C\(_{20}\) forms the smallest known fullerene, the Si\(_{20}\) cluster is of particular interest in this context. While the pure hollow Si\(_{20}\) cage is unstable due to the lack of \(sp^2\) hybridization, endohedral doping with a range of metal atoms has been considered to be an effective way to stabilize the cage structure. In order to seek out suitable embedded atoms for stabilizing Si\(_{20}\), a broad search has been made across elements with relatively large atomic radius. The rare earth elements have been found to be able to stabilize the Si\(_{20}\) cage in the neutral state by forming R@Si\(_{20}\) fullerene cages. Among these atoms, Eu@Si\(_{20}\) has been reported to yield a stable magnetic silicon fullerene. The central europium atom has a large magnetic moment of nearly 7.0 Bohr magnetons. In addition, based on a stable Eu\(_2\)Si\(_{30}\) tube, a magnetic silicon nanotube has been constructed and discussed. These magnetic silicon fullerenes and nanotubes may have potential applications in the fields of spintronics and high-density magnetic storage.