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Influence of electron correlation and degeneracy on the Fukui matrix and extension of frontier molecular orbital theory to correlated quantum chemical methods

Patrick Bultinck UGent, Dimitri Van Neck UGent, Guillaume Acke UGent and Paul W Ayers (2012) PHYSICAL CHEMISTRY CHEMICAL PHYSICS. 14(7). p.2408-2416
abstract
The Fukui function is considered as the diagonal element of the Fukui matrix in position space, where the Fukui matrix is the derivative of the one particle density matrix (1DM) with respect to the number of electrons. Diagonalization of the Fukui matrix, expressed in an orthogonal orbital basis, explains why regions in space with negative Fukui functions exist. Using a test set of molecules, electron correlation is found to have a remarkable effect on the eigenvalues of the Fukui matrix. The Fukui matrices at the independent electron model level are mathematically proven to always have an eigenvalue equal to exactly unity while the rest of the eigenvalues possibly differ from zero but sum to zero. The loss of idempotency of the 1DM at correlated levels of theory causes the loss of these properties. The influence of electron correlation is examined in detail and the frontier molecular orbital concept is extended to correlated levels of theory by defining it as the eigenvector of the Fukui matrix with the largest eigenvalue. The effect of degeneracy on the Fukui matrix is examined in detail, revealing that this is another way by which the unity eigenvalue and perfect pairing of eigenvalues can disappear.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
REACTIVITY, SIMILARITY, ENERGY, NUMBER, ATOMS, NON-NEGATIVITY, FUNCTION INDEXES, KOOPMANS THEOREM, DENSITY-FUNCTIONAL THEORY
journal title
PHYSICAL CHEMISTRY CHEMICAL PHYSICS
Phys. Chem. Chem. Phys.
volume
14
issue
7
pages
2408 - 2416
Web of Science type
Article
Web of Science id
000299505400036
JCR category
PHYSICS, ATOMIC, MOLECULAR & CHEMICAL
JCR impact factor
3.829 (2012)
JCR rank
6/34 (2012)
JCR quartile
1 (2012)
ISSN
1463-9076
DOI
10.1039/c2cp22543c
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
2041511
handle
http://hdl.handle.net/1854/LU-2041511
date created
2012-02-23 09:03:47
date last changed
2012-02-28 15:42:47
@article{2041511,
  abstract     = {The Fukui function is considered as the diagonal element of the Fukui matrix in position space, where the Fukui matrix is the derivative of the one particle density matrix (1DM) with respect to the number of electrons. Diagonalization of the Fukui matrix, expressed in an orthogonal orbital basis, explains why regions in space with negative Fukui functions exist. Using a test set of molecules, electron correlation is found to have a remarkable effect on the eigenvalues of the Fukui matrix. The Fukui matrices at the independent electron model level are mathematically proven to always have an eigenvalue equal to exactly unity while the rest of the eigenvalues possibly differ from zero but sum to zero. The loss of idempotency of the 1DM at correlated levels of theory causes the loss of these properties. The influence of electron correlation is examined in detail and the frontier molecular orbital concept is extended to correlated levels of theory by defining it as the eigenvector of the Fukui matrix with the largest eigenvalue. The effect of degeneracy on the Fukui matrix is examined in detail, revealing that this is another way by which the unity eigenvalue and perfect pairing of eigenvalues can disappear.},
  author       = {Bultinck, Patrick and Van Neck, Dimitri and Acke, Guillaume and Ayers, Paul W},
  issn         = {1463-9076},
  journal      = {PHYSICAL CHEMISTRY CHEMICAL PHYSICS},
  keyword      = {REACTIVITY,SIMILARITY,ENERGY,NUMBER,ATOMS,NON-NEGATIVITY,FUNCTION INDEXES,KOOPMANS THEOREM,DENSITY-FUNCTIONAL THEORY},
  language     = {eng},
  number       = {7},
  pages        = {2408--2416},
  title        = {Influence of electron correlation and degeneracy on the Fukui matrix and extension of frontier molecular orbital theory to correlated quantum chemical methods},
  url          = {http://dx.doi.org/10.1039/c2cp22543c},
  volume       = {14},
  year         = {2012},
}

Chicago
Bultinck, Patrick, Dimitri Van Neck, Guillaume Acke, and Paul W Ayers. 2012. “Influence of Electron Correlation and Degeneracy on the Fukui Matrix and Extension of Frontier Molecular Orbital Theory to Correlated Quantum Chemical Methods.” Physical Chemistry Chemical Physics 14 (7): 2408–2416.
APA
Bultinck, P., Van Neck, D., Acke, G., & Ayers, P. W. (2012). Influence of electron correlation and degeneracy on the Fukui matrix and extension of frontier molecular orbital theory to correlated quantum chemical methods. PHYSICAL CHEMISTRY CHEMICAL PHYSICS, 14(7), 2408–2416.
Vancouver
1.
Bultinck P, Van Neck D, Acke G, Ayers PW. Influence of electron correlation and degeneracy on the Fukui matrix and extension of frontier molecular orbital theory to correlated quantum chemical methods. PHYSICAL CHEMISTRY CHEMICAL PHYSICS. 2012;14(7):2408–16.
MLA
Bultinck, Patrick, Dimitri Van Neck, Guillaume Acke, et al. “Influence of Electron Correlation and Degeneracy on the Fukui Matrix and Extension of Frontier Molecular Orbital Theory to Correlated Quantum Chemical Methods.” PHYSICAL CHEMISTRY CHEMICAL PHYSICS 14.7 (2012): 2408–2416. Print.