Nonsingular two/one-component relativistic Hamiltonians accurate through arbitrary high order in α2

A series of nonsingular two-component relativistic Hamiltonians is derived from the Dirac Hamiltonian by first performing the free-particle Foldy–Wouthuysen transformation and then a block-diagonalizing transformation. The latter is defined in terms of operators which can be determined iteratively through arbitrary order in α, leading to transformed Hamiltonians with the two-component block accurate through α^2k, k=1, 2, 3,… . These Hamiltonians give relativistic energies which differ from Dirac's energies only in terms higher than α^2k. Their relation to other nonsingular methods of relativistic quantum chemistry (the Douglas–Kroll method, the regular Hamiltonian schemes) is discussed. By removing the spin-dependent operators, the derived Hamiltonians can be written in spin-free one-component form. The computational effort involved is essentially the same as in the case of the Douglas–Kroll scheme and amounts to relatively easy modification of the core Hamiltonian. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 225–239, 1997     

A variationally stable quasi-relativistic method: low-order approximation to the normalized elimination of the small component using an effective potential

A simple and variationally stable quasi-relativistic method based on a modified low-order (LO) approximation to the normalized elimination of the small component (NESC) method is presented. The modification of the original LO-NESC scheme implies the use of an energy-independent factor in the relativistic correction to the potential energy. This factor cuts off the potential energy at short distances from the nucleus and in this way restores the variational stability of LO-NESC. The new method, dubbed LO-NESC-effective potential (EP) was tested in calculations on one-, two- and many-electron atoms. The LO-NESC-EP can be easily implemented into the existing nonrelativistic quantum-chemical program codes because its Hamiltonian matrix can be expressed entirely in terms of the integrals appearing in a nonrelativistic calculation. Received: 1 April 2002 / Accepted: 23 June 2002 / Published online: 30 August 2002     

Spin‐orbit ZORA and four‐component Dirac–Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers

Hartree–Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange‐correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin‐orbit zeroth‐order regular approximation Hamiltonian in combination with the large Slater‐type basis set QZ4P as well as with the four‐component Dirac–Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization‐consistent basis sets aug‐pcSseg‐4 for He, Ne and Ar, aug‐pcSseg‐3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero‐point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed. © 2015 Wiley Periodicals, Inc.     

Synthesis and properties of a deuterated phenolic resin

A highly deuterated novolac‐type phenolic resin was prepared by polycondensation of deuterated phenol and formaldehyde using oxalic acid as an acid catalyst. The polycondensation of deuterated monomers and the formation of the highly deuterated phenolic resin were confirmed by the gel permeation chromatography, IR, and ¹H NMR analyses. With the exception of hydroxyl groups, the degree of deuteration was estimated to be more than 98%. The polymer conformation in THF solution was evaluated by the scaling exponent of the Mark–Houwink–Sakurada equation. The exponent of the deuterated phenolic resin is 0.26 in THF at 40 °C and is close to that of a nondeuterated phenolic resin, which suggests that phenolic resins behave like a compact sphere irrespective of deuteration. The curing behavior of the deuterated phenolic resin with hexamethylenetetramine was confirmed by differential scanning calorimetry analysis. The cured highly deuterated phenolic resin exhibits a lower incoherent neutron scattering background than that of the nondeuterated phenolic resin, which suggests that the former is suitable for matrix resins with low incoherent backgrounds for small‐angle neutron scattering studies of thermosetting resins. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011.     

Standardized basis sets for high-level-correlated relativistic calculations of atomic and molecular electric properties in the spin-averaged Douglas-Kroll (no-pair) approximation I. Groups Ib and IIb

Summary The technique developed earlier for the generation of the so-called first-order polarized basis sets for accurate non-relativistic calculations of molecular electric properties is used to obtain similar basis sets suitable for calculations in the Douglas-Kroll no-pair approximation. The corresponding (relativistic) basis sets are devised for atoms of the Groups Ib and IIb of the periodic table and tested in calculations of atomic polarizabilities and dipole moments of the coinage metal hydrides. Excellent performance of these basis sets has been found in the case of molecular calculations.     

Evaluation of mass spectrometric data using principal component analysis for determination of the effects of organic lakes on protein binder identification

Matrix‐assisted laser desorption/ionisation–time of flight (MALDI‐TOF) mass spectrometry is commonly used for the identification of proteinaceous binders and their mixtures in artworks. The determination of protein binders is based on a comparison between the m/z values of tryptic peptides in the unknown sample and a reference one (egg, casein, animal glues etc.), but this method has greater potential to study changes due to ageing and the influence of organic/inorganic components on protein identification. However, it is necessary to then carry out statistical evaluation on the obtained data. Before now, it has been complicated to routinely convert the mass spectrometric data into a statistical programme, to extract and match the appropriate peaks. Only several ‘homemade’ computer programmes without user‐friendly interfaces are available for these purposes. In this paper, we would like to present our completely new, publically available, non‐commercial software, ms‐alone and multiMS‐toolbox, for principal component analyses of MALDI‐TOF MS data for R software, and their application to the study of the influence of heterogeneous matrices (organic lakes) for protein identification. Using this new software, we determined the main factors that influence the protein analyses of artificially aged model mixtures of organic lakes and fish glue, prepared according to historical recipes that were used for book illumination, using MALDI‐TOF peptide mass mapping. Copyright © 2015 John Wiley & Sons, Ltd.     

