Der oxydative Abbau des (+)‐Cyclolavandulols

Simon, H. L.; Schinz, H.

doi:10.1002/hlca.19490320524

Cited by 8 publications

(5 citation statements)

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“…For instance, Z c ≈ 2.08 [16] for three-electron Zeee system which predicts the instability of He − and H 2− ions. However, from the mathematical analysis of Simon, [17] Zhislin, [18] Gridnev, [19] and the detailed review of Katriel et al, [20] it is evident that the Z c value cannot be higher than N − 1, but it can be equal to N − 1, where N is the number of electrons. Thus, there is a controversy regarding the critical nuclear charge of four-body Zeee system.…”

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confidence: 99%

Critical stability and quantum phase transition of screened two‐electron system

Sadhukhan

Dutta

Saha

2019

Int J of Quantum Chemistry

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The ground state energy and structural properties of a model two‐electron system (Zee), bound via screened Coulomb interaction with nuclear charge Z, have been studied under the variational framework. Hylleraas type basis has been adopted for explicit incorporation of the electron–electron correlation. Critical nuclear charges (Zc) of Zee system have been reported for different screening parameters (μ). Expectation values of different structural properties have been estimated to predict the internal structure of the Zee system. The variation of the structural properties with respect to Z for different μ reveals the signature of quantum phase transition (QPT) in the vicinity of Zc. Moreover, the nature of variation of these properties with respect to Z in case of bare Coulomb or free system (μ = 0) is completely opposite to those of screened system (μ ≠ 0). Radial two‐particle density (TPD) confirms the symmetry breaking of the electronic structure and therefore QPT in the vicinity of Zc.

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confidence: 99%

Critical stability and quantum phase transition of screened two‐electron system

Sadhukhan

Dutta

Saha

2019

Int J of Quantum Chemistry

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“…Therefore we shall only sketch the details. (ii) If a corresponds to a decomposition with all electrons in one end or the other, we take HhR' as in the general case, independent of R. If a is a different decomposition (we call all such a's, 9), we take an R-dependent operator as follows: For each a at least one of the N + 1 regions has no electrons, so choose j ( a ) so that 7 (3j -l)R ( 3 j + 1) (iii) Note that if a E 9 R -t m lim @u(JaHb(a)Ja) zp~oo (Hb(a)), since at least one electron in JaHb(,)Ja does not interact with either nucleus so that by the HVZ theorem pl(JaHb(a)Ja) Zpm(Hb(a)) + o(1). (vi) The steps above replace those in the proof of Theorem 2.4 when there may be somewhere negative potentials between "electrons."…”

Section: Basic Theoremsmentioning

confidence: 99%

Behavior of molecular potential energy curves for large nuclear separations

Morgan

Simon

1980

Int J of Quantum Chemistry

127

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AbstractsWe prove by elementary geometric methods and within the Born-Oppenheimer approximation that as the nuclei of a molecule are dissociated into spatially separated clusters, the discrete molecular energies approach sums of the energies of isolated subsystems. Our methods also show that the spectral projections associated with the discrete molecular spectrum asymptotically approach direct sums of suitable spectral projections for the isolated subsystems. These results apply to any system of particles interacting by asymptotically vanishing pair potentials. We prove that the 1/ R expansion for discrete molecular potential curves is asymptotic as R + 03, and we discuss the behavior of the coefficients of the 1 / R expansion for the ground state of H2+.Nous prouvons par des methodes gCom6triques tltrnentaires et dans le cadre de l'approximation de Born-Oppenheirner, que quand les noyaux d'une mol6cule sont dissocits en amas stparts dans l'espace, les tnergies moltculaires discrktes tendent vers la somme des tnergies des sous-systkmes isol6s. Nos mtthodes montrent aussi que les projections spectrales associkes au spectre mol6culaire discret tendent asymptotiquement vers des sommes directes de projections spectrales convenables pour les sous-systkmes isolts. Ces rksultats s'appliquent ti n'importe quel systkme de particules qui interagissent par des potentiels de paire s'annulant asymptotiquement. Nous prouvons que le dtveloppement en 1/R pour des courbes de potentiel moltculaires discrktes est asymptotique quand R + w , et nous discutons le comportement des coefficients de ce dtveloppement pour M a t fondamental de H2+.Wir beweisen durch elementare geometrische Methoden und im Rahmen der Born-Oppenheimer-Naherung, dass, wenn die Kerne eines Molekuls in raumlich separierten Clusters dissoziiert werden, die diskreteii Molekulenergien Summen der Energien der isolierten Untersysteme zustreben. Unsere Methoden zeigen auch, dass die mit dem diskreten Molekularspektrum assoziierten Spektralprojektionen asymptotisch direkten Summen von geeigneten Spektralprojektionen fur die isolierten Untersysteme zustreben. Diese Ergebnisse sind fur irgendein System von Teilchen gultig, die durch asymptotisch verschwindende Paarpotentiale wechselwirken. Wir beweisen, dass die Entwicklung in 1/R fur diskrete molekulare Potentialkurven wenn R + m asymptotisch ist, und wir diskutieren das Verhalten der Koeffizienten dieser Entwicklung fur den Grundzustand von HZ+.

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“…Indeed, under additional assumptions which are fulfilled for the Wiglitman theory of the free electromagnetic field, Simon [7] succeeded in recovering Euclidean region scalar fields showing just that property. This result is not surprising.…”

Section: Introductionmentioning

confidence: 99%