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

Zaccari, Daniel; Azúa, Martín C. Ruiz de; Melo, Juan I.; Giribet, C. G.

doi:10.1063/1.2162541

Cited by 21 publications

(13 citation statements)

References 27 publications

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“…Visscher suspects that missing positive-energy-negative-energy orbital rotations or the standard restricted kinetic-balance for negative-energy states might produce the differences [59]. In contrast to Visscher's pilot study, similar results were found by Zaccari et al [60] for the linear response within the elimination of the small component framework and Kutzelnigg's approach. In recent work, Xiao and co-workers have addressed the proper and efficient implementation of magneticfield like properties [35].…”

Section: Introductionsupporting

confidence: 55%

Electromagnetic fields in relativistic one-particle equations

2009

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Section: Introductionsupporting

confidence: 55%

Electromagnetic fields in relativistic one-particle equations

2009

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“…Zaccari and coworkers published the formal relation that relate the BBPT (Breit–Pauli perturbation theory) approach and another one formulated by Kutzelnigg . These three proposals appeared almost at the same time and started from different grounds.…”

Section: Models and Levels Of Approachmentioning

confidence: 99%

“…To assess the completeness of LRESC regarding its theoretical grounds, in Ref. , Zaccari et al focused on the formal relations that shows the gauge invariance of the LRESC method, and compared this scheme with two other similar descriptions for shielding constants, namely the Breit–Pauli approximation presented by Vaara and coworkers and the approach proposed by Kutzelnigg in Ref. .…”

Section: Applications Of the Lresc Modelmentioning

confidence: 99%

Foundations of the LRESC model for response properties and some applications

Aucar

Melo

Aucar

et al. 2017

Int J of Quantum Chemistry

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Accurate calculations of some response properties, like the NMR spectroscopic parameters, are quite exigent for the theoretical quantum chemistry models together with the computational codes that are written from them. They need to include a very good description of the electronic density in regions close to the nuclei. When heavy-atom containing systems are studied, those requirements become even higher. Given that relativistic effects must be included in one way or another on the calculation of response properties of heavy-atoms and heavy-atom containing molecules, different schemes were developed during the past decades to include them in as good as possible way. There are some four-component models, which include relativistic effects in a very compact way, although calculations have large time-consumption; one also needs to deal with new and unusual four-component operators. There are also two-component models, which in general may be less accurate, although their application to property calculations on medium-size and large-size molecules are feasible, and they maintain the application of usual operators. In this review, we give the fundamentals of the two-component linear response elimination of small component formalism, LRESC, together with some applications to few selected response properties.New physical insights do appear when the LRESC model is used to analyze the effect of the environment on magnetic shieldings, and when one search for the relativistic extension of well-known nonrelativistic relationships like Flygare's relation among the NMR magnetic shielding and the nuclear spin-rotation constant. A similar relationship is found for the g-tensor and the susceptibility tensor. K E Y W O R D Sg-tensor, NMR, response properties, spin-rotation tensor, two-component methods | I N TR ODU C TI ONThe strong influence of relativistic effects on atomic and molecular response properties of heavy-atom containing molecules was first shown few decades ago.[1] Pyykk€ o included relativistic effects in the calculations of NMR spectroscopic parameters by applying a relativistic model that resemble Ramsey's theory [2] and use relativistic molecular wave function of the relativistically parameterized extended H€ uckel method, REX.[3] Other more elaborated semi-empirical methods and codes were later on used to improve those first results. [4][5][6] The importance of including relativistic effects on the calculation of response properties compelled the theoretical chemists to develop new specific relativistic theories and models. Several formalisms and models appeared in the literature from that time, whose implementations gave more accurate results than that obtained using previous schemes. [7][8][9][10][11][12] We can split them into two broad groups: four-component methods and two-component methods. [12][13][14][15] Even though accurate calculations of response properties of medium-size molecules, meaning molecules containing more than 10 heavy atoms (belonging to the fourth row or below of the Periodic Ta...

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“…The equivalence of the total result of the usual Breit-Pauli and LRESC schemes was theoretically proven, although the particular operators involved are different. 37 The LRESC or Breit-Pauli schemes are interesting because they present several advantages compared to other approaches. First, from the physical point of view, they are based on the Schrödinger Hamiltonian and perturbation operators are amenable to physical interpretation in terms of usual nonrelativistic spin orbitals.…”

Section: Relativistic Two-component Geometric Approximation Of the Elmentioning

confidence: 99%

Relativistic two-component geometric approximation of the electron-positron contribution to magnetic properties in terms of Breit–Pauli spinors

Zaccari

Melo

Azúa

et al. 2009

The Journal of Chemical Physics

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An alternative approach for the calculation of the electron-positron (e-p) contribution to magnetic properties based on two-component Breit-Pauli spinors is presented. In it, the elimination of the small component scheme is applied to the inverse propagator matrix of e-p pairs. The effect of the positronic manifold is expressed as an operator acting on Breit-Pauli spinors. The operator form thus obtained sums up the relativistic correction as a geometric series and as a result a totally different behavior in the vicinity of a nucleus is obtained as compared to the one of the linear response approximation. This feature has deep influence in numerical values of the e-p contribution to the nuclear magnetic shielding of heavy atoms. Numerical calculations carried out for Kr, Xe, and I show that with this approach, the e-p contributions to this property are in good agreement with those of four-component methods.

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

Cited by 21 publications

References 27 publications

Electromagnetic fields in relativistic one-particle equations

Electromagnetic fields in relativistic one-particle equations

Foundations of the LRESC model for response properties and some applications

Relativistic two-component geometric approximation of the electron-positron contribution to magnetic properties in terms of Breit–Pauli spinors

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