Benchmark calculations of Rényi,Tsallis entropies,and Onicescu information energy for ground state helium using correlated Hylleraas wave functions

Accurate values of physical quantities serve as the stepping stone for further researches. Consequently, we provide benchmark values of Shannon, Rényi, Tsallis entropies, and Onicescu information energy for ground state helium. With the highly correlated Hylleraas wave functions, our calculations fully considered the effect of electron correlation. Presented numerical results converge with increasing size of basis set, fulfill analytic relations between the quantities, and satisfactorily agree with those in the literature. In particular, we present these information-theoretic quantities with high accuracy, and it is believed that the reported data would be a valuable reference for further research on information-theoretic quantities of atomic and molecular systems.     

Frequency moments,L_{q} norms and Rényi entropies of general hypergeometric polynomials

The basic variables of the information theory of quantum systems (e.g., frequency or entropic moments, Rényi and Tsallis entropies) can be expressed in terms of $L_{q}$ norms of general hypergeometrical polynomials. These polynomials are known to control the radial and angular parts of the wavefunctions of the quantum-mechanically allowed states of numerous physical and chemical systems. The computation of the $L_{q}$ norms of these polynomials is presently an interesting issue per se in the theory of special functions; moreover, these quantities are closely related to the frequency moments and other information-theoretic properties of the associated Rakhmanov probability density. In this paper we calculate the unweighted and weighted $L_{q}$ -norms $(q=2k, k\in {\mathbb {N}})$ of general hypergeometric real orthogonal polynomials (Hermite, Laguerre and Jacobi) and some entropy-like integrals of Bessel polynomials, in terms of $q$ and the parameters of the corresponding weight function by using their explicit expression and second order differential equation. In addition, the asymptotics $(q\rightarrow \infty )$ of the unweighted $L_{q}$ norms of the Jacobi polynomials is determined by the Laplace method.     

Rényi entropy of the U(3) vibron model

Rényi entropies and variances are determined in the vibron model. They provide a sharp detector for the quantum (shape) phase transition (from linear to bent) at the critical value ξ _c of a control parameter ξ. Numerical results are complemented and compared with a variational approximation in terms of parity-symmetry-adapted coherent (Schödinger’s catlike) states, which provide a good approximation to describe delocalization properties of the ground state of vibron models across the critical point for N-size molecules.     

Rényi entropy of the infinite well potential in momentum space and Dirichlet-like trigonometric functionals

The momentum entropic moments and Rényi entropies of a one-dimensional particle in an infinite well potential are found by means of explicit calculations of some Dirichlet-like trigonometric integrals. The associated spreading lengths and quantum uncertainty-like sums are also provided.     

Phase-space relative Rényi entropy in density functional theory

The phase-space relative Rényi entropy is introduced using the information theoretical and thermodynamic view of density functional theory. In the special case of constant inverse temperature the phase-space relative Rényi entropy is a sum of the position-space relative Rényi entropy and a term arising from the momentum space. This quantity can be considered as a measure of similarity. It includes more information than the position-space measures, since it also incorporates momentum-space knowledge.     

Solution of the mixed Dirichlet–Neumann problem for molecular orientation in liquid crystals

The orientation of the nematic director field under the action of an external time‐dependent field is theoretically investigated as a mixed Dirichlet–Neumann boundary‐value problem. This mathematical problem represents the situation in which a nematic liquid crystal sample is limited by two inhomogeneous flat surfaces, separated by a distance d, on which the anchoring is weak. By considering the one‐constant approximation and a parabolic approximation for the surface energy, the initial conditions and boundary‐value problem for the profile of the tilt angle can be analytically solved even in the case in which the surfaces are not identical, which represents the more general situation. The results are valid for small deviations from the homeotropic orientation and for θ?Θ?1, where θ is the actual tilt angle and Θ characterizes the easy direction imposed by the surface, and can be relevant to investigation of the molecular orientation in a nematic cell submitted to a small external voltage.     

Quantum information entropies of multiple quantum well systems in fractional Schrödinger equations

In this work, we study the position and momentum information entropies of multiple quantum well systems in fractional Schrödinger equations, which, to the best of our knowledge, have not so far been studied. Through a confining potential, their shape and number of wells (NOW) can be controlled by using a few tuning parameters; we present some interesting quantum effects that only appear in the fractional Schrödinger equation systems. One of the parameters denoted by the L_d can affect the position and momentum probability densities if the system is fractional (1 < α < 2). We find that the position (momentum) probability density tends to be more severely localized (delocalized) in more fractional systems (ie, in smaller values of α). Affecting the L_d on the position and momentum probability densities is a quantum effect that only appears in the fractional Schrödinger equations. Finally, we show that the Beckner Bialynicki-Birula-Mycieslki (BBM) inequality in the fractional Schrödinger equation is still satisfied by changing the confining potential amplitude V_conf, the NOW, the fractional parameter α, and the confining potential parameter L_d .     

