On a Singular Sturm–Liouville Problem in the Theory of Molecular Vibrations

In this paper, we study the angular part of the internal amplitude function of a diatomic molecule under an angular potential function depending only on cos θ and which is an entire even function on R. For the equation $$ \frac{1}{\sin \theta}\frac{{\rm d}}{{\rm d}\theta }\left(\sin\,\theta\frac {{\rm d}\psi} {{\rm d}\theta}\right) + \left(\lambda - V(\cos\,\theta ) - \frac{m^{2}}{\sin^{2}\,\theta}\right)\psi = 0, $$ we obtain a formula for the eigenvalues and we determine the corresponding eigenfunctions     

Exact solution of the Schrödinger equation with a new expansion of anharmonic potential with the use of the supersymmetric quantum mechanics and factorization method

The study involves finding exact eigenvalues of the radial Schrödinger equation for new expansion of the anharmonic potential energy function. All analytical calculations employ the mathematical formalism of the supersymmetric quantum mechanics. The novelty of this study is underlined by the fact that for the first time the recurrence formulas for rovibrational bound energy levels have been derived employing factorization method and algebraic approach. The ground state and the excited states have been determined by means of the hierarchy of the isospectral Hamiltonians. The Riccati nonlinear differential equation with superpotentials has been solved analytically. It has been shown that exact solutions exist when the potential and superpotential parameters satisfy certain supersymmetric constraints. The results obtained can be utilized both in computations of quantum chemistry and theoretical spectroscopy of diatomic molecules.     

Exact solution of the Schrödinger equation with a Lennard–Jones potential

The Schrödinger equation with a Lennard–Jones potential is solved by using a procedure that treats in a rigorous way the irregular singularities at the origin and at infinity. Global solutions are obtained thanks to the computation of the connection factors between Floquet and Thomé solutions. The energies of the bound states result as zeros of a function defined by a convergent series whose successive terms are calculated by means of recurrence relations. The procedure gives also the wave functions expressed either as a linear combination of two Laurent expansions, at moderate distances, or as an asymptotic expansion, near the singular points. A table of the critical intensities of the potential, for which a new bound state (of zero energy) appears, is also given.     

An analysis of the rate of isomerization in molecules with an asymmetric double well potential

The classical theory of the rate of unimolecular isomerization developed by Gray andRice as extended by Zhao and Rice is applied to the calculation of the rate of isomerization in modelsystems which have linear asymmetric double well potentials. We are interested in this system fortwo reasons. First, we are interested in the detailed dynamical processes for the mentioned systembecause it is widely related to practical chemical reactions. Second, the present model systemhas an asymmetric double well potential, which provides a different test of the accuracy of theapproximations used in the Gray-Zhao-Rice theory than posed by previous applications. We havecalculated relaxation rates and relaxation times for the model systems on different time scales.We find that for the systems under studies the Gray-Zhao-Rice version of the classical theory ofisomerization rate yields values in good agreement with those generated from trajectory calculationsand from the Reactive Island theory of De Leon et al.     

An SCF-CI method for determining the potential energy surface of a triatomic molecule

A self-consistent-field (SCF)-configuration interaction (CI) (SCF-CI) method for determining the potential energy surface of a triatomic molecule from the observed vibrational band origins has been suggested. By this method, the SCF-CI procedure in the internal coordinates is used to calculate the vibrational bond origins and their first derivatives with respect to parameters in the potential energy function using the exact vibrational Hamiltonian, and the optimizer LMF in the nonlinear-squares problem is employed to optimize parameters in the potential energy function. This approach is used to optimize the potential energy function of the water molecule. The standard deviation of this fitting to the 70 observed band origins is 1.154cm-1.     

Solutions of the Klein–Gordon equation with the improved Tietz potential energy model

We present the relativistic rotation–vibrational energy equation of a diatomic molecule which moves under the improved Tietz potential energy model in higher spatial dimensions. The nonrelativistic limits of the bound state solutions of the Klein–Gordon equation are the bound state solutions of the Schrödinger equation with the same potential energy function. Numerical analysis results show that there exists a critical point around which the solution behaviors bifurcate into two extreme cases. Below the critical point, the behavior of the relativistic vibrational energies for the ground electronic state of carbon monoxide in higher dimensions keeps similar to that of the three-dimensional system, while this symmetry phenomenon breaks and the Klein–Gordon equation has no stability solution upon the critical point.     

