Theoretical study of the relativistic molecular rotational g-tensor

et al. 2017

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...

Section: Models and Levels Of Approachmentioning

confidence: 86%

\begin{matrix} E = E_{0} - \frac{1}{2} B \otimes χ \otimes B - \frac{1}{2 m_{p} c} B \otimes g \otimes L - \sum_{K} I_{K} \otimes M_{K} \otimes L \\ - \sum_{K} bold-italicB \otimes true(1 - σ_{K} true) \otimes μ_{K} + \sum_{K > L} μ_{K} \otimes true(D_{K L} + J_{K L} true) \otimes μ_{L} \end{matrix}

where

bold-italicL

is the rotational angular momentum (related to the system angular velocity

bold-italicω

I^{- 1}

⊗

bold-italicL

, with

bold-italicI

the tensor of inertia). This momentum is given only by the rotational states of the nuclei of the system . In addition,

bold-italicB

is an external magnetic field, and

μ_{N} = \frac{g_{N} e}{2 m_{p} c} I_{N}

is the magnetic moment of nucleus N .…”

Section: Response Propertiesmentioning

confidence: 99%

“…In the case of the g‐tensor, we should mention that the action of the operator

boldL

J_{e}^{false(4 false)}

.…”

Section: Models and Levels Of Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Foundations of the LRESC model for response properties and some applications

et al. 2017

“…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

Maldonado

2019

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.

Relativistic corrections of the electric field gradient in dihalogen molecules XY (X, Y = F, Cl, Br, I, At) within the linear response elimination of the small component formalism

Maldonado

2021

We analyze the performance of the linear response elimination of the small component (LRESC) scheme to describe the electric field gradient (EFG), in dihalogen molecular systems, and also to give insight of the relativistic corrections. LRESC shows a good performance, providing results close to four-component (4c) ones for molecules containing atoms belonging up to the fifth row of the Periodic Table . When heavier nuclei are involved the difference among LRESC and 4c values reaches up to 5%. The main relativistic correction represents 80% of the nonrelativistic part for the heaviest molecule. LRESC can be applied at Hartree-Fock as well as Density Functional Theory levels, therefore we also analyze correlation effects on EFG showing that relativity enhances correlation effects and both effects are not additive. As an application of LRESC method, nuclear quadrupole moment calculations of some halogen nuclei are also carried out and compared with the most recent data.