🔬 mesoscale physics

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

This study experimentally demonstrates the many-body ground state of a singlet diradicaloid on an ultrathin NaCl surface by combining tip-induced generation, atomic-scale scanning probe characterization, and multiconfigurational calculations to reveal strong electronic correlations in its geometric and electronic structures.

Original authors: Elia Turco, Lara Tejerina, Gonçalo Catarina, Andres Ortega-Guerrero, Nils Krane, Leo Gross, Michal Juríček, Shantanu Mishra

Published 2026-10-02

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CC BY 4.0

Original authors: Elia Turco, Lara Tejerina, Gonçalo Catarina, Andres Ortega-Guerrero, Nils Krane, Leo Gross, Michal Juríček, Shantanu Mishra

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

For over a century, chemists and physicists have been fascinated by a peculiar class of molecules that seem to exist in two worlds at once. These are not the stable, predictable compounds that make up most of the material world, nor are they the fleeting, highly reactive fragments known as radicals. Instead, they occupy a gray zone in between, behaving as if they are simultaneously closed and open, stable and unstable. This ambiguity arises because the electrons inside these molecules do not settle into a single, neat arrangement. Instead, they exist in a complex, shared state where multiple possible arrangements overlap, creating a "many-body" ground state. Understanding this behavior is crucial because it challenges our basic definitions of how chemical bonds work and offers a path toward designing new materials for advanced electronics and computing. The question has long been whether these theoretical descriptions of overlapping electron states could be seen directly in a single molecule, rather than just inferred from bulk measurements.

A team of researchers has now answered this question by creating and examining a specific molecule on an atomic scale. They built a structure consisting of two triangular carbon rings connected by a short chain of four carbon atoms. In a standard chemical view, this chain might look like a series of alternating single and triple bonds, or perhaps a uniform string of double bonds. However, when the scientists placed this molecule on a thin layer of salt and probed it with an extremely sharp tip, they found that reality was far more subtle. The molecule did not choose one bonding pattern over the other. Instead, the bonds in the central chain showed a strength that was intermediate, a physical signature that the molecule is a hybrid of both possibilities. This observation confirms that the molecule exists in a state where its electrons are deeply entangled, refusing to be described by a single, simple picture.

To see this, the researchers first had to build the molecule atom by atom on a surface. They started with a precursor molecule that had extra hydrogen atoms attached, which kept it in a stable, closed form. Using the tip of a scanning tunneling microscope, they applied precise voltage pulses to strip away these hydrogen atoms. This process, known as dehydrogenation, transformed the stable precursor into the target molecule, a neutral species with a unique electronic character. The team then used two different types of microscopic imaging to study the result. One technique, atomic force microscopy, allowed them to feel the strength of the chemical bonds by measuring the repulsive force between the tip and the molecule. They found that the four-carbon chain did not show the sharp contrast between strong and weak bonds that would be expected if it were a simple chain of alternating single and triple bonds. Nor was it perfectly uniform. The bond strength was somewhere in between, suggesting that the molecule is a blend of two different structural forms.

The second part of the investigation involved looking at how the molecule interacts with electricity. By scanning the surface with a voltage that could add or remove electrons, the researchers mapped out the shape of the electron clouds. If the molecule behaved like a standard, closed-shell system, the images of these electron clouds would have matched simple, predictable patterns. Instead, the images showed something unexpected. At certain voltages, the electron density appeared to have a hole or a dip in the center of the chain, a feature that could not be explained by a single, static arrangement of electrons. The researchers realized that these images only made sense if they considered the molecule's ground state as a mixture of several different electron configurations. In this view, the molecule is not just one thing or another; it is a weighted combination of multiple possibilities, where the electrons are constantly shifting between different arrangements.

To confirm this interpretation, the team performed complex computer simulations that treated the electrons as a collective group rather than individual particles. These calculations supported the experimental images, showing that the molecule's behavior is best described by a state where multiple electron configurations coexist. The study demonstrates that strong electronic correlations—the way electrons influence each other in a crowded environment—can manifest in the physical shape and electrical properties of a single molecule. This work provides a clear, visual proof that the complex, multi-layered nature of quantum mechanics is not just a mathematical abstraction, but a real, observable feature of matter at the smallest scale. By showing how a single molecule can embody a blend of different chemical states, the research offers a new way to visualize and understand the fundamental nature of chemical bonds.

