Mathematical discoveries from program search with large language models.

Large language models (LLMs) have demonstrated tremendous capabilities in solving complex tasks, from quantitative reasoning to understanding natural language. However, LLMs sometimes suffer from confabulations (or hallucinations), which can result in them making plausible but incorrect statements1,2. This hinders the use of current large models in scientific discovery. Here we introduce FunSearch (short for searching in the function space), an evolutionary procedure based on pairing a pretrained LLM with a systematic evaluator. We demonstrate the effectiveness of this approach to surpass the best-known results in important problems, pushing the boundary of existing LLM-based approaches3. Applying FunSearch to a central problem in extremal combinatorics-the cap set problem-we discover new constructions of large cap sets going beyond the best-known ones, both in finite dimensional and asymptotic cases. This shows that it is possible to make discoveries for established open problems using LLMs. We showcase the generality of FunSearch by applying it to an algorithmic problem, online bin packing, finding new heuristics that improve on widely used baselines. In contrast to most computer search approaches, FunSearch searches for programs that describe how to solve a problem, rather than what the solution is. Beyond being an effective and scalable strategy, discovered programs tend to be more interpretable than raw solutions, enabling feedback loops between domain experts and FunSearch, and the deployment of such programs in real-world applications.

Discovering faster matrix multiplication algorithms with reinforcement learning.

Improving the efficiency of algorithms for fundamental computations can have a widespread impact, as it can affect the overall speed of a large amount of computations. Matrix multiplication is one such primitive task, occurring in many systems-from neural networks to scientific computing routines. The automatic discovery of algorithms using machine learning offers the prospect of reaching beyond human intuition and outperforming the current best human-designed algorithms. However, automating the algorithm discovery procedure is intricate, as the space of possible algorithms is enormous. Here we report a deep reinforcement learning approach based on AlphaZero1 for discovering efficient and provably correct algorithms for the multiplication of arbitrary matrices. Our agent, AlphaTensor, is trained to play a single-player game where the objective is finding tensor decompositions within a finite factor space. AlphaTensor discovered algorithms that outperform the state-of-the-art complexity for many matrix sizes. Particularly relevant is the case of 4 × 4 matrices in a finite field, where AlphaTensor's algorithm improves on Strassen's two-level algorithm for the first time, to our knowledge, since its discovery 50 years ago2. We further showcase the flexibility of AlphaTensor through different use-cases: algorithms with state-of-the-art complexity for structured matrix multiplication and improved practical efficiency by optimizing matrix multiplication for runtime on specific hardware. Our results highlight AlphaTensor's ability to accelerate the process of algorithmic discovery on a range of problems, and to optimize for different criteria.

Chalcogen- and Halogen-Bond-Donating Cyanoborohydrides Provide Imine Hydrogenation.

Sulfonium, selenonium, telluronium, and iodonium cyanoborohydrides have been synthesized, isolated, and fully characterized by various methods, including single-crystal X-ray diffraction (XRD) analysis. The quantum theory of atoms in molecules' analysis based on the XRD data indicated that the hydride···σ-hole short contacts observed in the crystal structures of each compound have a purely noncovalent nature. The telluronium and iodonium cyanoborohydrides provide a significantly higher rate of the model reaction of imine hydrogenation compared with sodium and tetrabutylammonium cyanoborohydrides. Based on the NMR and high-resolution electrospray ionization mass spectrometry data indicating that the reaction progress is accompanied by the cation reduction, a mechanism involving intermediate formation of elusive onium hydrides has been proposed as an alternative to conventional electrophilic activation of the imine moiety by its ligation to the cation's σ-hole.

One-pot Synthesis and Photophysical Studies of Α-cycloamino-substituted 5-aryl-2,2'-bipyridines.

A series of α-cycloamine substituted 2,2'-bipyridines 3ae'-3ce' was obtained via the one-pot approach based on ipso-substitution of a cyano-group in 1,2,4-triazines, followed by aza-Diels-Alder reaction in good yields. Photophysical properties, including fluorosolvatochromism, were studied for 3ae'-3ce' and were compared with α-unsubstituted 2,2'-bipyridines. In addition, dipole moments differences in ground and excited states were calculated by both Lippert-Mataga equation and DFT studies and were compared to each other. The correlation between the size of cycloamine unit and the dipole moments differences value (based on Lippert-Mataga equation) was observed. In addition charge transfer indices (DCT, Λ, H and t) were calculated to demonstrate influence of molecular structure on the intramolecular charge transfer degree.

New Fluorescent Dye for the Detection of Zn2+ in Living Cells and Fixed Sections of the Rat Pancreas.

