Toward an absolute NMR shielding scale using the spin-rotation tensor within a relativistic framework

Aucar, I. Agustín; Gómez, Sergio S.; Giribet, C. G.; Aucar, Gustavo A.

doi:10.1039/c6cp03355e

Cited by 12 publications

(31 citation statements)

References 46 publications

(83 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From the definitions of NMR shielding and SR tensors, we can rewrite this relationship as

\begin{matrix} σ_{N}^{false(e - e false) LRESC} = \frac{m_{p}}{g_{N}} M_{N}^{false(e - e false) LRESC} \otimes I \\ + σ_{N}^{OZ - normalK} + σ_{N}^{SZ - normalK} + σ_{N}^{normalB - SO} + \frac{1}{2} σ_{N}^{SO - normalS} . \end{matrix}

where

M_{N}^{false(e - e false) LRESC}

is given by the Equation . We can see that the NR Flygare's relation

σ_{N}^{NR - para} = \frac{m_{p}}{g_{N}} M_{N}^{NR - elec} \otimes I,

is fulfilled, together with the following relationships,

σ_{N}^{X} = \frac{m_{p}}{g_{N}} M_{N}^{X} \otimes I

being X = PSO‐K, para‐Mv/Dw, and SO‐L. The SO‐S contribution has a similar relationship although with an extra factor 2,

σ_{N}^{SO - normalS} = 2 \frac{m_{p}}{g_{N}} M_{N}^{SO - normalS} \otimes I .

…”

Section: Models and Levels Of Approachmentioning

confidence: 73%

“…Therefore, the LRESC expansion of the electronic ( e‐e ) part of the spin‐rotation, SR, constant of a nucleus N can be written as

\begin{matrix} M_{N}^{elec false(e - e false)} = - \frac{\partial^{2}}{\partial I_{N} \partial L} E^{M false(e - e false)} (α \cdot A_{N}, - ω \cdot J_{e}) \\ = M_{N}^{NR - elec} \\ + M_{N}^{PSO - normalK} + M_{N}^{para - M v / D w} + M_{N}^{SO - normalL} + M_{N}^{SO - normalS}, \end{matrix}

where

M_{N}^{NR - elec}

is the NR electronic contribution to

M_{N}, M_{N}^{PSO - normalK}

is a second‐order RSPT relativistic correction, and the remaining three terms are third‐order corrections.…”

Section: Models and Levels Of Approachmentioning

confidence: 99%

“…Recently, based on the fact that the OZ‐K, SZ‐K, and B‐SO mechanisms are core‐dependent, an extension of the Flygare's relationship was proposed, in which the shielding tensor can be obtained from the SR tensor employing the new M ‐ i (

i = I, I I, I I I, I V, V

) models . The M ‐ III model was the best model proposed in Ref.…”

Section: Models and Levels Of Approachmentioning

confidence: 99%

“…The M ‐ III model was the best model proposed in Ref. and it is expressed as:

σ_{N}^{M - I I I} = \frac{m_{p}}{g_{N}} M_{N} \otimes I + σ_{N}^{atom} + \frac{1}{2} σ_{N}^{SO - normalS}

…”

Section: Models and Levels Of Approachmentioning

confidence: 99%

See 3 more Smart Citations

Foundations of the LRESC model for response properties and some applications

Aucar

Melo

Aucar

et al. 2017

Int J of Quantum Chemistry

Self Cite

View full text Add to dashboard Cite

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...

show abstract

“…From the definitions of NMR shielding and SR tensors, we can rewrite this relationship as

\begin{matrix} σ_{N}^{false(e - e false) LRESC} = \frac{m_{p}}{g_{N}} M_{N}^{false(e - e false) LRESC} \otimes I \\ + σ_{N}^{OZ - normalK} + σ_{N}^{SZ - normalK} + σ_{N}^{normalB - SO} + \frac{1}{2} σ_{N}^{SO - normalS} . \end{matrix}

where

M_{N}^{false(e - e false) LRESC}

is given by the Equation . We can see that the NR Flygare's relation

σ_{N}^{NR - para} = \frac{m_{p}}{g_{N}} M_{N}^{NR - elec} \otimes I,

is fulfilled, together with the following relationships,

σ_{N}^{X} = \frac{m_{p}}{g_{N}} M_{N}^{X} \otimes I

being X = PSO‐K, para‐Mv/Dw, and SO‐L. The SO‐S contribution has a similar relationship although with an extra factor 2,

σ_{N}^{SO - normalS} = 2 \frac{m_{p}}{g_{N}} M_{N}^{SO - normalS} \otimes I .

