Role of Hartree-Fock and Kohn-Sham orbitals in the basis set superposition error for systems linked by hydrogen bonds

In this work the effect of the basis set superposition error (BSSE) is explored with the counterpoise method on the occupied and unoccupied Hartree-Fock (HF) and Kohn-Sham (KS) orbitals. Three different systems linked by hydrogen bonds, H(2)O...FH, H(2)O...H(2)O, and H(2)O...CFH(3), were studied by using the basis set families cc-pVXZ and aug-cc-pVXZ (X = D, T, Q). The basis sets were tested with the HF method and two approximations for the exchange-correlation functional of KS: a generalized gradient approximation and a hybrid approach. In addition to these methods, the second-order M?ller-Plesset perturbation theory, MP2, was considered. It was found that the presence of the "ghost" basis set affects the orbitals in two ways: (1) The occupied KS orbitals are more sensitive to the presence of this "ghost" basis set than the occupied HF orbitals. For this reason the BSSE observed in HF is less than that obtained with KS. (2) The unoccupied HF orbitals are more sensitive to the presence of the "ghost" basis set than their corresponding occupied orbitals. Because the MP2 method uses both, occupied and unoccupied HF orbitals, to compute the total energy, the contribution of the BSSE is bigger than that obtained with HF or KS methodologies.     

The synthesis and reactivity of the heptanuclear dianion [Os7(CO)20]2− including the synthesis and structural characterizations of the compounds [Os7(CO)20(AuPEt)3 2] and [Os8(CO)20(η6-C6H6]

Reduction of the heptaosmium cluster [Os₇(CO)₂₁] With [Et₄N][NH₄) gives the cluster dianion [Os₇(CO)₂₀]^2–,1, in high yield. The reaction of the dianion with [AuPR ₃Cl] (R=Et or Ph) in the presence of TlPF₆ forms [Os₇((CO)₂₀(AuPR ₃)₂] [R=Et (2a);R = Ph(2b)] in 80% yield, while the corresponding reaction with (Os(C₆H₆)(CH₃CN)₃]²⁺ gives [Os₈(CO)₂₀ ( ⁶-C₆H₆)] (3) in reasonable yield (ca. 30%). The dianion,1, and the clusters2 and3 have been fully characterized by bout spectroscopic and crystallographic methods. The crystal structure of the [Ph₄P]⁺ salt of1 shows that the metals in the anion adopt a capped octahedral geometry, with all twenty carbonyl ligands in terminal sites. The metal core geometry in2a is best described as a tricapped octahedron, and is based on the structure of the dianion1 with two adjacent octahedral faces capped by the Au atoms of the two AuPEt₃ groups. In a similar fashion, the geometry of3 is related to that of1 with the addition of an Os(C₆H₆) unit capped to a triangular face, to give a bicapped octahedral framework.     

Geometrization of the physics with teleparallelism. I. The classical interactions

A connection viewed from the perspective of integration has the Bianchi identities as constraints. It is shown that the removal of these constraints admits a natural solution on manifolds endowed with a metric and teleparallelism. In the process, the equations of structure and the Bianchi identities take standard forms of field equations and conservation laws.The Levi-Civita (part of the) connection ends up as the potential for the gravity sector, where the source is geometric and tensorial and contains an explicit gravitational contribution.Nonlinear field equations for the torsion result. In a low-energy approximation (linearity andlow energy-momentumtransfer), the postulate that only charge and velocities contribute to the source transforms these equations into the Maxwell system. Moreover, the affine geodesics become the equations of motion of special relativity with Lorentz force in the same approximation [J. G. Vargas,Found. Phys. 21, 379 (1991)]. The field equations for the torsion must then be viewed as applying to an electromagnetic/strong interaction.A classical unified theory thus arises where the underlying geometry confers their contrasting characters to Maxwell-Lorentz electrodynamics and to an Einstein's-like theory of gravity. The highly compact field equations must, however, be developed in phase-spacetime, since the connection is velocity-dependent, i.e., Finsler-like.Further opportunities for similarities with present-day physics are discussed: (a) teleparallelism allows for the formulation of the torsion sector of the theory as a flat space theory with concomitant point-dependent transformations; (b) spinors should replace Lorentz frames in their role as the subjects to which the connection refers; (c) the Dirac equation consistent with the frame bundle for a velocity-dependent metric with Lorentz signature generates a weak-like interaction in the torsion sector.Work done at the Department of Mathematics and Physics of the Interamerican University of Puerto Rico, San German, Puerto Rico 00683.     

Trace determination of lead by helium-4 activation analysis

The determination of lead via 30 MeV⁴He bombardment to produce the long-lived radioisotope²¹⁰Po was studied. The validity of the technique was tested by the analysis of a series of NBS glass samples doped with 61 different trace elements at nominal 500 to 1 ppm level concentrations. The measurement sensitivity of alpha counting with surface barrier detectors was evaluated. The detection limit was estimated at 0.1 ppm. The⁴He-activation technique coupled with -counting features a unique combination of sensitivity and accuracy for the trace determination of lead.     

