Towards density functional approximations from coupled cluster correlation energy densities

2019 ◽  
Vol 150 (24) ◽  
pp. 244116 ◽  
Author(s):  
Johannes T. Margraf ◽  
Christian Kunkel ◽  
Karsten Reuter
Keyword(s):  
Density Functional ◽  
Correlation Energy ◽  
Coupled Cluster ◽  
Cluster Correlation

Towards Density Functional Approximations from Coupled Cluster Correlation Energy Densities

2019 ◽  
Author(s):  
Johannes T. Margraf ◽  
Christian Kunkel ◽  
Karsten Reuter
Keyword(s):  
Surface Science ◽  
Density Functional ◽  
Correlation Energy ◽  
Local Density ◽  
Coupled Cluster ◽  
Electron Systems ◽  
Condensed Matter Theory ◽  
Matter Theory ◽  
Helium Isoelectronic Series ◽  
Cluster Correlation

<div> <div> <div> <p>(Semi-)local density functional approximations (DFAs) are the workhorse electronic structure methods in condensed matter theory and surface science. The correlation energy density εc(r) (a spatial function that yields the correlation energy Ec upon integration) is central to defining such DFAs. Unlike Ec, εc(r) is not uniquely defined, however. Indeed, there are infinitely many functions that integrate to the correct Ec for a given electron density ρ. The challenge for constructing useful DFAs is thus to find a suitable connection between εc(r) and ρ. Herein, we present a new such approach by deriving εc(r) directly from the coupled- cluster (CC) energy expression. The corresponding energy densities are analyzed for prototypical two-electron systems. To explore their usefulness for designing DFAs, we construct a semilocal functional to approximate the numerical CC correlation energy densities. Importantly, the energy densities are not simply used as reference data, but guide the choice of the functional form, leading to a remarkably simple and accurate correlation functional for the Helium isoelectronic series. </p> </div> </div> </div>

Towards Density Functional Approximations from Coupled Cluster Correlation Energy Densities

2019 ◽  
Author(s):  
Johannes T. Margraf ◽  
Christian Kunkel ◽  
Karsten Reuter
Keyword(s):  
Surface Science ◽  
Density Functional ◽  
Correlation Energy ◽  
Local Density ◽  
Coupled Cluster ◽  
Electron Systems ◽  
Condensed Matter Theory ◽  
Matter Theory ◽  
Helium Isoelectronic Series ◽  
Cluster Correlation

<div> <div> <div> <p>(Semi-)local density functional approximations (DFAs) are the workhorse electronic structure methods in condensed matter theory and surface science. The correlation energy density εc(r) (a spatial function that yields the correlation energy Ec upon integration) is central to defining such DFAs. Unlike Ec, εc(r) is not uniquely defined, however. Indeed, there are infinitely many functions that integrate to the correct Ec for a given electron density ρ. The challenge for constructing useful DFAs is thus to find a suitable connection between εc(r) and ρ. Herein, we present a new such approach by deriving εc(r) directly from the coupled- cluster (CC) energy expression. The corresponding energy densities are analyzed for prototypical two-electron systems. To explore their usefulness for designing DFAs, we construct a semilocal functional to approximate the numerical CC correlation energy densities. Importantly, the energy densities are not simply used as reference data, but guide the choice of the functional form, leading to a remarkably simple and accurate correlation functional for the Helium isoelectronic series. </p> </div> </div> </div>

Towards Density Functional Approximations from Coupled Cluster Correlation Energy Densities

2019 ◽  
Author(s):  
Johannes T. Margraf ◽  
Christian Kunkel ◽  
Karsten Reuter
Keyword(s):  
Surface Science ◽  
Density Functional ◽  
Correlation Energy ◽  
Local Density ◽  
Coupled Cluster ◽  
Electron Systems ◽  
Condensed Matter Theory ◽  
Matter Theory ◽  
Helium Isoelectronic Series ◽  
Cluster Correlation

<div> <div> <div> <p>(Semi-)local density functional approximations (DFAs) are the workhorse electronic structure methods in condensed matter theory and surface science. The correlation energy density εc(r) (a spatial function that yields the correlation energy Ec upon integration) is central to defining such DFAs. Unlike Ec, εc(r) is not uniquely defined, however. Indeed, there are infinitely many functions that integrate to the correct Ec for a given electron density ρ. The challenge for constructing useful DFAs is thus to find a suitable connection between εc(r) and ρ. Herein, we present a new such approach by deriving εc(r) directly from the coupled- cluster (CC) energy expression. The corresponding energy densities are analyzed for prototypical two-electron systems. To explore their usefulness for designing DFAs, we construct a semilocal functional to approximate the numerical CC correlation energy densities. Importantly, the energy densities are not simply used as reference data, but guide the choice of the functional form, leading to a remarkably simple and accurate correlation functional for the Helium isoelectronic series. </p> </div> </div> </div>

Making the Coupled Cluster Correlation Energy Machine-Learnable

2018 ◽  
Vol 122 (30) ◽  
pp. 6343-6348 ◽  
Author(s):  
Johannes T. Margraf ◽  
Karsten Reuter
Keyword(s):  
Correlation Energy ◽  
Coupled Cluster ◽  
Cluster Correlation

Exchange-Correlation Energy Densities and Response Potentials: Connection Between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