Energy and density analysis on the H2 molecule from the united atom to dissociation: The Σ, Π, Δ, ϕ, and Γ manifolds

We present 140 accurate potential energy curves, PECs, for the Σ, Π, Δ, ?, and Γ manifolds for the H₂ molecule, mapping all the states with energy below the H ground state. The full configuration interaction, nonrelativistic Born–Oppenheimer computations are performed with large and optimized basis sets of Slater‐type and spherical Gaussian functions; these new basis sets are somewhat larger than those used in recent published studies on the 60 Σ state PECs. The full CI computations are performed twice, with Hartree–Fock and with Heitler–London‐type functions, allowing the identification of the ionic component in the total energy. The computed energies are within 10^?5 hartree from the most accurate PECs in literature. We aim (a) at the evaluation of the PECs starting at very short and unexplored internuclear distances (0.01 bohrs) and ending at full dissociation, (b) at the systematic prediction of high excited state PECs dissociating as 1s + 4l and 1s + 5l, and (c) at the characterization of the evolution of the 140 PEC electronic densities from united atom to dissociation. With this work we fill a gap in today literature, which has dealt mainly with low excited states, generally excluding short internuclear distances. The electronic configuration at the united atom persists as dominant configuration well beyond the equilibrium separation, and it switches to that at dissociation often with energy patterns seemingly irregular, in particular when the values of the principal quantum number at dissociation and at the united atom differ by one or more unit. The Hund's singlet‐triplet splitting, which propagates from the united atom to the molecule, is discussed. The singlet and triplet states are rather close in energy in the Π manifolds, and approach degeneracy in the Δ and ? manifolds, to become fully degenerate in the Γ manifolds. Discussions on the correlation energy correction, adiabatic correction, spectroscopic constants and on general features of the H₂ excited states are presented. The H₂ molecule is a system, which—to be understood—needs consideration of both the very short internuclear distances in approaching the united atom and of the very high excited states below H. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Effizienz kommerziell erwerblicher Silikagele (dp=5 μm und 10 μm) in der Flüssigkeits-Chromatographie

Zusammenfassung 18 kommerziell erwerbliche Kieselgele mit Teilchengrößen (d _p) von 10 m und 5 m wurden systematisch untersucht. Die chromatographisch bestimmte mittlere Teilchengröße (d) ist etwa um 35% größer als die mit Hilfe des Coulter Counter bestimmte Größe (d _c). Die von den Herstellern angegebenend _p-Werte liegen meistens zwischend undd _c. Died-Werte streuten-für die mitd _p=10 m angegebenen Silikagele-zwischen 7,6 m und 12,2 m. Die Konstanten der vereinfachten (10 m Teilchen) bzw der vollständigen (5 m Teilchen) van Deemter Gleichung bei verschiedenen Kapazitäts verhältnissen (k=0–3) und die Asymmetriefaktoren (As) für die Inertsubstanzen wurden gemessen und tabelliert. Beiu=1 mm/s waren die reduzierten Bodenhöhen (h/d) kleiner als 3 für Substanzen mit 0k<3 fürd _p=10 m. Für sämtliche untersuchten Kieselgele waren die Kapazitätsverhältnisse der einzelnen Proben an einer gegebenen stationären Phase mit einer Genauigkeit von ±0.05 reproduzierbar. DieA, B undC Terme der van Deemter Gleichung (d _p=5 m) waren innerhalb von ±10% reproduzierbar, auch dann, wenn die Säule eine Woche trocken gelagert wurde. Die Abnahme vonU _min mit zunehmendenk-Werten hängt sowohl von der Qualität (z.B. geometrischer Form, Enge der Siebfraktion, etc.) der stationären Phase als auch von der Güte der Packungsmethode ab. Für kleinere Teilchen werden die reduzierten Bodenhöhen (h/d)_min größer. Da die Permeabilität der Säulen gemäß der Definition vond immer zud ² proportional ist, nimmt der Druckabfall an der Säule mit abnehmender Teilchengröße wesentlich zu. Die Lebensdauer von Säulen nimmt erfahrungsgemäß mit zunehmendem Druck ab. Die Bandenverbreiterung außerhalb der Säule ist oft bei kommerziell erwerblichen Geräten so groß, daß 10 cm lange Säule (i.D.=4 mm), die mit 5 m. Teichen gepackt wurden, identischen, jedoch mit 10 m Kieselgelen gepackten Säulen, in der Effizienz kaum überlegen sind. Obwohl die Definition vond sphärische Teilchen begünstigt, wenn reduzierte Bodenhöhen errechnet werden, ist die Effizienz von Säulen, die mit sphärischen und unregelmäßigen Teilchen gepackt sind, sehr ähnlich. die Bevorzugung der sphärischen Packungsmaterialien gegenüber den preiswerteren unregelmäßigen Silikagelen scheint experimentell nicht belegbar zu sein. DieA-Terme nehmen mit zunehmendenk-Werten immer zu, obwohl dies von der Theorie hier nicht zu erwarten ist. DieC Terme scheinen überwiegend von der Massentransportgeschwindigkeit in der Eluentenphase bestimmt zu sein. Diek-Abhängigkeit derC-Terme ist mit Hilfe des ausschließlichk-abhängigen Faktors derC _m-Terme der Golay-Gleichung gut zu beschreiben, fallsk>0,75 ist. Allerdings ist die Zunahme derC-Terme vonk=0 aufk=0,75 etwa um einen Faktor 3 kleiner als theoretisch errechenbar ist. Die Stabilität der Säulen wird demonstriert. Obwohl die 20 cm langen Säulen drei Monate lang trocken gelagert wurden, nahm die Effizienz nur vonn=17.000 aufn=15.000 ab. Mit 27 bar Druckabfall wurden 130 theoretische Böden pro Sekunde erreicht. Mittlerer Porendurchmesser, Porenvolumen und spezifische Oberfläche der kommerziell erwerblichen Kieselgele beeinflußten diek-Werte der Probesubstanzen. Obwohl die Variationsbreite dieser Faktoren bei den 18 untersuchten Kieselgelen nicht allzu eng war, beeinflußten diese Parameter die Effizienz der Säulenkaum.

