Natural spin orbital analysis of diatomic molecular wave functions in terms of generalized diatomic orbitals

Starting from the demi-H ₂ ⁺ -model for Rydberg states, ab initio calculations of the energy and the wave function for some excited states of H₂ have been carried out with the help of diatomic orbitals. The potential curves and wave functions for the following states: 2¹ _g< ^/+ , 3¹ _g< ^/+ , 1³ _g< ^/+ , 2³ _g< ^/+ , 1¹ _u< ^/+ , 2¹ _u< ^/+ , 1³ _u< ^/+ , 2³ _u< ^/+ , 3³ _u< ^/+ , 1¹ _g , 1³ _g , 1¹ _u , and 1³ _u , have been calculated by a complete CI (configuration interaction) calculation in the sense that all configurations of the state symmetry have been used which can be formed from a given basis set. From the wave functions thus obtained the natural spin orbitals are calculated subsequently to the variational calculations. The dependence of the occupation numbers of the natural spin orbitals on internuclear distance is interpreted according to the model and is used for the explanation of the special features like double minima and maxima which occur in the potential curves of H₂. For the curves of the occupation numbers a non-crossing rule in analogy to that for potential curves is valid. The potential curves for the states 1³ _g and 1³ _u have been improved by the use of linear combinations of diatomic orbitals with different nuclear charges, which allow a flexible transition to linear combinations of atomic orbitals.Dedicated to Professor Iwan N. Stranski on the occasion of his 80th birthday.     

Theoretical study of the6Σ+,6Π, and4Σ+ van der Waals states of NO

Summary Potential energy curves for the weakly bound⁶⁺,⁶, and⁴⁺ states of NO are presented at various levels of correlation treatment. The binding energies for the van der Waals minima vary from about 30 cm^–1 for the⁶⁺ state to about 20 cm^–1 for the⁴⁺ and⁶ states. We investigate the importance of constraining the wave function to dissociate to a spherically symmetric O atom where the oxygen 2p orbitals are equivalent. For high levels of correlation treatment, we find that these restrictions have little effect on the potential, while greatly increasing the length of the CI expansion.     

Additive prediction of thermodynamic functions of hydrofluorides

Summary The experimental data available on the thermodynamic functions ⁰ forMF·nHF hydrofluorides [M=Li, Na, K, Rb, Cs, NH₄, Ag(I) and Tl(I);n=1–3] have been evaluated additively. The unknown values of ⁰ forn=0÷7 are predicted.

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Additive Voraussagen der thermodynamischen Funktionen von Hydrogenfluoriden (Kurze Mitt.)

Zusammenfassung Die vorhandenen experimentellen Daten über die thermodynamischen Funktionen ⁰ von HydrogenfluoridenMF·nHF [M=Li, Na, K, Rb, Cs, NH₄, Ag(I) und Tl(I);n=1–3] werden linear ausgeglichen und die fehlendenden Werte für ⁰ mitn=0÷7 vorausgesagt.

     

Spectroscopic study of organosilicon derivatives of thiophene

It is shown that the chemical shifts of hydrogen atoms in the 3 position of the thiophene ring in the PMR spectra of 2-substituted thiophenes are linearly associated with the Hammett _n substituent constants. On the basis of this, it was concluded that silyl substituents in 2-silylthiophenes have electron-acceptor character. It was established that the degree of d–p conjugation between the d orbitals of the silicon atom and the p electrons of the thiophene ring depends on the nature of the other three substituents attached to the silicon atom. The data from the IR spectra of organosilylthiophenes that contain a Si-H bond also attest to the presence of d–p conjugation in these compounds.See [1] for communication I.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, pp. 911–915, July, 1972.     

