Topological classification of cycloadditions occurring on-surface and in the solid-state

doi:10.21203/rs.3.rs-1650627/v1

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Topological classification of cycloadditions occurring on-surface and in the solid-state

https://doi.org/10.21203/rs.3.rs-1650627/v1

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The study of cycloaddition mechanisms is central to the fabrication of extended sp² carbon nanostructures such as spin-chains. Reaction modeling in this context has focused mostly on putative, energetically preferred, exothermic products with limited consideration for symmetry allowed or forbidden mechanistic effects. To classify and optimize allowed reaction mechanisms modern topological tools can be explored. Here, we introduce a scheme for classifying symmetry-forbidden reaction coordinates in Woodward-Hoffmann correlation diagrams. Topological classifiers grant access to the study of reaction pathways and correlation diagrams in the same footing, for the purpose of elucidating mechanisms and products of polycyclic aromatic azomethine ylide (PAMY) cycloadditions with pentacene–yielding polycyclic aromatic hydrocarbons with an isoindole core in the solid-state and on surfaces, as characterized by mass spectrometry and scanning tunneling microscopy, respectively. By means of a tight-binding reaction model and density functional theory (DFT) we find topologically-allowed pathways for an endothermic reaction mechanism. Our work unveils topological classification as a crucial element of reaction modeling for nanographene engineering, and highlights its fundamental role in the design of cycloadditions in on-surface and solid-state chemical reactions, while underscoring that exothermic pathways can be topologically-forbidden.

Physical sciences/Chemistry/Surface chemistry

Physical sciences/Physics/Chemical physics

Cycloaddition reactions^{1, 2} are cornerstones in carbon nanomaterial engineering. Early examples include Diels-Alder^{3, 4} [4 + 2] and Prato-type⁵ [3 + 2] cycloadditions in solution environments, and Huisgen-type⁶ [3 + 2] as well as related [2 + 2] Bergman^{7, 8} cyclization on surfaces. With the advent of nanographene synthesis^{9,10, 11, 12}, a new chapter in organic chemistry has opened up, seeking a modular, highly selective, and high-yield synthesis^{6, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24} of extended conjugated macromolecules at interfaces without byproducts.²⁵ This endeavor embodying click-chemistry²⁶ has notably driven the adaptation of a large variety of organic reactions at interfaces, including Ullmann coupling, Glaser coupling and polycondensations. Recently, we have shown that polycyclic aromatic azomethine ylides^{27, 28, 29} (PAMYs, Fig. 1a) can be employed to form diaza-hexabenzocoronenes and N-containing polycyclic aromatic chains^{20, 30} in the solid-state and on surfaces, opening an avenue to cycloaddition polymerizations for extended polycyclic aromatic hydrocarbons (PAHs) or related nanographenes. In solution, the PAMY precursor, namely 8H-isoquinolino[4,3,2-de]phenanthridin-9-ium tetrafluoroborate (DBAP salt, 1, see Methods and SI), undergoes selective 1,3-dipolar [3 + 2] cycloaddition to electron-deficient dipolarophiles yielding N-containing PAHs.^{31, 32} Towards the engineering of extended N-containing PAHs on-surface and in the solid-state, a mechanistic, broadly accessible understanding of the chemical reactions and pathways accessible to PAMY^{33, 34} and similar cycloadditions is desirable.³⁵

