Comparison of cartesian and lobe function Gaussian basis sets

The lobe function and cartesian (spherical harmonic) gaussian are compared with reference to calculations for second-row atoms. Single and grouped gaussian basis sets which have been reported for cartesian functions are taken over directly to construct corresponding lobe function bases with identical sets of exponents and with lobe separations chosen by a scaling procedure. Total and orbital energies and SCF coefficients resulting from calculations on the second-row atoms using the two types of functions for both primitive and grouped gaussian basis sets are seen to be in excellent agreement, thereby emphasizing the essential equivalence of lobe functions and cartesian gaussians, at the very least with respect to calculation of energy surfaces.

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Zusammenfassung Die Lobe-Funktionen und kartesischen (Kugelfunktions-) Gaußfunktionen werden in Berechnungen von Atomen der zweiten Reihe des periodischen Systems verglichen. Schon bekannte einfache und gruppierte Gaußfunktionsbasissätze für kartesische Funktionen werden direkt übernommen, um entsprechende Lobe-Funktionsbasen mit identischen Exponenten zu konstruieren, wobei die zugehörigen Lobe-Abstände nach einer Koordinatenstreckungs-(scaling) Methode berechnet werden. Gesamt- und Orbitalenergien sowie SCF-Koeffizienten für die Atome der zweiten Reihe stimmen bei Benutzung der beiden verschiedenen Funktionstypen, sowohl bei einfacher als auch bei gruppierter Gaußfunktionsbasis, außerordentlich gut überein, wodurch die wesentliche Gleichwertigkeit von Lobe-Funktionen und kartesischen Gaußfunktionen betont wird, zum allermindesten hinsichtlich der Berechnung von Energieflächen.

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Résumé La fonction de lobe et la gaussienne cartésienne (harmonique sphérique) sont comparées sur des calculs d'atomes de la seconde ligne. Des bases de gaussiennes simples et groupées utilisées pour les fonctions cartésiennes sont directement employées pour construire les bases correspondantes de fonctions à lobes avec des ensembles d'exposants identiques et des séparations de lobes choisis par calibrage. L'emploi de ces deux types de fonctions donne des résultats concordants pour l'énergie totale, les énergies orbitales et les coefficients SCF, mettant l'accent sur l'équivalence essentielle des fonctions à lobe et des gaussiennes cartésiennes, tout au moins pour le calcul des surfaces d'énergie.

     

Theoretical study of the electronic spectrum of diimide by AB initio methods

A series of ab initio calculations is reported for the ground and low-lying valence and Rydberg states of diimide N₂H₂. Symmetric bending potential curves for both the cis and trans forms of this system have been obtained at the SCF level of treatment. In addition Cl calculations have been carried out for the trans-diimide ground state equilibrium nuclear conformation, using a configuration selection procedure described elsewhere; an associated energy extrapolation scheme is also employed which enables the effective solution of secular equations with orders of up to 40000. The ensuing Cl wavefunctions are interpreted in the discussion and the corresponding calculated energy differences between the various electronic states are compared with experimental transition energy results for both diimide and for related systems such as trans-azomethane. A more detailed analysis of the observed absorption bands in the ¹B_g-X¹A_g transition in N₂H₂ is also given, making use of calculated potential curve data as well as the pertinent Cl vertical energy difference. The dipole-forbiddenness of the excitation process is thereupon concluded to result in a distinct non-verticality for this electronic band system, causing its absorption maximum to occur at a position some 0.6 eV to the blue of the so-called vertical transition, i.e., that for which maximum vibrational overlap is obtained.     

Potential energy surfaces for the photodissociation H2O→O(1Dg + H2(X1Σ+g)

The minimum energy pathways for symmetrical dissociation of water into O(¹D_g + H₂(X¹Σ⁺_g) are calculated by the MRD Cl technique for various excited states of H₂O and possible mechanism for the photodissociation are discussed.     

