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

2013 ◽  
Vol 4 (16) ◽  
pp. 2674-2680 ◽  
Author(s):  
Ryan M. Richard ◽  
Ka Un Lao ◽  
John M. Herbert
Keyword(s):  
Molecular Clusters ◽  
Basis Set ◽  
Many Body ◽  
Counterpoise Corrections ◽  
The Many

Basis Set Superposition Errors in the Many-Body Expansion of Molecular Properties

2019 ◽  
Vol 123 (20) ◽  
pp. 4500-4511 ◽  
Author(s):  
Benjamin G. Peyton ◽  
T. Daniel Crawford
Keyword(s):  
Molecular Properties ◽  
Basis Set ◽  
Many Body ◽  
The Many

Understanding the Many-Body Basis Set Superposition Error: Beyond Boys and Bernardi

2018 ◽  
Vol 14 (5) ◽  
pp. 2386-2400 ◽  
Author(s):  
Ryan M. Richard ◽  
Brandon W. Bakr ◽  
C. David Sherrill
Keyword(s):  
Basis Set ◽  
Many Body ◽  
Basis Set Superposition Error ◽  
The Many

scholarly journals Frozen-Density Embedding Based Many-Body Expansions

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>

scholarly journals Photoemission Spectra from the Extended Koopman’s Theorem, Revisited

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.

Frozen-Density Embedding Based Many-Body Expansions

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>

scholarly journals Frozen-Density Embedding Based Many-Body Expansions

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>

scholarly journals Comparing many-body approaches against the helium atom exact solution

2019 ◽  
Vol 6 (4) ◽  
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.

On the many-body theory of nuclear reactions

1968 ◽  
Vol 111 (1) ◽  
pp. 392-416 ◽  
Author(s):  
K DIETRICH ◽  
K HARA
Keyword(s):  
Nuclear Reactions ◽  
Many Body ◽  
Many Body Theory ◽  
The Many ◽  
Body Theory
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