Determining the excited‐state substituent constants of meta‐substituent from 3,4'‐disubstituted stilbenes

In this paper, 61 samples of 3,4'‐disubstituted stilbenes and 18 samples of 3,3'‐disubstituted stilbenes were synthesized, and their UV data were measured in anhydrous ethanol. Based on the UV absorption energy (wavenumber) of 3,4'‐disubstituted stilbenes, the excited‐state substituent constants of meta‐substituent were determined by means of curve‐fitting. The availability of was confirmed by the good correlation with the UV absorption energy of 3,4'‐disubstituted stilbenes and 4,4'‐disubstituted stilbenes. Further, using the obtained constants and the correlation equation, we calculated the UV wavenumbers of 3,3'‐disubstituted stilbenes, and the calculated wavenumbers are in good agreement with the experimental values. These results verified that the excited‐state substituent constants of meta‐substituent are reliable parameter to scale the effect of meta‐substituent on the UV absorption energy. Copyright © 2012 John Wiley & Sons, Ltd.     

Quantum mechanical estimation of Abraham hydrogen bond parameters using 1:1 donor–acceptor complexes

Hydrogen bond donor strength () and acceptor strength () have been successfully used in models of many environmental and chemical systems, and a number of computational methods have been developed to predict them. In this work, a quantum chemical Møller–Plesset perturbation (MP2) method is applied to estimate the binding free energies (ΔG_hbond) of several 1:1 hydrogen‐bonded complexes. A correlation between the binding free energies and hydrogen bond strength is established. This relationship can be used to develop an accurate computational model for predicting and using binding free energies. The accuracy of the method in predicting Abraham (root mean squared deviation (RMSD) = 0.0693) and (RMSD = 0.0677) are comparable to the empirical, fragment‐based ABSOLV method (RMSD = 0.1144 and 0.1281 for and , respectively). The binding free energy has been decomposed into its thermodynamic components, and it is demonstrated that the linear relationships in the dataset and the existence of magic point can be attributed to a constant entropy of reaction. Copyright © 2014 John Wiley & Sons, Ltd.     

Synthesis and thermochemical study of quinoxaline‐N‐oxides: enthalpies of dissociation of the N–O bond

The synthesis of three new quinoxaline mono‐N‐oxides derivatives, namely, 2‐tert‐butoxycarbonyl‐3‐methylquinoxaline‐N‐oxide, 2‐phenylcarbamoyl‐3‐ethylquinoxaline‐N‐oxide, and 2‐carbamoyl‐3‐methylquinoxaline‐N‐oxide, from their corresponding 1,4‐di‐N‐oxides is reported. Samples of these compounds were used for a thermochemical study, which allowed derivation of their gaseous standard molar enthalpies of formation, , from their enthalpies of formation in the condensed phase, , determined by static bomb combustion calorimetry, and from their enthalpies of sublimation, , determined by Calvet microcalorimetry. Finally, combining the for the quinoxaline‐N‐oxides derived in this work with literature values for the corresponding 1,4‐di‐N‐oxides and atomic oxygen, the bond dissociation enthalpies for cleavage of the first N?O bond in the di‐N‐oxides, DH₁(N–O), were obtained and compared with existing data. Copyright © 2011 John Wiley & Sons, Ltd.     