Ab initio studies of ground and excited electronic states of MgAr,CdAr, and BeAr

Summary The ground state (X ¹⁺) and several excited state (A ³,c ³+,C ¹,D ¹⁺, andE ³⁺) potential energy surfaces for the diatomic molecules MgAr, CdAr, and BeAr have been computed using complete active space self-consistent field (CASSCF) wavefunctions and valence double- and triplezeta quality basis sets augmented with polarization and diffuse functions. Pump-and-probe laser experiments have examined the quenching, of excited singlet states of metal-rare gas complexes such as CdXe to produce triplets that dissociate to³ P _Jmetal atoms. This quenching, which is detected for CdXe but not for CdAr or MgAr, is thought to occur via a crossing or strong coupling of a repulsive triplet curve correlating to the underlying³ P state of the metal, with an attractive singlet curve that correlates to the higher¹ P state of the metal. The present work indicates that the attractiveC ¹ and repulsivec ³⁺ curves of MgAr and CdArdo not intersect in the energetically accessible region of theC ¹ surface, unlike the corresponding curves for the CdXe diatom. These data are consistent with the absence of³ P _J Cd atoms in the MgAr and CdAr experiments, respectively. However, an alternative quenching mechanism involving vibronic coupling between theC ¹ vibrational eigenstates and the continuum eigenstates of the underlying repulsive³⁺ surface may be operative; this possibility is examined qualitatively and predicted to be unlikely for MgAr (due to small spin-orbit coupling) and CdAr (due to unfavorable vibronic factors). BeAr, which has yet to be probed experimentally, is predicted to be bound by 770 and 900 cm^–1 in theD ¹⁺ state (which has metal 2s2p character) and theE ³⁺ state (which has Rydberg metal 2s3s character), respectively, and to display interesting potential curve intersections.Dedicated to Prof. Klaus Ruedenberg     

Optimal double-configuration study of the lowest excited Π states of H2

Various levels of approximation (Hartree-Fock, configuration interaction and double-configuration Hartree-Fock method) are compared for extensive and limited exponent optimization of the atomic orbitals of the wavefunctions. The potential energy curves for the lowest-lying ¹ _u, ³ _u, ¹ _g, ³ _g states of the hydrogen molecule are presented. The shapes of the curves on the highest level of approximation, i.e. with the optimal double-configuration wavefunction, are basically in agreement with previous, more sophisticated and time-consuming work. The influence of the various approximations is also studied for several one-electron properties: charge distribution of the wavefunction along and perpendicular to the molecular axis, quadrupole moment and core attraction energy distribution. Differences arise to the work of Zemke et al. [1], who used a limited exponent optimization with a larger basis set, in the _g states where the orbitals are very diffuse. The differences concern magnitude and location of minima and maxima of potential curves, as well as considerable changes in one-electron properties which depend strongly on the spatial distribution of the orbitals.

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Zusammenfassung Verschiedene Approximationsstufen (Hartree-Fock, Konfigurationenwechselwirkung und Doppelkonfigurationen-Hartree-Fock-Methode) werden für ausgedehnte und begrenzte Exponentenoptimisierung von Atomorbitalen der Wellenfunktionen verglichen. Die Potentialkurven für die niedrigsten ¹ _u, ³ _u, ¹ _g, ³ _g Zustände des Wasserstoffmoleküls werden angegeben. Die Form der Kurven im Rahmen der besten Näherung, d. h. mit Doppelkonfiguration, stimmen im wesentlichen mit früheren aufwendigeren Rechnungen überein. Der Einfluß der verschiedenen Approximationen wird auch an einigen Einelektroneneigenschaften studiert: Ladungsverteilung der Wellenfunktion längs und senkrecht zur Molekülachse, Quadrupolmoment und Verteilung der Rumpfenergie. Unterschiede erscheinen zur Arbeit von Zemke et al. [1], die einen größeren Basissatz mit begrenzter Optimisierung verwandten, bei den _g Zuständen, wo die -Orbitale sehr diffus sind. Die Unterschiede betreffen Größe und Lage der Minima und Maxima der Potentialkurven sowie beträchtliche Änderungen in solchen Einelektroneneigenschaften, die stark von der räumlichen Verteilung der Orbitale abhängen.

