Structural Study of Methyl Acrylate in a Nematic Liquid Crystal by 1H NMR with 13C Satellites

The molecular structure and conformation of methyl acrylate have been determined by analyzing the ¹H NMR spectrum with ¹³C satellites of the molecules dissolved in the liquid crystal ZLI 1132. In the structural analysis, direct coupling constants have been corrected for molecular vibrations and converted to those in the r structure. The correlation between reorientational motion and internal rotation has been taken into account by using the mean external potential described in terms of bond interaction tensors. The potential for the internal rotation about the bond has been represented as V() = (V ₁/2) (1 – cos ) + (V ₂/2)(1 – cos 2), where is zero for the s-cis configuration, and the determined values of V ₁ and V ₂ are 2.7(1) and 8.4(13) kJ mol^–1, respectively. The relative abundance of the s-cis conformer, 76(1)%, agrees with a gas-phase value, 67(11)%, determined by electron diffraction within experimental errors.     

Catalytic properties of vanadium bronzes, I. Decomposition of isopropanol

Decomposition of isopropanol on V₂O₅ and the bonzes Li_0.02V₂O₅, Na_0.02V₂O₅, Na_0.06V₂O₅, Li_0.33V₂O₅, and Na_0.33V₂O₅ has been studied in the temperature range 168–300°C. The main reaction was found to be dehydration to propene with negligible dehydrogenation to acetone on the first four catalysts. Dehydration on these catalysts increased with the alkali metal content, but the energy of activation remained unchanged. On the last two catalysts, dehydration and dehydrogenation proceeded at comparable rates. A tentative mechanism for the dehydration of isopropanol is proposed, based on the effect of the product on the initial rate, the electric conductivity of the catalysts and their ESR spectra.

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V₂O₅ : Li_0,02V₂O₅, Na_0,02V₂O₅, Na_0,06V₂O₅, Li_0,33V₂O₅ Na_0,33V₂O₅ 186–300°C. . , . . , , .

     

Etude thermique de la N-methylmorpholine N-oxyde et de sa complexation avec l'eau

Résumé La N-méthylmorpholine N-oxyde (MMNO) a une température de fusion de 184.2°, une enthalpie de fusion de 160.5 J/g et une chaleur de décomposition de 1340 J/g. Son hydratation a été étudiée par analyse calorimétrique différentielle et par gravimétrie. A l'air et à la température ambiante, la quantité totale d'eau qui a diffusé dans la MMNO correspond à quatre molécules d'eau par molécule de MMNO. Plusieurs complexes MMNO-H₂O cristallins ont été mis en évidence par analyse calorimétrique differentielle: un complexe MMNO-2.5 H₂O (T _f =40.5°,H _f =143.4 J/g), un complexe MMNO-1 H₂O (T _f = 75.6°,H _f =160.5 J/g) et un complexe dont la quantité d'eau n'a pas été déterminée (T _f =102°,H _f =95 J/g).

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N-methylmorpholine N-oxide (MMNO) has a melting temperature of 184.2°, an enthalpy of fusion of 160.5 J/g and a heat of decomposition of 1340 J/g. Its hydration has been investigated by differential scanning calorimetry (DSC) and by gravimetry.In air and at room temperature, the total amount of water diffusing into MMNO corresponds to four molecules of H₂O per molecule of MMNO.Several MMNO-H₂O crystalline complexes have been studied by DSC: an MMNO-2.5 H₂O complex (T _f =40.5°,H _f =143.4 J/g), an MMNO-1 H₂O complex (T _f =75.6°,H _f =160.5 J/g) and a complex with an unknown amount of water (T _f =102°,H _f =95 J/g).

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Zusammenfassung Das N-Methylmorpholin N-Oxid (MMNO) hat eine Schmelztemperatur von 184.2°, eine Schmelzenthalpie von 160.5 J/g und eine Zersetzungswärme von 1340 J/g. Seine Hydratisierung wurde durch differentialkalorimetrische Analyse und durch Thermogravimetrie untersucht.In Luft und bei Raumtemperatur entspricht die gesamte, in das MMNO diffundierte Wassermenge 4 Wassermoleküle pro Molekül MMNO.Durch die differentialkalorimetrische Analyse wurden verschiedene kristalline MMNO-H₂O-Komplexe nachgewiesen: ein Komplex MMNO-2.5 H₂O (T _f =40.5°,H _f =143.4 J/g), ein Komplex MMNO-1 H₂O (T _f =75.6°,H _f =160.5 J/g) und ein Komplex, dessen Wassergehalt nicht bestimmt wurde (T _f =102°,H _f =95 J/g).