Trends in properties of para‐substituted 3‐(phenylhydrazo)pentane‐2,4‐diones

Trends between the Hammett's σ_p and related normal , inductive σ_I, resonance σ_R, negative and positive polar conjugation and Taft's σ_p° substituent constants and the distance, δ_{N? H} NMR chemical shift, oxidation potential (E_p/2°x, measured in this study by cyclic voltammetry (CV)) and thermodynamic parameters (pK, ΔG⁰, ΔH⁰ and ΔS⁰) of the dissociation process of unsubstituted 3‐(phenylhydrazo)pentane‐2,4‐dione (HL₁) and its para‐substituted chloro (HL₂), carboxy (HL₃), fluoro (HL₄) and nitro (HL₅) derivatives were recognized. The best fits were found for σ_p and/or in the cases of , δ_{N? H} and E_p/2°x, showing the importance of resonance and conjugation effects in such properties, whereas for the above thermodynamic properties the inductive effects (σ_I) are dominant. HL₂ exists in the hydrazo form in DMSO solution and in the solid state and contains an intramolecular H‐bond with the distance of 2.588(3) Å. It was also established that the dissociation process of HL_1–5 is non‐spontaneous, endothermic and entropically unfavourable, and that the increase in the inductive effect (σ_I) of para‐substitutents (? H < ? Cl < ? COOH < ? F < ? NO₂) leads to the corresponding growth of the distance and decrease of the pK and of the changes of Gibbs free energy, of enthalpy and of entropy for the HL_1–5 acid dissociation process. The electrochemical behaviour of HL_1–5 was interpreted using theoretical calculations at the DFT/HF hybrid level, namely in terms of HOMO and LUMO compositions, and of reactivities induced by anodic and cathodic electron‐transfers. Copyright © 2010 John Wiley & Sons, Ltd.     

Nodal theorems for the Dirac equation in d ≥ 1 dimensions

A single particle obeys the Dirac equation in spatial dimensions and is bound by an attractive central monotone potential that vanishes at infinity. In one dimension, the potential is even, and monotone for The asymptotic behavior of the wave functions near the origin and at infinity are discussed. Nodal theorems are proven for the cases and , which specify the relationship between the numbers of nodes n₁ and n₂ in the upper and lower components of the Dirac spinor. For , whereas for if and if where and This work generalizes the classic results of Rose and Newton in 1951 for the case Specific examples are presented with graphs, including Dirac spinor orbits      

Refined comparison theorems for the Dirac equation in d dimensions

A single spin‐1/2 particle obeys the Dirac equation in spatial dimension and is bound by an attractive central monotone potential which vanishes at infinity (in one dimension the potential is even). This work refines the relativistic comparison theorems which were derived by Hall 1 . The new theorems allow the graphs of the two comparison potentials and to crossover in a controlled way and still imply the spectral ordering for the eigenvalues at the bottom of each angular momentum subspace. More specifically in a simplest case we have: in dimension , if , then ; and in dimensions, if , where and , then .

     

A generalized G‐function for the Quantum Rabi Model

The analytical solution of the quantum Rabi model is based on a transcendental function , the zeros of which determine the eigenenergies. is generalized here to a function , which allows a much better numerical control of the high‐energy part of the spectrum by an appropriate choice of the complex parameter z. Additionally, it is shown that all zeros of correspond to eigenvalues of the Hamiltonian as well as the zeros of for imaginary z.     

Quantum states and vortex patterns in nanosuperconductors

The quanum levels and corresponding vortex states in nanoscale superconductors are investigated within generalized Bogolubov‐de Gennes theory. For symmetric (square‐shaped) samples thermodynamically stable vortex phases form symmetry‐consistent patterns and no transition to conventional Abrikosov‐like vortex patterns occurs till T=0K for sizes not exceeding 25 nm. For vorticity a giant vortex is stabilized at temperatures in the vicinity of , which transforms into a giant antivortex and four normal vortices with lowering the temperature. On the other hand, the vortex pattern for vorticity corresponds to an antivortex and four normal vortices in the whole temperature domain.     

Quantum information entropies for an asymmetric trigonometric Rosen–Morse potential

Shannon entropy for the position and momentum eigenstates of an asymmetric trigonometric Rosen–Morse potential for the ground and first excited states is evaluated. The position and momentum information entropies and are calculated numerically. Also, it is found that is obtained analytically and increases with the potential depth and width. Some interesting features of the information entropy densities and are demonstrated graphically. The Bialynicki‐Birula–Mycielski inequality is also tested and found to hold good.     

