Ayers, Paul W

Bultinck, Patrick

Cooper, David L

van Aggelen, Helen

Van Neck, Dimitri

Verstichel, Brecht

English

Ghent University Academic Bibliography

Chemical Verification of Variationally Optimized Second Order Density Matrices   Helen van Aggelena, Brecht Verstichelb, Patrick Bultincka, Dimitri Van Neckb, Paul Ayersc, David Cooperd   aDepartment of Inorganic and Physical Chemistry, Ghent University, 281 S3, Krijgslaan, Ghent 9000, Belgium bCenter for Molecular Modeling, Ghent University, 86, Proeftuinstraat, Ghent 9000, Belgium cDepartment of Chemistry, McMaster University, Hamilton L8S 4M1, Canada dDepartment of Chemistry, University of Liverpool, Liverpool L69 76D, UK   Size-consistency is a highly desirable property for any quantum chemical method. Variational second order density matrix theory aims to replace the role of the wavefunction in quantum chemical calculations by a variationally optimized second order density matrix [1,2]. Practical implementations of this method are not size-consistent, because they apply  a necessary but not sufficient subset of N-representability constraints.  We identify several problems of this method in describing dissociating molecular systems under the approximate 2-positivity conditions [1,3] for N-representability. First of all, it tends to dissociate molecules incorrectly into fractionally charged dissociation products with too low energies, thereby violating size-consistency [4]. Secondly, the second order density matrix of a non-interacting system is not separable into density matrices for each of the non-interacting units. The first shortcoming, dissociation into fractionally charged products, is a consequence of the method’s  faulty relationship between energy and the number of electrons. We propose simple 2-index constraints to solve this problem [5].  Nonetheless, these constraints do not  solve the second problem, non-separability of the second-order density matrix for a system of non-interacting units.  References: 1. J. Coleman, Rev. Mod. Phys., 35, 668 (1963) 2. H. Kummer,  J. Math. Phys., 8, 2063 (1967) 3. C. Garrod, J.K. Percus, J. Math. Phys., 5, 1756 (1964) 4. H. van Aggelen, B. Verstichel, P. Bultinck, D. Van Neck, P.W. Ayers, J. Chem. Phys., 132, 114112 (2010) 5. B. Verstichel, H. van Aggelen, D. Van Neck, P.W. Ayers, P. Bultinck, J. Chem. Phys., 132, 114112 (2010)  

Chemical verification of variationally optimized second order density matrices

https://biblio.ugent.be/publication/1085371/file/4133966

Chemical verification of variationally optimized second order density matrices

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Ghent University Academic Bibliography