Fate of the open-shell singlet ground state in the experimentally accessible acenes: A quantum Monte Carlo study

Abstract

By means of the Jastrow correlated antisymmetrized geminal power (JAGP) wave function and quantum Monte Carlo (QMC) methods, we study the ground state properties of the oligoacene series, up to the nonacene. The JAGP is the accurate variational realization of the resonating-valence-bond (RVB) ansatz proposed by Pauling and Wheland to describe aromatic compounds. We show that the long-ranged RVB correlations built in the acenes' ground state are detrimental for the occurrence of open-shell diradical or polyradical instabilities, previously found by lower-level theories. We substantiate our outcome by a direct comparison with another wave function, tailored to be an open-shell singlet (OSS) for long-enough acenes. By comparing on the same footing the RVB and OSS wave functions, both optimized at a variational QMC level and further projected by the lattice regularized diffusion Monte Carlo method, we prove that the RVB wave function has always a lower variational energy and better nodes than the OSS, for all molecular species considered in this work. The entangled multi-reference RVB state acts against the electron edge localization implied by the OSS wave function and weakens the diradical tendency for higher oligoacenes. These properties are reflected by several descriptors, including wave function parameters, bond length alternation, aromatic indices, and spin-spin correlation functions. In this context, we propose a new aromatic index estimator suitable for geminal wave functions. For the largest acenes taken into account, the long-range decay of the charge-charge correlation functions is compatible with a quasi-metallic behavior.

Analytic Energy Gradients for Variational Two-Electron Reduced-Density Matrix Methods within the Density Fitting Approximation

“…These results constrast with the JSD-derived geometry for nonacene presented in Ref. 82. For JSD, the BLA pattern for the singlet and triplet states of nonacene clearly differ, and large oscillations (on the order of 0.02 A for the triplet) persist in the center of the molecule.…”

“…For dodecacene, the active space consists of 50 electrons in 50 orbitals. Figure 3 shows the adiabatic singlet-triplet excitation energies computed at the PQG/cc-pVDZ, DMRG-driven complete active space CI (CASCI)/DZ, [75] and quantum Monte Carlo (QMC) [82] levels of theory, along with vertical excitation energies derived from the particle-particle random phase approximation (PP-RPA, using the cc-pVDZ basis) [81] and experiment. [83][84][85][86] The QMC results taken from Ref.…”

“…[83][84][85][86] The QMC results taken from Ref. 82 were obtained using a Jastrow single determinant (JSD) wave function, optimized using lattice regularized diffusion Monte Carlo (LRDMC). PP-RPA, DMRG-CASCI, PQG, and experiment are all in reasonable agreement for the smaller members of − ω CI e ) obtained from full-valence v2RDM-and CI-CASSCF using the cc-pVDZ basis sets.…”

“…The frequencies considered correspond to those that are provided in Table V. [75] and JSD [82] along with vertical excitation energies using particle-particle random phase approximation [81] and experimental excitation energies. [83][84][85][86] the series.…”

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

“…DMRG-or v2RDM-based CASSCF) tend to overestimate the polyradical character of the larger members of the series when correlations among the σ/σ * network are ignored. [131][132][133][134] A detailed history of the progression of these controversies is recounted in Ref. 134.…”