Application des orbitales atomiques perturb�es au calcul de la constante de couplage entre les spins nucl�aires de la mol�cule HD

Delpuech, André; Paviot, Jacques; Hoarau, J.

doi:10.1007/bf00548476

Cited by 5 publications

(5 citation statements)

References 8 publications

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“…The following replacement (cf. Gregson et al [4]) has been made k(r) = r/(r + r'o) 41 -exp ( -r/ro), (9) ~ r' -!Z~2 is a fitting constant. wherer 0= o-2…”

Section: Ka + I(s a • (Ka)) (4)mentioning

confidence: 98%

“…Since the contact operator makes the dominant contribution to the spin-spin coupling constants involving the proton and first row nuclei [6] the Blinder operator has predictably found favour in many such calculations (cf. [7][8][9] contrast, the infinite second-order self coupling energy of the delta function operator makes it unusable in any energy minimization procedure [10, 1!] to second and higher orders.…”

Section: Introductionmentioning

confidence: 99%

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Second order hyperfine splitting with Blinder type contact operator : Finite nucleus models

Trivedi¹

1979

Molecular Physics

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Taking the nucleus as an extended magnetic dipole the hyperfine interaction operators derived from the Dirac hamihonian using the partitioning technique are written down. The second order hyperfine splitting in the ground state of the hydrogen atom is calculated from the contact operator for three different finite nucleus models. The results turn out to be strongly model dependent. The best (and physically reasonable) result is obtained for a nonsingular magnetic form factor. Singular form factors fail to yield physically acceptable results.

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“…The following replacement (cf. Gregson et al [4]) has been made k(r) = r/(r + r'o) 41 -exp ( -r/ro), (9) ~ r' -!Z~2 is a fitting constant. wherer 0= o-2…”

Section: Ka + I(s a • (Ka)) (4)mentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Second order hyperfine splitting with Blinder type contact operator : Finite nucleus models

Trivedi¹

1979

Molecular Physics

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“…Sänger and Voitländer [2] point out that all three expressions, i.e., (1), (3) and (5) which would ensure that JHD -JHD -^HD • This is readily verified by inserting (6) in (1), (3) and (4). Condition (6) is clearly invariant under scaling of the bases.…”

mentioning

confidence: 92%

“…Condition (6) is clearly invariant under scaling of the bases. We now proceed to construct bases functions which would a priori guarantee (6). Consider the somewhat unusual choice (7) where xp^ is an arbitrary function centred on the nucleus N. For instance, if we choose the negative sign and yx = j/e 3 /;!…”

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confidence: 99%

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On the Convergence of the Calculated Spin-spin Coupling Constant of HD

Trivedi

1979

Zeitschrift Für Naturforschung A

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It is shown that the concurrence of the results obtained by varying the self coupling energy, the total second order energy and the cross coupling energy independently can be readily accomplished. In addition, it is possible to arrange to obtain any pre-specified value for the coupling constant. On this basis it is suggested that it might be dangerous to construe the concurrence of calculated results as an indication of convergence in practice.Calculations of the spin-spin coupling constant of the HD molecule have been performed by many authors [1][2][3][4][5] in many different ways. This note deals with the class of calculations involving a less singular contact operator than the delta function. With such an operator and a suitable choice of variational functions it becomes possible to make the cross-coupling energy independent (to within a very small parameter) of the (finite) self-coupling energy [5], the value of which depends on the precise form of the contact operator [1][2][3][4][5]. Delpuech [6] et al. concluded from their study that it is necessary to use variational functions which mimic the true solution both in the immediate vicinity (that is, within a few Fermis) of the perturbing nucleus and in the inter-nuclear domain in order to get convergence. Sänger and Voitlander [2] using a non-singular contact operator did not directly address themselves to the question of convergence but they computed the coupling constant JHD in three different ways -by varying the self coupling energy, the total second order energy and the cross coupling energy -and obtained the same result, 39 Hz, in each case. The question poses itself whether this can be taken as an indication of convergence. In what follows we argue that it would be dangerous to do so. We demonstrate that a class of variational functions can be chosen for which this concurrence can be guaranteed and for which it is possible to obtain any pre-specified value for J HDAfter integrating out the spin the original two electron problems can be reduced to a one electron Reprint request to the author at Physical Chemistry Laboratory, South Parks Road, Oxford.' 0X1 3QZ, England. problem. Having postulated a short range and a long range part for the solution and observed that the cross coupling energy is independent of the self coupling energy [2,5] Sänger and Voitländer [2] point out that all three expressions, i.e., (1), (3) and (5), are equivalent if Hi,i. (5)

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Geometric approximation to nuclear spin–spin coupling constants in the water molecule

Lazzeretti

1979

Int J of Quantum Chemistry

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AbstractsThe geometric aproximation is used within the framework of triple perturbation theory to evaluate the contributions to nuclear spin-spin coupling constants in the water molecule provided by the Fermi contact, the spin-orbit, and the spin-dipolar interactions. The results, obtained with SCF wave functions expanded over Gaussian basis sets of increasing quality, are compared with corresponding coupled Hartree-Fock estimates. The limits of the geometric approximation to coupling constants are discussed.L'approximation geomttrique a ete utilisee dans le cadre de la theorie des perturbations triples pour calculer les contributions aux constantes de couplage spin-spin nucleaire dans la molecule d'eau, fournies par les interactions de contact de Fermi, de spin-orbite et de spin-dip8le. Les resultats, obtenus avec des fonctions d'onde de type SCF developpees en fonctions gaussiennes de plus en plus complexes, sont compares ?a des estimations obtenues i partir de fonctions Hartree-Fock couplees.Les limites de l'approximation gkornetrique dans le calcul des constantes de couplage sont discutees.Die geometrische Naherung wird im Rahmen der Theorie von Trippelstorungen angewandt, um die Beitrage (Ferrni-Kontakt-, Spin-Bahn-und Spin-Dipol-) zu den Kern-Spin-Spin-Kopplungskonstanten im Wassermolekiil zu berechnen. Die mit in Gaussatzen steigender Qualitat entwickelten SCF-Wellenfunktionen erhaltenen Resultate werden mit entsprechenden Abschatzungen von gekoppelten Hartree-Fock-Funktionen verglichen. Die Grenzen der geometrischen Naherungen in der Berechnung von Kopplungskonstanten werden diskutiert.

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Application des orbitales atomiques perturb�es au calcul de la constante de couplage entre les spins nucl�aires de la mol�cule HD

Cited by 5 publications

References 8 publications

Second order hyperfine splitting with Blinder type contact operator : Finite nucleus models

Second order hyperfine splitting with Blinder type contact operator : Finite nucleus models

On the Convergence of the Calculated Spin-spin Coupling Constant of HD

Geometric approximation to nuclear spin–spin coupling constants in the water molecule

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