Hard sphere expansion conformal solution theory with the Lennard–Jones (12-6) intermolecular potential

Modification of the hard sphere expansion conformal solution theory is presented concerning polarity of molecules, the Lennard–Jones (12-6) parameters, and mixing rules for unlike parameters. The theory was used for prediction of vapour–liquid equilibrium at constant temperature in binary, ternary and quaternary mixtures consisting of chlorobutanes and C₇ hydrocarbons. Excess molar volumes for binary systems are calculated, too.     

Characterization of isomeric cationic porphyrins with β-pyrrolic substituents by electrospray mass spectrometry: The singular behavior of a potential virus photoinactivator

Electrospray ionization mass spectrometry (ESI-MS) and tandem mass spectrometry (ESI-MS/MS) have been used to differentiate the 2- and 4-methylpyridyl isomers of free-base and metallated cationic beta-vinylpyridylporphyrins. The analysis by ESI-MS/MS of the deuterated analogs and semiempirical calculations of structural and electronic parameters were also undertaken. The two free-base isomers are easily differentiated by ESI-MS/MS but the presence of a metallic center renders differentiation of the metallated isomers less effective. The data acquired show that of all the studied compounds, the free-base 2-methylpyridyl isomer, which was operative in the in vitro photoinactivation of Herpes simples virus, has a different gas-phase behavior. Local distortion of the macrocycle due to the presence of the beta-vinylpyridyl substituent occurs for all the compounds, but a different electron density distribution can account for the observed gas-phase behavior of this potential virus photoinactivator.     

An evaluation of the dyeing behavior of sol–gel silica doped with direct dyes

A new dyeing process of sol–gel silica doped with direct dyes is investigated for improving color strength (K/S value) and dyeing fastness. Cotton fabrics are dyed in this direct dye silica solution. The results indicate that the K/S value of C.I. Direct Blue 86 and C.I. Direct Red 23 are enhanced by 12.8% and 16.8%, respectively. For C.I. Direct Blue 86, the washing staining fastness is improved by half a grade, and the rubbing fastness and the washing change fastness are enhanced by one grade, respectively. Compared to the fabric fixed with fixing reagent MMF-1, the K/S value is improved by about 23.7% and the wet rubbing fastness and washing change fastness are enhanced by half a grade. The formation of uniform continuous layers on the fiber surface dyed with direct dye silica solution is revealed by video microscope, and the calculated sol–gel weight gain on the fabric is 4.6%.     

An activated carbon with high capacitance from carbonization of a resorcinol–formaldehyde resin

A polymeric activated carbon (PAC) was synthesized from the carbonization of a resorcinol–formaldehyde resin with KOH served as an activation agent. The nitrogen adsorption–desorption at 77 K, X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS) were used to characterize the prepared PAC. Compared with the commercial activated carbon (Maxsorb: Kansai, Japan), PAC shows superior capacitive performance in terms of specific capacitance, power output and high energy density as electrode materials for supercapacitors. PAC presents a high specific capacitance of 500 F g^?1 in 6 mol l^?1 KOH electrolyte at a current density of 233 mA g^?1 which remained 302 F g^?1 even at a high current density of 4.6 A g^?1. The good electrochemical performance of the PAC was ascribed to well-developed micropores smaller than 1.5 nm, the presence of electrochemically oxygen functional groups and low equivalent series resistance.     

Bound state solutions of the Deng–Fan molecular potential with the Pekeris-type approximation using the Nikiforov–Uvarov (N–U) method

By employing the Pekeris-type approximation to deal with the centrifugal term, we solve the Schrödinger equation with the Deng–Fan molecular potential for all values of $l$ (orbital angular momentum quantum number). Using the Nikiforov–Uvarov (N–U) method, the approximate analytical bound state energy eigenvalues and the corresponding wave functions are obtained. The results obtained are in good agreement with those ones found in the literature. The bound state energy eigenvalues for a set of diatomic molecules (HCl, LiH, H $_{2}$ , ScH, TiH, VH, CrH, CuLi, TiC, NiC, ScN and ScF) corresponding to the Deng–Fan molecular potential for arbitrary values of n and $l$ quantum numbers are reported.     

