|Posted on November 11, 2016 at 11:10 AM|
The concept of electron correlation goes back as far as 1934, to the early stages of quantum-mechanics methods development, before the advent of coupled-cluster, CASSCF or density functional methods. Initially it was defined as the energy difference between the exact result and the Hartree-Fock energy but, soon enough, many different nuances were suggested. The computational lexicon now includes terms such as dynamic, static, angular, radial, short-range or long-range correlation. The most popular separation of electron correlation is done in terms of dynamic and nondynamic correlation types. The former and the latter are also known as weak and strong correlation, respectively. This nomenclature is often used to decide the most convenient computational tool to perform molecular simulations.
The account of electron correlation and its efficient separation into dynamic and nondynamic parts plays a key role in the development of computational methods. We have suggested a physically-sound matrix formulation to split electron correlation into dynamic and nondynamic parts using the two-particle cumulant matrix and a measure of the deviation from idempotency of the first-order density matrix. These matrices are applied to a two-electron model, giving rise to a simplified electron correlation index that (i) depends only on natural orbitals and their occupancies, (ii) can be straightforwardly decomposed into orbital contributions and (iii) splits into dynamic and nondynamic correlation parts that (iv) admit a local version. To the best of y knowledge, these expressions provide the first separation of dynamic and nondynamic correlation based on natural orbital occupancies. These expressions can be used in fractional-occupancy density functional theory (DFT) and density matrix functional theory (DMFT) to construct expressions that control the introduction of dynamic and nondynamic correlation.