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Many-body Perturbation Theory (many-body + perturbation_theory)

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Chemistry100%

Selected Abstracts

How many-body perturbation theory (MBPT) has changed quantum chemistry

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2009
Werner KutzelniggArticle first published online: 26 AUG 200
Abstract The history of many-body perturbation theory (MBPT) and its impact on Quantum Chemistry is reviewed, starting with Brueckner's conjecture of a linked-cluster expansion and the time-dependent derivation by Goldstone of such an expansion. A central part of this article is the time-independent formulation of quantum chemistry in Fock space and its diagrammatic representation including the particle-hole picture and the inversion of a commutator. The results of the time-independent derivation of MBPT are compared with those of Goldstone. It is analyzed which ingredients of Goldstone's approach are decisive. The connected diagram theorem is derived both in a constructive way based on a Lie-algebraic formulation and a nonconstructive way making use of the separation theorem. It is discussed why the Goldstone derivation starting from a unitary time-evolution operator, ends up with a wave operator in intermediate normalization. The Møller,Plesset perturbation expansions of Bartlett and Pople are compared. Examples of complete summations of certain classes of diagrams are discussed, for example, that which leads to the Bethe-Goldstone expansion. MBPT for energy differences is analyzed. The paper ends with recent developments and challenges, such as the generalization of normal ordering to arbitrary reference states, contracted Schrödinger k -particle equations and Brillouin conditions, and finally the Nakatsuji theorem and the Nooijen conjecture. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source]

Algebraic modifications to second quantization for non-Hermitian complex scaled hamiltonians with application to a quadratically convergent multiconfigurational self-consistent field method

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 6 2005
Danny L. Yeager
Abstract The algebraic structure for creation and annihilation operators defined on orthogonal orbitals is generalized to permit easy development of bound-state techniques involving the use of non-Hermitian Hamiltonians arising from the use of complex-scaling or complex-absorbing potentials in the treatment of electron scattering resonances. These extensions are made possible by an orthogonal transformation of complex biorthogonal orbitals and states as opposed to the customary unitary transformation of real orthogonal orbitals and states and preserve all other formal and numerical simplicities of existing bound-state methods. The ease of application is demonstrated by deriving the modified equations for implementation of a quadratically convergent multiconfigurational self-consistent field (MCSCF) method for complex-scaled Hamiltonians but the generalizations are equally applicable for the extension of other techniques such as single and multireference coupled cluster (CC) and many-body perturbation theory (MBPT) methods for their use in the treatment of resonances. This extends the domain of applicability of MCSCF, CC, MBPT, and methods based on MCSCF states to an accurate treatment of resonances while still using L2 real basis sets. Modification of all other bound-state methods and codes should be similarly straightforward. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source]

Ab-initio simulations of materials using VASP: Density-functional theory and beyond

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 13 2008
Jürgen Hafner
Abstract During the past decade, computer simulations based on a quantum-mechanical description of the interactions between electrons and between electrons and atomic nuclei have developed an increasingly important impact on solid-state physics and chemistry and on materials science,promoting not only a deeper understanding, but also the possibility to contribute significantly to materials design for future technologies. This development is based on two important columns: (i) The improved description of electronic many-body effects within density-functional theory (DFT) and the upcoming post-DFT methods. (ii) The implementation of the new functionals and many-body techniques within highly efficient, stable, and versatile computer codes, which allow to exploit the potential of modern computer architectures. In this review, I discuss the implementation of various DFT functionals [local-density approximation (LDA), generalized gradient approximation (GGA), meta-GGA, hybrid functional mixing DFT, and exact (Hartree-Fock) exchange] and post-DFT approaches [DFT + U for strong electronic correlations in narrow bands, many-body perturbation theory (GW) for quasiparticle spectra, dynamical correlation effects via the adiabatic-connection fluctuation-dissipation theorem (AC-FDT)] in the Vienna ab initio simulation package VASP. VASP is a plane-wave all-electron code using the projector-augmented wave method to describe the electron-core interaction. The code uses fast iterative techniques for the diagonalization of the DFT Hamiltonian and allows to perform total-energy calculations and structural optimizations for systems with thousands of atoms and ab initio molecular dynamics simulations for ensembles with a few hundred atoms extending over several tens of ps. Applications in many different areas (structure and phase stability, mechanical and dynamical properties, liquids, glasses and quasicrystals, magnetism and magnetic nanostructures, semiconductors and insulators, surfaces, interfaces and thin films, chemical reactions, and catalysis) are reviewed. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008 [source]