Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action

It is known that the actions of field theories on a noncommutative space-time can be written as some modified (we call them theta-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and the usual quantum mechanical features of the corresponding field theory. In the present article, we discuss the problem of constructing theta-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract theta-modified actions of the relativistic particles from path-integral representations of the corresponding noncommutative field theory propagators. We consider the Klein-Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as theta-modified actions of the relativistic particles. To confirm the interpretation, we canonically quantize these actions. Thus, we obtain the Klein-Gordon and Dirac equations in the noncommutative field theories. The theta-modified action of the relativistic spinning particle is just a generalization of the Berezin-Marinov pseudoclassical action for the noncommutative case.

CONSTRUCTING QUANTUM OBSERVABLES AND SELF-ADJOINT EXTENSIONS OF SYMMETRIC OPERATORS. III. SELF-ADJOINT BOUNDARY CONDITIONS

This paper completes the review of the theory of self-adjoint extensions of symmetric operators for physicists as a basis for constructing quantum-mechanical observables. It contains a comparative presentation of the well-known methods and a newly proposed method for constructing ordinary self-adjoint differential operators associated with self-adjoint differential expressions in terms of self-adjoint boundary conditions. The new method has the advantage that it does not require explicitly evaluating deficient subspaces and deficiency indices (these latter are determined in passing) and that boundary conditions are of explicit character irrespective of the singularity of a differential expression. General assertions and constructions are illustrated by examples of well-known quantum-mechanical operators like momentum and Hamiltonian.

Rankamaite from the Urubu pegmatite, Itinga, Minas Gerais, Brazil: Crystal chemistry and Rietveld refinement

A new occurrence of rankamaite is here described at the Urubu pegmatite, Itinga municipality, Minas Gerais, Brazil. The mineral forms cream-white botryoidal aggregates of acicular to fibrous crystals, intimately associated with simpsonite, thoreaulite, cassiterite, quartz, elbaite, albite, and muscovite. The average of six chemical analyses obtained by electron microprobe is (range in parentheses, wt%): Na(2)O 2.08 (1.95-2.13), K(2)O 2.61 (2.52-2.74), Al(2)O(3) 1.96 (1.89-2.00), Fe(2)O(3) 0.01 (0.00-0.03), TiO(2) 0.02 (0.00-0.06), Ta(2)O(5) 81.04 (79.12-85.18), Nb(2)O(5) 9.49 (8.58-9.86), total 97.21 (95.95-101.50). The chemical formula derived from this analysis is (Na(1.55)K(1.28))(Sigma 2.83)(Ta(8.45)Nb(1.64)Al(0.89)Fe(0.01)(3+)Ti(0.01))(Sigma 11.00)[O(25.02)(OH)(5.98)](Sigma 31.00). Rankamaite is an orthorhombic ""tungsten bronze"" (OTB), crystallizing in the space group Cmmm. Its unit-cell parameters refined from X-ray diffraction powder data are: a = 17.224(3), b = 17.687(3), c = 3.9361(7) angstrom, V = 1199.1(3) angstrom(3), Z = 2. Rietveld refinement of the powder data was undertaken using the structure of LaTa(5)O(14) as a starting model for the rankamaite structure. The structural formula obtained with the Rietveld analyses is: (Na(2.21)K(1.26))Sigma(3.37)(Ta(9.12)NB(1.30) Al(0.59))(Sigma 11.00)[O(26.29)(OH)(4.71)](Sigma 31.00). The tantalum atoms are coordinated by six and seven oxygen atoms in the form of distorted TaO(6) octahedra and TaO(2) pentagonal bipyramids, respectively. Every pentagonal bipyramid shares edges with four octahedra, thus forming Ta(5)O(14) units. The potassium atom is in an 11-fold coordination, whereas one sodium atom is in a 10-fold and the other is in a 12-fold coordination. Raman and infrared spectroscopy were used to investigate the room-temperature spectra of rankamaite.

Surface and Quantum Confinement Effects in ZnO Nanocrystals

ZnO nanocrystals are studied using theoretical calculations based on the density functional theory. The two main effects related to the reduced size of the nanocrystals are investigated: quantum confinement and a large surface:volume ratio. The effects of quantum confinement are studied by saturating the surface dangling bonds of the nanocrystals with hypothetical H atoms. To understand the effects of the surfaces of the nanocrystals, all saturation is removed and the system is relaxed to its minimum energy position. Several different surface motifs are reported, which should be observed experimentally. Spin-polarized calculations are performed in the nonsaturated nanocrystals, leading to different magnetic moments. We propose that this magnetic moment can be responsible for the intrinsic magnetism observed in ZnO nanostructures.

