Exact and approximate adiabatic connection formulae for the correlation energy in multireference ground and excited states

2018 ◽  
Vol 149 (20) ◽  
pp. 204101 ◽  
Author(s):  
Katarzyna Pernal
Keyword(s):  
Excited States ◽  
Correlation Energy ◽  
Connection Formulae

Embracing local suppression and enhancement of dynamic correlation effects in a CASΠDFT method for efficient description of excited states

2020 ◽  
Vol 224 ◽  
pp. 333-347
Author(s):  
Katarzyna Pernal ◽  
Oleg V. Gritsenko
Keyword(s):  
Excited States ◽  
Correlation Energy ◽  
Correlation Effects ◽  
Dynamic Correlation

In this work we show that the presence of covalent and ionic configurations in a wavefunction gives rise to spatial regions where the effects of suppression and enhancement of correlation energy, respectively, dominate.

An approximate ab initio method based on the DIM model

2000 ◽  
Vol 78 (12) ◽  
pp. 1575-1586 ◽  
Author(s):  
John M Cullen
Keyword(s):  
Ab Initio ◽  
Excited States ◽  
Electron Correlation ◽  
Correlation Energy ◽  
Basis Sets ◽  
Ab Initio Method ◽  
First Order ◽  
Hartree Fock ◽  
Modified Method ◽  
Electron Correlation Energy

Using a second quantized formulation, an approximate diatomics in molecules (DIM) theory is presented in which all three- and four-centered electronic integrals are neglected. To ameliorate the effects of this approximation, the DIM one electron operator is constructed so that the true ab initio first-order density matrix and total energy are reproduced at the Hartree–Fock level. The resulting model was extensively tested for a variety of basis sets for its capability of capturing both the dynamic and nondynamic components of the electron correlation energy as well as the energies of excited electronic states. A modified method in which the DIM one-electron operator is formed from the initial extended Hückel guess of the Hartree–Fock orbitals was also found to produce excellent results.Key words: DIM, electron correlation energy, excited states, semiempirical.

scholarly journals Correlation Energies of Many-Electron Ensembles Are More than the Sum of Their Parts

2018 ◽  
Author(s):  
Tim Gould ◽  
Stefano Pittalis
Keyword(s):  
Excited States ◽  
Variational Approach ◽  
Density Functional ◽  
Unique Feature ◽  
Correlation Energy ◽  
Energy Functional ◽  
Functional Approach ◽  
Passive State ◽  
Functional Theory ◽  
Natural Components

Density functional theory can be extended to excited states by means of a unified variational approach for passive state ensembles. This extension overcomes the restriction of the typical density functional approach to ground states, and offers useful formal and demonstrated practical benefits. The correlation energy functional in the generalized case acquires higher complexity than its ground state counterpart, however. Little is known about its internal structure nor how to effectively approximate it in general. Here we demonstrate that such a functional can be broken down into natural components, including what we call "state-" and "density-driven" correlations, with the latter being a unique feature of ensembles. Such a decomposition, summarised in eq. (10), is exact and also provides us with a pathway to general approximations.<br>

scholarly journals Density-driven correlations in many-electron ensembles: theory and application for excited states

2019 ◽  
Author(s):  
Tim Gould ◽  
Stefano Pittalis
Keyword(s):  
Excited States ◽  
Variational Approach ◽  
Density Functional ◽  
Unique Feature ◽  
Correlation Energy ◽  
Energy Functional ◽  
Functional Approach ◽  
Passive State ◽  
Functional Theory ◽  
Natural Components

Density functional theory can be extended to excited states by means of a unified variational approach for passive state ensembles. This extension overcomes the restriction of the typical density functional approach to ground states, and offers useful formal and demonstrated practical benefits. The correlation energy functional in the generalized case acquires higher complexity than its ground state counterpart, however. Little is known about its internal structure nor how to effectively approximate it in general. Here we show that such a functional can be broken down into natural components, including what we call ``state-'' and ``density-driven'' correlations, with the former amenable to conventional approximations, and the latter being a unique feature of ensembles. Such a decomposition, summarised in eq.(6), provides us with a pathway to general approximations that are able to routinely handle low-lying excited states. The importance of density-driven correlations is demonstrated, an approximation for them is introduced and shown to be useful.

Potential energy curves and dipole moment of NF molecule with inner electron correlation

2015 ◽  
Vol 93 (12) ◽  
pp. 1544-1550 ◽  
Author(s):  
Mingjie Wan ◽  
Huafeng Luo ◽  
Chengguo Jin ◽  
Duohui Huang ◽  
Fanhou Wang
Keyword(s):  
Potential Energy ◽  
Excited States ◽  
Correlation Energy ◽  
Dipole Moments ◽  
Electronic States ◽  
Spectroscopic Properties ◽  
Potential Energy Curves ◽  
Basis Set ◽  
Triplet States ◽  
Singlet And Triplet States

The potential energy curves and dipole moments for the low-lying electronic states of the NF molecule are found by using highly accurate multireference configuration interaction plus the Davidson correction with the AV5Z basis set. All 16 electrons are used in the correlation energy calculations, which are used to characterize the spectroscopic properties of a manifold for singlet and triplet states. X3Σ–, a1Δ, b1Σ+, A3Π, 23Σ–, 23Π, 21Δ, 33Σ–, 13Σ+, and 13Δ electronic states correlate with the two lowest dissociation channels N(4Su) + F(2Pu) and N(2Du) + F(2Pu) are investigated. Note that the b1Σ+ state has two depth wells, but only one depth well was observed in the experiment. The spectroscopic parameters (Re, ωe, ωeχe, De, Be, and Te) are derived, which are in excellent agreement with the available experimental data and the other theoretical values. The molecular parameters and dipole moments for the ground and excited states are also obtained.

scholarly journals Density-driven correlations in many-electron ensembles: theory and application for excited states

2019 ◽  
Author(s):  
Tim Gould ◽  
Stefano Pittalis
Keyword(s):  
Excited States ◽  
Variational Approach ◽  
Density Functional ◽  
Unique Feature ◽  
Correlation Energy ◽  
Energy Functional ◽  
Functional Approach ◽  
Passive State ◽  
Functional Theory ◽  
Natural Components

Density functional theory can be extended to excited states by means of a unified variational approach for passive state ensembles. This extension overcomes the restriction of the typical density functional approach to ground states, and offers useful formal and demonstrated practical benefits. The correlation energy functional in the generalized case acquires higher complexity than its ground state counterpart, however. Little is known about its internal structure nor how to effectively approximate it in general. Here we show that such a functional can be broken down into natural components, including what we call ``state-'' and ``density-driven'' correlations, with the former amenable to conventional approximations, and the latter being a unique feature of ensembles. Such a decomposition, summarised in eq.(6), provides us with a pathway to general approximations that are able to routinely handle low-lying excited states. The importance of density-driven correlations is demonstrated, an approximation for them is introduced and shown to be useful.<br>

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