The direct determination of Brueckner orbitals with application to the H2 molecule

An iterative procedure is presented which allows for the direct determination of approximate Brueckner orbitals for small atomic and molecular systems. Starting from the Hartree-Fock determinant one first determines pair natural orbitals (PNOs) of independent electron pairs in the HF-field of the remaining electrons. The use of the generalized Brillouin-theorem then leads to an approximate Brueckner orbital for each electron pair. This procedure must be repeated up to self-consistency which is reached generally after 4–5 macroiterations. Applications to the ground state of H₂ show how important the use of Brueckner orbitals is to get good expectation values of one-electron operators and the correct asymptotic behaviour of the potential energy curve for large internuclear distances.

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Zusammenfassung Es wird eine Iterationsmethode beschrieben, die eine direkte Bestimmung genäherter Bruecknerorbitale für kleine atomare und molekulare Systeme gestattet. Ausgehend von der Hartree-Fock-Determinante bestimmt man zunächst Paar-NOs (PNOs) der unabhängigen Elektronenpaare im HF-Feld der übrigen Elektronen des Systems. Mit Hilfe des verallgemeinerten Brillouin-Theorems erhält man dann ein genähertes Bruecknerorbital für jedes Elektronenpaar. Dies Verfahren muß bis zur Selbstkonsistenz wiederholt werden, die man im allgemeinen nach 4–5 solcher Makroiterationen erreicht. Anwendung auf den Grundzustand des H₂-Moleküls zeigt, wie wichtig die Benutzung von Bruecknerorbitalen ist, wenn man gute Erwartungswerte von Einelektronenoperatoren und das richtige asymptotische Verhalten der Potentialkurve bei großen Abständen erhalten will.

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Résumé On propose un schéma itératif qui permet le calcul direct des orbitales de Brueckner approchées pour les atomes et les petites molécules. Partant du déterminant Hartree-Fock on calcule d'abord les PNO (pair natural orbitals) des paires indépendantes d'électrons dans le champ effectif des autres électrons dans l'approximation Hartree-Fock. Ensuite le théorème de Brillouin généralisé permet de calculer les orbitales de Brueckner approchées pour chaque paire d'electrons. On recommence le calcul des PNO, la self-consistance de cette méthode itérative s'établit en général au bout de 4 ou 5 macroitérations. Les applications à la molécule H₂ démontrent que l'utilisation d'orbitales de Brueckner s'impose si l'on s'intéresse à des bonnes valeurs moyennes d'opérateurs monoélectroniques ou au comportement asymptotique correct des courbes de potentiel aux grandes distances.

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Dedicated to the memory of Prof. K. H. Hansen.     

On the (Emultiply sign in circlee)-Jahn-Teller conical intersections in the 3p(E') and 3d(E") Rydberg electronic states of triatomic hydrogen

The static and dynamic aspects of the Jahn-Teller (JT) interactions in the 3p(E') and 3d(E") Rydberg electronic states of H3 are analyzed theoretically. The static aspects are discussed based on recent ab initio quantum chemistry results, and the dynamic aspects are examined in terms of the vibronic spectra and nonradiative decay behavior of these states. The adiabatic potential-energy surfaces of these degenerate electronic states are derived from extensive ab initio calculations. The calculated adiabatic potential-energy surfaces are diabatized following our earlier study on this system in its 2p(E') ground electronic state. The nuclear dynamics on the resulting conically intersecting manifold of electronic states is studied by a time-dependent wave-packet approach. Calculations are performed both for the uncoupled and coupled state situations in order to understand the importance of nonadiabatic interactions due to the JT conical intersections in these excited Rydberg electronic states.     

On an inconsistency connected with koopman's theorem

On the basis of Koopmans' theorem two methodically different ways to estimate the effect of a spin-orbit perturbation on the ionization potentials of I₂ have been proposed. In the present paper a model system is constructed to show the equivalence of both methods.     

Low-energy dissociative recombination in small polyatomic molecules

Indirect dissociative recombination of low-energy electrons and molecular ions often occurs through capture into vibrationally excited Rydberg states. Properties of vibrational autoionization, the inverse of this capture mechanism, are used to develop some general ideas about the indirect recombination process, and these ideas are illustrated by examples from the literature. In particular, the Δv = -1 propensity rule for vibrational autoionization, i.e., that vibrational autoionization occurs by the minimum energetically allowed change in vibrational quantum numbers, leads to the prediction of thresholds in the dissociative recombination cross sections and rates at the corresponding vibrational thresholds. Capture into rotationally excited Rydberg states is also discussed in terms of recent low-temperature studies of the dissociative recombination of H(3)(+).     

Theory of vibronic interactions in D2 and H2: a comparison between multichannel-quantum-defect and coupled-equation approaches

New experimental energy levels for the 2pπC(1)Π(u)(-) state of D(2) are reported extending up to the dissociation limit and including rotational quantum numbers up to N = 10. These data are extracted from recent high resolution optical emission spectra, and they are used for a detailed comparison of two theoretical approaches, both of which are fully ab initio and are based on the same state-of-the-art clamped-nuclei potential energy curves. These are the coupled differential equations (CE) and the multichannel quantum defect theory (MQDT) approaches, each of which accounts for adiabatic corrections and non-adiabatic couplings. Both theoretical approaches reproduce the experimental levels to within a fraction of a wavenumber unit (cm(-1)) for the lower vibrational quantum numbers, with the MQDT surpassing the CE method. As the dissociation limit is approached, the residuals observed-calculated increase up to several cm(-1) and the MQDT method is up to a factor of two less accurate than the CE method. The same analysis is carried out with existing data for the H(2) isotopomer and yields similar results. An analogous comparison is also made for the 3pπD(1)Π(u)(-) and 4pπD('1)Π(u)(-) states for both isotopomers, where the MQDT is found to be superior to the CE approach.     

Sur les séries de Taylor n'ayant que des singularités algébrico-logarithmiques sur leur cercle de convergence

Sans résumé     

The Fix–Heiberger procedure for solving the generalized Ill-conditioned symmetric eigenvalue problem

We review a formalism introduced by Fix and Heiberger in 1972 for solving the generalized (or nonorthogonal) eigenvalue problem for ill-conditioned symmetric matrices and we discuss its application in quantum chemistry. A few examples dealing with the calculation of high Rydberg orbitals are presented.