Uma breve discussão sobre os possíveis estados ligados para uma classe de potenciais singulares

Investiga-se a equação de Schrödinger unidimensional com uma classe de potenciais V(|x|) que se anulam no infinito e apresentam singularidade dominante na origem na forma α/|x|β(0 < β < 2). A hermiticidade dos operadores associados com quantidades físicas observáveis é usada para determinar as condições de contorno apropriadas. Dupla degenerescência e exclusão de soluções simétricas, consoante o valor de β, são discutidas. Soluções explícitas para o átomo de hidrogênio e o potencial de Kratzer são apresentadas.

Spherical, cylindrical and tetrahedral symmetries; hydrogenic states at high magnetic field in Si:P

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Potenciais singulares na equação de Schrodinger unidimensional via transformada de Laplace

The present work has as its goal to treat well known and interesting unidimensional cases from quantum mechanics through an unusual approach within this eld of physics. The operational method of Laplace transform, in spite of its use by Erwin Schrödinger in 1926 when treating the radial equation for the hydrogen atom, turned out to be forgotten for decades. However, the method has gained attention again for its use as a powerful tool from mathematical physics applied to the quantum mechanics, appearing in recent works. The method is specially suitable to the approach of cases where we have potential functions with even parity, because this implies in eigenfunctions with de ned parity, and since the domain of this transform ranges from 0 to ∞, it su ces that we nd the eigenfunction in the positive semi axis and, with the boundary conditions imposed over the eigenfunction at the origin plus the continuity (discontinuity) of the eigenfunction and its derivative, we make the odd, even or both parity extensions so we can get the eigenfunction along all the axis. Factoring the eigenfunction behavior at in nity and origin, we take the due care with the points that might bring us problems in the later steps of the solving process, thus we can manipulate the Schrödinger's Equation regardless of time, so that way we make it convenient to the application of Laplace transform. The Chapter 3 shows the methodology that must be followed in order to search for the solutions to each problem

Finite-difference calculation of donor energy levels in a spherical quantum dot subject to a magnetic field

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A Combined Study Using Ligand-Based Design, Synthesis, and Pharmacological Evaluation of Analogues of the Acetaminophen Ortho-Regioisomer with Potent Analgesic Activity

A ligand-based drug design study was performed to acetaminophen regioisomers as analgesic candidates employing quantum chemical calculations at the DFT/B3LYP level of theory and the 6-31G* basis set. To do so, many molecular descriptors were used such as highest occupied molecular orbital, ionization potential, HO bond dissociation energies, and spin densities, which might be related to quench reactivity of the tyrosyl radical to give N-acetyl-p-benzosemiquinone-imine through an initial electron withdrawing or hydrogen atom abstraction. Based on this in silico work, the most promising molecule, orthobenzamol, was synthesized and tested. The results expected from the theoretical prediction were confirmed in vivo using mouse models of nociception such as writhing, paw licking, and hot plate tests. All biological results suggested an antinociceptive activity mediated by opioid receptors. Furthermore, at 90 and 120 min, this new compound had an effect that was comparable to morphine, the standard drug for this test. Finally, the pharmacophore model is discussed according to the electronic properties derived from quantum chemistry calculations.

The infrared fundamental intensities of some cyanopolyynes

Some cyanopolyynes, HCnN (n = 1, 3, ... , 17), are investigated by means of calculations at the MP2/cc-pVTZ and CCSD/cc-pVDZ levels. Although the MP2/cc-pVTZ results for geometries and molecular dipole moments are encouraging, the CCSD/cc-pVDZ level was superior for the study of infrared fundamental intensities. The main bands are also analyzed with a charge-charge flux-dipole flux (CCFDF) partition model based on quantities given by the Quantum Theory of Atoms in Molecules (QTAIM). The intensity of vibrations corresponding to the stretching of CH bonds (3471-3473 cm(-1)) increases in line with the number of carbon atoms (from 61 to 146 km mol(-1) between HCN and HC13N). This increase is due to the charge flux contribution while the other contributions remain roughly unaltered except for HCN. Moreover, the hydrogen atom loses an almost constant amount of electronic charge during the CH bond enlargement and a small fraction of this charge spreads to atoms farther and farther away from hydrogen as the molecule size increases. The band associated with the doubly degenerate CH bending vibrations (643-732 cm(-1)) presents approximately the same intensity in all the studied cyanopolyynes (from 67 to 76 km mol(-1)). The CCFDF/QTAIM contributions are also nearly the same for these bending modes in HC5N and larger systems. The intensity of the mode mostly identified as CN stretching (around 2378-2399 cm(-1) except for HCN) increases from HCN up to HC7N (from 0.3 to 83 km mol(-1)) and nearly stabilizes around 80-90 km mol(-1) for larger systems. The CCFDF/QTAIM contributions for this mode also change significantly up to HC7N and remain almost constant in larger systems. We also observed the appearing of a very relevant band between 2283 and 2342 cm(-1). This mode is mainly associated with the symmetric stretching of CC triple bonds near the molecule center and exhibits large charge fluxes while the other contributions are almost negligible in the largest cyanopolyynes. The two vibrational bands associated with the smallest frequencies are also studied and extrapolation equations are suggested to predict their positions in larger cyanopolyynes. (C) 2012 Elsevier B.V. All rights reserved.

