Exact two-component Hamiltonians revisited

Liu, Wenjian; Peng, Daoling

doi:10.1063/1.3159445

Cited by 355 publications

(295 citation statements)

References 18 publications

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“…(14). Much activity has been directed in recent years at the development of practical and efficient methods to construct a fully decoupled 2c one-electron Hamiltonian from matrix representations of the 4c Hamiltonian, [73][74][75][76][77] allowing for a full elimination of the lower components with explicit construction of a matrix representation of U. Information regarding the development of these methods, now collectively termed X2C ("eXact 2-Component"), and details about the construction of such operators, can be found in Refs.…”

Section: Relativistic Quantum Chemistry Methodsmentioning

confidence: 99%

Perspective: Relativistic effects

Autschbach

2012

The Journal of Chemical Physics

277

233

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Section: Relativistic Quantum Chemistry Methodsmentioning

confidence: 99%

Perspective: Relativistic effects

Autschbach

2012

The Journal of Chemical Physics

277

233

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“…In their implementation, the basis functions are first converted into an orthonormalized set and every matrix is then evaluated within the orthonormalized set, while the implementation in the BDF program uses the matrices expressed in unnormalized basis functions. Dyall's renormalization matrix turned out to be problematic [73] and a new implementation in the BDF program fixed this problem using a new renormalization matrix, which made the BDF implementation equivalent to the IOTC method of the DIRAC program. Finally, Liu and co-workers found the name XQR to be not suitable to describe this approach.…”

Section: One-step Transformationmentioning

confidence: 99%

Exact decoupling of the relativistic Fock operator

2012

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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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“…Later it was generalized to the so-called exact twocomponent (X2C) method by several groups. [33][34][35][36][37][38][39][40][41][42][43][44] Since the DKH method also employs matrix techniques to evaluate the Douglas-Kroll transformation, it is also able to exactly decouple the four-component Hamiltonian matrix. This has been shown within the arbitrary-order approach.…”

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confidence: 99%

Local relativistic exact decoupling

Peng

Reiher

2012

The Journal of Chemical Physics

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104

123

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An exact separation of the spin-free and spin-dependent terms of the Dirac-Coulomb-Breit Hamiltonian The Journal of Chemical Physics 100, 2118 (1994) We present a systematic hierarchy of approximations for local exact decoupling of four-component quantum chemical Hamiltonians based on the Dirac equation. Our ansatz reaches beyond the trivial local approximation that is based on a unitary transformation of only the atomic block-diagonal part of the Hamiltonian. Systematically, off-diagonal Hamiltonian matrix blocks can be subjected to a unitary transformation to yield relativistically corrected matrix elements. The full hierarchy is investigated with respect to the accuracy reached for the electronic energy and for selected molecular properties on a balanced test molecule set that comprises molecules with heavy elements in different bonding situations. Our atomic (local) assembly of the unitary exact-decoupling transformationcalled local approximation to the unitary decoupling transformation (DLU)-provides an excellent local approximation for any relativistic exact-decoupling approach. Its order-N 2 scaling can be further reduced to linear scaling by employing a neighboring-atomic-blocks approximation. Therefore, DLU is an efficient relativistic method well suited for relativistic calculations on large molecules. If a large molecule contains many light atoms (typically hydrogen atoms), the computational costs can be further reduced by employing a well-defined nonrelativistic approximation for these light atoms without significant loss of accuracy. We also demonstrate that the standard and straightforward transformation of only the atomic block-diagonal entries in the Hamiltonian-denoted diagonal local approximation to the Hamiltonian (DLH) in this paper-introduces an error that is on the order of the error of second-order Douglas-Kroll-Hess (i.e., DKH2) when compared with exact-decoupling results. Hence, the local DLH approximation would be pointless in an exact-decoupling framework, but can be efficiently employed in combination with the fast to evaluate DKH2 Hamiltonian in order to speed up calculations for which ultimate accuracy is not the major concern.

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Exact two-component Hamiltonians revisited

Cited by 355 publications

References 18 publications

Perspective: Relativistic effects

Perspective: Relativistic effects

Exact decoupling of the relativistic Fock operator

Local relativistic exact decoupling

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