Continuum, Discrete, and Explicit Solvation Models for Describing the Low-Lying Absorption Spectrum of the Pterin Acid in Aqueous Environment

The absorption spectrum of the acid form of pterin in water was investigated theoretically. Different procedures using continuum, discrete, and explicit models were used to include the solvation effect on the absorption spectrum, characterized by two bands. The discrete and explicit models used Monte Carlo simulation to generate the liquid structure and time-dependent density functional theory (B3LYP/6-31G+(d)) to obtain the excitation energies. The discrete model failed to give the correct qualitative effect on the second absorption band. The continuum model, in turn, has given a correct qualitative picture and a semiquantitative description. The explicit use of 29 solvent molecules, forming a hydration shell of 6 angstrom, embedded in the electrostatic field of the remaining solvent molecules, gives absorption transitions at 3.67 and 4.59 eV in excellent agreement with the S(0)-S(1) and S(0)-S(2) absorption bands at of 3.66 and 4.59 eV, respectively, that characterize the experimental spectrum of pterin in water environment. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110: 2371-2377, 2010

IxV Curves of Boron and Nitrogen Doping Zigzag Graphene Nanoribbons

We investigate the transport properties (IxV curves and zero bias transmittance) of pristine graphene nanoribbons (GNRs) as well as doped with boron and nitrogen using an approach that combines nonequilibrium Green`s functions and density functional theory (DFT) [NEGF-DFT]. Even for a pristine nanoribbon we verify a spin-filter effect under finite bias voltage when the leads have an antiparallel magnetization. The presence of the impurities at the edges of monohydrogenated zigzag GNRs changes dramatically the charge transport properties inducing a spin-polarized conductance. The IxV curves for these systems show that depending on the bias voltage the spin polarization can be inverted. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 111: 1379-1386, 2011

Luminescence studies on nitride quaternary alloys double quantum wells

We present theoretical photoluminescence (PL) spectra of undoped and p-doped Al(x)In(1-xy)Ga(y)N/Al(X)In(1) (X) (Y)Ga(Y)N double quantum wells (DQWs). The calculations were performed within the k.p method by means of solving a full eight-band Kane Hamiltonian together with the Poisson equation in a plane wave representation, including exchange-correlation effects within the local density approximation. Strain effects due to the lattice mismatch are also taken into account. We show the calculated PL spectra, analyzing the blue and red-shifts in energy as one varies the spike and the well widths, as well as the acceptor doping concentration. We found a transition between a regime of isolated quantum wells and that of interacting DQWs. Since there are few studies of optical properties of quantum wells based on nitride quaternary alloys, the results reported here will provide guidelines for the interpretation of forthcoming experiments. (C) 2008 Elsevier B.V. All rights reserved.

Empirical analysis of the Lieb-Oxford bound in ions and molecules

Universal properties of the Coulomb interaction energy apply to all many-electron systems. Bounds on the exchange-correlation energy, in particular, are important for the construction of improved density functionals. Here we investigate one such universal property-the Lieb-Oxford lower bound-for ionic and molecular systems. In recent work [J Chem Phys 127, 054106 (2007)], we observed that for atoms and electron liquids this bound may be substantially tightened. Calculations for a few ions and molecules suggested the same tendency, but were not conclusive due to the small number of systems considered. Here we extend that analysis to many different families of ions and molecules, and find that for these, too, the bound can be empirically tightened by a similar margin as for atoms and electron liquids. Tightening the Lieb-Oxford bound will have consequences for the performance of various approximate exchange-correlation functionals. (C) 2008 Wiley Periodicals Inc.

Electronic Structure of the Ground and Low-Lying Electronic States of MoB and MoB(+)

Multiconfigurational second-order perturbation theory (CASSCF//CASPT2) and quadruple-zeta ANO-RCC basis sets were employed to investigate the ground and low-lying electronic states of MoB and MoB(+). Spectroscopic constants, potential energy curves, wavefunctions, Mulliken population analyses, and ionization energies are given. The ground state of MoB is of X(6)Pi symmetry (R(e) = 1.968 angstrom, omega(e) = 664 cm(-1), and mu = 2.7 D), giving rise to a Omega = 7/2 ground state after including spin-orbit coupling. For MoB(+), the ground state is computed to be of X(7)Sigma(+) symmetry (R(e) = 2.224 angstrom, omega(e) = 141 cm(-1), and mu = 1.2 D), with an adiabatic ionization energy of 7.19 eV and a vertical one of 7.53 eV. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem 111: 3362-3370, 2011

Solvatochromic Shift of the pi -> pi* Transition in All-Trans, Cis-13, Cis-11, Cis-9, and Cis-7 Retinal Isomers Induced by Water and Methanol

