Information-theoretic approach to kinetic-energy functionals: the nearly uniform electron gas

We strengthen the connection between information theory and quantum mechanical systems using a recently developed dequantization procedure which results in a decomposition of the kinetic energy as the sum of a classical term and a purely quantum term. For the nearly uniform electron gas, we thereby approximate the noninteracting kinetic energy as the sum of the Thomas-Fermi term, which is exact for the uniform electron gas, and the Weizsäcker term, which is proportional to the Fisher information. Electron correlation is included via a nonlocal analytical expression which is a functional of the (N-1)-conditional probability density. This expression is evaluated via a statistically rigorous Monte-Carlo procedure to obtain the correlation energy as a functional of the electron density. We show that this functional is well aproximated by a term which is proportional to the Shannon entropy. Thus the kinetic energy is expressed as the standard Thomas-Fermi term plus terms which are proportional to two of the cornerstones of information theory: the Fisher information, which is a measure of localization, and the Shannon entropy, which is a measure of delocalization.     

General relativistic symmetry of electron spin vorticity

The general relativistic symmetry of quantum electrodynamics (QED) predicts that the spin vorticity of electron contributes to the kinetic momentum of electron. The canonical quantization of QED is performed by using new b-photon, f-electron, and \(f^{c}\)-positron algebras. These algebras work for interacting particles and are useful for nonperturbationally solving the dual Cauchy problems of QED.     

Effect of donor and acceptor properties of solvents on the kinetics of photoreduction of sterically hindered <Emphasis Type="Italic">о</Emphasis>-benzoquinones

Effect of the solvent nature on the kinetics of photoreduction of 3,6-di-tert-butyl-1,2-benzoquinone and its six derivatives in the presence of N,N-dimethylaniline and 4-(N,N-dimethylamino)benzaldehyde has been investigated. It has been found that for the о-quinone—amine pair, for which the free energy change of electron transfer is ΔG_e > +0.11 eV, the rate constant of о-quinone photoreduction k_H decreases proportionally to the increase in the acceptor number of the solvent. For the о-quinone—amine pair with ΔG_e < +0.11 eV, the k_H value decreases proportionally to the increase in the donor number of the solvent. It has been established that the enhancement of the electron-acceptor properties of the solvent leads to the emergence of kinetic isotope effect for the reactant pairs of 3,6-di-tert-butyl-1,2-benzoquinone and 4,5-dimethoxy-3,6-di-tert-butyl-1,2-benzoquinone with N,N-di-methylaniline (ΔG_e = +0.11 and +0.22 eV, respectively).     

Thermooxidative decomposition of heterocyclic <Emphasis Type="Italic">N</Emphasis>-oxides

Thermooxidative decomposition of pyridine N-oxide, 4-(4-dimethylaminostyryl)pyridine N-oxide, 4-(4-methoxystyryl)pyridine N-oxide, quinoline N-oxide, 2-methylquinoline N-oxide, 4-chloroquinoline N-oxide, 2-styrylquinoline N-oxide, and 2-(4-dimethylaminostyryl)quinoline N-oxide was studied. The kinetic parameters of the thermooxidative processes were calculated according to three independent procedures. The relation between the nature of heterocyclic N-oxide and its stability to thermal oxidation was analyzed.     

The response electron–electron repulsion energy and energy component analysis in CC/MBPT methods

Molecular properties are computed as responses to perturbations (energy derivatives) in coupled-cluster (CC)/many-body perturbation theory (MBPT) models. Here, the CC/MBPT energy derivative with respect to a general two-electron (2-e) perturbation is assembled from gradient theory for 2-e property evaluation, including the electron repulsion energy. The correlation energy (?E) is shown to be the sum of response kinetic (?T), electron–nuclear attraction (?V), and electron repulsion (?V _ee ) energies. Thus, evaluation of total V _ee for energy component analysis is simple: For total energy (E), total 1-e responses T and V, and nuclear–nuclear repulsion energy (V _NN ), V _ee  = E ? V _NN  ? T ? V is the true 2-e response value. Component energy analysis is illustrated in an assessment of steric repulsion in ethane’s rotational barrier. Earlier SCF-based results (Bader et al. in J Am Chem Soc 112:6530, 1990) are corroborated: The higher-energy eclipsed geometry is favored versus staggered in the two repulsion energies (V _NN and V _ee ), while decisively disfavored in electron–nuclear attraction energy (V). Our best quality calculations (CCSD/cc-pVQZ) attain practical Virial Theorem compliance (i.e., agreement among the kinetic energy, potential energy, and total energy representations) in assigning 2.70 ± 0.06 to the barrier height; ?195.80 kcal/mol is assigned to the drop in “steric” repulsion upon going to the eclipsed geometry. Steric repulsion is not responsible for any fraction of the ~3 kcal/mol barrier.     

