Journal Article10.1063/1.478189
Cumulant expansion of the reduced density matrices
290
TL;DR: In this paper, conditions for vanishing of certain k-particle cumulants are formulated for a multiconfiguration self-consistent field wave function, where the only nonvanishing matrix elements of the cumulant are those where all labels refer to active (partially occupied) spin orbitals.
read more
Abstract: k-particle cumulants λk (for 2⩽k⩽n) corresponding to the k-particle reduced density matrices γk for an n-fermion system are defined via a generating function. The two-particle cumulant λ2 describes two-particle correlations (excluding exchange), λ3 genuine three-particle correlations etc. The properties of these cumulants are analyzed. Conditions for vanishing of certain λk are formulated. Necessary and sufficient for λ2=0 is the well-known idempotency condition γ2=γ for γ≡γ1. For λ3=0 to hold, a general necessary condition is Tr{2γ3−3γ2+γ}=0, for three special forms of the wave function (arbitrary two-electron state, antisymmetrized product of strongly orthogonal geminals on antisymmetrized geminal power wave function of extreme type) 2γ3−3γ2+γ=0 turns out to be necessary and sufficient. For a multiconfiguration self-consistent field wave function the only nonvanishing matrix elements of the cumulants are those where all labels refer to active (partially occupied) spin orbitals. Spin-free cumulants Λk co...
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Density-functional methods for excited states
Nicolas Ferré,Michael Filatov,Miquel Huix-Rotllant +2 more
- 01 Jan 2016
TL;DR: In this article, a linear response time-dependent density matrix functional theory (TD-DFT) for excited states is proposed. But the authors focus on the non-linear response and multi-dimensional spectroscopy using timedependent DFT.
262
Perspective: Multireference coupled cluster theories of dynamical electron correlation.
TL;DR: This perspective discusses the recent progress and current challenges in multireference wave function methods for dynamical electron correlation, focusing on systematically improvable methods that go beyond the limitations of configuration interaction and perturbation theory.
162
A natural orbital functional for multiconfigurational states
TL;DR: A natural orbital functional is derived, the Piris Natural Orbital Functional 5, PNOF5, constrained to fulfill the D, Q, and G positivity necessary conditions of the N-representable 2-RDM, which yields a remarkable accurate description of systems bearing substantial (near)degeneracy of one-particle states.
139
References
The quantum theory of fields
Steven Weinberg
- 30 Jun 1995
TL;DR: Weinberg as discussed by the authors presented a self-contained, up-to-date and comprehensive introduction to supersymmetry, a highly active area of theoretical physics, including supersymmetric algebras.
5.8K
On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell-Type Expansion Using Quantum-Field Theoretical Methods
TL;DR: In this article, a method for the calculation of the matrix elements of the logarithm of an operator which gives the exact wavefunction when operating on the wavefunction in the one-electron approximation is proposed.
3K
Generalized cumulant expansion method
TL;DR: The notion of cumulants and cumulant functions was introduced in this paper, where a moment generating function of a set of stochastic variables defines the cumulus or the semi-invariants and the cumULant function, and the definition of average may be greatly generalized as far as the condition of the average of unity is unity.
1.7K
Structure of Fermion Density Matrices
TL;DR: In this paper, a new approach is presented to the many-particle problem in quantum mechanics by proposing a method of finding natural orbitals and natural geminals of a system without prior knowledge of the wave function.
1.5K