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Résumé Comparaison de différents niveaux d'approximation (Hartree-Fock, interaction de configuration et Hartree-Fock à deux configurations) pour des optimisations étendues et limitées des orbitales atomiques de base. Calcul des courbes d'énergie potentielle pour les plus bas états ¹ _u, ³ _u, ¹ _g, ³ _g de la molécule d'hydrogène. Pour la fonction d'onde la plus raffinée: H.F. à deux configurations, la forme des courbes est en accord avec les résultats obtenus dans des travaux précédents plus complexes et plus coûteux. On étudie aussi l'influence des diverses approximations sur plusieurs propriétés monoélectroniques: distribution de charge le long de l'axe moléculaire et perpendiculairement à celui-ci, moment quadrupolaire et distribution de l'énergie d'attraction de coeur. On trouve des différences avec le travail de Zemke et al. (1), qui utilisent une plus grande base partiellement optimisée, pour les états _g où les orbitales sont très diffuses. Les différences concernent la grandeur et la position des extrema des courbes de potentiel, ainsi que des variations importantes des propriétés monoélectroniques qui dépendent fortement de la distribution spatiale des orbitales.

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On leave to: Institut für Theoretische Chemie, Universität Stuttgart.

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On leave to: Office of Computing Activities, National Science Foundation, Washington, D.C.     

Quantum chemical study of allyl halides

Using the MNDO method we have shown that the bathochromic shift of the longwavelength region of absorption in the electronic spectrum of allyl bromide and allyl iodide on going to nonplanar conformers is due to the fact that, in this case, the transition ^* to the low-lying ^* orbital appears, which is forbidden in planar forms. In allyl fluoride and allyl chloride, , and the transition ^*, which depends little on conformation, is long-wavelength. In the gauche conformers of allyl halides, the frontier MOs are appreciably delocalized as a result of - interaction; in the s-trans conformer, the unshared pair of the heteroatom makes an insignificant contribution to the orbital only in allyl iodide.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2552–2557, November, 1989.     

Ru(III) catalyzed oxidation of some aliphatic alcohols by N-bromosuccinimide (NBS). A kinetic study

Kinetics of Ru(III) catalyzed oxidation of methanol, ethanol, n-propanol, n-butanol, isopropanol and iso-butanol by N-bromosuccinimide (NBS) in the presence of Hg(II) acetate have been studied in acid medium. The oxidation exhibits a fractional order in [alcohol] and first order in [NBS]. The applicability of Taft's equation was tested. The probable mechanism is discussed.

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, , -, -, - () Hg(II), Ru(III), . . . .

     

Energy dissipation and selectivity in the catalytic oxidation of ammonia

A qualitative interpretation of selectivity changes in ammonia oxidation, based on considerations of energy dissipation processes is presented.

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, .

     

Gasification in steam of a bituminous coal from Peñarroya (Cordoba,Spain) and of different samples prepared from it

The gasification with steam of a bituminous coal from Peñarroya (Cordoba, Spain) (H—O) and of several samples prepared from either by acid treatment (H—H, H—N, H—F and H—F(3)) or by thermal treatment (H—O—C) was studied under both dynamic and isothermal conditions (10 deg/min and 40 min at 1000°).It was found that only for the samples prepared by hydrofluoric acid treatment, H-F and H—F(3), did the gasification effected under such experimental conditions take place in a complete manner.

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Zusammenfassung Die Dampfvergasung von bituminöser Kohle (H—O) (Penarroya, Cordoba, Spanien) und von daraus durch Säurebehandlungen (H—H, H—N, H—F und H-F(3)) oder thermische Behandlung (H—O—C) hergestellten Proben wurde unter dynamischen und isothermen Bedingungen (10 °/min und 40 min bei 1000°) untersucht. Es wurde festgestellt, daß nur die durch Flußsäurebehandlung hergestellten Proben (H—F und H—F(3)) unter den experimentellen Bedingungen vollständig vergasbar sind.

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(10°/ 40 1000°) () , . , , , .

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The authors are grateful to the CAICYT of Spain for the financial support on Project No. 0794/82.     