The solvatochromic shift of the lowest singlet it pi -> pi* electronic transition in the all-trans, cis-13, cis-11, cis-9, and cis-7 retinal isomers were computed under the influence of water, methanol, and benzene solvents. Excitation energies were calculated in gas phase and in solution. The calculations in solution were performed considering the sequential Monte Carlo (MC) /Quantum Mechanical approach. The MC simulations were performed considering the full retinal isomer molecules and 900 water molecules, 900 methanol, or 400 benzene ones. The OPLS/AA parametrization was chosen for retinal, methanol, and benzene molecules and the SPC model was used for water one. From the MC calculations 100 independent configurations were selected, with 100 solvent molecules in thermodynamical equilibrium at T = 298.15 K. Average point-charges were obtained from those independent configurations for water, methanol, and benzene solvent. TDDFT and CASSCF//CASPT2 methodologies were used to compute the vertical excitation energy of the retinal isomers in different environment. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110: 2076-2087, 2010

Electronic Structure and Chemical Bonding in the Ground and Low-Lying Electronic States of Ta(2)

The electronic structure and chemical bonding of the ground and low-lying Lambda - S and Omega states of Ta(2) were investigated at the multiconfiguration second-order perturbation theory (CASSCF//CASPT2) level. The ground state of Ta(2) is computed to be a X(3)Sigma(-)(g) state (R(e) = 2.120 angstrom, omega(e) = 323 cm(-1), and D(e) = 4.65 eV), with two low-lying singlet states close to it (a(1) Sigma(+)(g) : T(e) = 409 cm(-1), R(e) = 2.131 angstrom, and omega(e) = 313 cm(-1); b(1) Gamma(g): T(e) = 1, 038 cm(-1), R(e) = 2.127 angstrom, and omega(e) = 316 cm(-1)). These electronic states are derived from the same electronic configuration: vertical bar 13 sigma(2)(g)14 sigma(2)(g)7 delta(2)(g)13 pi(4)(u)>. The effective bond order of the X(3) Sigma(-)(g) state is 4.52, which indicates that the Ta atoms are bound by a quintuple chemical bond. The a(1) Sigma(+)(g) state interacts strongly with the X(3)Sigma(-)(g) g ground state by a second-order spin-orbit interaction, giving rise to the (1)0(g)(+) (ground state) (dominated by the X(3)Sigma(-)(g) Lambda - S ground state) and (9)0(g)(+) (dominated by the a(1) Sigma(+)(g) Lambda - S state) Omega states. These results are in line with those reported for the group 5B homonuclear transition metal diatomics. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 111: 1306-1315, 2011

Raman spectra of polymer electrolytes based on poly(ethylene glycol) dimethyl ether, lithium perchlorate, and the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate

Raman spectra of polymer electrolytes based on poly(ethylene glycol) dimethyl ether (PEGdME) with LiClO(4), PEGdME/LiClO(4), and the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate, PEGdME/[bmim]PF(6), are compared. Raman spectroscopy suggests stronger interactions in PEGdME/LiClO(4) than PEGdmE/[bmim]PF(6), thus corroborating previous results obtained by molecular dynamics simulations. Quantum Chemistry methods have been used to calculate vibrational frequencies and the equilibrium structure of segments of the polymer chain around the cation. A consistent picture has been obtained from Raman spectroscopy, density functional theory (DFT) calculations, and molecular dynamics simulations for these polymer electrolytes. (C) 2010 Elsevier B.V. All rights reserved.

Ab Initio Analysis of Monomers and Dimers of Trialkylphosphine Oxides: Structural and Thermodynamic Stability

Structural and thermodynamic stabilities of monomers and dimers of trialkylphosphine oxides (TRPO) were Studied using quantum chemistry calculations. Density functional theory calculations were carried Out and the structures Of four TRPO have been determined: TMPO (methyl; R = CH(3)), TEPO (ethyl; R = CH(3)CH(2)), TBPO (n-butyl; R = CH(3)(CH(2))(3)), and TOPO (n-octyl; R = CH(3)(CH(2))(7)). TRPO homodimers were investigated considering two isomeric possibilities for each dimer. Relative binding energies and the enthalpic and entropic contributions to the Gibbs free energy were Calculated for all dimers. The formation of dimers from the individual monomeric TRPO species as a function of temperature was also analyzed. (C) 2008 Wiley Periodicals, Inc. Int J Quantum Chem 109: 250-258, 2009

Crystal structure and theoretical calculations of Julocrotine, a natural product with antileishmanial activity

Julocrotine, N-(2,6-dioxo-l-phenethyl-piperidin-3-yl)-2-methyl-butyramide, is a potent antiproliferative agent against the promastigote and amastigote forms of Leishmania amazonensis (L.). In this work, the crystal structure of Julocrotine was solved by X-ray diffraction, and its geometrical parameters were compared with theoretical calculations at the B3LYP and HF level of theory. IR and NMR spectra also have been obtained and compared with theoretical calculations. IR absorptions calculated with the B3LYP level of theory employed together with the 6-311G+(d,p) basis set, are close to those observed experimentally. Theoretical NMR calculations show little deviation from experimental results. The results show that the theory is in accordance with the experimental data. (C) 2007 Wiley Periodicals, Inc.