Semiempirical Study of the Bergman Reaction: Towards a Computationally Efficient and Accurate Method for Modeling Enediyne Anticancer Antibiotics

Over the past 7 years, the enediyne anticancer antibiotics have been widely studied due to their DNA cleaving ability. The focus of these antibiotics, represented by kedarcidin chromophore, neocarzinostatin chromophore, calicheamicin, esperamicin A, and dynemicin A, is on the enediyne moiety contained within each of these antibiotics. In its inactive form, the moiety is benign to its environment. Upon suitable activation, the system undergoes a Bergman cycloaromatization proceeding through a 1,4-dehydrobenzene diradical intermediate. It is this diradical intermediate that is thought to cleave double-stranded dna through hydrogen atom abstraction. Semiempirical, semiempiricalci, Hartree–Fock ab initio, and mp2 electron correlation methods have been used to investigate the inactive hex-3-ene-1,5-diyne reactant, the 1,4-dehydrobenzene diradical, and a transition state structure of the Bergman reaction. Geometries calculated with different basis sets and by semiempirical methods have been used for single-point calculations using electron correlation methods. These results are compared with the best experimental and theoretical results reported in the literature. Implications of these results for computational studies of the enediyne anticancer antibiotics are discussed.

Kyzylkumite, Ti2V3+O5(OH): new structure type, modularity and revised formula

The crystal structure of kyzylkumite, ideally Ti2V3+O5(OH), from the Sludyanka complex in South Baikal, Russia was solved and refined (including the hydrogen atom position) to an agreement index, R1, of 2.34 using X-ray diffraction data collected on a twinned crystal. Kyzylkumite crystallizes in space group P21/c, with a = 8.4787(1), b = 4.5624(1), c = 10.0330(1) Å, β = 93.174(1)°, V = 387.51(1) Å3 and Z = 4. Tivanite, TiV3+O3OH, and kyzylkumite have modular structures based on hexagonal close packing of oxygen, which are made up of rutile TiO2 and montroseite V3+O(OH) slices. In tivanite the rutile:montroseite ratio is 1:1, in kyzylkumite the ratio is 2:1. The montroseite module may be replaced by the isotypic paramontroseite V4+O2 module, which produces a phase with the formula Ti2V4+O6. In the metamorphic rocks of the Sludyanka complex, vanadium can be present as V4+ and V3+ within the same mineral (e.g. in batisivite, schreyerite and berdesinskiite). Kyzylkumite has a flexible composition with respect to the M4+/M3+ ratio. The relationship between kyzylkumite and a closely related Be-bearing kyzylkumite-like mineral with an orthorhombic norbergite-type structure from Byrud mine, Norway is discussed. Both minerals have similar X-ray powder diffraction patterns.

Excitation and charge transfer in H-H+ collisions at 5-80 keV and application to astrophysical shocks