Labelling spectroscopy on argonhydride and argondeuteride in a plasma beam penning tube

Rare gas hydride molecules and triatomic hydrogen molecules were produced in a Cossart-type plasma beam Penning tube specially designed for laser spectroscopic work. A cw dye laser was used to stimulate transitions from theB ² rovibrational levels to theA ²⁺ levels of argonhydride (⁴⁰ArH) and argondeuteride (⁴⁰ArD). The transitions were detected by measuring the decrease of the spontaneous emission from the upper levels, which clearly shows the expected population inversion between the two participating electronic states. With this first laserspectroscopic work on argonhydride and argon deuteride, the classification of the lines of theB ² A ²⁺ band as given by Johns 1970 could be checked and was found to be consistent*. Furthermore theQ branches of these bands for ArH and ArD could be completely resolved into their single lines and their wavelengths were measured. The latter allowed the difference between the rotational constants of theA andB electronic states to be directly determined. The method was also applied to triatomic hydrogen. D₃. It should be useful for classifying more complicated bands of ArH and of KrH and XeH, which can also be produced in this tube.In later theoretical work theB ² state was called 2² state [13] andE ² state [12], respectively     

Empirical equations of state for adsorption layer: Alkylthiopolyoxyethylene glycols

Surface tension isotherms ofn-alkylthiopolyoxyerhylene glycols:n-C _x H_2x+1S(CH₂CH₂O) _y H, wherex=5 to 8,y=3 or 4, were approximated with orthogonal polynomials to get good quality values of surface pressure (II) and molar area of the adsorbed layer (). The modified Volmer (*(–₀)=Z*R*T) van der Waals and virial equations of state were used to correlate and in terms of real two-dimensional gas. The combination of Volmer and van der Waals equations of state made it possible to determine the interaction energy, , which was prescribed to cohesion of hydrophobic chains in the adsorption layer. The value of for the amphiphiles in question was in the range 0.97–1.91R*T and the average contribution per methylene group was ca. 0.21R*T.The Lennard-Jones potentials calculated from second virial coefficient were of the same range as , but no clear relation was found between their values and number of structure elements of the alkylthiopolyoxyethlene glycols.Presented during 7th International Conference: Surface and Colloid Science, July 7–13, 1991, Compiegne, France     

Effect of stirring on the Belousov-Zhabotinskii reaction: A problem of interpretation

It is probable that different phenomena attributed to mechanical stirring during the Belousov-Zhabotinskii (BZ) reaction are caused by atmospheric oxygen and, as far as our experiments show, they have nothing to do with dissipative structures or with the turbulence of the reacting mixture.

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, , , -, .

     

The thermal decomposition of thaumasite from Mothae kimberlite pipe,Lesotho, Southern Africa

The endothermic decomposition of thaumasite from Mothae which has been investigated by DTA and TG shows a peak temperature of 138–203°, and reaction orders of 0.45–1.00, depending on the heating rate employed. The activation energy of the reaction was found to be about 19 kcal/mole; the enthalpy is 246 cal/g.The decomposition seems to be divided into one reaction withn=0.90, immediately followed by one withn=1.59. The first reaction is attributed to the loss of H₂O, the second one to the (partial) release of OH and CO₂.

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Zusammenfassung Die durch DTA und TG überprüfte endothermische Zersetzung von Thaumasit aus Mothae zeigt in Abhängigkeit der angewandten Aufheizgeschwindigkeiten Spitzentemperaturen zwischen 138 und 203° C, sowie Reaktionsordnungen von 0.45 bis 1.00. Die Aktivierungsenergie der Reaktion ergab sich zu 19 Kcal/Mol, die Enthalpie zu 246 cal/g.Die Zersetzung scheint in eine Reaktion vonn=0.90 und eine sofort darauffolgende vonn=1.59 geteilt zu sein. Die erste Reaktion wird dem Verlust von H₂O, die zweite der (teilweisen) Freisetzung von OH und CO₂ zugeschrieben.

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Résumé La décomposition endothermique de la thaumasite de Mothae a été étudiée par ATD et TG. Suivant la vitesse de chauffage utilisée la température au sommet du pic varie de 138 à 203° C et l'ordre de réaction de 0.45 à 1.00. On a trouvé que l'énergie d'activation s'élevait à 19 kcal, mol^–1 et l'enthalpie à 246 cal. g^–1.Il semble que la décomposition s'effectue suivant une réaction d'ordren=0.90, immédiatement suivie par une autre oùn=1.59. On attribue la première réaction à la perte d'eau et la seconde à la libération (partielle) d'hydroxyles OH et d'anhydride carbonique CO₂.

