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.     

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     

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.     

A calculation of the spin-orbit splitting of the X 2Π state of NO

Using Brion, Moser and Yamazaki's SCF LCAO MO the spin orbit splitting of the X ² state of NO has been calculated using various potentials. Experimentally W (² _3/2) –W (² _1/2) is known to be 122 cm^–1. Using an unscreened nuclear field we find a value of 328 cm^–1. Inclusion of screening due to electronic repulsions reduces this value to 283 cm^–1. Agreement with the experimental value may be obtained by reducing the orbital exponents in the 2 molecular orbital by 30% over the value given by Slater's rules.

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Zusammenfassung Die Spin-Bahn-Aufspaltung des X ² -Zustandes von NO wurde mit verschiedenen Potentialen unter Verwendung der SCF LCAO MOs von Brion, Moser und Yamazaki berechnet. Der experimentelle Wert für W (² _3/2) –W (² _1/2) beträgt 122 cm^–1. Die Rechnung mittels eines reinen Kernfeldes liefert den Wert 328 cm^–1 und unter Einschluß der Abschirmung durch die Elektronen 283 cm^–1. Übereinstimmung mit dem experimentellen Wert läßt sich erzielen, wenn man den Exponenten des 2-Zustandes 30% kleiner als nach den Slater Regeln macht.

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Résumé Avec les orbitals moléculaires SCF LCAO de Brion, Moses et Yamazaki, nous avons calculé le dédoublement spin-orbitale de l'état X ² de NO. La valeur expérimentale W (² _3/2) –W (² _1/2) est 122 cm^–1. Dans un champ nucléaire «sans écran» on trouve 328 cm^–1. L'inclu-sion de l'effet d'écran dû aux répulsions interélectroniques réduit cette valeur à 283 cm^–1. La valeur expérimentale s'obtient, si l'on réduit de 30% les exposants d'après Slater dans l'orbi-tale moléculaire 2.

     

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.

     

Influence des charges nucléaires effectives σ et π sur les calculs LCAO-MO-SCF-π

Application of the LCAO-MO-SCF- method to conjugated hydrocarbons leads with the effective nuclear Slater's charges, Z_eff = Z_eff = 3.25 to electronic transitions higher than experimental ones by about 50%.We show that in the case of all trans linear polyenes and fulvene, one may obtain satisfying results by the same method, without any reference to experience, by taking Z_eff = 3.0 Z_eff = 3.55. There the effective nuclear charges are near of these of the valence state of carbon V ₄1s²t₁t₂t₃2pt_z:Z_eff = 2.971 Z_eff = 3.382 [10].     

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.     

Etats de valence 2Π et 2Δ des molécules isoélectroniques N 2 + , CN et CO+

Résumé On a calculé les courbes d'énergie potentielle de plusieurs états excités de N₂ ⁺, CN et CO⁺, en utilisant les fonctions d'onde LCAO MO SCF. Les valeurs calculées des constantes spectroscopiques et spin orbite sont en bon accord avec l'expérience. Notre calcul prévoit qu'on ne peut pas observer de transition ² -A ² dans CO⁺, et confirme que l'état supérieur de la transition récemment observée est un état ² et non ² .

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Potential energy curves have been calculated for several excited states of N₂ ⁺, CN and CO⁺, using LCAO MO SCF functions. Good agreement with experiment has been obtained for spectroscopic and spin orbit constants. From our calculation, ² -A ² transition in CO⁺ is predicted to be non observable, but we confirm that the upper state of the experimentally observed transition is ² _r and not ² .

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Zusammenfassung Für verschiedene angeregte Zustände der iso-elektronischen Moleküle N₂ ⁺, CN und CO⁺ wurden unter Verwendung von LCAO-MO-SCF-Funktionen die Potentialkurven berechnet. Für die spektroskopischen und die Spin-Bahn-Kopplungskonstanten wurde gute Übereinstimmung mit dem experimentellen Befund erreicht. Unseren Berechnungen nach sollte der ² -A ² -Übergang in CO⁺ nicht beobachtbar sein, während die Rechnung bestätigt, daß der obere Zustand des experimentell beobachteten Überganges ein ² _r -Zustand und nicht ein ² -Zustand ist.