THz and above THz electron or hole oscillations in DNA dimers and trimers

A non conventional source or receiver of THz and above THz electromagnetic radiation is proposed. Specifically, electron or hole oscillations in DNA dimers (two interacting DNA base‐pairs or monomers) are predicted, with frequency in the range 0.25–100 THz (period 10–4000 fs) i.e. potentially absorbing or emitting electromagnetic radiation mainly in the mid‐ and far‐infrared with wavelengths ≈ 3–1200 μm. The efficiency of charge transfer between the two monomers which make up the dimer is described with the maximum transfer percentage p  and the pure maximum transfer rate . For dimers made of identical monomers , but for dimers made of different monomers . The investigation is extended to DNA trimers (three interacting DNA base‐pairs or monomers). For trimers made of identical monomers the carrier oscillates periodically with 0.5–33 THz ( 30–2000 fs); for 0 times crosswise purines , for 1 or 2 times crosswise purines . For trimers made of different monomers the carrier movement may be non periodic. Generally, increasing the number of monomers above three, the system becomes more complex and periodicity is lost; even for the simplest tetramer the carrier movement is not periodic.     

Theory of the Robin quantum wall in a linear potential. I. Energy spectrum,polarization and quantum‐information measures

Information‐theoretical concepts are employed for the analysis of the interplay between a transverse electric field applied to a one‐dimensional surface and Robin boundary condition (BC), which with the help of the extrapolation length Λ zeroes at the interface a linear combination of the quantum mechanical wave function and its spatial derivative, and its influence on the properties of the structure. For doing this, exact analytical solutions of the corresponding Schrödinger equation are derived and used for calculating energies, dipole moments, position and momentum quantum information entropies and their Fisher information and and Onicescu information energies and counterparts. It is shown that the weak (strong) electric field changes the Robin wall into the Dirichlet, (Neumann, ), surface. This transformation of the energy spectrum and associated waveforms in the growing field defines an evolution of the quantum‐information measures; for example, it is proved that for the Dirichlet and Neumann BCs the position (momentum) quantum information entropy varies as a positive (negative) natural logarithm of the electric intensity what results in their field‐independent sum . Analogously, at and the position and momentum Fisher informations (Onicescu energies) depend on the applied voltage as () and its inverse, respectively, leading to the field‐independent product (). Peculiarities of their transformations at the finite nonzero Λ are discussed and similarities and differences between the three quantum‐information measures in the electric field are highlighted with the special attention being paid to the configuration with the negative extrapolation length.

     

DFT study and NBO analysis of the mutual interconversion of cumulene compounds

The B3LYP/6‐31G* method was used to investigate the configurational properties of allene (1,2‐propadiene) ( 1 ), 1,2,3‐butatriene ( 2 ), 1,2,3,4‐pentateriene ( 3 ), 1,2,3,4,5‐hexapentaene ( 4 ), 1,2,3,4,5,6‐heptahexaene ( 5 ), 1,2,3,4,5,6,7‐octaheptaene ( 6 ), 1,2,3,4,5,6,7,8‐nonaoctaene ( 7 ), and 1,2,3,4,5,6,7,8,9‐decanonaene ( 9 ). The calculations at the B3LYP/6‐31G* level of theory showed that the mutual interconversion energy barrier in compounds 1 – 8 are: 209.73, 131.77, 120.34, 85.00, 80.91, 62.19, 55.56, and 46.83 kJ mol^?1, respectively. The results showed that the difference between the average C?C double bond lengths ( ) values in cumulene compounds 1 and 2 , is larger than those between 7 and 8 , which suggest that with large n (number of carbon atoms in cumulene chain), the values approach a limiting value. Accordingly, based on the plotted data, the extrapolation to n = ∞, gives nearly the same limiting (i. e., ). Also, NBO results revealed that the sum of π‐bond occupancies, , decrease from 1 to 8 , and inversely, the sum of π‐antibonding orbital occupancies, , increase from compound 1 to compound 8 . The decrease of values for compounds 1 – 8 , is found to follow the same trend as the barrier heights of mutual interconversion in compounds 1 – 8 , while the decrease of the barrier height of mutual interconversion in compounds 1 – 8 is found to follow the opposite trend as the increase in the number of carbon atom. Accordingly, besides the previously reported allylic resonant stabilization effect in the transition state structures, the results reveal that the values, , Δ(E_HOMO ? E_LUMO), and the C atom number could be considered as significant criteria for the mutual interconversion in cumulene compounds 1 – 8 . This work reports also useful predictive linear relationships between mutual interconversion energy barriers ( ) in cumulene compounds and the following four parameters: , , Δ(E_HOMO ? E_LUMO), and C_Number. Copyright © 2007 John Wiley & Sons, Ltd.     