In on-surface and solid-state thermochemistry, chemical reaction modeling beyond adiabatic energetic diagrams (e.g. nudge elastic band method for determining transition structure and energy barrier³⁶) is rarely explored since the potential energy surfaces of ground states are often assumed to follow the noncrossing rule³⁷ or void of electronic state hopping. Because of this limitation, it remains often unclear in the literature whether cyclization and dehydrogenation reactions are symmetry-allowed, that is, occur adiabatically or otherwise. Symmetry-forbidden reactions, that is, reactions in which molecular orbitals cross, are indicative of nonadiabatic dynamics that are known to play a fundamental role in PAH synthesis and cycloadditions^{38, 39}. Several models are available to attempt to formally define forbidden nonadiabatic reaction pathways from on-surface reaction mechanisms. Woodward and Hoffmann (WH)^{40, 41, 42, 43, 44} attribute the reactivity of a chemical reaction to the atomic orbital symmetries under adiabatic conditions. The WH rules provide qualitative selection rules for pericyclic cycloaddition reactions^{45,46, 47, 48, 49} whereby molecular orbital symmetry and crossings are commonly treated by means of Fukui reaction theory⁵⁰, Marcus theory of electron transfer and the surface hopping method⁵¹. More accurate mechanistic predictions relying on the Born-Oppenheimer⁵² approximation, are challenging when dealing with more than one reaction pathway in the presence of nonadiabatic quantum effects such as tunneling and surface hopping. These effects make it difficult to validate qualitative WH rules. Yet the WH approach remains a powerful well-known concept for reaction engineering. In this regard, quantitative and chemically-intuitive WH visualization tools treating ionic, radical and pericyclic reactions on the same footing would be desirable for the rapid prototyping of PAH reactions, and the study of nonadiabaticity. During the last decades, the classification of orbital crossings^{53, 54, 55} aided by differential geometry and algebraic topology has emerged as a promising method to study nonadiabaticity in condensed matter physics.^{56, 57, 58, 59, 60, 61, 62, 63} Topological physical properties⁶⁴ in quantum matter and metamaterials can now be engineered with an extraordinary level of sophistication, aided by the interplay between effective (‘toy’) models, ab initio calculations and experiments. Such methodology has been rarely employed for the study of chemical phase transitions and corresponding reactions. Recently, the concept of topology classification for mirror-symmetric reaction pathway models to study reactions by means of topological invariants was introduced^{65, 66}, whereby the reactions with distinct topologically classifiers are adiabatically forbidden (such as the [2 + 2] thermal reaction of two ethylene molecules)^{65, 66}. Topological classifications could epitomize a turning point to accelerate cycloaddition reaction engineering, especially on-surface, where reactions are surface templated and highly symmetric. Particularly, such topological models expand and unify the WH-Fukui approach: They enforce the geometrical symmetry and concertedness of reaction pathways to summarize and formalize chemical notions, simplifying reaction interpreting and rational design. Additionally, they illustrate that reaction coordinates can be mathematically defined to study nonadiabaticity and (non-interacting) orbital intersections from a topological standpoint.^{67, 68}

Here, we study the solid-state and on-surface cycloaddition of a PAMY precursor and pentacene to yield internally N-containing PAH with a tetracenoisoindole core (Fig. 1a) as characterized by ultra-high vacuum (UHV) scanning tunneling microscopy (STM) and matrix-assisted laser desorption-ionization mass spectrometry (MALDI-MS).⁶⁹ By investigating the frontier orbital symmetries of gas-phase reaction pathways by means of intrinsic reaction coordinates which are assumed conclusive for the study of the on-surface and in the solid-state reactions, we describe the [3 + 2] reaction (Fig. 1b) between singlet diradicaloid PAMY (rPAMY) and pentacene and show that its de-aromatization pathway is adiabatic and therefore thermally allowed in the gas phase. We formally classify the WH rules via topological invariants, extending the recently proposed topological classification⁶⁵ to a tight-binding Hückel reaction model combining first-principles calculations (Fig. 1c). Different from the frontier orbital model, our topological WH model differentiates the allowed, concerted adiabatic pathways from the nonadiabatic, crossings by a \(\:\mathbb{Z}\)-classified topological invariant \(\:C\left(t\right)={N}_{+}\left(t\right)-{N}_{-}\left(t\right)\), where \(\:{N}_{+}\left(t\right)\) (\(\:{N}_{-}\left(t\right)\)) is the number of mirror symmetric (antisymmetric) molecular orbitals (MOs) in all occupied Mos, and \(\:\varDelta\:C={C}_{react}-{C}_{prod}\) is the difference of the topological invariants between reactants and products (Fig. 1c). We find that singlet diradicaloid PAMY lateral addition to acenes is endothermic but topologically WH allowed, while central ring addition is exothermic but topological forbidden. Our work introduces a methodological and theoretical approach for the study of cycloaddition selectivity, particularly PAMY reactions which are relevant in development of N-containing PAHs as substrates for N-doped nanographenes, spin-chains^{70, 71}, metal-free catalysis^{72, 73} and sensors^{74, 75}.

Unlike homocoupling solution reactions³⁰, previous heterocoupling solid-state studies⁷⁶ employing DBAP salt have not identified key intermediates which unambiguously evidence cycloaddition reaction pathways. Therefore, we set to investigate on-surface and solid-state intermediates and products between the DBAP and pentacene in Fig. 2 employing mass spectrometry (MS) and STM. Upon heating to 250°C a 1:1 solid-state mixture of pentacene and DBAP salt, a peak of m/z = 543.198 is identified in the matrix-assisted laser desorption/ionization (MALDI) mass spectrum (Fig. 2a), assigned to the heterocoupling product with a hydrogenated tetracenoisoindole core, together with the expected competing homocoupling products³⁰. A tentative structure for the product is DH (Fig. 1a, 2a) ensuing from a hydrogenated tetracenoisoindole core and partial dehydrogenation of pentacene. Such product could occur following pathway R1 (Fig. 1a) as a probable adiabatic cycloaddition mechanism. A direct, unknown pathway R2 could occur but is less plausible. These pathways consider that a hydrogen of the unreactive species of DBAP is removed, to form diradicaloid PAMY (rPAMY, Fig. 1a), which has been previously characterized on surfaces^30,76. The diradicaloid term is used to address both potential spin states of rPAMY, whereby the singlet and triplet frontier orbitals are depicted in Fig. 1a with intrinsic bond orbital (IBO) analysis. It is worth noting that triplet diradical PAMY is 25 kcal mol^− 1 higher in energy, which is around 8 kcal mol^− 1 above than the highest energy barrier found in this work, and therefore not considered as the reactive species.