…”

Section: Models and Levels Of Approachmentioning

confidence: 73%

“…Therefore, the LRESC expansion of the electronic ( e‐e ) part of the spin‐rotation, SR, constant of a nucleus N can be written as

\begin{matrix} M_{N}^{elec false(e - e false)} = - \frac{\partial^{2}}{\partial I_{N} \partial L} E^{M false(e - e false)} (α \cdot A_{N}, - ω \cdot J_{e}) \\ = M_{N}^{NR - elec} \\ + M_{N}^{PSO - normalK} + M_{N}^{para - M v / D w} + M_{N}^{SO - normalL} + M_{N}^{SO - normalS}, \end{matrix}

where

M_{N}^{NR - elec}

is the NR electronic contribution to

M_{N}, M_{N}^{PSO - normalK}

is a second‐order RSPT relativistic correction, and the remaining three terms are third‐order corrections.…”

Section: Models and Levels Of Approachmentioning

confidence: 99%

i = I, I I, I I I, I V, V

) models . The M ‐ III model was the best model proposed in Ref.…”

Section: Models and Levels Of Approachmentioning

confidence: 99%

“…The M ‐ III model was the best model proposed in Ref. and it is expressed as:

σ_{N}^{M - I I I} = \frac{m_{p}}{g_{N}} M_{N} \otimes I + σ_{N}^{atom} + \frac{1}{2} σ_{N}^{SO - normalS}

…”

Section: Models and Levels Of Approachmentioning

confidence: 99%

See 2 more Smart Citations

Foundations of the LRESC model for response properties and some applications

Aucar

Melo

Aucar

et al. 2017

Int J of Quantum Chemistry

Self Cite

View full text Add to dashboard Cite

show abstract

“…In doing so, second‐order RSPT expressions in a relativistic context were driven to RSPT corrections to Schrödinger molecular states plus relativistic correcting terms. LRESC has been applied successfully since then to nuclear spin‐rotation constant, the molecular rotational g‐tensor, and the susceptibility tensor . A recent review presents a sketch of all described properties where LRESC has been applied …”

Section: Introductionmentioning

confidence: 99%

Relativistic corrections to the electric field gradient given by linear response elimination of the small component formalism

Melo

Maldonado

2019

Int J of Quantum Chemistry

View full text Add to dashboard Cite

This article is concerned with the analysis of relativistic corrections to the electric field gradients (EFGs) via the linear response elimination of the small component scheme (LRESC). Originally developed for magnetic shielding constant, LRESC has been applied in many molecular properties and presented in this work describing EFG for the first time. Within LRESC we obtain relativistic corrections to EFG in terms of 1/c (the speed of light) formally showing that, up to first order (1/c2), there are no virtual pair contributions; recovering the so‐called “no‐pair” approximation. Virtual pair contributions and triplet corrections arise at second order (1/c4). To assess the LRESC description of EFGs at Hartree‐Fock and DFT levels, we applied it to a simple heavy atom containing set of benchmark molecular systems, HX (X = F, Cl, Br, I, and At), and to linear HgX2 (X = Cl, Br, and I) molecules. Fully relativistic four‐component calculations were also done and taken as reference. The most important relativistic correction given by LRESC is a Mass‐velocity related contribution (ΔMv) which represents close to 80% of the nonrelativistic result for At in HAt molecule. For Hg in HgX2 molecular systems, ΔMv is also the most important correction representing close to 60% of the nonrelativistic part. We also describe the overall behavior of LRESC corrections in HgX2 molecules showing low varying results when the weight of the halogen, X, increases. In this kind of molecular system, correlation effects appear in combination to relativity, making them a challenging group to be studied. LRESC results are in very good agreement with previous results for halogen halides, but it shows a need of inclusion of higher order contributions, beyond 1/c2, when applied to Hg in HgX2 set, although LRESC describes accurately At atom, heavier than Hg.

show abstract

Recent Developments in Absolute Shielding Scales for NMR Spectroscopy

Aucar

2019

Annual Reports on NMR Spectroscopy

View full text Add to dashboard Cite

Toward an absolute NMR shielding scale using the spin-rotation tensor within a relativistic framework

Cited by 12 publications

References 46 publications

Foundations of the LRESC model for response properties and some applications

Foundations of the LRESC model for response properties and some applications

Relativistic corrections to the electric field gradient given by linear response elimination of the small component formalism

Recent Developments in Absolute Shielding Scales for NMR Spectroscopy

Contact Info

Product

Resources

About