scholarly journals Towards a formal definition of static and dynamic electronic correlations

2017 ◽  
Vol 19 (20) ◽  
pp. 12655-12664 ◽  
Author(s):  
Carlos L. Benavides-Riveros ◽  
Nektarios N. Lathiotakis ◽  
Miguel A. L. Marques
Keyword(s):  
Electron Correlation ◽  
Density Functional ◽  
Recent Progress ◽  
Electronic Correlation ◽  
Body Density ◽  
Hartree Fock ◽  
Static Electron ◽  
Pure States ◽  
The One ◽  
Definition Of

Some of the most spectacular failures of density-functional and Hartree–Fock theories are related to an incorrect description of the so-called static electron correlation. Motivated by recent progress in the N-representability problem of the one-body density matrix for pure states, we propose a way to quantify the static contribution to the electronic correlation.

scholarly journals Information Entropy and Information Distances in Atoms, Nuclei and Bosonic Systems

2019 ◽  
Vol 14 ◽  
pp. 191
Author(s):  
K. Ch. Chatzisavvas ◽  
Ch. C. Moustakidis ◽  
C. P. Panos
Keyword(s):  
Information Entropy ◽  
Atomic Clusters ◽  
Wave Functions ◽  
Body Density ◽  
Bose Gases ◽  
Hartree Fock ◽  
Density Distributions ◽  
The One ◽  
Jensen Shannon Divergence ◽  
Short Range Correlations

The universal property for the information entropy S = a + h In Ζ is verified for atoms using a systematic study with Roothaan-Hartree-Fock (RHF) wave functions with atomic number Ζ — 2 — 54. The above relation was proposed previously for atoms, nuclei, atomic clusters and correlated atoms in a trap. Kullback-Leibler relative entropy Κ and Jensen-Shannon divergence J are employed to compare RHF with Thomas-Fermi (TF) density of atoms as well as another phenomenological density obtained by Sagar et al. Two-body density distributions in position- and momentum-space are used to calculate and compare the corresponding information entropies for correlated and uncorrelated nuclei and bosonic systems (correlated atoms in a trap). It is seen that short-range correlations (SRC) increase the values of S. One-body information entropy entropy S\ is compared with two-body information entropy and a conjecture is made for TV-body information entropy SN- The entropy Κ and the divergence J are also used to evaluate the information distance between correlated and uncorrelated densities both at the one- and the two-body levels for nuclei and trapped Bose gases.

Mathematical Approach to N-Centered DFT and Associated Methods for the Study of Open Systems

2021 ◽  
Author(s):  
Guillaume Grente
Keyword(s):  
Density Functional ◽  
Optimal Transport ◽  
Open Systems ◽  
Fundamental Aspect ◽  
Electronic Systems ◽  
Electronic Density ◽  
Mathematical Properties ◽  
Seminal Article ◽  
The One ◽  
Definition Of

Abstract A fundamental aspect of the study of N−electronic systems (systems containing N electrons) is to obtain information on the states in which these systems have minimal energy. In practice a numerical search of such states is impossible to carry out, so that alternative approaches have been developped, the one around which this work revolves being to consider electronic systems through their electronic density rather than their state. This approach, known today as Density Functional Theory (DFT), was formalised in Kohn and Sham’s seminal article [1] and its mathematical aspects were studied a few years later by Lieb [2]. Since then, the ideas leading to the construction of DFT have been adapted to the context of electronic systems with a fractionnal number of electrons (open systems), first through PPLB DFT[3] and more recently through the definition of N−centered DFT[4, 5]. In both cases it is unclear wherether the mathematical properties established for classical DFT can be expected to hold true. This question is the main problematic of our work, in which we shall study the analogy between N−centered and classical DFT, from their construction to the methods that are derived from them. This will lead us to construct a Kohn-Sham scheme for N−centered DFT, investigate the links between this theory and optimal transport and present the Hubbard Dimer in this particular situation.

THEORETICAL STUDY OF ONE- AND TWO-PHOTON ABSORPTION PROPERTIES FOR THREE SERIES OF DIPHENYLAMINE AND DIFLUORENYLAMINE SUBSTITUTED CONJUGATED COMPOUNDS

2012 ◽  
Vol 11 (05) ◽  
pp. 1033-1056 ◽  
Author(s):  
JIN-YUN WANG ◽  
CHEN-SHENG LIN ◽  
MIN-YI ZHANG ◽  
GUO-LIANG CHAI ◽  
WEN-DAN CHENG
Keyword(s):  
Density Functional ◽  
Photon Absorption ◽  
Transition Strength ◽  
Absorption Properties ◽  
Geometrical Structures ◽  
Hartree Fock ◽  
Two Photon ◽  
Three State Model ◽  
The One ◽  
Conjugated Compounds

The one-photon (OPA) and two-photon (TPA) absorption properties of three series of symmetrically substituted quadrupolar compounds with structure of donor-π bridge-donor (D–π–D) were investigated by time-dependent density functional theory (TDDFT) based on the Hartree–Fock (HF)-optimized geometrical structures. These compounds were constructed with either phenyl or fluorenyl groups connected by vinylene unit as the central π-conjugated bridges and either diphenylamine or difluorenylamine groups as terminal electron donors. The calculated OPA spectra are dominated by two strong transitions which are attributed to the charge transfers from the donor groups to central conjugated chains. The OPA and TPA transition strength all increase with the extension of conjugated chain length in each series and the corresponding wavelength shifts red in general. The transition strength in either OPA or TPA process also increases from series one to series two or three by replacing the phenyl groups with fluorenyl groups. The intramolecular charge transfers make significant contributions to the TPA activity. According to the three-state model, the enhanced TPA activity comes from the enhancement of transition moment between states–states as conjugated chain increases.