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N- -N- (MMNO) 184.2°, - 160.5 /, -1340 /. () MMNO. , MMNO , MMNO. MMNO ₂: MMNO · 2.5 ₂, _f =40.5°,H _f =143.4 /, MMNO · 1₂-T _f = 75.6°,H _f = 160.5 / , _f =102°,H _f =95 /.

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Nous tenons à remercier Monsieur H. Chanzy, Maître de Recherche au Centre de Recherches sur les Macromolécules Végétales (Grenoble), et son équipe de leur aide et de leurs conseils pour la préparation des produits.     

V2O5/TiO2 oxidation catalysts. II. Texture properties

The texture properties (specific surface area and porosity) of V₂O₅/TiO₂ catalysts obtained from VO(acetylacetonate)₂ have been studied. The presence of sodium leads to a marked decrease in the S_BET values, probably as a consequence of the formation of Na-V bronzes, which lead to a rutilization of the support.

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( ) V₂O₅/TiO₂, - VO()₂. S_BET, , Na-V, .

     

The phenomenon of conglomerate crystallization. XX. Spontaneous resolution in coordination compounds. XVIII.

The title compound, [cis-Co(en)₂(NO₂)₂](NO₂) (1), crystallizes in the polar, nonenantiomorphic, monoclinic space group, Cc, with lattice constants:a=9.198(2) Å,b=12.444(2),c=9.963(3), and=96.76(2)°;V=1132.39 ų andd(calc;Z=4) =1.860 g cm^–3. Thus, with NO_2– as the counteranion, [cis-Co(en)₂(NO₂)₂] crystallizes in a heterochiral lattice containing racemic pairs of cations. A total of 2699 data were collected over the range of 4°270°; of these, 1859 (independent and withI3(I)) were used in the structural analysis. Data were corrected for absorption (=15.465 cm^–1) and the relative transmission coefficients ranged from 0.9934 to 0.7112. Refinement was carried out for both lattice polarities and the finalR(F) andR _w (F) residuals were, respectively, 0.0242 and 0.0202 for (–––) and 0.0264 and 0.0243 for (+++). Thus, the former was selected as correct for our specimen.Unlike all previous X-ray diffraction studies of the structural properties of the cation [cis-Co(en)₂(NO₂)₂]⁺, which are found to have a pair of oppositely configured en rings [i.e., () or ()], we find that in1 the cations are in the lowest energy conformation and configuration; i.e., () or (). We attribute this change in configuration to the formation of strong interionic hydrogen bonds between nitrite anion oxygens and the axial—NH₂ hydrogens, which markedly weaken the intermolecular and intramolecular hydrogen bonds between ligand—NO₂ oxygens and the hydrogens of those same amine moieties. Thus, the nitrite anions behave exactly as nitrate anions, except that the hydrogen bonds found here are stronger than those formed by the latter. This is as expected since the negative charge is delocalized over two, instead of three, oxygens.     

Thiolactame als Reagenzien in der quantitativen Analyse. IX

Zusammenfassung Thiocaprolactam (T) eignet sich zur Goldbestimmung im Konzentrationsbereich 10 bis 130 g Au/ml mit einem Fehler von ±0,5g. Thiocaprolactam bildet mit [AuCl₄]^– eine Verbindung im molaren Verhältnis TAuCl=112, mit [AuJ₄]^– im molaren Verhältnis TAuJ=213. Dagegen bilden sich im System T:Au:Br zwei verschiedene Verbindungen: Ein Bromidkomplex mit höherem Goldgehalt TAu=12, der mit Chloroform extrahierbar ist, und eine sich als Niederschlag ausscheidende Verbindung mit dem Verhältnis TAuBr=112.

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Thiolactams as reagents in quantitative analysis. IX

Summary Thiocaprolactam (T) is suitable for the determination of gold in the concentration range 10–130g Au/ml with an error of ±0.5g. Thiocaprolactam yields with [AuCl₄]^– a compound in the molar ratio TAuCl=112, with [Aul₄]^– in the molar ratio TAuI=213. On the other hand various compounds result in the system TAu Br. The molar ratio in the case of the bromide complex has a higher gold content, namely TAu=12; this product is extractable with chloroform and a compound that comes down as a precipitate shows the ratioT Au Br=112.

