Calculations of the electronic structures of cage molecules using free-electron orbitals as a basis

A non-empirical molecular orbital method, particularly suitable for calculations on cage-like molecules, is described. The method uses as basis functions the set of free-electron functions which are the solutions of Schrödinger's equation for an electron confined between two concentric, spherical potential energy barriers. Application of the theory to the SCF calculation of the energies of the delocalized electrons in benzene and tetrasulphur tetranitride shows that the model is capable of interpreting the properties of such systems. However, it does highlight a difficulty in the calculation of excited state energies with one-centre models which appears to be largely unrecognized.Extension of the method to a consideration of all the valence electrons, using P₄ as an example, reveals problems the origin of which is an inadequate treatment of the core electrons. It is suggested that these problems may best be dealt with by use of a suitable pseudo potential.     

Vaporisation et dissociation thermique des sulfures de phosphore P4S3, P4S7 et P4S10 a l'etat gazeux

Résumé Nous avons montré par spectrométrie Raman à chaud et mesure des tensions de vapeur que P₄S₃ se vaporise de façon congruente tandis que P₄S₇ et P₄S₁₀ se dissocient dès le début de leur vaporisation. P₄S₇ donne réversiblement P₄S₃ et soufre. P₄S₁₀ se dissocie irréversiblement en P₄S₇ et soufre. A l'état de vapeur non saturante, P₄S₃ se dissocie au-dessus de 600° avec formation de phosphore, de soufre et d'autres espèces non identifiées.Nous avons mesuré expérimentalement la capacité calorifique de P₄S₃ liquide, calculé celle de P₄S₃ gazeux et son entropie standard. Nous avons aussi estimé l'enthalpie standard de vaporisation de P₄S₃ à l'aide des mesures des tensions de vapeur saturante. Nous en avons déduit l'entropie standard de P₄S₃ liquide et son point d'ébullition.

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It is shown by Raman spectroscopy at high temperature and by vapor tensimetric measurements that the vaporisation of P₄S₃ is congruent, whereas P₄S₇ and P₄S₁₀ dissociate at the beginning of vaporisation. P₄S₇ gives P₄S₃ and sulfur reversibly. The dissociation of P₄S₁₀ into P₄S₇ and sulfur is irreversible. Above 600°, in non-saturated vapour the dissociation of P₄S₃ gives phosphorus, sulfur and some unidentified gaseous species. The heat capacity of liquid P₄S₃ has been measured. That of gaseous P₄S₃ and its standard entropy have been calculated. The vaporisation standard enthalpy of P₄S₃ has been estimated from the experimental results on the saturated vapour pressures. The standard entropy of liquid P₄S₃ and its boiling point have been derived from these data.

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Zusammenfassung Mittels Raman-Spektrometrie bei erhöhter Temperatur und durch Messung der Dampfdrucke wurde festgestellt, daß sich P₄S₃ verflüchtigt, während P₄S₇ und P₄S₁₀ mit Beginn der Verflüchtigung dissoziieren. P₄S₇ ergibt reversibel P₄S₃ und Schwefel. Im Zustand ungesättigten Dampfes dissoziiert P₄S₃ oberhalb von 600° unter Bildung von Phosphor, Schwefel und anderer nicht identifizierter Substanzen.Die Wärmekapazität von flüssigem P₄S₃ wurde gemessen, während die vom gasförmigem P₄S₃ sowie seine Standard-Entropie berechnet wurden. Die Standard-Enthalpie der Verflüchtigung des P₄S₃ wurde durch Messungen der Sättigungs-Dampfdrucke ermittelt. Daraus wurden die Standard-Entropie des flüssigen P₄S₃ sowie sein Siedepunkt berechnet.

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- - , P₄S₃ , P₄S₇ P₄S₁₀ . P₄S₇ P₄S₃ , P₄S₁₀ P₄S₇ . 600° P₄S₃ , . P₄S₃, P₄S₃ . P₄S₃. P₄S₃ .

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Nous remercions Monsieur Letoffe du laboratoire du Professeur J. Bousquet, INSA de Lyon, 20 Avenue Albert Einstein 401, 69621 Villeurbanne, qui a r6alis6 pour nous les déterminations expérimentales des capacités calorifiques de P₄S₈ liquide.     

Relativistic molecular orbitals for the double group D3h

Relativistic symmetry orbitals are given for the double group D_3h. For atomic orbitals at the symmetry center a general expression is presented. The atomic orbitals of the s, p_½, and p_3/2 variety outside the center are also considered. The representation matrices are given in explicit form.     

The determination of sulphur in copper,nickel and aluminium alloys by proton activation analysis

The ³⁴S(p, n)^34mCl reaction induced by 13-MeV protons is used for the determination of sulphur in copper, nickel and aluminium alloys. The ^34mCl is separated by repeated precipitation as silver chloride. The results obtained were 3.08 ± 0.47, 1.47 ± 0.17 and <1μg g^-1 for copper, nickel and aluminium alloys, respectively.     