     

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     

Determination of gaseous nitrogen in gas mixtures using low pressure microwave induced plasma emission spectrometry

A microwave induced plasma emission spectrometer operating at low energy (30 W) and low plasma gas pressure (2.510^-2 Pa) has been used for the quantitative measurement of molecular nitrogen in natural gases. The samples have been introduced into the plasma using a counterflow principle to produce emission spectra of diatomic molecular fragments in low excitation states (advantage: minimized interferences). The N₂ concentration has been determined by measuring the intensity of the N₂-line at 337.13 nm (C³_u-B³_g-system; (0,0)vibrational transition) and of the NH-line at 336.03 nm (A³_i-X^2--system; (0,0)-vibrational transition). A linear correlation between concentration and signal intensities has been obtained in the range of 0.00% to 14.24% (v/v). The method possesses a detection limit of 0.01 ppm (v/v) for the determination of N₂, and a reproducibility of 1.33% (RSD).     

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.     

Adiabatic corrections for thei 3Π g state of the hydrogen molecule

Summary The adiabatic corrections of thei ³_g state of H₂ are calculated for a wide range of internuclear distances using an explicitly correlated wavefunction. The vibrational structure of this state is calculated in the adiabatic approximation. It is shown that forN=1 levels of the – substate, for which the nonadiabatic corrections are negligible, the agreement between theory and experiment is excellent; the small mass independent discrepancy of the order of 0.5–3 cm^–1 is due to the convergence error in the Born-Oppenheimer calculations. For higherN the discrepancy is much larger. However, it is mass andN-dependent and it is almost entirely due to the nonadiabatic effects caused by³_g-³_g interactions. The still larger discrepancy for the + substate of thei state is evidently caused by additional interactions of thei state with close-lying states of³ _g ⁺ symmetry.Dedicated to Prof. Klaus Ruedenberg on the occasion of his 70th birthday     

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.     

Slow Li + He Collisions: A Molecular State Treatment

Low-energy state-changing cross sections involving the ground state of He atoms and ground states of Li atoms are calculated using the semiclassical impact parameter close-coupling method based on a molecular states expansion to represent the electronic wave function. The plane wave translation factor is used considering a classical trajectory for the motion of the heavy particles. We approximate this many electrons system to a one-electron problem by using the l-dependent pseudopotential technique. In order to obtain cross sections, we retain nine molecular states including six and three states in our close coupling calculations, but, in the structure calculations, we have included 16 states (ten and six states) so the excitation of 5s levels of the target Li atoms is possible. Our cross sections for Li (2p) excitation agree well with previous theoretical and available experimental results.     

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.     

Thermal studies on metal complexes of 5-nitroso-pyrimidine derivatives

Four Hg(II) complexes, containing as ligands 6-amino-5-nitrosouracil (AH), 6-amino-3-methyl-5-nitrosouracil (BH) or 6-amino-1-methyl-5-nitrosouracil (CH), have been synthesized and their thermal behaviour studied by TG and DSC techniques: Hg₃Cl₆(AH)₄, HgCl₂(BH)₂· 2 H₂O, HgCl₂(BH)₂ · H₂O and HgC₂· 2 H₂O.The dehydration processes take place in only one step, with enthalpies in the range 40.2–60.0 kJ · mole^–1 H₂O.Pyrolytic processes start between 200 and 250°, in all cases the thermal stability of the corresponding pyrimidine derivative being lower than that of the free ligand. These processes finish between 600 and 750°, with no residue.

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Zusammenfassung Vier 6-Amino-5-nitrosouracil (AH), 6-Amino-3-methyl-nitrosouracil (BH) oder 6-Amino-1-methyl-5-nitrosouracil (CH) als Liganden enthaltende Hg(II)-Komplexe wurden synthetisiert: Hg₃Cl₆(AH)₄, HgCl₂(BH)₂ · 2 H₂O, HgCl₂(BH)₂ · H₂O und HgC₂ · 2 H₂O. Die Dehydratisierungsprozesse verlaufen in nur einem Schritt mit Enthalpien im Bereich von 40.2–60.0 kJ pro mol H₂O. Pyrolitische Prozesse setzen zwischen 200 und 250° ein. In allen Fällen ist die thermische Stabilität der entsprechenden Pyrimidin-Derivate geringer als die der freien Liganden. Diese Prozesse sind zwischen 600 und 750° beendet, wobei kein Rückstand zurückbleibt.

