An analysis of the four nuclear quadrupole problem: The microwave spectrum of cyanogen azide

We have derived expressions for the Hamiltonian matrix elements for the coupling of any number of quadrupolar nuclei with the molecular rotation using the Wigner n-j formalism. These expressions have been used to analyse the nuclear quadrupole hyperfine structure of the rotational spectrum of cyanogen azide, NCN₃. The analysis was effected by comparing the experimental high resolution spectral traces with computer simulated traces from which the nuclear quadrupole coupling constants obtained are (MHz)

$\text{x}{}_{\mathrm{aa}}\text{(1) = 4.82 ± 0.02,}\text{x}{}_{\mathrm{bb}}\text{(1) = ?0.70±0.08,}$

$\text{x}{}_{\mathrm{aa}}\text{(2) = ?0.85 ± 0.07,}\text{x}{}_{\mathrm{bb}}\text{(2) = 0.70±0.08,}$

$\text{x}{}_{\mathrm{aa}}\text{(3) = ?0.75 ± 0.07,}\text{x}{}_{\mathrm{bb}}\text{(3) = 0.70±0.05,}$

$\text{x}{}_{\mathrm{aa}}\text{(4) = ?2.27 ± 0.04,}\text{x}{}_{\mathrm{bb}}\text{(4) = 0.70±0.07,}$

Small corrections to the previously reported rotational constants are given.     

The chlorinalion of 3,5-dimethyl-1,2,4-oxadiazole

The clilorination of 3,5-dimethyl-1,2,4-oxadiazole has been studied using both photo and thermal initiation. It has been found that photoinitiation allows reaction at both the 3- and 5-methyl group, the former being preferred by a factor of 3-4 at moderate (up to 75° ) temperature. The difference in reactivity is related to a difference in electron availability at the two reaction sites. The thermally initiated chlorination occurs almost exclusively at the 5-methyl group. Overall, 3,5-dimethyl oxadiazole is much less active than toluene or cyclo-liexane toward chlorination.     

Lasers for plasma diagnostics,time resolved measurement and molecular fluorometry in analytical science

In chemical measurement and characterization, lasers are playing a unique role in improving sensitivity, enhancing spatial and spectral resolution, and enabling time resolution on the fastest time scales that are chemically significant. Furthermore, lasers have permitted entirely new classes of measurements to be undertaken that would not be possible without the high radiant power, directionality, and coherence of a laser beam. In this paper, a number of these capabilities are illustrated with examples from the authors' laboratory. Prominent among these examples is the use of a high-power pulsed laser for producing scattering and fluorescence from species in an inductively coupled plasma (ICP). With the appropriate laser and photometric equipment, such measurements enable the determination of time-resolved and spatially resolved values for electron concentration, electron energy distribution, gas-kinetic temperature, and the concentrations of important sample and intrinsic species that the plasma contains. Another example shows how either a continuous wave (CW) or repetitively pulsed laser can be coupled with relatively simple electronic instrumentation to permit measurements to be obtained on a sub-nanosecond time scale. Interestingly, a recent development might obviate the need for a sophisticated laser in such schemes. Lastly, a relatively simple experimental configuration can be used to determine as few as 10⁶ molecules in a real sample. In this arrangement, a single aliquot of the sample is dispensed in a volume as small as 6 nL. This aliquot, in droplet from, then constitutes the sample cell itself. As the droplet falls through the focused laser beam, its contents can be determined with extraordinarily high sensitivity. Methods to improve even this detection capability will be outlined.     

Optimum parametrization of the Pople-Santry-Segal method of treating all valence electrons

An optimised version of the simple all-valence-electron SCF MO method of Pople, Santry and Segal has been developed by deriving the basic core hamiltonian matrix elements U ^AA for 2p and 1s orbitals empirically by a least-squares fitting of calculated to observed dipole moments. The calculated moments were found to be relatively insensitive to U _2s2s ^AA and resonance integrals and so for the present the values suggested by Pople, Santry and Segal have been used for them. Optimum values for U _2p2p ^AA and U _1s1s ^AA are surprisingly close to the CNDO/2 values of these authors. Calculated dipole moments are sometimes sensitive to the assumed geometries and attention is drawn to several instances in which the idealised geometries assumed by Pople and Gordon lead to values notably different from those obtained by starting with the experimentally determined geometry. The present optimised scheme becomes less satisfactory for molecules in which large electron shifts occur or in which the atomic dipole is a dominant term.

