Characterization of the Active Species in the Afterglow of a Nitrogen and Helium Atmospheric-Pressure Plasma

The concentrations of the neutral active species in the afterglow of a nitrogen and helium atmospheric-pressure plasma have been determined by optical emission and absorption spectroscopy and by numerical modeling. For operation with 10 Torr N₂ and 750 Torr He, at 15.5 W/cm³ rf power, 30.4 L/min flow rate, and a neutral temperature of 50°C, the plasma produced 4.8×10¹⁵ cm^–3 of ground state nitrogen atoms, N(⁴S), 2.1×10¹³ cm^–3 of N₂(A³_u), 1.2×10¹² cm^–3 of N₂(B³_g), and 3.2×10⁹ cm^–3 of N₂(C³_u). The concentration of nitrogen atoms and metastable state nitrogen molecules, N₂(A), increased gradually with the rf power and the nitrogen partial pressure. Both the model and experiments indicate that ground-state nitrogen atoms are the dominant active species in the afterglow beyond 2.0 ms.     

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).     

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.

     

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.     

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.

     

Effects of an avoided crossing on linewidths of resonances in the H2 i3Π g state

We have investigated the influence of nonadiabatic effects on the linewidths of quasi-bound rovibrational levels in the i³ _g state of molecular hydrogen. This state has a potential barrier due to the interaction of then=3³ _g Rydberg series and the Q1³ _g valence state. The radial coupling with the higher lying³ _g states has been modelled into a diabatic problem. The widths of thev=4 and 5 levels, a measure for their lifetimes, have been determined both in the adiabatic i³ _g potential, and in the two-state system. The results show small shifts of the i³ _g (v=4,5;N=1) levels of a few wavenumbers, and a significant increase of 49% in the lifetimes of these levels. Both effects are large enough to be important in spectroscopic experiments. The magnitude of the effect is in accordance with observed linewidths obtained in recent experiments. Model calculations for differently shaped potential barriers have been carried out to study the generality of the above conclusions.     

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.     

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.     

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.     

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.

     

Exact spin-pairing energies at the crossovers in octahedral d 4, d 5, d 6, and d 7 transition metal complexes

Exact spin-pairing energies are calculated by direct diagonalization of the relevant ligand field plus interelectronic repulsion matrices for the configurations d ⁴, d ⁵, d ⁶, and d ⁷ of octahedral transition metal ions. The results are presented in terms of /B as function of = C/B for the range of values =3.0 to 8.0. Comparison with the quantity resulting from a simplified approach in which configuration interaction is neglected or considered on an approximate basis only reveals significant differences. Useful estimates of spin-pairing energies are provided, in addition, on the basis of empirical magnetic and electronic spectral data.

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Zusammenfassung Exakte Spinpaarungsenergien für die Konfigurationen d ⁴, d ⁵, d ⁶ und d ⁷ oktaedrischer Übergangsmetallionen werden durch direkte Diagonalisierung der entsprechenden Matrizen des Ligandenfeldes sowie der Elektronenwechselwirkung berechnet. Die Ergebnisse für /B werden in Abhängigkeit von = C/B für den Wertebereich =3.0 bis 8.0 angegeben. Ein Vergleich mit der Größe , die bei einer vereinfachten Behandlung unter Vernachlässigung oder näherungsweiser Berücksichtigung der Konfigurationswechselwirkung erhalten wird, zeigt auffallende Unterschiede. Nützliche Abschätzungen der Spinpaarungsenergie werden außerdem unter Benutzung empirischer magnetischer und elektronenspektroskopischer Daten erhalten.

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Résumé Les énergies exactes de couplage de spin sont calculées par diagonalisation directe du champ de ligand correspondant en plus des matrices de répulsion électronique pour les configurations d ⁴, d ⁵, d ⁶ et d ⁷ des ions octaédriques des métaux de transition. Les résultats sont présentés en termes de /B en fonction de = C/B dan l'intervalle =3,0 à 8,0. On trouve des différences significatives par comparaison de avec les valeurs résultant d'une approche simplifiée sans interaction de configuration ou avec interaction de configuration approchée. De plus, des estimations des énergies de couplage de spin sont obtenues à partir de données empiriques magnétiques et spectrales.