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g₃l₆()₄, gl₂( )₂ · 2 ₂O, gl₂()₂ · ₂O, g₂ · 2 ₂, — 6- -5-, — 6--3- — 6---5- . , 40.2–60.0 · ^–1 ₂. 200 250° 600–750° - . , .

     

A new possibility of construction of the CD ring systems of the steroid molecule

Summary We have carried out the cyclization of 2-(-cyclohexylidene ethyl)-2-cyclohexen-1-one (I) into trans-1-keto-^4a,10a-dodecahydrophenanthrene (II) under the influence of phosphoric acid.     

Some remarks on the periodical change of the stability constants of the lanthanide complexes

The correlations between the values of the lgK (K = stability constant of the lanthanide complex) and the reciprocal of the ionic radius 1/r or the sum of the ionization potentials ₁ ³ I for the lanthanide ions were reviewed for different ligands. A straight-line relationship (lgK – lgK)/lgK vs. (1/r – 1/r)/(1/r) or vs. ( ₁ ³ I – ₁ ³ I)/ ₁ ³ I was found within the tetrads La-Nd, Gd-Ho, and Er-Lu.

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Bemerkungen zum periodischen Wechsel der Stabilitätskonstanten von Lanthaniden-Komplexen

Zusammenfassung Es wurde eine Übersicht der Korrelationen zwischen den Werten von logK (K = Stabilitätskonstante der Lanthanidenkomplexe) und den reziproken Ionenradien 1/r oder der Summe der Ionisierungspotentiale ₁ ³ I für die Lanthanidenionen für verschiedene Liganden gegeben. Dabei wurde eine lineare Korrelation für (lgK – lgK)/lgK gegen (1/r – 1/r)/(1/r) oder gegen ( ₁ ³ I – ₁ ³ I)/_1/3 I innerhalb der Tetraden La-Nd, Gd-Ho und Er-Lu aufgefunden.

     

Variations in the cooling transitions of potassium nitrate

Because of questions concerning the suitability of potassium nitrate as a dynamic temperature standard for DTA, the relation between the experimental procedure and the resulting curves was ascertained for the Standard Reference Material KNO₃. The material behaves differentlyon cooling in open pans than in cylindrical holders because confinement in the latter case initiates reversion to the room temperature form. Under the conditions of use as a dynamic temperature reference material, the curves are accurately reproducible.

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Zusammenfassung Zur Überprüfung der Eignung von Kaliumnitrat als dynamische Temperatur-Eichsubstanz für die DTA, wurde der Zusammenhang des Versuchsvorganges und der erhaltenen Kurven für das Standard-Referenz-Material KNO₃ untersucht. Die Substanz verhält sich bei der Kühlung in offenen Tiegeln und in zylindrischen Behältern unterschiedlich, da in letzteren die Begrenztheit die Reversion zur Zimmertemperatur-Form in Gang setzt. Unter den für das dynamische Temperatur-Referenz-Material gegebenen Bedingungen sind die Kurven gut reproduzierbar.

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Résumé En raison de l'emploi du nitrate de potassium comme étalon de température en ATD, on a étudié l'influence des conditions d'expérience sur les courbes obtenues. Le comportement de ce corps est différent si on effectue le refroidissement dans des capsules ouvertes ou dans des creusets cylindriques. Dans ce dernier cas, le manque d'espace initie le retour à la forme stable delà température ambiante. Dans les conditions d'emploi comme matériau de température étalon, les courbes sont exactement reproductibles.

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One of us is indebted to the U. S. National Science Foundation for support of part of this study.     

Study of the heterogeneous decomposition of tertiary-butyl alcohol and di-tertiary-butyl peroxide on SiO2 by temperature programmed desorption

In the study of the interaction of tertiary-butyl alcohol and di-tertiary-butyl peroxide with SiO₂ treated with KCl by means of temperature programmed desorption, pulsation desorption (oscilatory behavior) is observed.

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- - SiO₂, KCl - , ( ).