When mixing 2.2 equivalents of DDQ in the solid-state reaction to further dehydrogenate the DH intermediate (see Methods), a fully dehydrogenated product, tentative P1, bearing a tetracenoisoindole core is found (Fig. 2b). The energy diagram in Fig. 2e depicts that the expected heterocoupling intermediate product of the R1 pathways TS1 is 13.6 kcal/mol above the reactants, whereby the intermediate with two detached hydrogens (DH) is more stable than the final product P1, consistent with the MALDI result.

Low temperature (LT) STM measurements on the Ag(100) surface (Fig. 2c and 2d) were carried out to further investigate surface-confined reaction products. Upon sublimation of pentacene and DBAP onto Ag(100) and annealing treatment at around 400°C, the major product of the reaction is identified as bearing mirror symmetry with the 2,3 position of pentacene as studied in Fig. 3. Metal substrates are known to catalyze dehydrogenation, such that the reaction on Ag(100) is comparable to the solid-state reaction with DDQ and the reaction product is inferred as the expected final product P1 with a tetracenoisoindole core. Moreover, the three-dimensional structure of Int1, with an angle of 125° between the PAMY and pentacene, strongly biases the reaction towards planarization through partial dehydrogenation products DH and P1. An additional minor product P2 derived from the pentacene molecules reacting on the 1,2 positions is observed (Fig. S11).

To study isomeric reaction pathways, we focus on the cycloaddition between singlet diradicaloid PAMY (rPAMY), and pentacene by broken-symmetry DFT calculations. Figure 2e depicts the energy profile obtained from intrinsic reaction coordinate (IRC) calculation of the R1 proposed reaction pathway leading to P1 via on-surface dehydrogenation as detailed in supporting information. There are at least two additional plausible reaction pathways (R2-R3) which could explain the on-surface and solid-state data (Fig. 3). The calculated frontier orbitals of the starting configuration can be defined as symmetric (S) or antisymmetric (AS) with respect to the molecular mirror plane. These symmetries are conserved in the endothermic R1 [3 + 2] cycloaddition IRC pathway (Fig. 3a, b) and therefore WH allowed. In pathway R2, which considers the cycloaddition reaction with dehydrogenated pentacene, the symmetry of the highest occupied molecular orbital is conserved and hence equally WH allowed. Here, attempts to locate a transition structure via IRC were unsuccessful, whereas nudge-elastic band identifies the reaction as barrierless and highly exothermic (Fig. 3c, d). Finally, the solid-state reaction could admit an isomer of product P1 through pathway R3, in which orbitals symmetries are changed. Accordingly, the transition structure search fails to locate a concerted [3 + 4] cycloaddition mechanism, despite the Int2 being exothermic (Fig. 3e, f). Apart from the concerted mechanism being WH forbidden, the pathway towards Int2 is obstructed through hydrogen migration, see hydrogen in Fig. 3f. Further generalization to acenes in Table S1 confirms that the reaction of rPAMY with acenes is a type-I HOMO-controlled [3 + 2] cycloaddition⁴⁸ since rPAMY is the electron donor, in line with suggested mechanisms for high-temperature on-surface and in-solution rPAMY dimerization³⁰ and a recently reported heterocycloaddition, the polymerization of cyano-rPAMY⁷⁶ to be further explored below. Classifying forbidden and allowed reaction pathways according to WH rules, offers qualitative criteria for the design of reaction pathways⁷⁷, yet a formal, topological classification could qualitative convey the symmetries and obstructions involved in cycloadditions.