Kinetic study of angiotensin converting enzyme activity by capillary electrophoresis after in-line reaction at the capillary inlet

The in-capillary reaction of angiotensin converting enzyme (ACE) with the tripeptide substrate hippuryl-L-histidyl-L-leucine was studied. ACE activity was determined by the quantitation of the product, hippuric acid, at 230 nm. Reaction occurred at the capillary inlet during a predetermined waiting period, followed by the electrophoretic separation of the compounds. When the set-up was reversed, i.e. reaction at the opposite side after short-end injection of enzyme and substrate, separation was achieved in less than 5 min. Using the Lineweaver-Burk equation, an average Michaelis constant for ACE from rabbit lung was calculated to be 1.16 +/- 0.12 mM, a value consistent with previously reported data.     

Synthese und Kristallstrukturen der Phosphaniminato-Komplexe [MCl2(NPPh3)]2 mit M = Al und Ga, [SbCl2(NPMe3)(DMF)]2 sowie des Phosphanimin-Komplexes [Ph3PNH · BF3] · THF

Syntheses and Crystal Structures of the Phosphorane Iminato Complexes [MCl₂(NPPh₃)]₂ with M = Al and Ga, [SbCl₂(NPMe₃)(DMF)]₂, and of the Phosphorane Imine Complex [Ph₃PNH · BF₃] · THF The phosphorane iminato complexes [MCl₂(NPPh₃)]₂ with M = Al and Ga and [SbCl₂(NPMe₃)(DMF)]₂ are formed as colourless crystals by reactions of the anhydrous trichlorides MCl₃ (M = Al, Ga, Sb) with the corresponding silylated phosphorane imines Me₃SiNPR₃ in acetonitrile and in dimethyl formamide, respectively. The phosphorane imine derivative [Ph₃PNH · BF₃] · THF is formed from Me₃SiNPPh₃ and boron trifluoride etherate in boiling tetrahydrofuran. The compounds are characterized by their i. r. spectra and by crystal structure analyses. [AlCl₂(NPPh₃)]₂ : Space group P1 , Z = 1, structure solution with 1 585 observed unique reflections, R = 0.061. Lattice dimensions at ?70°C: a = 917.6, b = 1 053.5, c = 1 145.2 pm, α = 111.72°, β = 100.80°, γ = 109.95°. [GaCl₂(NPPh₃)]₂ : Space group P1 , Z = 1, structure solution with 2 586 observed unique reflections, R = 0.066. Lattice dimensions at ?70°C: a = 917.5, b = 1 058.3, c = 1 153.7 pm, α = 105.52°, β = 107.75°, γ = 109.88°. In both compounds the metal atoms are linked to planar M₂N₂ four-membered rings via the N-atoms of the phosphorane iminato groups. [SbCl₂(NPMe₃)(DMF)]₂ : Space group P2₁/n, Z = 4, structure solution with 3 805 observed unique reflections, R = 0.038. Lattice dimensions at ?70°C: a = 1 913.0, b = 726.8, c = 2 040.7 pm, β = 113.62°. The unit cell contains two symmetry independent dimeric molecules, in which the antimony atoms are centrosymmetricly μ₂ linked via the N-atoms of the phosphorane iminato groups. Along with the oxygen atom of the dimethyl formamide molecule the Sb atoms achieve a ψ-octahedral environment. [Ph₃PNH · BF₃] · THF : Space group C2/c, Z = 8, structure solution with 2 048 observed unique reflections, R = 0.058. Lattice dimensions at ?70°C: a = 2 460.4, b = 869.2, c = 1 978.0 pm, β = 116.35°.     