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Zusammenfassung Die Pople-Santry-Segal-Methode wurde modifiziert, indem die Rumpfintegrale U ^AA für 1s- und 2p-Orbitale unter Verwendung der Fehlerquadratmethode an gemessenen Dipolmomenten angepaßt wurden; sie unterschieden sich nur wenig von den CNDO/2-Parametern. Die berechneten Dipolmomente sind ziemlich unempfindlich gegen Variationen von U _2s2s ^AA und der Resonanzintegrale; hier wurden die Werte von Pople, Santry und Segal verwendet. Die berechneten Momente sind in einigen Fällen stark von der Geometrie abhängig und können sich für idealisierte und experimentelle Geometrien merklich unterscheiden. Bei Molekülen mit starker Elektronenverschiebung oder bei welchen die atomaren Dipole bedeutsam sind, ist unser Parametersatz nicht befriedigend.

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Résumé Développement d'une version optimisée de la méthode des électrons de valence SCF MO de Pople-Santry-Segal par déduction empirique des éléments de matrice de coeur U ^AA des orbitales 2p et 1s par ajustement quadratique des moments dipolaires calculés à ceux observés. Les moments calculés sont relativement insensibles à U _2s2s ^AA et aux intégrales de résonance; les valeurs proposées par Pople Santry et Segal ont donc été utilisées dans ces cas. Les valeurs optimales de U _2p2p ^AA et U _1s1s ^Emphasis>1AA sont étonnament voisines des valeurs CNDO/2 de ces auteurs. Les moments dipolaires calculés sont parfois sensibles aux géométries utilisées et l'on cite plusieurs cas où les valeurs obtenues à partir de géométries idéalisées et de geometries expérimentales sont notablement différentes. Ce schéma optimisé s'avère moins satisfaisant pour les molécules où de déplacement d'électrons importants se produisent ou bien dans lesquelles les dipôles atomiques sont des termes dominants.

     

Simplified ab-initio calculations on hydrogen-containing molecules

The simplified ab-initio method described in an earlier paper is tested on some hydrogen-containing molecules. The performance is slightly below that found previously for molecules composed entirely of first-row atoms but should be suitable for applications where limited numerical accuracy is sufficient. The hope of improved performance through limited expansion of the basis, especially on hydrogen, is not realised and so alternative treatments of the two-electron many-centre integrals should be sought if greater numerical accuracy is required.     

Optimum atomic orbitals for molecular calculations A review

This review is intended to give a broad outline of the many techniques used in the calculation of atomic structure and the methods of using the information gained from this work in molecular calculations. Consequently, no topic is considered in full depth and only selected examples from the literature are used to illustrate the main points. Extensive tabulatios of atomic and molecular properties are already available in the literature, and these serve as additional sources of examples. Only methods within the Hartree-Fock framework, where a single Slater determinant (or in some cases a linear combination of Slater determinants) and the variation principle form the basis of the model, are considered in detail. Extensions of the independent particle model to include correlation have been considered briefly and smaller corrections, such as magnetic and relativistic effects are omitted.

We describe, in the first part of the review, the partical requirements of the functional form of the basis set and consider examples of the types of functions available in the literature. These include exponential- and Gaussian type-functions and many others. For' chemical accuracy' the total energy of the electronic system should be estimated to within one kilocalorie or better, requiring at least Hartree-Fock accuracy for the isolated atoms and optimization or augmentation of the bases in the molecule. Smaller, less accurate basis sets for the atoms are still useful, however, in the prediction of certain atomic and molecular properties, and in supplying simple orbital pictures of interest to chemists, although producing poorer representations of the total wave function.

In order to produce good wave functions there are certain criteria that they may satisfy. These, when coupled with the independent particle model, produce many methods of obtaining wave functions of varying accuracy depending in the size and type of functions comprising the basis set. Some of the criteria considered include the minimal energy principle, the best approximation to operators other than the Hamiltonian and other less known, and perhaps less practical, methods.

The quality of the atomic wave functions, produced from Hartree-Fock equations, using different types of basis functions, may be investigated with the aid of many operators, and in particular the position operators, <rⁿ >, and tested in the prediction of such quantities as the electron-electron interaction operators. The atomic <rⁿ > values are extremely useful in choosing a basis for the calculation of a particular molecular property that depends heavily on the same region of space.

In order to allow for the polarization of an atom in a molecular environment, and hence achieve better molecular properties, one may either reoptimize or augment the existing basis. If large basis sets are used initially for the atom, then they may be contracted without appreciable loss of ‘chemical accuracy’ before being used in the molecular calculations. These points are illustrated, using different basis sets produced by several methods, for the molecules HF, H₂O, NH₃ and HCN. Rules for orbital exponents (non-linear parameters of the basis set) for atoms and molecules are also discussed.