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Herrn Dr.K. Czerepko möchte ich hiermit meinen Dank für die Diskussion der Ergebnisse aussprechen.     

Predissociation lifetime of the 1σ g 2 2σ g diabatic state of He 2 + : a one-channel approach

Summary This work is concerned with the application of a one-channel model to obtaining predissociation lifetimes and transition rates in a system of crossing diabatic states. The calculation focuses on the first shape resonance of the 1 _g ² 2 _g diabatic state of He ₂ ⁺ , which is relatively stable with respect to tunneling. This resonance predissociates as a result of the 1 _g ² 2 _g state being crossed by the 1 _g 1 _u ² dissociative diabatic state near the resonance level. We have estimated its predissociation lifetime to be of the order of 10^–11 s.     

Conformational studies of sequential polypeptides of L-Alanine and β-Alanine

Summary In order to investigate the effect of the -alanine residue on the conformational stability of -helical poly(L-alanine), studies have been made on the conformations of sequential copolypeptides having the following repeating sequences: (L-Ala--Ala) _n , (L-Ala-L-Ala--Ala) _n , (L-Ala--Ala-L-Ala-L-Ala) _n and (L-Ala-L-Ala-X) _n , where X is D,L--amino-isobutyric acid residue. Conformations of these polypeptides were measured both in the solution and solid states by means of optical rotatory dispersion, infrared and far-infrared spectroscopies and X-ray diffractions. All the copolypeptides studied here did not give the -helix. It may be, therefore, concluded that the -alanine residue is not incorporated in but impairs the -helix of poly(L-alanine), since the hydrogen bond periodicity in the -helical chain is disturbed by the introduction of such a -amino acid as -alanine.With 5 figures and 2 tables     

Single-Ion Contributions to Activity Coefficient Derivatives, Second Moment Coefficients, and the Liquid Junction Potential

We discuss several interrelated single-ion thermodynamic properties required to calculate the liquid junction potential between two solutions of the same binary electrolyte. According to a previously reported molecular theory of nonuniform electrolyte solutions in nonequilibrium, is determined by the transport numbers of the ions, and by the second moment coefficients H ⁽²⁾ of the charge densities around the ions. The latter may be viewed as the single-ion contributors to the second moment condition of Stillinger and Lovett. For a solution of a single binary electrolyte, we relate the H ⁽²⁾ (R) to the derivatives of the single-ion activity coefficients with respect to the ionic strength. In the light of these results, we examine, in some detail, the role played by the specific short-range interionic interactions in determining . We investigate this matter by means of integral equation calculations for realistic models of LiCl and NaCl aqueous solutions in the 0–1 mol-dm^–3 range. In addition to the hypernetted-chain (HNC) relation, we perform calculations under a new integral equation closure that is a hybrid between the HNC and Percus–Yevick closures. Like the HNC approximation, the new closure satisfies the Stillinger and Lovett condition. However, for the models considered in this study, the two closures predict different dependence of the H ⁽²⁾ and of on the specific part of the interionic interactions.     

Thermal analysis standards. need and realization

Several organizations, internationally and in North America, have a current interest in thermal analysis standards. Of these, the activities of the Committee on Standardization, International Confederation for Thermal Analysis (ICTA) are the most advanced, with a group of temperature standards for DTA scheduled for approval in 1970. A review will be given of the experimental program leading to issuance of these standards, as well as programs underway in the ICTA on other aspects of thermal analysis standards. The current activities of other interested groups will also be reviewed.

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Zusammenfassung Das Standardisationskomitee der International Confederation for Thermal Analysis (ICTA) hatte eine Gruppe von DTA-Temperaturstandarden im Jahr 1970 vorgeschlagen. Es wird ein Bericht über das experimentelle Programm gegeben, das zur Ausgabe der thermischen Standarden führte, weiterhin über andere Programme der ICTA für weitere Standarde. Die Tätigkeit von anderen an dieser Frage interessierten Gruppen und Organisationen wird ebenfalls behandelt.

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Résumé Le comité de standardisation de l'International Confederation for Thermal Analysis (ICTA) a elaboré un groupe de standards de température de ATD présentés à approbation en 1970. On donne un rapport du programme expérimental conduisant à l'emission des standards thermiques et d'autres programmes de l'ICTA concernant ce sujet ainsi que sur les activités d'autres groupes intéressés.

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, , . (ICTA) , 1970 . , , , ICTA . .

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This paper appeared in Thermochim. Acta, 1 (1970) 325 is published also in this place, regarding the great importance of standardization.