Reaktionen von MoNCl3 und WNCl3 mit elementarem Fluor. Kristallstrukturen von [MoO2F2(THF)2] und [WF4(NCl)(CH3CN)]

Reactions of MoNCl₃ and WNCl₃ with Elemental Fluorine. Crystal Structures of [MoO₂F₂(THF)₂] and [WF₄(NCl)(CH₃CN)] The nitrido chlorides MoNCl₃ and WNCl₃ as well as WCl₄(NCl) react with elemental fluorine forming the N-chloro imido complexes MoF₄(NCl) and WF₄(NCl), which were characterized by IR spectroscopy. With tetrahydrofurane MoF₄(NCl) reacts to give [MoF₄(NCl)(THF)], which in THF solution slowly converts into [MoO₂F₂(THF)₂]. From WF₄(NCl) with acetonitrile the complex [WF₄(NCl)(CH₃CN)] is obtained. Both donor acceptor complexes were characterized by crystal structure determinations. [MoO₂F₂(THF)₂] : Space group P2₁/n, Z = 4, structure solution with 1823 unique reflections, R = 0.033 for reflections with I > 2σ(I). Lattice dimensions at ?40°C: a = 636.2, b = 1119.5, c = 1625.2 pm; β = 93.92(1)º. The compound has a monomeric molecular structure with the fluorine atoms in trans-position to one another and with the oxygen atoms of the THF molecules in trans to the oxo ligands. [WF₄(NCl)(CH₃CN)] : Space group P2₁/m, Z = 2, structure solution with 1119 unique reflections, R = 0.038 for reflections with I > 2σ(I). Lattice dimensions at 20°C: a = 511.7, b = 714.9, c = 1002.5 pm; β = 102.59(10)º. The compound has a monomeric molecular structure in which the nitrogen atom of the acetonitrile molecule coordinates in trans-position to the N-chloro imido group W?N? Cl. The structural parameters of this group are WN = 172.2 pm, NCl = 161.1 pm, WNCl = 178.6º.     

On data-guided optimal control simulation of human motion

This work investigates the combination of optical motion capturing data with optimal control simulations of human motion, which can be important in a wide range of applications in the professional as well as the private sector, ranging from health and ergonomics over human-machine-interaction to sports and games [1–3]. There are methodically very different approaches to include optical measurement data in the simulation of human motion, see e.g. [4–6]. Two different approaches to combine data and simulation are investigated in this work. Either we use a soft constraints approach, where the difference of simulated and measured marker positions is part of the objective function (1), or we formulate an hard constraints approach with nonlinear constraints that set an upper bound on this difference (2), while the objective function is purely physiologically motivated. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variational multirate integration in multi-body dynamics

For systems that contain slow and fast dynamics, variational multirate integration schemes are used. These schemes split the system into parts which are simulated using two time grids consisting of micro and macro nodes. This formulation can be extended for multi-body systems. The rigid multi-body system is described by the so called director formulation and constraints describing the joints connecting the bodies. With the Lagrange multiplier method, the constraints are introduced into the equations of motion. A way to implement the null space method into the variational multirate framework is shown and the influence on the number of unknowns is investigated. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vertical Electronic Spectra of the Isovalent Molecules H2CNH,H2SiNH,H2CPH and H2SiPH on the Basis of MRD-CI Calculations

Abstract

Large-scale multi-reference single and double-excitation configuration interaction (MRD-CI) calculations are employed for the study of the isovalent compounds H₂CNH, HLSiNH, hLCPH and H₂SiPH in their ground state equilibrium geometry. The dipole moments and charge distributions are given. The vertical excitation energies to the intravalence states ^3,1 (n, π*) and ^3,1(π,π*) and to the first members of the Rydberg series originating from n and - MO's respectively are predicted; the first two ionization potentials and the Rydberg term values are also calculated. In H₂CNH, mixing of Rydberg and valence-shell states with CN stretching is analyzed. The trends in relative stability of electronic and ionized states can be directly related to increased orbital stability of n relative to π as soon as a first-row constituent is replaced by a second-row atom. The calculations explain the diffuse character of the uv spectrum of imines; they treat the molecules H₂SiNH and H₂SiPH for the first time and present a large number of data for all four molecules which can serve as a basis for future experimental investigations on these and related compounds.