Kinetic balance: A partial solution to the problem of variational safety in Dirac calculations

Stanton, Richard; Havriliak, S.

doi:10.1063/1.447865

Cited by 561 publications

(310 citation statements)

References 28 publications

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“…2,4,56 Here, we focus mostly on the theoretical foundations of the relativistic matrix Dirac-Kohn-Sham (mDKS) method as implemented in the ReSpect program package, 57 involving a restricted kinetically balanced basis set for the small component of the wave function. [58][59] Consistent with ref. 42, in the following we use the Hartree system of atomic units.…”

Section: Theorysupporting

confidence: 80%

Four-Component Relativistic Density Functional Theory Calculations of EPRg- and Hyperfine-Coupling Tensors Using Hybrid Functionals: Validation on Transition-Metal Complexes with Large Tensor Anisotropies and Higher-Order Spin–Orbit Effects

et al. 2015

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The four-component matrix Dirac-Kohn-Sham (mDKS) implementation of EPR g-and hyperfine A-tensor calculations within a restricted kinetic balance framework in the ReSpect code has been extended to hybrid functionals. The methodology is validated for an extended set of small 4d 1 and 5d 1 [MEXn] q systems, and for a series of larger Ir(II) and Pt(III) d 7 complexes (S=1/2) with particularly large g-tensor anisotropies. Different density functionals (PBE, BP86, B3LYP-xHF, PBE0-xHF) with variable exact-exchange admixture x (ranging from 0% to 50%) have been evaluated, and the influence of structure and basis set has been examined. Notably, hybrid functionals with exact-exchange admixture of about 40% provide the best agreement with experiment and clearly outperform the generalized-gradient approximation (GGA) functionals, in particular for the hyperfine couplings. Comparison with computations at the one-component second-order perturbational level within the DouglasKroll-Hess framework (1c-DKH), and a scaling of the speed of light at the four-component mDKS level, provide insight into the importance of higher-order relativistic effects for both properties. In the more extreme cases of some iridium(II) and platinum(III) complexes, the widely used leading-order perturbational treatment of SO effects in EPR calculations fails to reproduce not only the magnitude but also the sign of certain g-shift components (with the contribution of higher-order SO effects amounting to several hundreds of ppt in 5d complexes). The four-component hybrid mDKS calculations perform very well, giving overall good agreement with the experimental data.

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Section: Theorysupporting

confidence: 80%

Four-Component Relativistic Density Functional Theory Calculations of EPRg- and Hyperfine-Coupling Tensors Using Hybrid Functionals: Validation on Transition-Metal Complexes with Large Tensor Anisotropies and Higher-Order Spin–Orbit Effects

et al. 2015

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“…One cannot simply employ the same basis set for the large and small components. This would lead to variationally unstable results as already observed in the first attempt by Kim [5,55] and to a wrong non-relativistic limit [56], The correct non-relativistic limit is obtained if the kinetic-balance (KB) condition [28,[57][58][59][60] which relates the basis sets for large and small components,…”

Section: Algorithmic Aspects Of ''Exact'' Decoupling Methodsmentioning

confidence: 99%

Exact decoupling of the relativistic Fock operator

Peng¹,

Reiher²

2012

Perspectives on Theoretical Chemistry

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It is generally acknowledged that the inclusion of relativistic effects is crucial for the theoretical description of heavy-element-containing molecules. Four-component Dirac-operator-based methods serve as the relativistic reference for molecules and highly accurate results can be obtained-provided that a suitable approximation for the electronic wave function is employed. However, four-component methods applied in a straightforward manner suffer from high computational cost and the presence of pathologic negative-energy solutions. To remove these drawbacks, a relativistic electron-only theory is desirable for which the relativistic Fock operator needs to be exactly decoupled. Recent developments in the field of relativistic two-component methods demonstrated that exact decoupling can be achieved following different strategies. The theoretical formalism of these exact-decoupling approaches is reviewed in this paper followed by a comparison of efficiency and results.Keywords Relativistic electronic structure theory Á Fock operator Á Douglas-Kroll-Hess method Á X2C method Á Picture change error 1 Introduction

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“…In the NR limit, X = (1/2c)σ · p. In calculations with basis functions, it has been demonstrated that, when using a basis set {χ } for the upper components and a basis for the lower components that includes the function set {σ · pχ }, the aforementioned variational collapse in four-component relativistic calculations can be kept under control. This is referred to as 'kinetic balance' [44]. Restricting the lower-component basis to only functions {σ · pχ } is referred to as 'restricted kinetic balance' (RKB); other schemes exist as well.…”

Section: From Four To Two Componentsmentioning

confidence: 99%

Relativistic calculations of magnetic resonance parameters: background and some recent developments

Autschbach

2014

Phil. Trans. R. Soc. A.

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This article outlines some basic concepts of relativistic quantum chemistry and recent developments of relativistic methods for the calculation of the molecular properties that define the basic parameters of magnetic resonance spectroscopic techniques, i.e. nuclear magnetic resonance shielding, indirect nuclear spin-spin coupling and electric field gradients (nuclear quadrupole coupling), as well as with electron paramagnetic resonance g-factors and electron-nucleus hyperfine coupling. Density functional theory (DFT) has been very successful in molecular property calculations, despite a number of problems related to approximations in the functionals. In particular, for heavy-element systems, the large electron count and the need for a relativistic treatment often render the application of correlated wave function ab initio methods impracticable. Selected applications of DFT in relativistic calculation of magnetic resonance parameters are reviewed.

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Kinetic balance: A partial solution to the problem of variational safety in Dirac calculations

Cited by 561 publications

References 28 publications

Four-Component Relativistic Density Functional Theory Calculations of EPRg- and Hyperfine-Coupling Tensors Using Hybrid Functionals: Validation on Transition-Metal Complexes with Large Tensor Anisotropies and Higher-Order Spin–Orbit Effects

Four-Component Relativistic Density Functional Theory Calculations of EPRg- and Hyperfine-Coupling Tensors Using Hybrid Functionals: Validation on Transition-Metal Complexes with Large Tensor Anisotropies and Higher-Order Spin–Orbit Effects

Exact decoupling of the relativistic Fock operator

Relativistic calculations of magnetic resonance parameters: background and some recent developments

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