In astrophysical regimes where the collisional excitation of hydrogen atoms is relevant, the cross-sections for the interactions of hydrogen atoms with electrons and protons are necessary for calculating line profiles and intensities. In particular, at relative velocities exceeding ∼1000 km s−1, collisional excitation by protons dominates over that by electrons. Surprisingly, the H–H+ cross-sections at these velocities do not exist for atomic levels of n≥ 4, forcing researchers to utilize extrapolation via inaccurate scaling laws. In this study, we present a faster and improved algorithm for computing cross-sections for the H–H+ collisional system, including excitation and charge transfer to the n≥ 2 levels of the hydrogen atom. We develop a code named BDSCX which directly solves the Schrödinger equation with variable (but non-adaptive) resolution and utilizes a hybrid spatial-Fourier grid. Our novel hybrid grid reduces the number of grid points needed from ∼4000n6 (for a ‘brute force’, Cartesian grid) to ∼2000n4 and speeds up the computation by a factor of ∼50 for calculations going up to n= 4. We present (l, m)-resolved results for charge transfer and excitation final states for n= 2–4 and for projectile energies of 5–80 keV, as well as fitting functions for the cross-sections. The ability to accurately compute H–H+ cross-sections to n= 4 allows us to calculate the Balmer decrement, the ratio of Hα to Hβ line intensities. We find that the Balmer decrement starts to increase beyond its largely constant value of 2–3 below 10 keV, reaching values of 4–5 at 5 keV, thus complicating its use as a diagnostic of dust extinction when fast (∼1000 km s−1) shocks are impinging upon the ambient interstellar medium.

Comparison of structures and energies of CH52+• with CH4+• and their possible role in superacidic methane activation

Contrary to previous theoretical studies at the UHF/6-31G* level, the methonium radical dication CH52+ is not a Cs symmetrical structure with a 2e—3c bond but a C2v symmetrical structure 1 with two 2e—3c bonds (at the UHF/6-31G**, UMP2/6-31G**, and UQCISD(T)/6-311G** levels). The Cs symmetrical structure is not even a minimum at the higher level of calculations. The four hydrogen atoms in 1 are bonded to the carbon atom by two 2e—3c bonds and the fifth hydrogen atom by a 2e—2c bond. The unpaired electron of 1 is located in a formal p-orbital (of the sp2-hybridized carbon atom) perpendicular to the plane of the molecule. Hydrogen scrambling in 1 is however extremely facile, as is in other C1 cations. It is found that the protonation of methane to CH5+ decreases the energy for subsequent homolytic cleavage resulting in the exothermic (24.1 kcal/mol) formation of CH4+•. Subsequent reaction with neutral methane while reforming CH5+ gives the methyl radical enabling reaction with excess methane to ethane and H2. The overall reaction is endothermic by 11.4 kcal/mol, but offers under conditions of oxidative removal of H2 an alternative to the more energetic carbocationic conversion of methane.

Designing safer chemicals: predicting the rates of metabolism of halogenated alkanes.

A computational model is presented that can be used as a tool in the design of safer chemicals. This model predicts the rate of hydrogen-atom abstraction by cytochrome P450 enzymes. Excellent correlations between biotransformation rates and the calculated activation energies (delta Hact) of the cytochrome P450-mediated hydrogen-atom abstractions were obtained for the in vitro biotransformation of six halogenated alkanes (1-fluoro-1,1,2,2-tetrachloroethane, 1,1-difluoro-1,2,2-trichloroethane, 1,1,1-trifluro-2,2-dichloroethane, 1,1,1,2-tetrafluoro-2-chloroethane, 1,1,1,2,2,-pentafluoroethane, and 2-bromo-2-chloro-1,1,1-trifluoroethane) with both rat and human enzyme preparations: In(rate, rat liver microsomes) = 44.99 - 1.79(delta Hact), r2 = 0.86; In(rate, human CYP2E1) = 46.99 - 1.77(delta Hact), r2 = 0.97 (rates are in nmol of product per min per nmol of cytochrome P450 and energies are in kcal/mol). Correlations were also obtained for five inhalation anesthetics (enflurane, sevoflurane, desflurane, methoxyflurane, and isoflurane) for both in vivo and in vitro metabolism by humans: In[F(-)]peak plasma = 42.87 - 1.57(delta Hact), r2 = 0.86. To our knowledge, these are the first in vivo human metabolic rates to be quantitatively predicted. Furthermore, this is one of the first examples where computational predictions and in vivo and in vitro data have been shown to agree in any species. The model presented herein provides an archetype for the methodology that may be used in the future design of safer chemicals, particularly hydrochlorofluorocarbons and inhalation anesthetics.

