Calculation of optical characteristics of atoms with a closed shell by the Hartree-Fock-Roothaan method

Adamov, M. N.; Malykhanov, Yu. B.; Meshkov, V. V.; Chadin, R. M.

doi:10.1134/1.1651242

Cited by 5 publications

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“…With these modifications their results compare well with those obtained by correlated ab initio methods. Adamov et al 11 have calculated the dynamic dipole polarizability and a number of spectroscopic properties of Ar, Ca, Sr and Xe using the Hartree-Fock-Roothaan method.…”

Section: Introductionmentioning

confidence: 99%

Polarizabilities, Hyperpolarizabilities and Analogous Magnetic Properties

Hinchliffe¹

2006

Chemical Modelling

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Section: Introductionmentioning

confidence: 99%

Polarizabilities, Hyperpolarizabilities and Analogous Magnetic Properties

Hinchliffe¹

2006

Chemical Modelling

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“…In [7,10] it is shown that in the perturbation theory for closed-shell systems this way of solving equations does not cause difficulties, because in this case, by definition, the matrices L (±) have only positive eigenvalues and one can calculate the matrices (L (±) ) ±1 ⁄ 2 , with the aid of which the nonsymmetrical matrix Λ in Eqs. (3) and (5) can be transformed into a symmetrical one (as a specific case, Eqs.…”

mentioning

confidence: 99%

“…In such an approach, the calculation of polarizability for the assigned values of frequency or Cauchy moments is performed purely algebraically by reversing a symmetrical matrix [9]. Such calculations have been performed for rather heavy atoms with a closed shell [7,10] and with an open shell [8,9]. Moreover, for the closed-shell atoms a technique of solving the NCPT equations has been suggested, which allows one to find the dynamic polarizability as an explicit function of the incident radiation frequency in terms of the basic spectroscopic quantities -frequencies and oscillator strengths [7].…”

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confidence: 99%

Calculation of the dynamic polarizability of open-shell atoms

Malykhanov

Chadin

2005

J Appl Spectrosc

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539.184The application of the authors' nonstationary theory of perturbations in the Hartree-Fock approximation to calculation of the dynamic polarizability of open-shell atoms as an explicit function of the incident radiation frequency in terms of the principal spectroscopic quantities -the frequency and strength of the oscillators of electronic transitions -is considered. The poles of the dynamic polarizability representing the energies of transitions are calculated in the approximation corresponding to the well-known method of random phases. For open-shell atoms from B to Sc and Fe the frequencies and oscillator strengths of all allowed (in the basis selected) dipole transitions are calculated, whereby the dipole dynamic polarizability of atoms is found. Introduction.Calculations of the polarizability of atoms and molecules in the Hartree-Fock (HF) approximation are urgent, since the polarizability determines a variety of measured optical parameters. In calculating static polarizabilities one can dispense with the perturbation theory in the Hartree-Fock approximation, provided one stays within the framework of the method of finite perturbations [1,2]. However, to calculate the dynamic polarizability, one has to solve the equations of nonstationary "coupled" perturbation theory (NCPT), the formulation of which for open-shell systems presents certain difficulties, which accounts for the small number of pertinent calculations [3][4][5][6]. In calculations of atoms, the equations of the perturbation theory for corrections to orbitals are usually solved with the aid of numerical methods [5,6]. Here, the dynamic polarizability can be found for specific values of the incident radiation frequency or in the form of a series in powers of the incident radiation frequency (Cauchy moments). As shown in [7-10], it is more convenient to seek corrections to orbitals in the form of expansions in nonperturbed orbitals that are assumed to be calculated in an analytical form in the LCAO approximation. In this case, the system of integrodifferential NCPT equations is transformed into an algebraic system for the expansion coefficients. In such an approach, the calculation of polarizability for the assigned values of frequency or Cauchy moments is performed purely algebraically by reversing a symmetrical matrix [9]. Such calculations have been performed for rather heavy atoms with a closed shell [7,10] and with an open shell [8,9]. Moreover, for the closed-shell atoms a technique of solving the NCPT equations has been suggested, which allows one to find the dynamic polarizability as an explicit function of the incident radiation frequency in terms of the basic spectroscopic quantities -frequencies and oscillator strengths [7]. The equations for the frequencies of transitions resulting from the NCPT equations are the equations of the method of random phases widely used in the theory of systems of particles [11,12].Such calculations for open-shell systems involve certain mathematical difficulties, which apparently have not yet been ove...

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