Exact quantum and TST-CEQ study of the collinear reaction O+HCl

Exact quantum calculations of reaction probabilities have been carried out using hyperspherical coordinates for the collinearr reaction O+HCl(v <1) -OH(v'<1)+Cl . A generalized LEPS potential energy surface with a barrier height of 8.12 kcal/mol has been used in the calculations. According to the calculated results we found that (1) the reaction probability oscillates with energy, (2) the reaction probability shows vibrational adiabaticity, although it is poorer than that for symmetric reaction Cl + HC1. The analysis of resonance has also been done. The reaction rate constants and average cross sections have been calculated by TST-CEQ method. The rate constants are in agreement with that by QCT and smaller than the experimental one. Finally, the threshold has been estimated and is in good agreement with that of the literature.     

Crystal structure and electrical conductivity of the “one-dimensional solid electrolyteN,N-dimethylmorpholinium pentaiodotetraargentate

The new solid electrolyteN, N-dimethylmorpholinium pentaiodotetraargentate, [(CH₃)N(CH₂)₂-(CH₂)₂O]Ag₄I₅ (DMMAg₄I₅), has a crystal structure which allows the Ag⁺ ions to move effectively in only one dimension. The channels for this motion result from the sharing of opposite faces of icosahedra, having iodides at their centers, forming infinite chains of icosahedra along thea axis. The joining of the icosahedra forms three more face-sharing tetrahedra at each junction, or a total of 23 tetrahedra per eight Ag⁺ ions, which are distributed non-uniformly over the tetrahedral sites. The limited number of pathways for the Ag⁺ ion diffusion leads to a low average conductivity, 1 × 10⁻⁴ Ω⁻¹ cm⁻¹ and a high activation enthalpy, 0.35 eV. Crystals of DMMAg₄I₅ belong to space groupP2₁2₁2₁ (D⁴₂) witha = 13.167(4), b = 23.437(3), c = 12.758(3)A˚; the unit cell contains eight formula units. The structure of dimethylmorpholinium iodide (DMMI) confirms the chair model for the DMM⁺ ion. Crystals of DMMI belong to space groupP2₁m(C²_2h), witha = 8.861(4), b = 8.020(2), c = 6.685(2)A˚, β = 101.07(3)°; each unit cell contains two formula units.     

Calculation of direct and indirect excitons in GaAs–Ga1−xAlxAs coupled double quantum wells: Electric and magnetic fields and hydrostatic pressure effects

A study of the electronic and optical properties of coupled double quantum wells is presented. Within the framework of the effective mass and parabolic-band approximations we have calculated the electron–hole and photoluminescence energy transitions under simultaneous effects of electric and magnetic fields. For that purpose, a variational procedure has been used, taking into account the effect of hydrostatic pressure. The electric field is taken to be oriented along the growth direction of the heterostructure whereas for the magnetic field both in-plane and in-growth directions have been considered. The results show that hydrostatic pressure is a useful tool to tune the direct and indirect exciton transitions in such heterostructures. It is shown that the photoluminescence peak energy transitions strongly depend on the external fields and hydrostatic pressure studied here. Furthermore, our numerical outcome is in good agreement with previous experimental findings at zero pressure in double quantum wells under applied electric and magnetic fields.     

Calculation of the quantum yield of the photochemical isomerization reaction → methoxybutadiene methoxycyclobutene

The methoxybutadiene → methoxycyclobutene photoisomerization process was simulated and the quantum yield of the product was calculated. The validity of the theoretical ideas and model concepts used in the proposed method for the calculation of quantum yields of photochemical reactions was confirmed. It was shown that the empirical parameter used in the model (broadening parameter) is stable in value and has the inherent property of transferability over a series of related molecules and analogous reactions. The cause of a substantial difference between the experimental quantum yields of reactions of the same type for a number of molecules bearing different substituents was revealed: this is a change in the form of vibrations and/or in the magnitude of structural rearrangement that directly involves the substituent.     

Influence of quantum effects on the mechanism of adsorption and phase diagram of rare gases in carbon nanotubes

We present results of grand canonical Monte Carlo simulations of rare gases (He, Ne, Ar, Kr and Xe) adsorption in carbon nanotubes. The interaction model includes both quantum effects (via effective Feymann-Hibbs potential) and the atomic roughness of the tube. We show that the quantum contribution to interactions does not suppress the energetic corrugation of carbon nanotube but decreases only its average strength. In the case of Ne, the phase diagram and, in particular, the melting temperature for layers adsorbed on and within an individual tube does not depend on tube chirality. However, the structure of layers adsorbed on outer surface of the tube is strongly related to the atomic structure of the underlying tube.     