The electron-furfural scattering dynamics for 63 energetically open electronic states

We report on integral-, momentum transfer-and differential cross sections for elastic and electronically inelastic electron collisions with furfural (C5H4O2). The calculations were performed with two different theoretical methodologies, the Schwinger multichannel method with pseudopotentials (SMCPP) and the independent atom method with screening corrected additivity rule (IAM-SCAR) that now incorporates a further interference (I) term. The SMCPP with N energetically open electronic states (N-open) at either the static-exchange (N-open ch-SE) or the static-exchange-plus-polarisation (N-open ch-SEP) approximation was employed to calculate the scattering amplitudes at impact energies lying between 5 eV and 50 eV, using a channel coupling scheme that ranges from the 1ch-SEP up to the 63ch-SE level of approximation depending on the energy considered. For elastic scattering, we found very good overall agreement at higher energies among our SMCPP cross sections, our IAM-SCAR+I cross sections and the experimental data for furan (a molecule that differs from furfural only by the substitution of a hydrogen atom in furan with an aldehyde functional group). This is a good indication that our elastic cross sections are converged with respect to the multichannel coupling effect for most of the investigated intermediate energies. However, although the present application represents the most sophisticated calculation performed with the SMCPP method thus far, the inelastic cross sections, even for the low lying energy states, are still not completely converged for intermediate and higher energies. We discuss possible reasons leading to this discrepancy and point out what further steps need to be undertaken in order to improve the agreement between the calculated and measured cross sections. (C) 2016 AIP Publishing LLC.

Entangled subspaces and quantum symmetries

Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt decomposition of the projection operator defines a string of Schmidt coefficients for each subspace, and this string is assumed to characterize its entanglement, so that a first subspace is more entangled than a second, if the Schmidt string of the second majorizes the Schmidt string of the first. The idea is applied to the antisymmetric and symmetric tensor products of a finite-dimensional Hilbert space with itself, and also to the tensor product of an angular momentum j with a spin 1/2. When adapted to the subspaces of states of the nonrelativistic hydrogen atom with definite total angular momentum (orbital plus spin), within the space of bound states with a given total energy, this leads to a complete ordering of those subspaces by their Schmidt strings.

Organic reactions in ionic liquids: N-alkylation of phthalimide and several nitrogen heterocycles

N-Alkylation of heterocyclic compounds bearing an acidic hydrogen atom attached to nitrogen with alkyl halides is accomplished in ionic liquids ([bmim]BF4 = 1-butyl-3-methylimidazolium tetrafluoroborate, [bmim]PF6 = 1-butyl-3-methylimida-zolium hexafluorophosphate, [buPy]BF4 = butylpyridinium tetra­fluoroborate) in the presence of potassium hydroxide as a base. In this manner, phthalimide, indole, benzimidazole, succinimide can be successfully alkylated. The procedure is convenient, efficient, and generally affords the N-alkylated product exclusively.

Study of neutral Fe(III) complexes of pyridoxal-N-substituted thiosemicarbazone with desolvation induced spin-state transformation above room temperature

The preparation and characterization of two new neutral ferric complexes with desolvation-induced discontinuous spin-state transformation above room temperature are reported. The compounds, Fe(Hthpy)(thpy).CH3OH.3H2O (1) and Fe(Hmthpy)(mthpy).2H2O (2), are low-spin (LS) at room temperature and below, whereas their nonsolvated forms are high-spin (HS), exhibiting zero-field splitting. In these complexes, Hthpy, Hmthpy, and thpy, mthpy are the deprotonated forms of pyridoxal thiosemicarbazone and pyridoxal methylthiosemicarbazone, respectively; each is an O,N,S-tridentate ligand. The molecular structures have been determined at 100(1) K using single-crystal X-ray diffraction techniques and resulted in a triclinic system (space group P1) and monoclinic unit cell (space group P21/c) for 1 and 2, respectively. Structures were refined to the final error indices, where RF = 0.0560 for 1 and RF = 0.0522 for 2. The chemical inequivalence of the ligands was clearly established, for the "extra" hydrogen atom on the monodeprotonated ligands (Hthpy, Hmthpy) was found to be bound to the nitrogen of the pyridine ring. The ligands are all of the thiol form; the doubly deprotonated chelates (thpy, mthpy) have C-S bond lengths slightly longer than those of the singly deprotonated forms. There is a three-dimensional network of hydrogen bonds in both compounds. The discontinuous spin-state transformation is accompanied with liberation of solvate molecules. This is evidenced also from DSC analysis. Heat capacity data for the LS and HS phases are tabulated at selected temperatures, the values of the enthalpy and entropy changes connected with the change of spin state were reckoned at DeltaH = 12.5 0.3 kJ mol-1 and DeltaS = 33.3 0.8 J mol-1 K-1, respectively, for 1 and DeltaH = 6.5 0.3 kJ mol-1 and DeltaS = 17.6 0.8 J mol-1 K-1, respectively, for 2