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The author's contribution to the ICTA program has been sponsored from a research grant to the Ontario Research Foundation from the Province of Ontario received through the Department of Economics and Development. This support is gratefully acknowledged.The work of other Committee members has been supported from many different sources. The Committee deeply appreciates all such support.     

Steroid glycosides from the starfishSolaster dawsoni (Verrill)

Two novel glycosides from the starfishSolaster dawsoni (Verrill) have been isolated and characterized: 24-O-(-D-xylopyranosyl)-5-cholestane-3,6,15,24,26-pentaol (solasteroside S₁) and (24R)-29-O-[-D-galactofuranosyl-(16)--D-galactofuranosyl]-24-ethyl-5-cholestane-3, 6,8,15,16,29-hexaol (solasteroside S₂).Translated fromIzvestiya Akademu Nauk. Seriya Khimicheskaya, No. 5, pp. 980–982, May, 1993.     

Binding/antibinding analyses for diatomic interactions H 2 + system

The region-functional concept of electron density has been quantitatively examined for 1s_g, 2p_u, 2p_u, and 3d_g states of H ₂ ⁺ system on the basis of Berlin diagram which divides the three-dimensional molecular space into binding and antibinding regions. The electronic charge, Hellmann-Feynman (H-F) force, and stabilization energy of the system are partitioned into the binding and antibinding contributions by the regional integrations.Dynamic behaviors of the electron density (i.e. electron-cloud preceding and following) during the interaction processes are also clarified using the centers of electron density and force density.Differences in attractive and repulsive, and - and -type interactions are discussed from the force and density point of view.     

Activity coefficients for ternary systems: VI. The system HCl + MgCl2 + H2O at different temperatures; application of Pitzer's equations

Electromotive-force measurements have been made on HCl–MgCl₂–H₂O mixtures at 5, 15, 25, 35 and 45°C at eleven different ionic strengths from 0.1–5.0 mol-kg ^–1 . The results are interpreted in terms of the simple Harned's equations, as well as the more complicated Pitzer ion-component treatment of multicomponent electrolyte mixtures. Activity coefficients for HCl in the salt mixtures obey Harned's rule up to and including I=5.0. For the salt in the acid mixtures, Harned's rule holds true up to and including I=0.5. The contribution of higher-order electrostatic terms (E and E') in the Pitzer equations is important for accurate evaluations of unlike cation-cation interactions (_H,Mg), and cation-anion-cation interactions (_H,Mg,Cl). The values of^S_H,Mg and _H,Mg,Cl (determined with E and E'), _H,Mg and _H,Mg,Cl (determined without E and E'), as well as the trace activity coefficients of HCl, _tr ^A , in solutions of MgCl₂ (where ionic strength fraction of the salt,y _B = 1) at all the experimental temperatures and ionic strengths, are reported. Results of this study are compared with those for similar systems. At I=0.1 and 25°C, the results of the Brönsted-Guggenheim specific interaction theory are discussed briefly.     

On the crystal chemistry of three copper(II)-arsenates: Cu3(AsO4)2-III,Na4Cu(AsO4)2, and KCu4(AsO4)3