Compositions and structures of nanoparticles of pentagonal axial symmetry <Emphasis Type="Italic">D</Emphasis><Subscript>5<Emphasis Type="Italic">d</Emphasis></Subscript>: Nanotubes

The method of determination of the structure and the number of atoms in the shells of nanoparticles as a function of the arrangement of atoms at the symmetry elements of a symmetry group has been developed. The formulas for the calculation of the number of particles with symmetry group D _5d are reported. The number of particles in these shells is determined by three structurally invariant numbers and the “quantum number” of the group order n. The classification of all possible nanostructures with symmetry group D _5d is given: C _θ+10z , z = 0, 1, 2, …, where the basic shells are C _θ = C ₂, C ₁₀, C ₁₂. The sum rule has been obtained for the coordination numbers of shell sites located at symmetry axes. Pentagonal axial nanoparticles are shown to be the initial shells for obtaining (5,5) and (10,10) armchair nanotubes or (5,0) and (10,0) zigzag nanotubes. The general formula of these nanotubes closed with icosahedral and dodecahedral caps is N _20+10p , N _60+10p (p = 1, 2, …). The graphical constructions of all classes of nanoparticles and nanotubes of the pentagonal axial type are reported.     

Compositions and structures of nanoparticles of trigonal symmetry <Emphasis Type="Italic">D</Emphasis><Subscript>3<Emphasis Type="Italic">d</Emphasis></Subscript>: Nanotubes

A method has been developed for the determination of the structure and number of atoms in the shells of nanoparticles as a function of the arrangement of atoms at the symmetry elements of a symmetry group. The formulas for calculation of the number of particles of symmetry D _3d have been reported. It has been shown that the number of atoms in trigonal shells is determined by three structurally invariant numbers and the quantum number of the group order n. All possible nanostructures of symmetry D _3d have been classified: C_{θ + 6z} , z = 0, 1, 2, ..., where the basic shells are C_θ = C₆, C₈, and C₁₄. A sum rule has been obtained for the coordination numbers of the shell sites located on symmetry axes. Trigonal nanoparticles are parent ones for obtaining (3,0), (6,0), and (9,0) nanotubes of trigonal type. The general formulas of these nanotubes with icosahedral, dodecahedral, and cubic caps are N_{8 + 12p} , N_{20 + 24p} , and N_{60 + 36p} (p = 1, 2, ...), respectively. The graphical constructions of all classes of trigonal nanoparticles and nanotubes are reported.     

Dissociation Constants of Silanol Groups of Silic Acids: Quantum Chemical Estimations

Dissociation constants of silanol groups on the silica surface are calculated with the DFT quantum chemical method using B3LYP and M06 functionals. Structural features of silanol fragments and the presence of hydrogen-bonded water clusters are shown to have significant effects on pK_a values of silanol groups. In particular, pK_a values are shown to vary widely depending on the features of the system of hydrogen bonds.     

Alkylation of 2-(methylsulfanyl)-6-polyfluoroalkylpyrimidin-4(3<Emphasis Type="Italic">H</Emphasis>)-ones with haloalkanes

The alkylation of ambident anions of 2-(methylsulfanyl)-6-(polyfluoroalkyl)pyrimidin-4(3H)-ones with 4-bromobutyl acetate leads to concurrent formation of O- and N-(4-acetoxybutyl) derivatives. Polar aprotic solvents favor formation of the O-isomer, and weakly polar dioxane favors N-alkylation. The reaction of 2-(methylsulfanyl)-6-(trifluoromethyl)pyrimidin-4(3H)-one with an equimolar amount of 1,2-dibromoethane in polar acetonitrile gives a mixture of N,N-, O,O-, and N,O-bridged bis-pyrimidines, as well as N- and O-[2-(methylsulfanyl)ethyl] derivatives, whereas in the presence of 10 equiv of 1,2-dibromoethane the N,O-isomer is formed as the only product. The reaction in weakly polar tetrahydrofuran yields N,N- and N,O-bispyrimidines.     