2019 ◽  
Author(s):  
S. Giarrusso ◽  
Paola Gori-Giorgi
Keyword(s):  
Density Functional Theory ◽  
Strong Coupling ◽  
Density Functional ◽  
Correlation Energy ◽  
Order Term ◽  
Strong Coupling Limit ◽  
Local Form ◽  
Coupling Constant ◽  
Functional Theory ◽  
Exchange Correlation

We analyze in depth two widely used definitions (from the theory of conditional probablity amplitudes and from the adiabatic connection formalism) of the exchange-correlation energy density and of the response potential of Kohn-Sham density functional theory. We introduce a local form of the coupling-constant-dependent Hohenberg-Kohn functional, showing that the difference between the two definitions is due to a corresponding local first-order term in the coupling constant, which disappears globally (when integrated over all space), but not locally. We also design an analytic representation for the response potential in the strong-coupling limit of density functional theory for a model single stretched bond.<br>

Electronic Structure Benchmark Calculations of Inorganic and Biochemical Carboxylation Reactions

2018 ◽  
Author(s):  
Oscar A. Douglas-Gallardo ◽  
David A. Sáez ◽  
Stefan Vogt-Geisse ◽  
Esteban Vöhringer-Martinez
Keyword(s):  
Electronic Structure ◽  
Chemical Reactions ◽  
Density Functional ◽  
Correlation Energy ◽  
Electronic Energy ◽  
Basis Sets ◽  
Electronic Correlation ◽  
Correct Description ◽  
Carbon Dioxide Co2 ◽  
High Level

<div><div><div><p>Carboxylation reactions represent a very special class of chemical reactions that is characterized by the presence of a carbon dioxide (CO2) molecule as reactive species within its global chemical equation. These reactions work as fundamental gear to accomplish the CO2 fixation and thus to build up more complex molecules through different technological and biochemical processes. In this context, a correct description of the CO2 electronic structure turns out to be crucial to study the chemical and electronic properties associated with this kind of reactions. Here, a sys- tematic study of CO2 electronic structure and its contribution to different carboxylation reaction electronic energies has been carried out by means of several high-level ab-initio post-Hartree Fock (post-HF) and Density Functional Theory (DFT) calculations for a set of biochemistry and inorganic systems. We have found that for a correct description of the CO2 electronic correlation energy it is necessary to include post-CCSD(T) contributions (beyond the gold standard). These high-order excitations are required to properly describe the interactions of the four π-electrons as- sociated with the two degenerated π-molecular orbitals of the CO2 molecule. Likewise, our results show that in some reactions it is possible to obtain accurate reaction electronic energy values with computationally less demanding methods when the error in the electronic correlation energy com- pensates between reactants and products. Furthermore, the provided post-HF reference values allowed to validate different DFT exchange-correlation functionals combined with different basis sets for chemical reactions that are relevant in biochemical CO2 fixing enzymes.</p></div></div></div>

Computational Study on the Kinetics and Mechanisms of Unimolecular Reactions of (Z)-(Z)-N-(λ5-phosphanylidene) Formohydrazonic Formic Anhydride: Intramolecular aza-Wittig Reaction in Competition with Mumm Rearrangement

2020 ◽  
Vol 17 (11) ◽  
pp. 884-889
Author(s):  
Somayeh Mirdoraghi ◽  
Hamed Douroudgari ◽  
Farideh Piri ◽  
Morteza Vahedpour
Keyword(s):  
Rate Constants ◽  
Density Functional ◽  
Wittig Reaction ◽  
Computational Study ◽  
Single Step ◽  
Low Energy ◽  
Coupled Cluster ◽  
Unimolecular Reaction ◽  
Single Step Reaction ◽  
Good Agreement

For (Z)-(Z)-N-(λ5-phosphanylidene) formohydrazonic formic anhydride, Aza-Wittig reaction and Mumm rearrangement are studied using both density functional and coupled cluster theories. For this purpose, two different products starting from one substrate are considered that are competing with each other. The obtained products, P1 and P2, are thermodynamically favorable. The product of the aza-Wittig reaction, P1, is more stable than the product of Mumm rearrangement (P2). For the mentioned products, just one reliable pathway is separately proposed based on unimolecular reaction. Therefore, the rate constants based on RRKM theory in 300-600 K temperature range are calculated. Results show that the P1 generation pathway is a suitable path due to low energy barriers than the path P2. The first path has three steps with three transition states, TS1, TS2, and TS3. The P2 production path is a single-step reaction. In CCSD level, the computed barrier energies are 14.55, 2.196, and 10.67 kcal/mol for Aza-Wittig reaction and 42.41 kcal/mol for Mumm rearrangement in comparison with the corresponding complexes or reactants. For final products, the results of the computational study are in a good agreement with experimental predictions.

scholarly journals A computational study for the reaction mechanism of metal-free cyanomethylation of aryl alkynoates with acetonitrile

RSC Advances ◽  
2021 ◽  
Vol 11 (30) ◽  
pp. 18246-18251
Author(s):  
Selçuk Eşsiz
Keyword(s):  
Density Functional Theory ◽  
Reaction Mechanism ◽  
Density Functional ◽  
Computational Study ◽  
Coupled Cluster ◽  
Functional Theory ◽  
Metal Free ◽  
Coupled Cluster Methods ◽  
High Level ◽  
Cluster Methods

A computational study of metal-free cyanomethylation and cyclization of aryl alkynoates with acetonitrile is carried out employing density functional theory and high-level coupled-cluster methods, such as [CCSD(T)].

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