An effective modification of the Benedict–Webb–Rubin equation of state

A modification of the BWR equation of state is proposed, which is a simplified form of a previously proposed one. It applies to systems formed by hydrocarbons and related compounds, with particular attention to the critical conditions. The range of treatable compounds was extended to a value 0.9 of the acentric factor, corresponding to C₂₀ hydrocarbons. The critical compressibility factor Z_c was made independent of the acentric factor, for a more accurate prediction of pure-component properties (the previous equation did not give the same improvement). Mixing rules require one binary interaction constant for each component pair. Zero binary constants can be used for methane–alkane and alkane–alkane pairs. Examples of applications to pure hydrocarbons and their mixtures are given.     

Descriptor of a Structure–Property Model for Calculating the Critical Temperature of a Liquid–Vapor Phase Transition with the Topological Characteristics of Alkene Molecules

Russian Journal of Physical Chemistry A - A nonlinear multidimensional model is proposed for calculating the critical temperature of normal and substituted alkenes through the topological...     

Synthesis and biological evaluation of potential new inhibitors of the bacterial transferase MraY with a β-ketophosphonate structure

Stable analogs of bacterial transferase MraY substrate or product with a pyrophosphate surrogate in their structure are described. β-ketophosphonates were designed as pyrophosphate bioisosteres and were investigated as UDP-GlcNAc mimics. The developed strategy allows introduction of structural diversity at a late stage of the synthesis. The biological activity of the synthesized compounds was evaluated on the MraY enzyme.     

Study of binary systems of β-cyclodextrin with a highly potential anti-mycobacterial drug

The present research paper is dedicated to the obtaining and physicochemical characterization of a highly potential anti-mycobacterial drug candidate with β-cyclodextrin (βCD). The active substance is a 1,3,4-oxadiazole derivative, 2-phenyl-5-{[(2-phenyl-1,3-dioxolan-2-yl)methyl]sulfanyl}-1,3,4-oxadiazole, further named DIOX. DIOX–βCD binary systems were obtained as a physical mixture and a lyophilized product with molar ratio between the main components equal to 1:1 and 1:2. The obtained systems were submitted to physicochemical characterization applying the following instrumental methods: infrared spectrometry, differential scanning calorimetry, and X-ray crystallographic analysis. Besides, a molecular modeling analysis has been performed. The research data suggested certain intermolecular interaction between DIOX and βCD, suggesting formation of a three-molecular inclusion complex DIOX:βCD, including one DIOX molecule and two molecules of βCD. The main parts of the DIOX molecule included in the hydrophobic cavity of the cyclodextrin molecules most probably are dioxolane cycle and two benzene rings.     

Gaseous products of the bombardment of a tetrafluoroethylene–hexafluoropropylene copolymer with accelerated MeV protons

The action of 1- to 4-MeV protons on a copolymer of tetrafluoroethylene and hexafluoropropylene (FEP) in a vacuum is accompanied by the release of more than 25 gaseous products and a decrease in its thermal stability. During the course of proton bombardment, the predominant rupture of lateral C–CF₃ bonds with the release of CF₃ particles occurs along with the detachment of fluorine and hydrogen atoms yielding H₂ and HF. Unlike polytetrafluoroethylene, a distinctive feature of the radiolysis of FEP is a decrease by a factor of 5 in the probability of fluorine detachment from the FEP macromolecule by accelerated protons.     

An efficient synthesis of the C27–C45 fragment of lagunamide A,a cyclodepsipeptide with potent cytotoxic and antimalarial properties

An efficient and stereoselective synthesis of the entire C27–C45 moiety of lagunamide A has been achieved from 1-[(4S)-4-benzyl-2-thioxothiazolidin-3-yl]propan-1-one in six steps with 22% overall yield. The key step in the synthesis is an asymmetric acetal aldol reaction featuring the enantioselective addition of a chiral thiazolidinethione-derived titanium enolate to an acetal to establish the stereochemistry at C39.     

Equivalence of the deformed Rosen–Morse potential energy model and Tietz potential energy model

By applying the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved expression for the deformed Rosen–Morse potential energy model. It is found that the deformed Rosen–Morse potential model and the well-known Tietz potential model are the same empirical potential function for diatomic molecules. With the help of the energy spectrum expression of the deformed Rosen–Morse potential model, we obtain exact closed-form expressions of diatomic anharmonicity constants $\omega _e x_e $ ω e x e and $\omega _e y_e $ ω e y e .