3-(1-Methyl-1-nitroethyl-1-<Emphasis Type="Italic">ONN</Emphasis>-azoxy)-4-aminofuroxan. Synthesis and transformations of the amino group

A four-step procedure to convert 4-(1-methyl-1-nitroethyl-1-ONN-azoxy)-3-cyanofuroxan into 3-(1-methyl-1-nitroethyl-1-ONN-azoxy)-4-aminofuroxan was developed. The pathways of transformation of the amino group of the synthesized compound into N-nitramino-, N-alkyl-N-nitramino-, N,N’-methylenediamino-, N,N’-methylene-N,N’-dinitramino-, and azo groups were studied.     

Graphene oxide promoted synthesis of <Emphasis Type="Italic">p</Emphasis>-phenylenediamine antioxidants

Three p-phenylenediamine antioxidants (p-phenylenediamine-N,N,N′,N′-tetrapropionic acid tetramethyl ester, p-phenylenediamine-N,N,N′-tripropionic acid trimethyl ester, and p-phenylenediamine-N, N′-dipropionic acid dimethyl ester) were successfully synthesized via atom-economic aza-Michael addition of pphenylenediamine to methyl acrylate p-romoted by graphene oxide in water. The synthesized compounds were characterized by NMR, ESI-MS spectra, and elemental analyses. The effects of the solvent and graphene oxide on the reaction were investigated.     

Kinetics of mechanochemical dissolution of chromium in iron

The kinetics of solid Fe–Cr solution formation has been studied during mechanical alloying of Fe and Cr powders taken in an atomic ratio of 80: 20. X-ray diffraction and Mössbauer spectroscopy data have been analyzed within the framework of the energetic approach. It has been established that, in this system, reaction product yield N is related to mechanical energy dose D and specific surface area S of Fe nanograin boundaries in an ideal manner: N ~ D² at S ~ D and N ~ D at S = const.     

Photoprocesses in <Emphasis Type="Italic">N</Emphasis>-ammonioalkyl derivatives of azacrown-containing styryl dyes and their complexes with metal perchlorates

Photophysical processes and photochemical reactions in the N-ammonioalkyl derivatives of the azacrown-containing styryl dyes and their complexes with lead and barium perchlorates in MeCN and CH₂Cl₂ were studied by ¹Н NMR spectroscopy, absorption spectroscopy, luminescence spectroscopy, laser kinetic spectroscopy, and quantum chemistry. Molecules of the styryl dyes and their complexes are able to undergo normal (fast) and delayed fluorescence and trans–cis-photoisomerization. The molecules in the triplet state participate in degradation processes of the electron excitation energy.     

Cyclization of trifluoro-<Emphasis Type="Italic">N</Emphasis>-(prop-2-yn-1-yl)methanesulfonamides to <Emphasis Type="Italic">N</Emphasis>-(hydroxymethyl)-1,2,3-triazoles

Three-component heterocyclizations of trifluoro-N-(prop-2-yn-1-yl)methanesulfonamide, trifluoro-N-pheny-N-(prop-2-yn-1-yl)methanesulfonamide, and trifluoro-N,N-di(prop-2-yn-1-yl)methanesulfonamide with formaldehyde and sodium azide afforded N-{[2-(hydroxymethyl)-2H-1,2,3-triazol-4-yl]methyl}-, N-{[2-(hydroxymethyl)-2H-1,2,3-triazol-4-yl]methyl}-N-phenyl-, and N,N-bis{[2-(hydroxymethyl)-2H-1,2,3-triazol-4-yl]methyl}trifluoromethanesulfonamides as the major products together with minor 1-(hydroxymethyl)-1H-1,2,3-triazole isomers.     