We report the synthesis and characterization of a new 4-methoxyphenyl-2,2'-bipyridine-based ligand, such as 12, bearing dipicolylaminomethyl core as a receptor unit, as a probe for the fluorescence "turn-on" detection of Zn2+. Thus, in the presence of Zn2+ the probe 12 exhibited a fluorescence enhancement with a Stokes shift of ~ 180 nm and photoluminescence quantum yields value of ~ 1.0. In addition, 12 exhibited higher binding constant for Zn2+ (~ 2 × 105 M-1) with the LOD reaching the nanomolar level (~ 0.1 × 10-9 M) compare to the previously reported probe 1. The stoichiometry and structure of the [Zn(12)]2+ and [Zn(1)]2+ complexes were supported by XRD analysis, DFT calculations and 1H NMR experiments. It was postulated that, as a result of binding of Zn2+, the sample exhibited a bright "on" state via the PET-ICT processes. Molecular docking studies and confocal fluorescence microscopy experiments demonstrated that the probe 12 could be used for the fluorescence detection of Zn2+ not only in artificially enriched with zinc salts live cells, but also in fixed tissues with cations are in a bound state. The high binding constant of compound 12 to Zn2+ cation allows it to be used for the accurate localization of pancreatic beta cells (islets of Langerhans).

Iridium(III)-Incorporating Self-Healing Polysiloxanes as Materials for Light-Emitting Oxygen Sensors.

Polymer-metal complexes (PMCs) based on poly(2,2'-bipyridine-4,4'-dicarboxamide-co-polydimethylsiloxanes) with cyclometalated di(2-phenylpyridinato-C2,N')iridium(III) fragments and cross-linked by Zn2+ (Zn[Ir]-BipyPDMSs) or Ir3+ (Ir[Ir]-BipyPDMSs) represent flexible, stretchable, phosphorescent, and self-healing molecular oxygen sensors. PMCs provide strong phosphorescence at λem = 595-605 nm. Zn[Ir]-BipyPDMS with PDMS chain length of Mn = 5000 has the highest quantum yield of 9.3% and is a molecular oxygen sensor at different O2 concentrations (0-100 vol%) compared to Ir[Ir]-BipyPDMSs. A Stern-Volmer constant is determined for Zn[Ir]-BipyPDMS as KSV = 0.014%-1, which is similar to the reported oxygen-sensitive iridium(III) complexes. All synthesized PMCs exhibit high elongation at break (up to 1100%) and self-healing efficiency (up to 99%).

Halogen Bond-Assisted Supramolecular Dimerization of Pyridinium-Fused 1,2,4-Selenadiazoles via Four-Center Se2N2 Chalcogen Bonding.

The synthesis and structural characterization of α-haloalkyl-substituted pyridinium-fused 1,2,4-selenadiazoles with various counterions is reported herein, demonstrating a strategy for directed supramolecular dimerization in the solid state. The compounds were obtained through a recently discovered 1,3-dipolar cycloaddition reaction between nitriles and bifunctional 2-pyridylselenyl reagents, and their structures were confirmed by the X-ray crystallography. α-Haloalkyl-substituted pyridinium-fused 1,2,4-selenadiazoles exclusively formed supramolecular dimers via four-center Se···N chalcogen bonding, supported by additional halogen bonding involving α-haloalkyl substituents. The introduction of halogens at the α-position of the substituent R in the selenadiazole core proved effective in promoting supramolecular dimerization, which was unaffected by variation of counterions. Additionally, the impact of cocrystallization with a classical halogen bond donor C6F3I3 on the supramolecular assembly was investigated. Non-covalent interactions were studied using density functional theory calculations and topological analysis of the electron density distribution, which indicated that all ChB, XB and HB interactions are purely non-covalent and attractive in nature. This study underscores the potential of halogen and chalcogen bonding in directing the self-assembly of functional supramolecular materials employing 1,2,4-selenadiazoles derived from recently discovered cycloaddition between nitriles and bifunctional 2-pyridylselenyl reagents.

Reaction of Pyrrolobenzothiazines with Schiff Bases and Carbodiimides: Approach to Angular 6/5/5/5-Tetracyclic Spiroheterocycles.

1H-Pyrrole-2,3-diones, fused at [e]-side with a heterocycle, are suitable platforms for the synthesis of various angular polycyclic alkaloid-like spiroheterocycles. Recently discovered sulfur-containing [e]-fused 1H-pyrrole-2,3-diones (aroylpyrrolobenzothiazinetriones) tend to exhibit unusual reactivity. Based on these peculiar representatives of [e]-fused 1H-pyrrole-2,3-diones, we have developed an approach to an unprecedented 6/5/5/5-tetracyclic alkaloid-like spiroheterocyclic system of benzo[d]pyrrolo[3',4':2,3]pyrrolo[2,1-b]thiazole via their reaction with Schiff bases and carbodiimides. The experimental results have been supplemented with DFT computational studies. The synthesized alkaloid-like 6/5/5/5-tetracyclic compounds have been tested for their biotechnological potential as growth stimulants in the green algae Chlorella vulgaris.