A symmetry forbidden WH pathway can be defined as orbitals crossing, and this crossing or obstruction topologically classified by a non-zero change of topological invariants. The topological invariants classify the discontinuities between eigenvector spaces of reaction matrices (see SI Fig. S1 block diagonalization Hückel reaction in Fig. 4 and topological classification). Mirror-symmetric (i.e. mirror symmetry-enforced) Hückel reaction models for the reaction between rPAMY and hydrocarbons can be constructed as depicted in Fig. 4. As an extended formal framework for WH rules, topological classification models can handle pericyclic and radical cycloadditions^{78, 79, 80} and are highly useful for visualizing plausible reaction pathways with enforced reaction symmetry (mirror plane depicted in Fig. 4a). Compared with classic WH diagrams, this model grants explicit access to the quantitative exploration of concerted cycloadditions which conserve the matrix symmetry by means of tunable bonding strengths. The model could be extended, in principle, to biradical cases^{38, 39} and complex geometrical transformations of molecules, provided certain symmetries are included.

In a Hückel reaction, we construct a general 6 × 6 or 8 × 8 Hückel matrix of the four-atom [3 + 2] or [3 + 4] representation of the reaction between the p orbitals of a rPAMY fragment and butadiene or benzene in Fig. 4a, b or 4c-e, respectively. Figure 4e shows 8 × 8 Hückel matrix for the forbidden [3 + 4] R3-like cycloaddition. It shows how to the key quantifying reaction coordinate t in the Hückel reaction model is inversely related to the distance between the reactants t = 1/d and crossings are identified through discontinuities in the frontier orbitals and their symmetries. Here, we assume that the valence electrons of the nitrogen are bonded to the carbons with strength a, and the onsite energy p1 (p1*) differs from p2 due to the heteroatom effect. To enforce symmetry and account for both p electrons of nitrogen, we consider a virtual sp² nitrogen where the lone pair occupies a degenerate pair of p_z and p_z* orbitals, thereby virtually increasing the order of the cycloaddition from a [3 + n] ring to a [4 + n] ring. The two reactants interact by a single variable parameter t < 0 with |t| as the reaction coordinate. Forbidden pathways in the model indicated by crossings of molecular orbitals that are \(\:\mathbb{Z}\)-classified by the topological invariant \(\:C\left(t\right)={N}_{+}\left(t\right)-{N}_{-}\left(t\right)\) (see Fig. S2 and previous section). The topological analysis of the frontier orbital evolution in Fig. 4b, d (see details in Fig. S2) shows that the diradicaloid reaction is allowed with benzene (\(\:\varDelta\:C=0\)), but forbidden with the 1,4-positions of butadiene (\(\:\varDelta\:C=2\)). Fig. S4, S5 provides details of how to obtain the parameters by fitting the Hückel-like parameters with DFT orbitals. The tight-binding Hückel reaction R3-like pathway is extended with DFT calculations in Fig. 4f, g. The DFT reaction pathway is only approximately forbidden, as strict eigenstate crossings seldom occur beyond tight-binding models. In such cases, Green function formalism can be employed to classify topological crossings in highly correlated reaction pathways^{81, 82}. In summary, cycloaddition WH reaction matrix models help formalize WH rules and vastly extend the scope of the engineering of adiabatically forbidden or allowed radicaloid reaction pathways.

We studied the on-surface and solid-state reaction of PAMY with pentacene from a Woodward-Hoffmann topological classification point of view, and computationally identified pathway R1 as most plausible. Pathway R1 entails a Woodward-Hoffmann topologically allowed, highly endothermic, de-aromatization of pentacene and subsequent dehydrogenation yielding a novel internally N-containing polycyclic aromatic P1 on Ag(100) and in the solid-state. In addition, we studied a plausible barrierless pathway R2, with pre-dehydrogenated pentacene, opening up avenues for the design of more efficient reaction pathways with PAMY. A more reactive pathway R3, plausible in the solid-state, is rationalized as Woodward-Hoffmann forbidden from frontier orbital analysis and topologically Woodward-Hoffmann forbidden in a symmetry-enforced tight-binding, Hückel reaction, model. Topological Woodward-Hoffmann models offer a pedagogic entry to the analytical study of mathematically-defined reaction pathways and radicaloid cycloadditions, and pave the road for the engineering of solid-state or on-surface AB-type cycloaddition polymerization and related nanographenes; building on three levels of interdisciplinarity common in quantum matter design: Topological classification of analytical models, verification or parameterization with quantum chemistry, and experimental realization.

Experimental

The precursor (DBAP molecule) was characterized by NMR-spectroscopy in d₂-dichloromethane (SI). The exact molecular weight of DBAP and pentacene additives was detected by high resolution matrix-assisted laser desorption/ionization time of flight (HR-MALDI-TOF) mass spectrometry (MS, see Fig. S12).

