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

(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:
http://hdl.handle.net/1854/LU-2041511

- author
- Bultinck, Patrick UGent, Van Neck, Dimitri UGent, Acke, Guillaume UGent and Ayers, Paul W
- organization
- year
- 2012
- 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
- 2016-12-19 15:39:30

@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.