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, , 138–203° 0,45–1,00 . , 19 /, - 246 /. , n=0,90, n=1,59. , - OH CO₂.

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The material used for this study has been kindly supplied by Dr. P. H. Nixon, former chief geologist, Department of Mines, Maseru, Lesotho.     

Effect of the medium on the oxidation of aliphatic monocarboxylic acids

Oxidation rates and k₂/k₆ ratios are given for some acids from propionic to lauric. The k₂/k₆ ratio is shown to be influenced by the electrostatic effect of the solvent. A linear dependence between the isodielectric values of k₂/k₆ and the number of methylene groups in the acid molecules is described.

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k₂/k₆ . k₂/k₆ k₂/k₆ .

     

Dissociative Excitation of MnII and MnCl in Electron Collisions with Manganese Dichloride

The dissociative excitation of MnII spectral lines and MnCl spectral bands upon e–MnCl₂ collisions was experimentally studied. Dissociative excitation is most effective for the low-lying ⁵ P° and ⁷ P° levels of MnII. Two sequences = 0 in the – systems of the MnCl molecule were detected. Possible pathways of dissociative excitation of MnII are discussed.     

Upper bounds to atomic electron densities in position and momentum spaces

Modified functions r ^–(r) and p ^–(p) of the spherically averaged electron densities (r) in position space and (p) in momentum space are found to be convex (i.e., the second derivatives are nonnegative everywhere) for all the 103 ground-state atoms from hydrogen (atomic number Z=1) to lawrencium (Z=103), if the parameters are chosen to be 0.6 and 1.4. The convex property of r ^–(r) and p ^–(p) is used to derive upper bounds to the density functions (r) and (p) in terms of their radial moments r ^s and p ^s or frequency moments ^t and ^t . In most cases, the present bounds are shown to be more general and more accurate than those reported in the literature.     

Molal volumes of sucrose in aqueous solutions of NaCl,KCl, or urea at 25°C

The apparent molal volume _v of sucrose in water has been measured at 25°C in the concentration range 0.04–4.4m from precise density measurements. The same property was also determined for dilute solutions of sucrose in mixed aqueous solvents containing NaCl, KCl, or urea. The limiting values _v ^° and the slopesS _v ^* were obtained in each case, and their significance has been discussed briefly. The mean apparent molal volumes _v of the ternary systems were also calculated, and the predictive accuracy of Ward and Millero's modified Young's rule for _v was found to be comparable to that for other electrolyte-nonelectrolyte solutions. For the system H₂O-sucrose-urea, an additivity rule based simply on total molality predicted _v with similar accuracy.Deceased January 15, 1976.     

Chemical,dehydration, differential thermal and X-ray analysis of Salal bauxite deposits

Chemical, dehydration, differential thermal and X-ray analysis data on four samples of mineral deposits from the Salal region (J & K) have been determined to assess their mineral compositions. All the samples appear to be kaolinitic in character, though in association with other mineral impurities, such as boehmite, diaspore and dickite, in varying proportions.

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Zusammenfassung Vier Proben von Minerallagerstätten der Salal-Region (J & K) wurden chemisch sowie mittels DTA und röntgenographischer Analyse untersucht, um ihre Mineralzusammensetzung zu ermitteln. Alle Proben sind dem Charakter nach kaolinitisch, allerdings in unterschiedlichen Verhältnissen mit anderem mineralischem Material wie Boehmit, Diaspor und Dickit verunreinigt.

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, , , . , - , .

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The authors are grateful to the Head of the Department of Physics, Jammu University, for his interest in the research programme.     

Catalytic isomerization of phenylcyclohexane in the presence of aluminium chloride

Intermolecular migration accompanied by deuterium atom rearrangement between the cycloalkyl fragment carbon atoms has been found during the interaction of phenylcyclohexane-1d₁ in benzene-¹⁴C with aluminium chloride. Relative rates of these conversions have been estimated. The reaction mechanism is discussed.

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, -1d₁ -¹⁴C , . .