     

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].     

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.     

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.     

Computation of electronic transition moments: the length versus the velocity representation

Summary We have compared transition moments (TMs) obtained using the length and velocity representations for transitions from the ground state of H₂ to the lowest two¹ _u and two¹ _u ⁺ Rydberg states, theA ¹–X ¹⁺ transition in BH, and theA ¹ _u –X ¹ _g ⁺ transition in C₂. For H₂, the TMs in the length and velocity representations agree well even in cases where the one-particle basis is incomplete and the TM has not converged. For BH and C₂ the TM in the length representation converges rapidly with improvements in the one-particle basis set and is insensitive to inner-shell correlation. In contrast, in the velocity representation convergence with improvements in the one-particle basis is much slower, especially for C₂, and the TMs are significantly changed by inner-shell correlation. Thus the difference between the TMs in the length and velocity representations would not appear to be a viable diagnostic of TM convergence.     

Concentrations of Active Species in the Flowing Afterglow of a Nitrogen Microwave Plasma

Measurements of nitrogen atom density, by means of NO chemical titration, along with an evaluation of the densities of some excited species N ₂ (B, v=11), N ₂ (B, v=2), N ₂ (C, v=0), and N ₂ ⁺ (B,v=0), by means of a spectroscopic study of some bands of dinitrogen, are achieved along the flowing afterglow of a dinitrogen microwave plasma (2450 MHz) for several pressures. The concentrations obtained are in the following range: [N]10 ⁺¹⁵ , [N ₂ (B, 2)]10 ⁺⁹ –10 ⁺¹⁰ , [N ₂ (B, 11)]10 ⁺⁸ –10 ⁺⁹ , [N ₂ (C, 0)]10 ⁺⁶ –10 ⁺⁷ , [N ₂ ⁺ (B,0)]10 ⁺⁶ -10 ⁺⁸ (cm^-3). From a kinetic study of the formation and decay of excited and charged species, an estimation of N ₂ (A, v), N ₂ (X, v, and N ₂ ⁺ (X) densities can be derived: [N ₂ (A, v)]10 ⁺¹² , [N ₂ (X, v6)]10 ⁺¹⁵ –10 ⁺¹⁶ , [N ₂ (X, v12)]10 ⁺¹⁴ –10 ⁺¹⁵ , [N ₂ ⁺ (X)]10 ⁺¹⁰ (cm ^-3 ).     

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     

Influence of Gadolinium on Carbon Arc Plasma and Formation of Fullerenes and Nanotubes

Gadolinium-doped (0.8 at.%) graphite anodes were dc arced to produce different nanocarbons. Emission spectroscopy was performed to determine the temperature and column density distributions of C₂ (a³_u=0) in the arc plasma under 13.3 and 60 kPa pressures in helium atmosphere. The solid products were analyzed by UV-VIS, TOF MS, HR SEM, and TEM techniques. The influence of metal catalyst on the formation of C₆₀, and endohedral fullerenes, and carbon nanotubes is discussed.     

Test study on the excitation spectra of the N<Subscript>2</Subscript>–He van der Waals molecule

We have performed ab initio fourth-order Møller–Plesset perturbation theory calculations in the framework of the supermolecule approach on the vertical excitation spectra of the weakly bound van der Waals N₂–He dimer. They indicate a ``T-shaped' stablest ground N<sub>2</sub>(X<sup>1</sup><sub>g</sub><sup>+</sup>)–He(<sup>1</sup>S) electronic state with a well depth, D<sub>e</sub>, of 21.63 cm<sup>–1</sup> at a minimum distance, R<sub>e</sub>, of 3.44 Å and zero-point vibration correction, D<sub>o</sub>, of 7.07 cm<sup>–1</sup>. They also indicate a ``T-shaped' stablest excited conformer with R_e=3.25 Å, D_e=36.85 cm^–1 and D_o=17.06 cm^–1 for the N₂(B³_g)–He(¹S) triplet electronic level. In order to investigate the use of less-demanding correlation methods, test density functional theory calculations using the mPW1PW exchange–correlation functional are also presented for comparison.