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Efficiency of commerically available silicas in HPLC

Summary Eighteen commercially available silicas having nominal particle sizes (d _p) of 10 m and 5 m, have been systematically studied. The chromatographically determined average particle size (d) is about 35% greater than the average particle size as estimated using a Coulter Counter (d _c). The particle sizes quoted by the manufacturers mostly lie betweend andd _c. Thed values for the silicas with a quotedd _p of 10 m lay between 7.6 m and 12.2 m. The constants of the simplified (for 10 m particles) or the complete (for 5 m particles) van Deemter equation were measured and tabulated for varying capacity ratios (k=0–3) as were the asymmetry factorsAs for an inert substance. When u=1 mm/s the reduced plate height (h/d) was less than 3 for substances with 0k<3 whend _p=10 m. The capacity ratios of individual samples on a given stationary phase were reproducible with an accuracy of ±0.05 for all the silicas studied. TheA, B andC terms of the van Deemter equation (d _p=5 m) were reproducible to within ±10%, even when the column was stored dry for a week. The decrease inu _min with increasingk value depended both on the quality of the stationary phase (e.g., its geometrical form, the narrowness of the sieve fraction) and on the packing method. The reduced plate heights (h/d)_min were bigger for smaller particles. In consequence of the definition ofd, the permeability of a column is always proportional tod ² and the pressure drop in columns with smaller size particles increased substantially. It is a matter of experience that the column life decreases with increasing pressure drop. The extracolumn band broadening of commercial instruments is often so large that 10 cm long columns (i.d.=4 mm) packed with 5 m particles are scarcely more efficient than identical columns packed with 10 m particles. Although the definition ofd favours spherical particles if reduced plate heights are to be calculated, the efficiencies of columns packed with spherical particles are very similar to those packed with irregular particles. The preference for spherical packing material over the cheaper irregular silica does not seems to be supported by experiment. TheA term always increases with increasingk values, although this is theoretically unexpected. TheC terms seems to be overwhelmingly determined by the speed of mass transport in the mobile phase. The dependence of theC term onk is, whenk is >0.75, well described using the exclusivelyk dependent factions of theC _m term of the Golay equation. However, the increase in theC term whenk is increased from 0 to 0.75 is about a factor three less than the theoretically calculated value. The stability of the columns has been demonstrated. Although columns (20 cm long in length) were stored dry for three months the efficiency only decreased slightly. With a 26 bar pressure drop 130 theoretical plates per second were obtained. The average pore diameters, pore volumes and specific surface areas of the commerical silicas influenced thek values of the sample substances. These factors however scarcely affected the column efficiencies even though their range of variation was not very narrow in the 18 silicas studied.

     

Equation of state for aqueous electrolyte systems based on the semirestricted non-primitive mean spherical approximation

The semirestricted non-primitive mean spherical approximation (npmsa) is used in combination with the PC-SAFT equation of state to model completely dissociating aqueous alkali halide systems. The salts are described using ion-specific parameters from tables and correlations. Upon analyzing aqueous electrolyte systems at infinite dilution of the salt it was concluded that for the arithmetic mean ion diameter of anion and cation, the semirestricted npmsa contribution gives no reliable results. Therefore, this parameter is adjusted in this work. The model was applied to aqueous alkali halide systems up to the solubility limit at T = 298.15 K. Mean ionic activity coefficients and osmotic coefficients were correlated with good results. The model was subsequently applied to temperatures up to T = 373.15 K and compared to liquid densities and to system pressures up to the solubility limit of the salts in water. The agreement between experimental data and the proposed equation of state is satisfactory for the liquid densities and excellent in case of the system pressures.