Theory of the Robin quantum wall in a linear potential. II. Thermodynamic properties

A theoretical analysis of the thermodynamic properties of the Robin wall characterized by the extrapolation length Λ in the electric field that pushes the particle to the surface is presented both in the canonical and two grand canonical representations and in the whole range of the Robin distance with the emphasis on its negative values which for the voltage‐free configuration support negative‐energy bound state. For the canonical ensemble, the heat capacity at exhibits a nonmonotonic behavior as a function of the temperature T with its pronounced maximum unrestrictedly increasing for the decreasing fields as and its location being proportional to . For the Fermi‐Dirac distribution, the specific heat per particle is a nonmonotonic function of the temperature too with the conspicuous extremum being preceded on the T axis by the plateau whose magnitude at the vanishing is defined as , with N being a number of the particles. The maximum of is the largest for and, similar to the canonical ensemble, grows to infinity as the field goes to zero. For the Bose‐Einstein ensemble, a formation of the sharp asymmetric feature on the ‐T dependence with the increase of N is shown to be more prominent at the lower voltages. This cusp‐like dependence of the heat capacity on the temperature, which for the infinite number of bosons transforms into the discontinuity of , is an indication of the phase transition to the condensate state. Some other physical characteristics such as the critical temperature and ground‐level population of the Bose‐Einstein condensate are calculated and analyzed as a function of the field and extrapolation length. Qualitative and quantitative explanation of these physical phenomena is based on the variation of the energy spectrum by the electric field.     

Orientations of ZnO grown on GaN

On semipolar epitaxial ZnO grown by chemical vapor deposition consists of two distinct orientations as evidenced by transmission electron microscopy and X‐ray diffraction. The initially grown ZnO on GaN follows the GaN lattice with the epitaxial relationship of // and The other oriented ZnO domains then grow on faceted with and with good coherency with the ‐oriented grains. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Hierarchy of the non‐covalent interactions in the alanine‐based secondary structures. DFT study of the frequency shifts and electron‐density features

The alanine (Ala)‐based cluster models of C5, C7, and C10 H‐bonds are studied at the DFT/B3LYP level. CPMD/BLYP simulations of the infinite polyalanine α‐helix (C13 H‐bond) and the two‐stranded β‐sheets are performed. Combined use of frequency shifts and electron‐density features enable us to detect and describe quantitatively the non‐covalent interactions (H‐bonds) defining the intrinsic properties of Ala‐based secondary structures. The energies of the primary N? H O H‐bonds are decreasing in the following way: C13 > C5 ≥ C7 > C10. The energies of the secondary N? H O, N?H N, and H H interactions are comparable to those of the primary H‐bonds (～4.5 kcal/mol). Side chain–backbone C? H O interaction is found to be the weakest non‐covalent interaction in the considered species. Its energy is ～0.5 kcal/mol in the infinite polyalanine α‐helix. Quantum‐topological electron‐density analysis is found to be a powerful tool for the detection of secondary non‐covalent interactions (C?O H? C and H H) and bifurcated H‐bonds, while the frequency shift study is useful for the identification and characterization of primary or secondary H‐bonds of the N? H O type. Copyright © 2008 John Wiley & Sons, Ltd.     

