Incorporating dynamic correlation into the variational determination method of the second‐order reduced density matrix in the doubly occupied configuration interaction space

Abstract

The variational determination of the second‐order reduced density matrices arising from N‐electron doubly occupied configuration interaction wave functions has recently been proposed as a method to describe systems possessing static correlation in their ground states. In this work, we propose to combine this approach with the on‐top pair density functional theory in order to incorporate dynamic correlations and improve the description of systems possessing both types of electron correlation. The procedure requires ensuring that the second‐order reduced density matrix elements satisfy determined N‐representability variational conditions, as well as other constraints arising from the doubly‐occupied configuration interaction wave function features. An analysis of the results obtained through this method, in studies of strongly correlated many‐electron systems, shows the usefulness of our proposals.

Variational determination of the two‐electron reduced density matrix: A tutorial review

“…28,30 Other interesting use cases include alternative schemes for capturing strong correlation effects, such as v2RDM-based approximations to DOCI. [37][38][39][40][41][42] In either case, one must contend with missing dynamical correlation, which can be done with standard post-CASSCF (or DOCI) methods, such as multiconfiguration pair density functional theory 64,65,109 or multireference adiabatic connection techniques. 41,110 The machinery of v2RDM is also potentially useful in the context of error mitigation for quantum chemical calculations on noisy intermediate scale quantum (NISQ) devices.…”

Localized Active Space Pair-Density Functional Theory

“…Various methods have been proposed to address the difficulties related to the exponential cost scaling of CASSCF with respect to the size of the active space. The restricted active space (RAS) 17,18 and generalized active space (GAS) 19 (DMRG), 20 doubly occupied configuration interaction, 21,22 and active-space two-electron reduced-density-matrix methods 23 can be implemented with polynomial, rather than exponential, cost scaling. The MC-PDFT has also been successfully employed with other reference wave functions, such as RASSCF, 24 GASSCF, 25−27 DMRG-SCF, 28,29 and RASCI 30 (where RASCI denotes RAS configuration interaction).…”

“…The restricted active space (RAS) , and generalized active space (GAS) approximations allow the user to reduce the number of configurations by defining subspaces based on chemical intuition. The density matrix renormalization group (DMRG), doubly occupied configuration interaction, , and active-space two-electron reduced-density-matrix methods can be implemented with polynomial, rather than exponential, cost scaling. The MC-PDFT has also been successfully employed with other reference wave functions, such as RASSCF, GASSCF, − DMRG-SCF, , and RASCI (where RASCI denotes RAS configuration interaction).…”

Variational determination of the two-electron reduced density matrix within the doubly occupied configuration interaction scheme: An extension to the study of open-shell systems

“…The Journal of Chemical Physics ARTICLE scitation.org/journal/jcp systems possessing the so-called strong or static correlation. [4][5][6][7][8][9][10][11][12] As is well known, the strongly correlated N-electron systems require linear combinations of Slater determinants in order to achieve a suitable zeroth-order wave function description, which is a characteristic of the multi-reference methods. However, the applicability of the DOCI method is also limited by its high computational cost, since it scales factorially with the size of the one-electron basis set used.…”