The multiconfigurational ground state of a diradicaloid characterized at the atomic scale

TL;DR

The paper investigates the multiconfigurational ground state of a singlet diradicaloid formed by two phenalenyl units linked by an sp-hybridized C4 chain on ultrathin NaCl. Using AFM and STM, paired with multiconfigurational calculations (DMRG and CASSCF) and Dyson-orbital–based analysis, the authors show that the neutral ground state $S_0$ is a weighted superposition of open- and closed-shell configurations, with $|A_1|^2 \approx 0.60$ and $|A_2|^2 \approx 0.06$ for the dominant bonding component and a non-negligible doubly excited contribution $|A_2|^2$. The STM charge-state transitions and the observed bond-order contrasts in the C4 bridge together reveal strong electronic correlations at the atomic scale, illustrating how multiconfigurational character manifests in real-space observables. This work provides a concrete atomic-scale demonstration of correlation-driven bonding motifs and offers a blueprint for studying diradicaloids on surfaces.

Abstract

We report the tip-induced generation and scanning probe characterization of a singlet diradicaloid, consisting of two phenalenyl units connected by an sp-hybridized C$_{4}$ chain, on an ultrathin insulating NaCl surface. The bond-order contrast along the C$_{4}$ chain measured by atomic force microscopy and mapping of charge-state transitions by scanning tunneling microscopy, in conjunction with multiconfigurational calculations, reveal that the molecule exhibits a many-body ground state. Our study experimentally demonstrates the manifestation of strong electronic correlations in the geometric and electronic structures of a single molecule.

Figures (3)

• Figure 1: (a, b) Chemical structures and sublattice representations of phenalenyl radical (a) and compound 1 (b). The two sublattices are represented with different colors. For 1, two possible resonance structures are shown, namely, an open-shell with a polyynic C4 chain, and a closed-shell with a cumulenic C4 chain. For the closed-shell resonance structure, the bond orders of bA, bB and bC should be similar, while for the open-shell resonance structure, bB should have a higher bond order than bA and bC.
• Figure 2: Structural characterization of 1p and 1. (a, b) From left to right: chemical structures, AFM images and corresponding Laplace-filtered AFM images of 1p (a) and 1 (b); STM set-point: $V = 0.2$ V and $I = 1.0$ pA on NaCl, tip height $\Delta z=0.5$ Å. a.u. denotes arbitrary units. (c) $\Delta f$ line profiles along the C4 chains of 1p (red) and 1 (blue). Scale bars: 0.5 nm.
• Figure 3: Electronic characterization of 1. (a) Constant-height $I(V)$ spectrum and the corresponding dI/dV(V) spectrum acquired on 1 (open feedback parameters on the molecule: $V = -2.2$ V, $I = 0.4$ pA). The acquisition position is indicated by the filled white circle in (c). PIR and NIR denote the positive and negative ion resonances, respectively. (b) Scheme of the many-body transitions relevant for the measured ion resonances. The transitions are labeled according to the orbital involved: H (HOMO) or L (LUMO). The $S_0 \rightarrow D_1^+$ transition was not accessible in the experimental voltage range. (c) Constant-height STM images at the ion resonances (from left to right, open feedback parameters on NaCl: $V =-1.8$ V, $I = 1.0$ pA, $\Delta z = 1.9$ Å; $V = 0.9$ V, $I = 1.0$ pA, $\Delta z = 2.3$ Å; $V = 1.5$ V, $I = 1.0$ pA, $\Delta z = 3.5$ Å). (d) Transition probability maps at the voltages corresponding to the experimental images in (c) (see Figs. S18, S22 and S23). The molecular structure of 1 is overlaid on the maps. (e) Sketch illustrating triplet trapping for tip positions above the LUMO nodal plane (left), and no trapping for tip positions above finite LUMO density (right). The data in (a, c) were acquired with a metallic tip. Scale bars: 0.5 nm.