Calculation of nuclear magnetic shieldings. XV. <i>Ab initio</i> zeroth-order regular approximation method

Fukui, H.; Baba, T.

doi:10.1063/1.1510118

Cited by 58 publications

(83 citation statements)

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“…It has been suggested 6 that it would be interesting to compare the individual terms in Kutzelnigg's approach to the outcome of the perturbative quadratic response by Manninen et al 8 and Melo et al 9,10 Approximate two-component methods to calculate nuclear-magnetic shieldings also yield different decompositions into para-and diamagnetic components of magnetic properties. [8][9][10][11][12][13][14][15][16] Among them, in the linear response within the elimination of small component ͑LR-ESC͒ approach, 9 the separation into para-and diamagnetic terms is explicitly obtained by considering separately the contributions from electronic excited states on one hand, and contributions from electron-positron pair-creation terms on the other. This decomposition is therefore fully consistent with the one carried out in the four-component linear-response calculations 1,2 which considers separately the contributions from electronic and positronic states to a given positive-energy fourcomponent spinor in order to define the paramagnetic and diamagnetic components.…”

Section: Formal Relations Connecting Different Approaches To Calculatmentioning

confidence: 99%

Formal relations connecting different approaches to calculate relativistic effects on molecular magnetic properties

Zaccari

Azúa

Melo

et al. 2006

The Journal of Chemical Physics

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Articles you may be interested in A fully relativistic method for calculation of nuclear magnetic shielding tensors with a restricted magnetically balanced basis in the framework of the matrix Dirac-Kohn-Sham equationa) J. Chem. Phys. 128, 104101 (2008) In the present work a set of formal relations connecting different approaches to calculate relativistic effects on magnetic molecular properties are proven. The linear response ͑LR͒ within the elimination of the small component ͑ESC͒, Breit Pauli, and minimal-coupling approaches are compared. To this end, the leading order ESC reduction of operators within the minimal-coupling four-component approach is carried out. The equivalence of all three approaches within the ESC approximation is proven. It is numerically verified for the NMR nuclear-magnetic shielding tensor taking HX and CH 3 X ͑X =Br,I͒ as model compounds. Formal relations proving the gauge origin invariance of the full relativistic effect on the NMR nuclear-magnetic shielding tensor within the LR-ESC approach are presented.

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Section: Formal Relations Connecting Different Approaches To Calculatmentioning

confidence: 99%

Formal relations connecting different approaches to calculate relativistic effects on molecular magnetic properties

Zaccari

Azúa

Melo

et al. 2006

The Journal of Chemical Physics

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“…The results of this BS double finite perturbation (BS/FPT-2) approach are shown in the fifth column of table 1. The basis set sizes used here [23] are (10s6p) for H, (15s10p3d) for F, (17s14p6d) for Cl, (21s17p8d4f) for Br and (25s21p12d8f) for I. The magnitudes of finite perturbations in atomic units were as follows:…”

Section: Resultsmentioning

confidence: 99%

“…The present authors have already presented relativistic calculations of nuclear magnetic shieldings in hydrogen halides based on the DKH method [20][21][22][23] and zerothorder regular approximation (ZORA) [23]. However, the results of these two approaches differ considerably, rendering it still necessary to establish an accurate and reliable scheme for evaluating nuclear magnetic shielding tensors.…”

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confidence: 98%

Calculation of nuclear magnetic shieldings: infinite-order Foldy–Wouthuysen transformation

et al. 2004

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A scheme for calculating nuclear magnetic shieldings using the infinite-order Foldy-Wouthuysen (FW) transformation proposed by Barysz and Sadlej (BS) is presented. The nuclear magnetic shieldings of hydrogen halides are calculated by three variant BS schemes; a double finite perturbation method for the external magnetic flux density (B 0 ) and the nuclear magnetic dipole moment ( M ) (BS/FPT-2), a single finite perturbation method for B 0 with analytical differentiation of energy with respect to ( M ) (BS/FPT-1), and an approximate analytical differentiation method with respect to both B 0 and M (BS/CHF). Although the BS/FPT-2 method is exact theoretically, the actual computation for heavy nuclei includes large error due to reduction of the number of significant figures. The BS/FPT-1 and BS/CHF approaches, on the other hand, yield reasonable values for all of the shieldings. Although several results could not be obtained by the BS/FPT-2 method, no serious contradictions were recognized among these three results. From a comparison of our results with values in the literature, our shieldings for the halogen nuclei are lower than those determined by the four-component relativistic random phase approximation (4-RPA), but the reason for this is not obvious. IntroductionFully relativistic treatments [1, 2], based on the fourcomponent spinor form of the one-electron wave functions, are still very costly, primarily due to the cost for a proper description of the small two-component spinor. In most relativistic quantum chemistry problems, however, explicit consideration of the negative energy states or the electron-positron pair creation processes is unnecessary. For example, the information included in the four-component Dirac equation [3] is excessive for the majority of problems encountered in relativistic quantum chemistry. Thus, the investigation and development of more appropriate two-component methods is particularly attractive. Many methods have been proposed to reduce the four-component Dirac formalism to computationally much simpler two-component schemes. Two groups of approximate two-component methods have been successful thus far; methods based on the Douglas-Kroll-Hess (DKH) approach [4][5][6][7][8] and those based on the regular Hamiltonian approximation (RA) [9][10][11][12][13][14][15][16].A powerful approach to decoupling positive energy states (electronic states) and negative energy states

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“…This is the case of the zeroth order regular approximation 8,9 ͑ZORA͒ and related approaches, the Douglas-Kroll-Hess formalism [10][11][12] or Breit Pauli [13][14][15][16][17] twocomponent formalism. In most cases, these approaches are based on one-body operators only or make explicit use of the no-pair approximation to the Hamiltonian which contains the magnetic field interaction.…”

Section: Introductionmentioning

confidence: 99%

Mean field linear response within the elimination of the small component formalism to evaluate relativistic effects on magnetic properties

Roura

Melo

Azúa

et al. 2006

The Journal of Chemical Physics

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Articles you may be interested inThe linear response within the elimination of the small component formalism is aimed at obtaining the leading order relativistic corrections to magnetic molecular properties in the context of the elimination of the small component approximation. In the present work we extend the method in order to include two-body effects in the form of a mean field one-body operator. To this end we consider the four-component Dirac-Hartree-Fock operator as the starting point in the evaluation of the second order relativistic expression of magnetic properties. The approach thus obtained is the fully consistent leading order approximation of the random phase approximation four-component formalism. The mean field effect on the relativistic corrections to both the diamagnetic and paramagnetic terms of magnetic properties taking into account both the Coulomb and Breit two-body interactions is considered.

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Calculation of nuclear magnetic shieldings. XV. Ab initio zeroth-order regular approximation method

Cited by 58 publications

References 50 publications

Formal relations connecting different approaches to calculate relativistic effects on molecular magnetic properties

Formal relations connecting different approaches to calculate relativistic effects on molecular magnetic properties

Calculation of nuclear magnetic shieldings: infinite-order Foldy–Wouthuysen transformation

Mean field linear response within the elimination of the small component formalism to evaluate relativistic effects on magnetic properties

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