The three copper(II)-arsenates were synthesized under hydrothermal conditions; their crystal structures were determined by single-crystal X-ray diffraction methods:Cu₃(AsO₄)₂-III:a=5.046(2) Å,b=5.417(2) Å,c=6.354(2) Å, =70.61(2)°, =86.52(2)°, =68.43(2)°,Z=1, space group ,R=0.035 for 1674 reflections with sin / 0.90 Å^–1.Na₄Cu(AsO₄)₂:a=4.882(2) Å,b=5.870(2) Å,c=6.958(3) Å, =98.51(2)°, =90.76(2)°, =105.97(2)°,Z=1, space group ,R=0.028 for 2157 reflections with sin / 0.90 Å^–1.KCu₄(AsO₄)₃:a=12.234(5) Å,b=12.438(5) Å,c=7.307(3) Å, =118.17(2)°,Z=4, space group C2/c,R=0.029 for 1896 reflections with sin / 0.80 Å^–1.Within these three compounds the Cu atoms are square planar [4], tetragonal pyramidal [4+1], and tetragonal bipyramidal [4+2] coordinated by O atoms; an exception is the Cu(2)^[4+1] atom in Cu₃(AsO₄)₂-III: the coordination polyhedron is a representative for the transition from a tetragonal pyramid towards a trigonal bipyramid. In KCu₄(AsO₄)₃ the Cu(1)^[4]O₄ square and the As(1)O₄ tetrahedron share a common O—O edge of 2.428(5) Å, resulting in distortions of both the CuO₄ square and the AsO₄ tetrahedron. The two Na atoms in Na₄Cu(AsO₄)₂ are [6] coordinated, the K atom in KCu₄(AsO₄)₃ is [8] coordinated by O atoms.Die drei Kupfer(II)-Arsenate wurden unter Hydrothermalbedingungen gezüchtet und ihre Kristallstrukturen mittels Einkristall-Röntgenbeugungsmethoden ermittelt:Cu₃(AsO₄)₂-III:a = 5.046(2) Å,b = 5.417(2) Å,c = 6.354(2) Å, = 70.61 (2)°, = 86.52(2)°, = 68.43(2)°,Z = 1, Raumgruppe ,R = 0.035 für 1674 Reflexe mit sin / 0.90 Å^–1.Na₄Cu(AsO₄)₂:a = 4.882(2) Å,b = 5.870(2) Å,c = 6.958(3) Å, = 98.51(2)°, = 90.76(2)°, = 105.97(2)°,Z = 1, Raumgruppe ,R = 0.028 für 2157 Reflexe mit sin / 0.90 Å^–1.KCu₄(AsO₄)₃:a = 12.234(5) Å,b = 12.438(5) Å,c = 7.307(3) Å, = 118.17(2)°,Z = 4, Raumgruppe C2/c,R = 0.029 für 1896 Reflexe mit sin / 0.80 Å^–1.Die Cu-Atome in diesen drei Verbindungen sind durch O-Atome quadratisch planar [4], tetragonal pyramidal [4 + 1] und tetragonal dipyramidal [4 + 2]-koordiniert; eine Ausnahme ist das Cu(2)^{[4 + 1]}-Atom in Cu₃(AsO₄)₂-III: Das Koordinationspolyeder stellt einen Vertreter des Übergangs von einer tetragonalen Pyramide zu einer trigonalen Dipyramide dar. In KCu₄(AsO₄)₃ haben das Cu(1)^[4]O₄-Quadrat und das As(1)O₄-Tetraeder eine gemeinsame O—O-Kante von 2.428(5) Å, was eine Verzerrung der beiden Koordinationsfiguren CuO₄-Quadrat und AsO₄-Tetraeder bedingt. Die zwei Na-Atome in Na₄Cu(AsO₄)₃ sind durch O-Atome [6]-koordiniert, das K-Atom in KCu₄(AsO₄)₃ ist [8]-koordiniert.

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Zur Kristallchemie dreier Kupfer (II)-Arsenate: Cu₃(AsO₄)₂-III, Na₄Cu(AsO₄)₂ und KCu₄(AsO₄)₃

     

Hypervirial theorems and symmetry

It is pointed out that to ensure that an optimal variational wave function having a certain symmetry satisfies the hypervirial theorem forW, it is sufficient thatiSW, whereS is the projector onto the symmetry type in question, be a possible variation of . Application is made to the tensor hypervirial theorem for atoms.     

The electronic structure of molecules by a many-body approach

The vertical valence ionization potentials of cyclopropane, ethylene oxide and ethylene imine are calculated by a many-body Green's function method. For C₃H₆ the ordering of the ionization potentials is 2e(), 1e(), 2a₁(), 1a₂(), 1e(). The assignment of the 2a₁ and the 1a₂ ionization potentials which has been controversial is thus clarified. The ordering is in agreement with the result obtained via Koopmans' theorem. For ethylene oxide and ethylene imine Koopmans' theorem fails in predicting the correct order of ionic states. For C₂H₄O the ordering of the ionization potentials is 2b ₁(), 4a ₁, 1a ₂(), 2b ₂,3a ₁, 1b ₁(), 1b ₂, 2a ₁ and for C₂H₅N 6a, 5a, 3a, 2a, 4a, 3a, 1a, 2a. The agreement of the computed ionization potentials with the experimental values is very satisfactory.     

Kinetics of the basic condensation of triphenylsilane in ethanol. The role of water

In order to elucidate the role of water in the basic condensation of triphenylsilane in moist ethanol, the kinetic law, the activation energy and entropy were determined. A two-step mechanism discarding ethanol as reactant is proposed.

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- , , . , .