For STM characterization, all samples were prepared in a custom-designed UHV chamber with a base pressure below 2.0 × 10 ^− 10 mbar. The Ag substrate was cleaned by repeated cycles of argon ion sputtering (800 V, 4.5 mA, 15 min) and annealing (flash heating to 450°C). DBAP and pentacene were deposited on the Ag(100) substrate using the organic molecular beam epitaxy (OMBE) method. The quartz crucibles were held at 300°C and 180°C, respectively, with a deposition time of 4 min and a pressure remaining below 5.0 × 10 ^− 9 mbar. Subsequently, the sample was transferred to the STM. After cooling down to ~ 20 K, constant current STM measurements were performed using a commercial low temperature STM (CreaTec Fischer & Co. GmbH) with a tungsten tip.

Computational

Broken-symmetry density functional theory (BS-DFT) calculations were performed in gas phase utilizing unrestricted B3LYP functional^{83, 84, 85, 86} with Grimme’s dispersion correction and Becke–Johnson damping [D3(BJ)].^{87, 88} Full geometry optimization and intrinsic reaction coordinate calculations were initially performed using the minimal basis set⁸⁹ and then reoptimized using def2-SVP basis set⁹⁰ in ORCA quantum chemistry package⁹¹. The Intrinsic Bond Orbital (IBO) analysis is a powerful tool for understanding molecular structure and bonding. It localizes molecular orbitals directly from the wavefunction, enabling the interpretation of the electronic structure in chemical systems^{92, 93}. The intrinsic bond orbital (IBO) analysis was done in PySCF⁹⁴ using the wavefunctions obtained in ORCA for singlet and triplet PAMY. The DFT gaps and the reaction energy profile in Fig. S14 were obtained using 6-31G(d) basis set⁹⁵ in Gaussian 09 Software⁹⁶ by varying inter-molecular distance. The inter-molecular distance was varied in the dimer system by shifting both molecules slightly along the perpendicular direction of the molecular planes to avoid the geometry frustration when they are too close.

The slab calculations involving Ag(100) substrate are performed using Vienna Ab-initio Simulation Package⁹⁷ (VASP). The Perdew-Burke-Ernzerhof (PBE) parametrization⁹⁸ of generalized gradient approximation (GGA) is adopted for exchange correlational functions. We considered van der Waals (vdW) corrections via Grimme's D3 method⁸⁷. The energy cutoffs of plane-wave basis are set as 400 eV. A single k-point (Γ) is used for structural optimization and the k-mesh of 3 × 3 × 1 was used for the density of states. The convergence criteria for the electronic self-consistent loop and atomic structural optimization are 10^− 6 eV for electronic energy and 0.02 eV/Å for the atomic force, respectively. The energy profile for detaching one hydrogen atom is calculated in the climb image nudged elastic band (CI-NEB) scheme.

Acknowledgments

This research was financially supported by the EU Graphene Flagship (Graphene Core 3, 881603), the Chinese Academy of Sciences (nos. QYZDBSSW-SLH038, XDB33000000, XDB33030300), National Natural Science Foundation of China (Grant Nos. 11974403, 11974045, 12374172, 62488201), the German Research Foundation (DFG) within the Clusters of Excellence “Center for FiAdvancing Electronics Dresden (cfaed)”, “Matters of Activity”, the DFG-SNSF Research Project (EnhanceTopo, No. 429265950), the K. C. Wong Education Foundation of Chinese Academy of Sciences, the National Key Research and Development Program of China (Grant No. 2020YFA0308800) and the Alexander von Humboldt Foundation. We thank Tilo Lübken (Dresden University of Technology) for NMR measurements, Knud Seufert for help with the STM. We gratefully acknowledge Akimistu Narita, Oliver Dumele and Prince Ravat for critical discussions.

Author contributions

A. M., W.-H. D. and L. M. performed the theoretical analysis. J. L., W. A., J.V. B. and C.-A. P. performed the microscopy measurements and data interpretation. A. M., L. M., W.-H. D., X.-S. D. and J.-T. S. performed and coordinated the calculations. K. L., M. R., X. W., R. B., J. M., A. N., K. M and X. F. performed MS measurements and synthesized the compounds. C.-A. P. designed the research and supervised the project. All authors participated in discussing and editing the manuscript.

J. L., A. M. and W.-H. D. contributed equally to this work.

Competing interests

The authors declare no competing interests.

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Topological classification of cycloadditions occurring on-surface and in the solid-state

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Abstract

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Introduction

Cycloaddition between rPAMY and pentacene: MALDI-MS and STM

Cycloaddition between rPAMY and pentacene: Intrinsic reaction coordinate calculations

Adiabatic vs. nonadiabatic pathways: Topological classification

Summary

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References

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