Computational determination of the à state absorption spectrum of NH3 and of ND3 using a new quasi-diabatic representation of the X and à states and full six-dimensional quantum dynamics

A recently developed method to represent adiabatic electronic states coupled by conical intersections has been used to construct a full six-dimensional quasi-diabatic representation of the 1(1)A and 2(1)A states of NH(3). This representation is expected to be appropriate to simulate the photodissociation of ammonia when it is excited to the 2(1)A electronic state. In this work, the electronic structure aspects of this quasi-diabatic representation are analyzed. This representation is then used as the basis for a simulation of the ? ← X absorption spectrum, dominated by a progression in the v(2) mode, using a full six-dimensional quantum mechanical treatment of the nuclear motion. Results are reported for both NH(3) and ND(3). This simulation provides the most accurate computational determination of this absorption spectrum reported to date. These results serve to validate the quasi-diabatic representation and set the stage for subsequent studies of vibrationally mediated photodissociation of NH(3).     

Generalisations of the pitzer—gwinn and feynman—hibbs approximations for quantum partition functions

By using an expression of Feynman and Hibbs for the partition function Z = Tr[exp[- β(p²/2m + V)]) in terms of integrals over paths with fixed means, and substituting for the potential V a local harmonic approximant (following Miller), we obtain an improved Pitzer—Gwinn approximation, as simple to use as the original one, but applicable to a much broader class of potentials. Systematic corrections, in the form of cumulant and Wigner—Kirkwood expansions are then obtained.     

Is the problem of molecular structure just the quantum measurement problem?

In a recent article entitled “The problem of molecular structure just is the measurement problem”, Alexander Franklin and Vanessa Seifert argue that insofar as the quantum measurement problem is solved, the problems of molecular structure are resolved as well. The purpose of the present article is to show that such a claim is too optimistic. Although the solution of the quantum measurement problem is relevant to how the problem of molecular structure is faced, such a solution is not sufficient to account for the structure of molecules as understood in the field of chemistry.

     

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.     

A quantum chemical study on the mechanism of the consecutive addition of HCN to propionitrile

MINDO/3 MO method has been used to study the mechanism of the consecutive addition of HCN to propionitrile. The results obtained for the first five steps show that the reaction is exothermic, and step 1 is the rate determining step.     

How does the NMR thermometer work? Application of combined quantum molecular dynamics and GIPAW calculations into the study of lead nitrate

Lead nitrate is an inorganic salt, commonly used for the accurate temperature determination in the solid state NMR spectroscopy, due to the strong temperature dependence of the ²⁰⁷Pb chemical shift. As the reason for this phenomenon remained unknown, the main purpose of this study was to explain this temperature dependence at the molecular level. To achieve this, combined CASTEP geometry optimization, quantum molecular dynamics at chosen temperatures and GIPAW NMR computations were performed. Due to the previous literature reports on inaccuracy in the calculation of ²⁰⁷Pb NMR parameters using GIPAW, a large emphasis was put on the optimization of computational method. The application of quantum molecular dynamics provided the simulation of the temperature-dependent vibrational motions and enabled to accurately compute the changes in the value of Pb δ_iso resulting from them. © 2018 Wiley Periodicals, Inc.     

Synthesis and characterization of a one-dimensional polymeric copper(Ⅱ)-tetrathioporphyrazine

The title polymer PCuS4Pz was synthesized by reaction of 2,3-dicyano-5,6-dihydro-1,4-dithiin,pyromellitic dianhydride and urea with cuprous salt in optimized gentle method.The structure and properties of the PCuS4Pz were characterized by elemental analysis,X-ray powder diffraction,IR,UV-Vis,fluorescence and EPR spectra and variable-temperature magnetic susceptibility.The polymer is black sublimable crystallite and the degree of polymerization has been found to be n>4.The PCuS4Pz in H2SO4 exhibits intensive absorption bands at 236,342,656 and 767 nm and intensive fluorescence band at 410 nm or 464 nm under the excitation of the ultraviolet light of a determined wavelength at room temperature.It has been found that the polymer exhibits a weaker antiferromag-netic interaction (J=-2.cm-1,εff=1.68 B.M.) with an apparent spin S<1/2 in the ground state and its conductivity 298K is 1.01×10-5 S-cm-1 at 13.73 MPa.