Epitaxy of m ‐plane ZnO on (112) LaAlO3 substrate

Heteroepitaxial growth of non‐polar m ‐plane (10 0) ZnO has been demonstrated on (112) LaAlO₃ single crystal substrates using the pulsed laser deposition method. X‐ray diffraction, reflection high energy electron diffraction, and cross‐sectional transmission electron microscopy with selected‐area diffraction, have been used to characterize the structural properties of deposited ZnO films. The epitaxial relationship between ZnO and LAO is shown to be (10 0)_ZnO ∥ (112)_LAO, (11 0)_ZnO ∥ ( 1)_LAO and [0001]_ZnO ∥ [ 10]_LAO. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparative analysis of electric field influence on the quantum wells with different boundary conditions.

Analytical solutions of the Schrödinger equation for the one‐dimensional quantum well with all possible permutations of the Dirichlet and Neumann boundary conditions (BCs) in perpendicular to the interfaces uniform electric field are used for the comparative investigation of their interaction and its influence on the properties of the system. Limiting cases of the weak and strong voltages allow an easy mathematical treatment and its clear physical explanation; in particular, for the small , the perturbation theory derives for all geometries a linear dependence of the polarization on the field with the BC‐dependent proportionality coefficient being positive (negative) for the ground (excited) states. Simple two‐level approximation elementary explains the negative polarizations as a result of the field‐induced destructive interference of the unperturbed modes and shows that in this case the admixture of only the neighboring states plays a dominant role. Different magnitudes of the polarization for different BCs in this regime are explained physically and confirmed numerically. Hellmann‐Feynman theorem reveals a fundamental relation between the polarization and the speed of the energy change with the field. It is proved that zero‐voltage position entropies are BC independent and for all states but the ground Neumann level (which has ) are equal to while the momentum entropies depend on the edge requirements and the level. Varying electric field changes position and momentum entropies in the opposite directions such that the entropic uncertainty relation is satisfied. Other physical quantities such as the BC‐dependent zero‐energy and zero‐polarization fields are also studied both numerically and analytically. Applications to different branches of physics, such as ocean fluid dynamics and atmospheric and metallic waveguide electrodynamics, are discussed.

     

Equivalence and hermiticity of Dirac Hamiltonians in the Kerr gravitational field

In the paper, for the Kerr field, we prove that Chandrasekhar's Dirac Hamiltonian and the self‐adjoint Hamiltonian with a flat scalar product of the wave functions are physically equivalent. Operators of transformation of Chandrasekhar's Hamiltonian and wave functions to the η representation with a flat scalar product are defined explicitly. If the domain of the wave functions of Dirac's equation in the Kerr field is bounded by two‐dimensional surfaces of revolution around the z axis, Chandrasekhar's Hamiltonian and the self‐adjoint Hamiltonian in the η representation are Hermitian with equality of the scalar products, .

     

Relic photon temperature versus redshift and the cosmic neutrino background

Presuming that CMB photons are described by the deconfining phase of an SU(2) Yang‐Mills theory with the critical temperature for the deconfining‐preconfining phase transition matching the present CMB temperature K (SU(2)_CMB), we investigate how CMB temperature T connects with the cosmological scale factor a in a Friedmann‐Lemaître‐Robertson‐Walker Universe. Owing to a violation of conformal scaling at late times, the tension between the (instantaneous) redshift of reionisation from CMB observation () and quasar spectra () is repealed. Also, we find that the redshift of CMB decoupling moves from to which questions ΛCDM cosmology at high redshifts. Adapting this model to the conventional physics of three flavours of massless cosmic neutrinos, we demonstrate inconsistency with the value N_eff ～ 3.36 extracted from Planck data. Interactions between cosmic neutrinos and the CMB implies a common temperature T of (no longer separately conserved) CMB and neutrino fluids. N_eff ～ 3.36 then entails a universal, temperature induced cosmic neutrino mass with . Our above results on z_re and z_dec, derived from SU(2)_CMB alone, are essentially unaffected when including such a neutrino sector.