Static second hyperpolarizability of twisted ethylene: A comprehensive computational study

2015 ◽  
Vol 14 (08) ◽  
pp. 1550060 ◽  
Author(s):  
Avijit Mondal ◽  
Kaushik Hatua ◽  
Prasanta K. Nandi
Keyword(s):  
Electron Correlation ◽  
Density Functional ◽  
Computational Study ◽  
Present Calculation ◽  
Functional Theory ◽  
Second Hyperpolarizability ◽  
Dominant Feature ◽  
Diradical Character ◽  
Static Electron ◽  
Good Agreement

Twisted conformations of ethylene molecule have diradical character and the second hyperpolarizability of these conformations is best described by the multiconfigurational self consistence field theory (MCSCF) wave function. Present calculation indicates that unrestricted density functional theory (UDFT) predicts second hyperpolarizability which is qualitatively correct for the intermediate diradical region. However, for the two extremities, i.e. rear diradical region and near diradical region, the second hyperpolarizability obtained by UDFT methods differ significantly from the MRCISD result. The BHHLYP and LC-BLYP ([Formula: see text]) results of [Formula: see text] are found to be in good agreement with the MRCISD result. Using the spin-projected UDFT methods almost similar results are obtained. The reasonably fair agreement between the calculated results of second hyperpolarizability obtained at the MRCISD and CASSCF(4,4) levels demonstrates that static electron correlation is the dominant feature of twisted ethylene.

EFFECT OF ELECTRON CORRELATION ON THE TWO-PARTICLE DYNAMICS OF A HELIUM ATOM IN A STRONG LASER PULSE

2002 ◽  
Vol 16 (03) ◽  
pp. 415-452 ◽  
Author(s):  
NILS ERIK DAHLEN
Keyword(s):  
Laser Pulse ◽  
Helium Atom ◽  
Electron Correlation ◽  
Density Functional ◽  
Femtosecond Laser Pulses ◽  
Time Dependent ◽  
Electron Dynamics ◽  
Dimensional Model ◽  
One Dimensional ◽  
Hartree Fock

This review discusses the complicated two-electron dynamics of a helium atom in an intense, short laser pulse. A helium gas in femtosecond laser pulses at long wave lengths (λ~700 nm) and high intensities (I~1015 W /cm2) produces surprisingly high numbers of He2+ ions. These laser fields cause large and fast electron oscillations, which makes a solution of the time-dependent Schrödinger equation numerically demanding. The system can be studied using a one-dimensional model atom, which has many of the same properties as the He atom. Using the one-dimensional model, the importance of including electron correlation in a simplified description of the two-electron dynamics is demonstrated. It is shown that electron correlation becomes much less important if the laser field has a short wave length, in which case the electron oscillations are smaller and slower. The problem of including electron correlation in the calculations is discussed in terms of approaches such as time-dependent Hartree–Fock, time-dependent density functional theory and time-dependent extended Hartree–Fock. Some of the commonly used semi-classical models for describing the double-ionization process are presented.

Comparison of Experimental and Theoretical Structure Amplitudes and Valence Charge Densities of GaAs

1998 ◽  
Vol 54 (3) ◽  
pp. 231-239 ◽  
Author(s):  
J. Stahn ◽  
M. Möhle ◽  
U. Pietsch
Keyword(s):  
Ab Initio ◽  
Density Functional ◽  
Theoretical Data ◽  
Charge Densities ◽  
Hartree Fock ◽  
Structure Factors ◽  
Nearest Neighbours ◽  
Kinematic Limit ◽  
Order Of Magnitude ◽  
The One

The current best sets of X-ray structure amplitudes for GaAs, gallium arsenide, are completed by highly precise data recorded at 0.50 < sin θ/λ < 1.35 Å−1. For the strong reflections the required accuracy of ΔF/F ≤ 1% was realized by the use of Pendellösung measurements at λ = 0.30 Å, recording the integral intensities as a function of the effective thickness from ∼500 µm thick GaAs wafers. Additionally, several weak reflections were determined from their integral intensities within the kinematic limit at wavelengths λ = 0.3, 0.56 and 0.71 Å. From these data individual Debye–Waller factors for gallium and arsenic were determined using the model of independent spherical atoms [B Ga = 0.666 (4) and B As = 0.566 (4) Å2]. The extended set of experimental structure factors now available is compared with those obtained by ab initio solid-state Hartree–Fock (HF) and density functional (DF) calculations. Therefore, the theoretical data were adapted to room temperature using the experimentally evaluated Debye–Waller factors and the model mentioned above. The valence and difference charge densities obtained from experimental and theoretical data show the expected charge accumulation between nearest neighbours slightly shifted towards the arsenic site. The disagreement remaining between the experimental and theoretical data, on the one hand, and between those of both ab initio methods, on the other hand, are of the same order of magnitude.

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