     

The kinetic energy components of LCAO-molecular orbitals: A comment on the “Electron-in-a-Box”-“LCAO-MO-Model” analogy

In many textbooks attention is drawn to the close analogy that seems to exist between the Electron-in-a-Box-wave functions _n and their LCAO-MO counterparts _J (J = n) for the movement of an electron in a -system. It is often implied that the wave lengths of _n and of _J (J = n) which satisfy to a high degree the relation =, have the same physical meaning. It is shown that this is not the case. for a linear system (e.g. a one-dimensional Electron-in-a-Box-model) is directly connected with the momentum of the electron and therefore with its kinetic energy according to the deBroglie relation. However, there is no such simple relationship between A and the corresponding kinetic energy component in LCAO-MO's _J . (The necessary two-center kinetic energy integrals have been computed for 1s-type atomic orbitals.)

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Zusammenfassung In vielen elementaren Textbüchern wird die Aufmerksamkeit auf die scheinbar enge Verwandtschaft hingelenkt, die zwischen den Wellenfunktionen _n für ein Electron-in-a-Box-Modell und den entsprechenden LCAO-MOs _J (J=n) für die Bewegung eines Elektrons in einem -System besteht. Unter anderem wird oft implizit angenommen, daß die Wellenlängen der Funktion _n und von _J (J=n), die weitgehend der Bedingung = genügen, die gleiche physikalische Bedeutung haben. In dieser Arbeit wird gezeigt, daß dies nicht der Fall ist. Für ein lineares System (z. B. ein eindimensionales Electron-in-a-Box-Modell) ist über die deBroglie'sche Beziehung direkt mit dem Impuls und damit mit der kinetischen Energie des Elektrons verknüpft. Im Gegensatz dazu existiert keine einfache Beziehung zwischen und der entsprechenden Komponenten der kinetischen Energie in einem LCAO-MO _J . (Die notwendigen Zweizentrenintegrale der kinetischen Energie wurden für Atomorbitale vom 1s-Typus berechnet.)

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Résumé Dans les textes élémentaires de chimie théorique on attire souvent l'attention sur l'analogie qui semble exister entre les fonctions d'onde _n pour un modèle «Electron-in-a-Box» et les fonctions correspondantes LCAO-MO _J (J=n) décrivant le mouvement d'un électron dans un système . En particulier cette comparaison implique que les «longueurs d'onde» de _n et de _J (J=n), qui satisfont pratiquement la relation =, ont la même signification physique. Dans ce travail on montre, que ceci n'est pas le cas. Pour un système linéaire (c.à.d. un modèle linéaire du type «Electron-in-a-Box») est reliée directement à la quantité de mouvement et par là à l'énergie cinétique, par la relation de deBroglie. Par contre on ne trouve pas une dépendance analogue entre et la composante correspondante de l'énergie cinétique dans une orbitale moléculaire LCAO _J. (Les intégrales bicentriques pour les composantes d'énergie cinétique nécessaires à ce calcul ont été déterminées pour des orbitales atomiques du type 1s.)

     

Invariant sets for kinetic equations

Some sets in the space of compositions possessing an invariance property are considered for a closed system, where a complex chemical reaction of a known mechanism proceeds. If the vector of concentrations belongs to such a set at a certain moment of time, it will remain within it at any succeeding moment. Some possible applications are discussed.

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, , , : , . .

     

r 12-Dependent terms in the wave function as closed sums of partial wave amplitudes for large l

The ansatz = (1+1/2r₁₂)+ with the bare nuclear (or screened nuclear) wave function and expanded in products of one-electron functions is explored for second-order perturbation theory and for variational calculations of the ground state of Helium-like ions.The energy increments E _l ⁽²⁾ corresponding to the partial wave expansion of go asymptotically as l^–8, while conventional partial wave increments go as l^–4. is coupled to by a residual interaction U₁₂ that has no singularity for r₁₂=0. With the present ansatz it is sufficient to include l-values up to 5 in order to get the second-order energy accurate to one microhartree. For the same accuracy l4 is sufficient in a CI with correlated reference function while in conventional CI one must go to l50. The surprisingly faster convergence of the variational approach as compared to second-order perturbation theory is explained. The slow convergence of the traditional partial wave expansion is entirely due to the attempt to represent the quantity 1=¦r₁₂r₁₂ ^–1¦ by its partial wave expansion. The best reference function shows very little shielding and resembles closely the eigenstate of the bare nuclear Hamiltonian. The generalization to arbitrary systems is discussed and it is pointed out that the calculation of difficult integrals can be avoided without a significant loss in accuracy.