Achieving the CCSD(T) Basis-Set Limit in Sizable Molecular Clusters: Counterpoise Corrections for the Many-Body Expansion

<div>Fragmentation methods allow for the accuratequantum-chemical treatment of large molecular clusters and materials. Here, we explore the combination of two complementary approaches to the development of such fragmentation methods: the many-body expansion (MBE) on the one hand and subsystem density-functional theory (DFT) or frozen-density embedding (FDE) theory on the other hand. First, we assess potential benefits of using FDE to account of the environmentin the subsystem calculation performed within the MBE. Second, we use subsystem DFT to derive a density-based MBE, in which a many-body expansion of the electron density is used to calculate the systems' total energy. This provides a correctionto the energies calculated with a conventional, energy-based MBE that only depends on the subsystem's electron densities. For the test case of clusters of water and of aspirin, we show that such a density-based MBE converges faster than the conventional energy-based MBE. For our test cases, truncation errors in the interaction energies are below chemical accuracy already with a two-body expansion. The density-based MBE thus provides a promising avenue for accurate quantum-chemical calculation of molecular clusters and materials.</div>

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Frozen-Density Embedding Based Many-Body Expansions

10.26434/chemrxiv.11816739.v1 ◽

2020 ◽

Author(s):

Daniel Schmitt-Monreal ◽

Christoph R. Jacob

Keyword(s):

Density Functional ◽

Molecular Clusters ◽

Test Case ◽

Chemical Calculation ◽

Many Body ◽

Functional Theory ◽

Truncation Errors ◽

Potential Benefits ◽

The Many ◽

The One

<div>Fragmentation methods allow for the accuratequantum-chemical treatment of large molecular clusters and materials. Here, we explore the combination of two complementary approaches to the development of such fragmentation methods: the many-body expansion (MBE) on the one hand and subsystem density-functional theory (DFT) or frozen-density embedding (FDE) theory on the other hand. First, we assess potential benefits of using FDE to account of the environmentin the subsystem calculation performed within the MBE. Second, we use subsystem DFT to derive a density-based MBE, in which a many-body expansion of the electron density is used to calculate the systems' total energy. This provides a correctionto the energies calculated with a conventional, energy-based MBE that only depends on the subsystem's electron densities. For the test case of clusters of water and of aspirin, we show that such a density-based MBE converges faster than the conventional energy-based MBE. For our test cases, truncation errors in the interaction energies are below chemical accuracy already with a two-body expansion. The density-based MBE thus provides a promising avenue for accurate quantum-chemical calculation of molecular clusters and materials.</div>

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Photoemission Spectra from the Extended Koopman’s Theorem, Revisited

Frontiers in Chemistry ◽

10.3389/fchem.2021.746735 ◽

2021 ◽

Vol 9 ◽

Author(s):

S. Di Sabatino ◽

J. Koskelo ◽

J. Prodhon ◽

J. A. Berger ◽

M. Caffarel ◽

...

Keyword(s):

Spectral Function ◽

Secular Equation ◽

Basis Set ◽

Effective Energy ◽

Bulk Silicon ◽

Many Body ◽

Optimal Basis ◽

Diagonal Approximation ◽

Energy Theory ◽

The Many

The Extended Koopman’s Theorem (EKT) provides a straightforward way to compute charged excitations from any level of theory. In this work we make the link with the many-body effective energy theory (MEET) that we derived to calculate the spectral function, which is directly related to photoemission spectra. In particular, we show that at its lowest level of approximation the MEET removal and addition energies correspond to the so-called diagonal approximation of the EKT. Thanks to this link, the EKT and the MEET can benefit from mutual insight. In particular, one can readily extend the EKT to calculate the full spectral function, and choose a more optimal basis set for the MEET by solving the EKT secular equation. We illustrate these findings with the examples of the Hubbard dimer and bulk silicon.

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Frozen-Density Embedding Based Many-Body Expansions

10.26434/chemrxiv.11816739.v2 ◽

2020 ◽

Author(s):

Daniel Schmitt-Monreal ◽

Christoph R. Jacob

Keyword(s):

Density Functional ◽

Molecular Clusters ◽

Test Case ◽

Chemical Calculation ◽

Many Body ◽

Functional Theory ◽

Truncation Errors ◽

Potential Benefits ◽

The Many ◽

The One

<div>Fragmentation methods allow for the accuratequantum-chemical treatment of large molecular clusters and materials. Here, we explore the combination of two complementary approaches to the development of such fragmentation methods: the many-body expansion (MBE) on the one hand and subsystem density-functional theory (DFT) or frozen-density embedding (FDE) theory on the other hand. First, we assess potential benefits of using FDE to account of the environmentin the subsystem calculation performed within the MBE. Second, we use subsystem DFT to derive a density-based MBE, in which a many-body expansion of the electron density is used to calculate the systems' total energy. This provides a correctionto the energies calculated with a conventional, energy-based MBE that only depends on the subsystem's electron densities. For the test case of clusters of water and of aspirin, we show that such a density-based MBE converges faster than the conventional energy-based MBE. For our test cases, truncation errors in the interaction energies are below chemical accuracy already with a two-body expansion. The density-based MBE thus provides a promising avenue for accurate quantum-chemical calculation of molecular clusters and materials.</div>

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Comparing many-body approaches against the helium atom exact solution

SciPost Physics ◽

10.21468/scipostphys.6.4.040 ◽

2019 ◽

Vol 6 (4) ◽

Cited By ~ 7

Author(s):

Jing Li ◽

N. D. Drummond ◽

Peter Schuck ◽

Valerio Olevano

Keyword(s):

Exact Solution ◽

Helium Atom ◽

Quantum Monte Carlo ◽

Nuclear Physics ◽

Density Functional ◽

Random Phase ◽

Basis Set ◽

Many Body ◽

Functional Theory ◽

The Many

Over time, many different theories and approaches have been developed to tackle the many-body problem in quantum chemistry, condensed-matter physics, and nuclear physics. Here we use the helium atom, a real system rather than a model, and we use the exact solution of its Schrödinger equation as a benchmark for comparison between methods. We present new results beyond the random-phase approximation (RPA) from a renormalized RPA (r-RPA) in the framework of the self-consistent RPA (SCRPA) originally developed in nuclear physics, and compare them with various other approaches like configuration interaction (CI), quantum Monte Carlo (QMC), time-dependent density-functional theory (TDDFT), and the Bethe-Salpeter equation on top of the \boldsymbol{GW}𝐆𝐖 approximation. Most of the calculations are consistently done on the same footing, e.g. using the same basis set, in an effort for a most faithful comparison between methods.

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