Theoretical study of PbO and the PbO anion

Iliaš, Miroslav; Jensen, Hans Jørgen Aa.; Kellö, Vladimı́r; Roos, Björn O.; Urban, Miroslav

doi:10.1016/j.cplett.2005.04.027

Cited by 89 publications

(66 citation statements)

References 26 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

279

233

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Section: Relativistic Quantum Chemistry Methodsmentioning

confidence: 99%

Perspective: Relativistic effects

Autschbach

2012

The Journal of Chemical Physics

279

233

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“…The theoretical results of bond length and dissociation energy of PbO molecule together with experimental values are given in Table IV. We also report 1-component CCSD(T) combined with 2-component MRCI studies [17,24] both in PP and allelectron, frozen-core settings. The bond length r e with the SO interaction shows an excellent agreement with experiment value, compared to an underestimation by ∼0.04Å in static-spin PP calculations.…”

mentioning

confidence: 99%

“…The method opens QMC to variety of systems across the periodic table such as materials with non-collinear states, spin waves and other electronic phases for which particle spins are of the key importance. [17] c all-electron spin-free CCSD(T) [24] d all-electron SO CCSD(T) [24] e Experimental data [25] …”

mentioning

confidence: 99%

Spin-orbit interactions in electronic structure quantum Monte Carlo methods

et al. 2016

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We develop generalization of the fixed-phase diffusion Monte Carlo method for Hamiltonians which explicitly depend on particle spins such as for spin-orbit interactions. The method is formulated in zero variance manner and is similar to treatment of nonlocal operators in commonly used staticspin calculations. Tests on atomic and molecular systems show that it is very accurate, on par with the fixed-node method. This opens electronic structure quantum Monte Carlo methods to a vast research area of quantum phenomena in which spin-related interactions play an important role.PACS numbers: 02.70. Ss, 31.30.jc Quantum Monte Carlo (QMC) methods are making significant contributions to our understanding of manybody effects in quantum systems. Although hampered by the infamous fermion sign problem, a number of approaches have been explored for dealing with inefficiencies whenever sampled distributions possess varying signs or complex values. One of the commonly used strategies is the fixed-node approximation that replaces the fermionic antisymmetry with boundaries given by trial wave function nodes. For broken time-reversal Hamiltonians or for twisted boundary conditions [1] with inherently complex eigenstates, the fixed-node condition has been generalized to the fixed-phase approximation [2]. Benchmark quality results for both models and real materials have been obtained in many settings such as molecules, solids, non-covalently bonded complexes, ultracold condensates and other systems [3,4].Electronic structure QMC calculations are usually done with particle spins being assigned fixed labels, up or down. Since spins commute with Hamiltonians without explicit spin terms, the problem simplifies to the spatial solution of the stationary Schrödinger equation. Treating the spins as quantum variables for more complicated Hamiltonians was explored very early [5] in variational Monte Carlo (VMC) of nuclear systems. However, extending this to projection methods such as the diffusion Monte Carlo (DMC) in position space [3,4] is much more involved. Building upon results for nuclear systems [6][7][8], a DMC method has been proposed and applied to a 2D electron gas with Rashba spin-orbit interaction [9]. In this approach the spinors are stochastically updated by the action of the spin-orbit operator that is absorbed into the path sampling part of the propagator. It effectively samples the space of spinor states rather than (spin) coordinates and a similar VMC approach has been implemented for spin-orbit in atoms [10] very recently.Here we propose a new development that is formulated as the DMC method in coordinate space with spinors in the trial state kept intact during the imaginary time evolution. This implies the zero variance property, ie, the bias in the obtained energy is proportional to the square of the trial function error.The method builds upon our previous work [11] on nonlocal pseudopotentials (PP) since the spin-orbit operator is just another case of inherent nonlocality. It is also well suited for calculations of re...

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“…One exception that used the prescription of Jensen was given in Ref. [75] for calculations on PbO. The scheme is usually called the ''BSS approach'' [4,45,46], but later Barysz et al preferred the abbreviation ''IOTC''.…”

Section: Two-step Transformationmentioning

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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Theoretical study of PbO and the PbO anion

Cited by 89 publications

References 26 publications

Perspective: Relativistic effects

Perspective: Relativistic effects

Spin-orbit interactions in electronic structure quantum Monte Carlo methods

Exact decoupling of the relativistic Fock operator

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