Atmospheric chemistry of dimethyl phosphonate, dimethyl methylphosphonate, and dimethyl ethylphosphonate

Rate constants for the reactions of OH radicals and NO3 radicals with dimethyl phosphonate [DMHP, (CH3O)2P(O)H], dimethyl methylphosphonate [DMMP, (CH3O)2P(O)CH3], and dimethyl ethylphosphonate [DMEP, (CH3O)2P(O)C2H5] have been measured at 296 +/- 2 K and atmospheric pressure using relative rate methods. The rate constants obtained for the OH radical reactions (in units of 10(-12) cm3 molecule(-1) s(-1)) were as follows: DMHP, 4.83 +/- 0.25; DMMP, 10.4 +/- 0.6; and DMEP, 17.0 +/- 1.0, with a deuterium isotope effect of k(OH + DMMP)/k(OH + DMMP-d9) = 4.8 +/- 1.2. The rate constants obtained for the NO3 radical reactions (in units of 10(-16) cm3 molecule(-1) s(-1)) were as follows: DMHP, < 1.4; DMMP, 2.0 +/- 1.0; and DMEP, 3.4 +/- 1.4. Upper limits to the rate constants for the O3 reactions of < 8 x 10(-20) cm3 molecule(-1) s(-1) for DMHP and < 6 x 10(-20) cm3 molecule(-1) s(-1) for DMMP and DMEP were determined. Products of the reactions of OH radicals with DMHP, DMMP, and DMEP were investigated in situ using atmospheric pressure ionization mass spectrometry (API-MS) and, for the DMMP and DMEP reactions, Fourier transform infrared (FT-IR) spectroscopy. API-MS analyses showed the formation of products of molecular weight 96 and 126, attributed to CH3OP(O)(H)OH and (CH3O)2P(O)OH, respectively, from DMHP; of molecular weight 110, attributed to CH3OP(O)(CH3)OH, from DMMP; and of molecular weight 124 and 126, attributed to CH3OP(O)(C2H5)OH and (CH3O)2P(O)OH, respectively, from DMEP. FT-IR analyses showed formation (values given are % molar yields) of the following: from DMMP, CO, 54 +/- 6; CO2, 5 +/- 1 in dry air; HCHO, 3.9 +/- 0.7; HC(O)OH, < 1.4 in dry air; RONO2, approximately 4; and formate ester, approximately 8; and from DMEP, CO, 50 +/- 7; CO2, 11 +/- 4; CH3CHO, 18 +/- 8; HCHO, < 7; HC(O)OH, < 6; RONO2, < or = 5; and formate ester, 5.0 +/- 1.5. Possible reaction mechanisms are discussed.     

Laguerre Wavelet Approach for a Two-Dimensional Time–Space Fractional Schrödinger Equation

This article is devoted to the determination of numerical solutions for the two-dimensional time–spacefractional Schrödinger equation. To do this, the unknown parameters are obtained using the Laguerre wavelet approach. We discretize the problem by using this technique. Then, we solve the discretized nonlinear problem by means of a collocation method. The method was proven to give very accurate results. The given numerical examples support this claim.     

Discriminating Bacterial Infection from Other Causes of Fever Using Body Temperature Entropy Analysis

Body temperature is usually employed in clinical practice by strict binary thresholding, aiming to classify patients as having fever or not. In the last years, other approaches based on the continuous analysis of body temperature time series have emerged. These are not only based on absolute thresholds but also on patterns and temporal dynamics of these time series, thus providing promising tools for early diagnosis. The present study applies three time series entropy calculation methods (Slope Entropy, Approximate Entropy, and Sample Entropy) to body temperature records of patients with bacterial infections and other causes of fever in search of possible differences that could be exploited for automatic classification. In the comparative analysis, Slope Entropy proved to be a stable and robust method that could bring higher sensitivity to the realm of entropy tools applied in this context of clinical thermometry. This method was able to find statistically significant differences between the two classes analyzed in all experiments, with sensitivity and specificity above 70% in most cases.     

Tetragonal to monoclinic phase transition observed during Zr anodisation

Plasma electrolytic oxidation (PEO) is a coating procedure that utilises anodic oxidation in aqueous electrolytes above the dielectric breakdown voltage to produce oxide coatings that have specific properties. These conditions facilitate oxide formation under localised high temperatures and pressures that originate from short-lived microdischarges at sites over the metal surface and have fast oxide volume expansion. Anodic ZrO₂ films were prepared by subjecting metallic zirconium to PEO in acid solutions (H₂C₂O₄ and H₃PO₄) using a galvanostatic DC regime. The ZrO₂ microstructure was investigated in films that were prepared at different charge densities. During the anodic breakdown, an important change in the amplitude of the voltage oscillations at a specific charge density was observed (i.e., the transition charge density (Q ^T)). We verified that this transition charge is a monotonic function of both the current density and temperature applied during the anodisation, which indicated that Q ^T is an intrinsic response of this system. The oxide morphology and microstructure were characterised using SEM and X-ray diffraction experiments (XRD) techniques. X-ray diffraction analysis revealed that the change in voltage oscillation was correlated with oxide microstructure changes during the breakdown process.