### New Measures of Dynamic Electron Correlation in Terms of Natural Orbitals and Their Occupancies

###
E. Matito a),b),*, Eloy Ramos-Cordoba b) Mauricio Rodriguez-Mayorga b),c)
and Pedro Salvador c)

*a)IKERBASQUE, Basque Foundation for Science, Bilbao, Euskadi, 48011, Spain
b)Faculty of Chemistry. University of the Basque Country UPV/EHU and Donostia International Physics Centre (DIPC), Donostia, Euskadi, 20080, Spain
c)Department of Chemistry and Institut de Química Computacional i Catàlisi (IQCC), Girona, Catalonia, 17071, Spain.
*email: ematito@gmail.com
*

**Abstract:**

The concept of electron correlation goes back as far as 1934 [1], to the early stages of quantum-mechanics methods development, before the advent of coupled-cluster (CC), complete active-space self-consistent field (CASSCF) or density functional theory (DFT) methods. Initially it was defined as the energy difference between the exact result and that obtained with a Hartree-Fock wavefunction [2]. Soon enough, many different nuances of electron correlation were suggested. In fact, the computational lexicon now includes terms such as dynamic, static, angular, radial, short-range or long-range correlation [3], which are used on a routine basis. For instance, his nomenclature is often employed to decide the most convenient computational tool to accurately reproduce the properties of a given system. For instance, a CASSCF calculation introduces nondynamic correlation, while CC includes mainly dynamic correlation effects. In addition, the distinction between different electron correlation regimes can be used to identify key components missing in current density functional expressions.
In this talk we present new means to quantify some of these electron correlation signatures using natural orbitals and their occupancies. In particular, we present two simple expressions to account for dynamic electron correlation employing natural orbitals and their occupancies [5]. These expressions will be used in conjuction with the almost idempotency index, which measures nondynamic correlation effects, to quantify extent of electron correlation effects in a variety of molecules and a simple model system with tunable electron correlation commonly known as harmonium of Hooke's atom [6]. These new indicators might prove useful in the context of natural orbital functional theory (NOFT), where the introduction of dynamic electron correlation effects remains a difficult problem [4].
[1] E. Wigner and F. Seitz, Phys. Rev. 46, 509 (1934).
[2] P.-O. Löwdin, Adv. Chem. Phys. 2, 207 (1959).
[3] D. Cremer, Mol. Phys. 99, 1899 (2001).
[4] M. Piris and J. Ugalde, Int. J. Quant. Chem. 114, 1169 (2014).
[5] E. Ramos-Cordoba, P. Salvador, E. Matito (submitted).
[6] J. Cioslowski, E. Matito, J. Chem. Theory Comput. 7, 915 (2011)