Nonvariational Orbital Optimization Techniques for the AP1roG Wave Function

Boguslawski, Katharina; Tecmer, Paweł; Bultinck, Patrick; Baerdemacker, Stijn De; Neck, Dimitri Van; Ayers, Paul W.

doi:10.1021/ct500759q

Cited by 84 publications

(137 citation statements)

References 102 publications

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“… Orbital‐pair mutual information and single‐orbital entropy for stretched H 2 (

d_{H ‐ H} = 2.0

Å, cc‐pVTZ) determined from the antisymmetric product of one‐reference orbital geminals . The orbitals labeled by indices (1) and (2) correspond to the σ‐ and

σ^{*}

‐orbitals.…”

Section: Orbital Entanglement For An Interpretive Picturementioning

confidence: 94%

Orbital entanglement in quantum chemistry

Boguslawski

Tecmer

2014

Int J of Quantum Chemistry

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148

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The basic concepts of orbital entanglement and its application to chemistry are briefly reviewed. The calculation of orbital entanglement measures from correlated wavefunctions is discussed in terms of reduced n-particle density matrices. Possible simplifications in their evaluation are highlighted in case of seniority-zero wavefunctions. Specifically, orbital entanglement allows us to dissect electron correlation effects in its strong and weak contributions, to determine bond orders, to assess the quality and stability of active space calculations, to monitor chemical reactions, and to identify points along the reaction coordinate where electronic wavefunctions change drastically. Thus, orbital entanglement represents a useful and intuitive tool to interpret complex electronic wavefunctions and to facilitate a qualitative understanding of electronic structure and how it changes in chemical processes.

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“… Orbital‐pair mutual information and single‐orbital entropy for stretched H 2 (

d_{H ‐ H} = 2.0

Å, cc‐pVTZ) determined from the antisymmetric product of one‐reference orbital geminals . The orbitals labeled by indices (1) and (2) correspond to the σ‐ and

σ^{*}

‐orbitals.…”

Section: Orbital Entanglement For An Interpretive Picturementioning

confidence: 94%

Orbital entanglement in quantum chemistry

Boguslawski

Tecmer

2014

Int J of Quantum Chemistry

Self Cite

148

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“…A different, computationally feasible approach suitable for strongly-correlated systems uses seniority-zero wavefunctions to describe the static/nondynamic part of the electron correlation en-ergy. [31][32][33][34][35][36][37][38][39][40][41][42][43][44] The missing dynamic electron correlation effects are included a posteriori in these ansätze using, for instance, many-body perturbation theory [45][46][47], coupled-cluster theory [48][49][50][51][52], extended random phase approximation [53], and density functional theory (DFT) corrections [54,55].…”

Section: Introductionmentioning

confidence: 99%

Benchmark of Dynamic Electron Correlation Models for Seniority-Zero Wave Functions and Their Application to Thermochemistry

Boguslawski

Tecmer

2017

J. Chem. Theory Comput.

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Wavefunctions restricted to electron-pair states are promising models to describe static/nondynamic electron correlation effects encountered, for instance, in bond-dissociation processes and transition-metal and actinide chemistry. To reach spectroscopic accuracy, however, the missing dynamic electron correlation effects that cannot be described by electron-pair states need to be included a posteriori. In this article, we extend the previously presented perturbation theory models with an Antisymmetric Product of 1-reference orbital Geminal (AP1roG) reference function that allow us to describe both static/nondynamic and dynamic electron correlation effects. Specifically, our perturbation theory models combine a diagonal and off-diagonal zero-order Hamiltonian, a single-reference and multi-reference dual state, and different excitation operators used to construct the projection manifold. We benchmark all proposed models as well as an a posteriori linearized coupled cluster correction on top of AP1roG against CR-CCSD(T) reference data for reaction energies of several closed-shell molecules that are extrapolated to the basis set limit. Moreover, we test the performance of our new methods for multiple bond breaking processes in the N2, C2, and BN dimers against MRCI-SD and MRCI-SD+Q reference data. Our numerical results indicate that the best performance is obtained from a linearized coupled cluster correction as well as second-order perturbation theory corrections employing a diagonal and off-diagonal zero-order Hamiltonian and a single-determinant dual state. These dynamic corrections on top of AP1roG allow us to reliably model molecular systems dominated by static/nondynamic as well as dynamic electron correlation.

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“…Such a basis can be obtained self-consistently within the AP1roG method as, for instance, described in Refs. [43,46,48,50]. Note that correlation and entanglement measures are basis dependent and thus the one-site(orbital) and two-orbital correlations within the optimized AP1roG basis will differ from those in the local on-site basis.…”

Section: The Half-filled One-dimensional Hubbard Hamiltonianmentioning

confidence: 99%

“…Recent studies demonstrate that AP1roG can reliably model strongly-correlated systems [47][48][49][50][51][52], even heavyelement containing molecules with multiple degenerate single-particle states [51]. However, most of the analysis presented so far was based on energetic arguments or onebody correlation functions like occupation numbers.…”

Section: Introductionmentioning

confidence: 99%

Analysis of two-orbital correlations in wave functions restricted to electron-pair states

2016

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Wavefunctions constructed from electron-pair states can accurately model strong electron correlation effects and are promising approaches especially for larger many-body systems. In this article, we analyze the nature and the type of electron correlation effects that can be captured by wavefunctions restricted to electron-pair states. We focus on the Antisymmetric Product of 1-reference orbital Geminal (AP1roG) method combined with an orbital optimization protocol presented in [Phys. Rev. B, 89, 201106(R), 2014] whose performance is assessed against electronic structures obtained form DMRG reference data. Our numerical analysis covers model systems for strong correlation: the one-dimensional Hubbard model with periodic boundary condition as well as metallic and molecular hydrogen rings. Specifically, the accuracy of AP1roG is benchmarked using the single-orbital entropy, the orbital-pair mutual information as well as the eigenvalue spectrum of the one-orbital and two-orbital reduced density matrices. Our study indicates that contributions from singly occupied states become important in the strong correlation regime which highlights the limitations of the AP1roG method. Furthermore, we examine the effect of orbital rotations within the AP1roG model on correlations between orbital pairs.

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Nonvariational Orbital Optimization Techniques for the AP1roG Wave Function

Cited by 84 publications

References 102 publications

Orbital entanglement in quantum chemistry

Orbital entanglement in quantum chemistry

Benchmark of Dynamic Electron Correlation Models for Seniority-Zero Wave Functions and Their Application to Thermochemistry

Analysis of two-orbital correlations in wave functions restricted to electron-pair states

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