Combining Pair-Density Functional Theory and Variational Two-Electron Reduced-Density Matrix Methods

Abstract

Complete active space self-consistent field (CASSCF) computations can be realized at polynomial cost via the variational optimization of the active-space two-electron reduced-density matrix (2-RDM). Like conventional approaches to CASSCF, variational 2-RDM (v2RDM)-driven CASSCF captures nondynamical electron correlation in the active space, but it lacks a description of the remaining dynamical correlation effects. Such effects can be modeled through a combination of v2RDM-CASSCF and on-top pair-density functional theory (PDFT). The resulting v2RDM-CASSCF-PDFT approach provides a computationally inexpensive framework for describing both static and dynamical correlation effects in multiconfigurational and strongly correlated systems. On-top pair-density functionals can be derived from familiar Kohn-Sham exchange-correlation (XC) density functionals through the translation of the v2RDM-CASSCF reference densities [Li Manni et al., J. Chem. Theory Comput. 10, 3669-3680 (2014)]. Translated and fully-translated on-top PDFT versions of several common XC functionals are applied to the potential energy curves of N2, H2O, and CN − , as well as to the singlet/triplet energy splittings in the linear polyacene series. Using v2RDM-CASSCF-PDFT and the translated PBE functional, the singlet/triplet energy splitting of an infinitely-long acene molecule is estimated to be 4.87 kcal mol −1 .

Pushing the Limits of Acene Chemistry: The Recent Surge of Large Acenes

“…The existence of a spin‐contaminated, spin‐unrestricted solution of the Hartree–Fock (HF) [11, 12] or Kohn–Sham (KS) equations [13] for acenes suggests that strong nondynamic (also called static) correlation effects are present and that a single determinant description (as provided by HF and KS‐DFT) of the ground state is qualitatively insufficient. Nonetheless, the singlet ground‐state nature of larger acenes finds general support from studies that employ a wide variety of computational methods, including multiconfiguration treatments that are deemed more appropriate for systems with strong static correlation [14, 108–122] …”

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

“…A partitioning of the matrix elements according to the well‐known Coulomb, exchange, and correlation components [ 38,39 ] and a subsequent formulation of the last two ones within the PDFT framework [ 2,22 ] allow one to express the energy as where E ot is a functional of the total DOCI density and on‐top pair density . [ 40,41 ] In this work, we will evaluate the quantity E ot by means of the procedure described in ref.…”

“…[ 40,41 ] In this work, we will evaluate the quantity E ot by means of the procedure described in ref. [22] where defines the spin polarization factor , [2,22 ] and E XC is the translated functional of the corresponding quantities, where no dependence on |∇ Π( r )| is assumed. Notwithstanding, in order to avoid the known shortcomings derived from the double counting of the correlation, we follow ref.…”

“…The search for more accurate results in quantum mechanical methodologies has motivated researchers to include the dynamic or weak correlation effects into the procedures aimed at treating the so‐called static or strong correlation present in many N ‐electron systems. [ 1–3 ] This is currently one of the challenges faced in many‐electron theories of atoms and molecules. As is well known, strongly correlated systems are those requiring multiple Slater determinants to express their zeroth‐order wave functions, while weakly correlated ones are systems for which a single Slater determinant constitutes a suitable zeroth‐order wave function approximation.…”

“…Likewise, methods that describe proper dynamic correlation in N ‐electron systems that are dominated by a single‐determinant wave function may not satisfactorily account for the multiconfigurational strong correlation effects. [ 2 ] In particular, the treatments based on density functional theory (DFT) [ 4 ] have played an important role in the description of systems with mainly dynamic correlation, but they present remarkable drawbacks dealing with those possessing a static one. [ 5,6 ]…”