Synthesis,Spectroscopic and Computational Studies of CT Complexes of Amino Acids with Iodine as σ Acceptor

Understanding the charge transfer process between bioactive molecules and inorganic or organic molecules is significant as this interaction can be used to interpret bioactive molecule–receptor interactions. A comprehensive spectrophotometric study has been performed to explore the complexation chemistry of the amino acids, tyrosine, lysine and arginine, with iodine as σ acceptor. The molecular structure, spectroscopic characteristics and the interactive modes have been deduced from UV–Vis and IR spectra. The binding ratio of complexation has been determined to be 1:1 for iodine with the amino acids. The association constant (K), extinction coefficient (ε _max), ionization potential (IP), energy of the charge transfer complex (E _CT), resonance energy (R _N ), dissociation energy (W) and standard Gibbs energy (ΔG°) have been computed. An in silico study has been carried out using GAMESS computations to understand the structural features. Highest occupied molecular orbital and lowest unoccupied molecular orbital calculations helped us in characterizing the chemical reactivity and kinetic stability of the molecules. A good consistency between experimental and computational results has been found.     

Compositions of nanoparticles of hexagonal symmetry

The formulas for calculation of the number of atoms in nanoparticles with symmetry group D _6h are reported. The numbers of atoms are determined by six structurally invariant numbers and the “quantum number” of the group order n. Eight classes of nanostructures with symmetry group D _6h are revealed: C _{? + 12z} , where z = 0, 1, 2, …, and C _? is C ₂, C ₆, C ₈, or C ₁₄. The sum rule for the coordination numbers of all atoms of subshells related to symmetry elements is established. Two-dimensional nanoparticles are considered.     

Arenesulfonylation of <Emphasis Type="Italic">N</Emphasis>-alkylanilines: reaction kinetics and mechanism

Kinetic regularities of arenesulfonylation of N-alkylanilines in binary water-organic solvents of variable composition have been studied. The rate constants for these reactions increase with increasing the water content in a system. The steric factor has the decisive influence on reactivity of N-alkylamines. The character of the influence of the composition and nature of a solvent on the rate constants for arenesulfonylation was discussed with the assistance of results of quantum chemical simulation of molecular complexes of the nucleophiles studied with the components of the binary systems. Calculation of potential energy surface for the reaction of N-methylaniline with benzenesulfonyl chloride showed that in the gas phase the process occurs by the S_N2 mechanism.     

On the chemical bonding features in palladium containing compounds: A combined QTAIM/DFT topological analysis

Topological analyses of the electron density on N-benzoyl-L-pheylalanine and its palladium(II) complexes are carried out using the quantum theory of atoms in molecules (QTAIM) at the M06/6-31G(d) theoretical level. The topological parameters derived from the Bader theory are also analyzed; these are characteristics of Pd bond critical points and ring critical points. The calculated structural parameters are the highest occupied molecular orbital energy (E _HOMO), the lowest unoccupied molecular orbital energy (E _LUMO), the hardness (η), the softness (S), the absolute electronegativity (χ), the electrophilicity index (ω), and the fractions of electrons transferred (ΔN) from ethylenediamine, 2,2′-bipyridine and 1,10-phenanthroline complexes to N-benzoyl-L-pheylalanine. The numerous correlations and dependences between the energy terms of the symmetry adapted perturbation theory approach, geometrical, topological, and energy parameters are detected and described.     

Dynamics of the photoinduced desorption of nitric oxide molecules from the surface of pure and modified platinum

The distribution of NO molecules desorbed from a Pt(111) surface due to valence electron excitation over rotational energy levels N(J) is analyzed using a simple impulse-induced model. A linear dependence is found between lnN(J) and (E_r)^1/2, where E_r is the rotational energy of the desorbed molecules. The lifetime of the excited state and the critical time of residence in the excited state estimated using this dependence are found to be close to one another (~10^?15 s). The frequency and amplitude of the tilting vibrations of the adsorbed molecules in the excited state are estimated.     

The impact of the stretching exponent on fragility of glass-forming liquids

The paper compared two factors governing fragility. The first one is thermodynamic, depending on the change in configurational entropy. The second one is kinetic and is determined by the stretching exponent β. Using a simple mathematical development, we show that the kinetic term \(m_{\text{K}} = f( {\beta_{{T_{\text{g}} }} } )\partial \ln \beta \left( T \right)/\partial \ln T|_{{T = T_{\text{g}} }}\) is always smaller than 1, where T _g is the glass transition temperature and \(f( {\beta_{{T_{\text{g}} }} } )\) is the given functions of the stretching exponent at T = T _g. As a result, the contribution of the kinetic term on the fragility of strong glasses is <6 %. Fragile glasses have a larger value of fragility index m, and for them, the influence of the kinetic term is significantly smaller. In any case, the thermodynamic term plays the main role in fragility and the kinetic one can be neglected.