Capturing the Dynamic Correlation for Arbitrary Spin-Symmetry CASSCF Reference with Adiabatic Connection Approaches: Insights into the Electronic Structure of the Tetramethyleneethane Diradical

Abstract

The recently proposed approach to multireference dynamic correlation energy based on the adiabatic connection (AC) is extended to an arbitrary spin symmetry of the reference state. We show that both the spin-free AC approach and its computationally inexpensive approximation, AC0, when combined with a complete active space wave function, constitute viable alternatives to the perturbation-based and density-functional-based multiconfiguration methods. In particular, the AC0 approach, thanks to its favorable scaling with the system size and the size of the active space, allows for treating larger systems than its perturbation-based counterparts while maintaining comparable accuracy. We show the method’s robustness on illustrative chemical systems, including the elusive tetramethyleneethane (TME) diradical, potential energy surfaces of which present a challenge to most computational approaches. For the latter system, AC0 outperforms other methods, staying in close agreement with the full configuration interaction quantum Monte Carlo benchmark. A careful analysis of the contributions to the correlation energy of TME’s lowest singlet and triplet states reveals the subtle interplay of the dynamic and static correlation as the key to understanding the shape of the diradical’s potential energy surfaces.

Organic Emitters Showing Excited-States Energy Inversion: An Assessment of MC-PDFT and Correlation Energy Functionals Beyond TD-DFT

“…In the following, we will denote ρ 2 (r) = ρ 2 (r 1 , r 2 )| r 1 =r 2 as the function at the twoelectron coalescence point, whose modelling has been extensively pursued in the past [24][25][26], as well as its integration into excited-state formalisms [27,28], as the next step for the description of electronic structure beyond the use of merely the electronic density ρ(r).…”

Density matrix renormalization group with dynamical correlation via adiabatic connection

“…Since we have not modified these methods, but rather connected them, we refer readers interested in more details to comprehensive DMRG reviews [17][18][19]21 or original papers presenting AC/AC0 methods. 34,35,42 Density matrix renormalization group and matrix product states…”

“…It was demonstrated numerically in Refs. 35,42 that one can avoid the expensive integration in Eq. 10 by linearized-AC-integrand approximation, W α = W (0) + αW (1) α=0 , named AC0, without losing much accuracy.…”

“…This results in an overall scaling n 2 sec n 4 act , n sec n 5 act , n 6 act , where n act denotes the number of active orbitals and n sec denotes the number of secondary (virtual) orbitals. Numerical accuracy of the AC0 method has been tested on several examples, 34,35 including the complex electronic structure of the tetramethyleneethane diradical 42 and it was shown that AC0 offers accuracy sim-ilar or exceeding that of NEVPT2. 35 Recently, it has been shown how to amend the AC0 with the contributions from the negative-transition component of the linear response function, in order to achieve good accuracy in description of the singlet excitation energies of organic chromophores.…”

Range separation of the Coulomb hole

“…See DOI: 10.1039/cXCP00000x/ Systems presenting dynamic and nondynamic correlation have become one of the greatest challenges in modern electronic structure methods. The ability to simultaneously tackle both types of correlation is present in very few electronic structure methods, such as the complete active space with second-order perturbation theory (CASPT2), 35,36 multireference configuration interactions (MRCI) 37,38 or, most recently, the adiabatic-connection MCSCF (AC-MCSCF) 39 , ∆NO, 40 and GNOF. 41 Nevertheless, these methods are far from exact and their computational cost represents a big drawback.…”