Technical Summary: The Multiconfigurational Ground State of a Diradicaloid Characterized at the Atomic Scale

Problem and Context
Diradicaloids occupy an intermediate electronic space between closed-shell molecules and open-shell diradicals, characterized by a small energy gap between the highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO). This small gap facilitates mixing between multiple electronic configurations in the singlet ground state, a phenomenon quantified by the diradical index. While theoretical frameworks often struggle to define the electronic structure of these systems due to their multiconfigurational nature, experimental characterization at the atomic scale has been limited. Specifically, understanding how strong electronic correlations manifest in the geometric (bond order) and electronic (orbital density) structures of a single molecule remains a challenge. Previous studies on derivatives of the target molecule in single-crystalline forms suggested temperature-dependent changes in bond lengths indicative of diradical character, but direct atomic-scale observation of the ground state's nature was lacking.

Methodology
The study employs a combination of on-surface synthesis, scanning probe microscopy, and advanced theoretical modeling:

Synthesis and Preparation: The target molecule, a diradicaloid 1 (C $_{30}$ H $_{16}$ ), consisting of two phenalenyl units connected by an $sp$-hybridized C $_4$ chain, was generated on a bilayer NaCl/Cu(111) surface. The precursor 1p was sublimed onto the surface, and 1 was produced via tip-induced homolytic cleavage of C(sp $^3$ )-H bonds using voltage pulses from a scanning tunneling microscope (STM) tip.
Experimental Characterization:
- Atomic Force Microscopy (AFM): Non-contact AFM with CO-functionalized tips was used to image the molecular geometry and measure bond-order contrasts via frequency shift ( $\Delta f$ ) signals.
- Scanning Tunneling Microscopy (STM): Constant-height STM and differential conductance ( $dI/dV$ ) spectroscopy were performed to map orbital densities and identify ion resonances (positive and negative).
Theoretical Modeling:
- Density Functional Theory (DFT): Used for initial geometry optimization and single-reference orbital analysis.
- Multiconfigurational Methods: Complete Active Space Self-Consistent Field (CASSCF) and Density Matrix Renormalization Group (DMRG) calculations were employed to model the ground state as a linear combination of Slater determinants.
- Rate Equation Modeling: A master equation approach incorporating Dyson orbitals derived from DMRG was used to simulate tunneling pathways, charge-state transitions, and the population of excited states (including triplet states) to reproduce experimental STM images.

Key Results

Geometric Characterization (Bond Order): AFM imaging revealed that the C $_4$ chain in the precursor 1p exhibits a polyynic bonding motif (alternating single and triple bonds), evidenced by distinct $\Delta f$ modulation. In contrast, the generated molecule 1 shows a markedly reduced bond-order contrast in the C $_4$ chain. The observed bond lengths are intermediate between a polyynic structure (diradical character) and a cumulenic structure (closed-shell character), suggesting a resonance hybrid rather than a pure diradical or closed-shell form.
Electronic Characterization (Orbital Densities): STM spectroscopy identified three ion resonances: a positive ion resonance (PIR) at –1.8 V, and two negative ion resonances (NIR) at 0.9 V and 1.5 V.
- The PIR image (–1.8 V) displayed a central nodal plane in the C $_4$ chain, which contradicts the expected HOMO density of a simple closed-shell system.
- The NIR+1 image (1.5 V) showed a density distribution that did not match the superposition of LUMO and LUMO+1 orbitals predicted by single-reference models; instead, it aligned better with a superposition of HOMO and LUMO densities.
Multiconfigurational Explanation: The experimental anomalies were resolved by modeling 1 as having a multiconfigurational ground state ( $S_0$ $S_{0}$ ), described as a weighted combination of a bonding configuration (doubly occupied HOMO) and an antibonding configuration (doubly occupied LUMO).
- Calculations (DMRG and CASSCF) confirmed a singlet ground state with a predominantly bonding character ( $|A_1|^2 \approx 0.60$ ) but a significant contribution from the excited configuration ( $|A_2|^2 \approx 0.06$ ).
- The "nodal plane" observed at –1.8 V was attributed to the trapping of the system in a neutral triplet excited state ( $T_1$ ) following electron detachment, a process dependent on the tip position relative to the LUMO nodal plane.
- The 1.5 V resonance was explained by the contribution of the antibonding configuration ( $\psi_{AB}$ ) in the ground state, allowing electron attachment to the HOMO, a transition forbidden in a pure closed-shell picture.

Significance and Claims
The authors claim that this work provides direct experimental evidence of strong electronic correlations manifesting at the atomic scale in real space. By combining AFM bond-order mapping with STM orbital density imaging and multiconfigurational theory, the study demonstrates that the diradicaloid 1 cannot be adequately described by single-determinant (single-reference) theories. Instead, its ground state is a resonance hybrid of open- and closed-shell structures. The study highlights that the "failure" of single-particle pictures in STM imaging is not an artifact but a signature of the many-body nature of the molecule's ground state. This approach establishes a framework for characterizing complex electronic states in molecular systems where traditional definitions of chemical bonding and electronic structure are ambiguous.

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