Revision of the Douglas-Kroll transformation

Jansen, Georg; Heß, Bernd A.

doi:10.1103/physreva.39.6016

Cited by 853 publications

(519 citation statements)

References 3 publications

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“…Therefore, sooner or later we shall face the problem of evaluation of the matrix elements of the orbitorbit and spin-orbit operators with the exponential functions. For heavy atoms, where the perturbation theory breaks down, different approaches need to be considered such as Douglas-Kroll-Hess transformations [108][109][110][111] or use of effective core potentials [112,113]. Neither of the above methods can straightforwardly be combined with the STOs basis sets.…”

Section: Discussionmentioning

confidence: 99%

Reexamination of the calculation of two-center, two-electron integrals over Slater-type orbitals. III. Case study of the beryllium dimer

et al. 2015

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In this paper we present results of ab-initio calculations for the beryllium dimer with basis set of Slater-type orbitals (STOs). Nonrelativistic interaction energy of the system is determined using the frozen-core full configuration interaction calculations combined with high-level coupled cluster correction for inner-shell effects. Newly developed STOs basis sets, ranging in quality from double to sextuple zeta, are used in these computations. Principles of their construction are discussed and several atomic benchmarks are presented. Relativistic effects of order α 2 are calculated perturbatively by using the Breit-Pauli Hamiltonian and are found to be significant. We also estimate the leading-order QED effects. Influence of the adiabatic correction is found to be negligible. Finally, the interaction energy of the beryllium dimer is determined to be 929.0 ± 1.9 cm −1 , in a very good agreement with the recent experimental value. The results presented here appear to be the most accurate ab-initio calculations for the beryllium dimer available in the literature up to date and probably also one of the most accurate calculations for molecular systems containing more than four electrons.

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Section: Discussionmentioning

confidence: 99%

Reexamination of the calculation of two-center, two-electron integrals over Slater-type orbitals. III. Case study of the beryllium dimer

et al. 2015

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“…The initial publication in this direction targeted the alkali and alkaline earth metals, [23] introduced scalar relativistic effects via the use of a Douglas-Kroll-Hess (DKH) Hamiltonian, [24,25] and substituted the CISD method with complete-active-space selfconsistent field (CASSCF) and complete-active-space secondorder perturbation theory (CASPT2). [26,27] The same design principles have since been used in the development of ANO-RCC sets for the main group elements (groups 13-18), [28] the transition metal elements [including spin-orbit (SO) effects], [29] and the actinides and lanthanides (again including SO effects).…”

Section: Atomic Natural Orbital Basis Setsmentioning

confidence: 99%

Gaussian basis sets for molecular applications

Hill¹

2012

Int J of Quantum Chemistry

188

155

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The choice of basis set in quantum chemical calculations can have a huge impact on the quality of the results, especially for correlated ab initio methods. This article provides an overview of the development of Gaussian basis sets for molecular calculations, with a focus on four popular families of modern atom-centered, energy-optimized bases: atomic natural orbital, correlation consistent, polarization consistent, and def2. The terminology used for describing basis sets is briefly covered, along with an overview of the auxiliary basis sets used in a number of integral approximation techniques and an outlook on possible future directions of basis set design.

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“…For a finite basis-function space, {k k }, Hess [15,32,62] suggested that the exact momentum eigenfunctions h i are to be replaced by the eigenfunctions of the matrix representation of p 2 ; fhk k jp 2 jk l ig: A transformation into this basis is easily achieved as the non-relativistic kinetic energy matrix, which is available in every quantum chemistry program package, is proportional to p 2 and can be diagonalized after multiplication by -2m e . Within this scheme, the KB condition is satisfied since any p -1 k k belongs to the space {k k }.…”

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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Revision of the Douglas-Kroll transformation

Cited by 853 publications

References 3 publications

Reexamination of the calculation of two-center, two-electron integrals over Slater-type orbitals. III. Case study of the beryllium dimer

Reexamination of the calculation of two-center, two-electron integrals over Slater-type orbitals. III. Case study of the beryllium dimer

Gaussian basis sets for molecular applications

Exact decoupling of the relativistic Fock operator

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