A comparison of SCF-Xα and extended Hückel methods for metal clusters

A comparison of some results from Xα-scattered wave (Xα-SW) and extended Hückel (EH) calculations for metal clusters is given. It is found that small clusters of atoms (≈ 13 atoms) using the Xα-SW method reproduce many of the features of the electronic structure of the bulk metals, whereas this is not the case for the same clusters using the EH method. A more systematic approach to EH parametrizations is suggested in order to make this method a more viable approach to treating metal clusters.     

Infrared intensities of the external modes of crystalline nitrous oxide

The absorption intensities of two infrared active lattice modes of crystalline N₂O have been measured. Both the frequencies and intensities of the external modes of N₂O have been found to be very similar to those of CO₂, and most of the differences between the spectra of CO₂ and N₂O can be explained by the differences in the quadrupole moments.     

Salze von Halogennophosphorsäuren. VII Darstellung und Eigenschaften von Siliciumdichlorphosphaten

Salts of Halogenophosphoric Acids. VII. Preparation and Properties of Silicon Dichlorophosphates By reaction of SiCl₄ or SiHCl₃ with dichlorophosphoric acid the compounds H[Si(PO₂Cl₂)₅] · C₂H₅OC₂H₅, H[Si(PO₂Cl₂)₅] or Si(PO₂Cl₂)₄ have been prepared, the composition of which depends on the solvents used. Some properties of these compounds are described and possible Constitutions are discussed.     

Bestimmung der molaren Masse und der Ladungszahl von Polymerelektrolyten mit der Ultrazentrifuge

Zusammenfassung In der vorliegenden Arbeit wird das Sedimentationsgleichgewicht der Systeme Na₆[H₂W₁₂O₄₀]—NaCI—H₂O und Na₆[H₂W₁₂O₄₀]—NaClO₄— H2O untersucht. Die scheinbare molare Masse Mapp des Natriummetawolframats wird in beiden Systemen als Funktion der Natriummetawolfrarnat-Anfangspartialdichte ₀ ^PX _z gemessen. Durch lineare Extrapolation der Funktion Mapp = Mapp (PP,, ) auf die Polymerelektrolyt-Anfangspartialdichte Null können die Grenzwerte der scheinbaren molaren Masse (Mapp)o ermittelt werden. Aus den (Mapp)o-Werten wird die Abhängigkeit der Größe (ln _PXz /m _BX ) _mPXz von der NaCI- bzw. NaClO₄-Molalität berechnet.Die Bestimmung der molaren Masse und der (stöchiometrischen) Ladungszahl eines Polymerelektrolyten aus den experimentell ermittelten (Mapp)o-Werten unter Anwendung der Lamm-Williams-Gleichung wird diskutiert. Zur Ermittlung der beiden Größen müssen mehrere Versuchsreihen mit zwei verschiedenen Fremdelektrolyten durchgeführt werden. Externe Messungen sind nicht erforderlich.Man erhält auf diese Weise verläßliche Werte so-wohl der molaren Masse als auch der (stächiometrischen) Ladungszahl.

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Summary The sedimentation equilibria of the systems sodium metatungstate-sodium chloride-water and sodium metatungstate-sodium perchlorate-water are investiated. In both systems the apparent molecular mass Mapp of sodium metatungstate (PX _z) is measured in dependence on partial density ₀ ^PX _z before centrifugation. By linear extrapolation of the function Mapp = Mapp ( ₀ ^PX _z the limiting value (Mapp)o for ₀ ^PX _z = 0 is obtained. The variation with sodium chloride and sodium perchlorate molality of the quantity (ln _{PX z} ^m _BX )mPX_z is calculated from (Mapp)o data.The determination of the molecular mass and the algebraic valency of a polymeric ion by means of the (Mapp)o values calculated by Lamm-Williams equation is discussed. In order to obtain these two quantities at least two series of experiments are required, each of which using a different supporting electrolyte. External measurements are not necessary. In this way reliable values for the molecular mass as well as for the stoichiometric valency are obtained.

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Mit 5 Abbildungen und 3 Tabellen     

Neue Verbindungen mit Granatstruktur. III. Arsenate des Typs {NaCa2} [M] (As3)O12

Attempts to prepare phosphate granates were without success. However, three arsenate granates of the type {NaCa₂}[M](As₃)O₁₂ with M^II ? Mg, Co, Ni have been prepared by solid state reaction and their lattice constants determined. All these arsenates are characterised by a thermal transformation into a high-temperature form, proceeding monotropically for the Mg compound, and reversibly for the Ni and Co compound.