Memristive Effect in Ti3 C2 Tx (MXene) Polyelectrolyte Multilayers.

The emerging novel class of two-dimensional materials - MХenes - have attracted significant research attention. However, there are only few reports on using the most prominent member of the MXene family, Ti3 C2 Tx , as an active material for memristive devices within a polyelectrolyte matrix and its deposition on inert electrodes like ITO and Pt. In this study, we systematically investigate Ti3 C2 Tx MXenes synthesized with two classical delamination agents, such as lithium chloride and tetramethylammonium hydroxide, to identify the most suitable candidate for memristive device applications. The characteristics of memristors based on the hybrid structures consisting of MXene-polyelectrolyte multilayers, specifically polyethyleneimine (PEI) and poly(sodium 4-styrenesulfonate) (PSS) are explored. The PEI(MXene)/PSS memristor exhibits a voltage threshold (VSET/RESET ) range of 1.5-2.0 V, enabling the transition from a high-resistive state (HRS) to a low-resistive state (LRS), along with a significant current switching ratio of approximately two orders of magnitude. The observed VSET/RESET difference of approximately 4 V is further supported by density functional theory (DFT) calculated redox potential. These findings underscore the potential of polyelectrolyte-based memristors, such as the in PEI-Ti3 C2 Tx -PSS system, in facilitating the development of highly functional, self-assembled memristive devices with diverse applications.

Xenon Derivatives as Aerogen Bond-Donating Catalysts for Organic Transformations: A Theoretical Study on the Metaphorical "Spherical Cow in a Vacuum" Provides Insights into Noncovalent Organocatalysis.

Computations indicate that cationic and noncharged xenon derivatives should exhibit higher catalytic activity than their iodine-based noncovalent organocatalytic congeners. Perfluorophenyl xenonium(II) is expected to demonstrate the best balance between catalytic activity and chemical stability for use in organocatalysis. Comparing its catalytic activity with that of isoelectronic perfluoroiodobenzene indicates that the high catalytic activity of cationic noncovalent organocatalysts is predominantly attributed to the electrostatic interactions with the reaction substrates, which cause the polarization of ligated species during the reaction progress. In contrast, the electron transfer and covalent contributions to the bonding between the catalyst and substrate have negligible effects. The dominant effect of electrostatic interactions results in a strong negative correlation between the calculated Gibbs free energies of activation for the modeled reactions and the highest potentials of the σ-holes on the central atoms of the catalysts. No such correlation is observed for noncharged catalysts.

Substrate-Controlled Three-Component Synthesis of Diverse Fused Heterocycles.

A chemoselective strategy toward a variety of fused heterocyclic scaffolds relying on a three-component condensation of heterocyclic ketene aminals (HKAs) or corresponding thioaminals with aryl glyoxals and cyclic 1,3-dicarbonyl compounds has been developed and explored. Depending on the applied combination of substrates, the strategy can be tuned to provide straightforward access to imidazo[1,2-a]quinoline, pyrrolo[1,2-a]imidazole, and pyrrolo[2,1-b]thiazole frameworks.

Noncovalent Dualism in Perylene-Diimide-Based Keggin Anion Complexes: Theoretical and Experimental studies.

We report the synthesis and comprehensive characterization of organic-inorganic hybrid salts formed by bis-cationic N,N'-bis(2-(trimethylammonium)ethylene)perylene-3,4,9,10-tetracarboxylic acid bisimide (PTCD2+) and Keggin-type [XW12O40]n- (X = Si, n = 4; X = P, n = 3) polyoxometalates. (PTCD)3[PW12O40]2·3DMSO·2H2O (2) and (PTCD)2[SiW12O40]·DMSO·2H2O (3) were structurally characterized by single crystal X-ray diffraction. The cations in both structures exhibited infinite chainlike arrangements through π-π interactions, contrasting with the previously reported cation-anion stacking observed in naphthalene diimide derivatives. A detailed theoretical study employing topological analysis of the electron density distribution within the quantum theory of atoms in molecules approach provided further insights into this structural dualism. Atomic force microscopy analyses revealed the formation of self-assembled supramolecular structures on graphite from molecular monolayers (3 nm of thick) to submicrometer aggregates for 2. Hyperspectral Raman spectroscopy imaging revealed that such heterostructures are likely formed by an enhanced π-π interactions. Both complexes demonstrated interesting electrochemical behavior, photoluminescence and X-ray-induced luminescence. Electron spin resonance analysis confirmed charge separation in both compounds, with enhanced efficiency observed in compound 2. Our findings of these perylene-based organic-inorganic hybrid salts offer the potential for their application in optoelectronic devices and functional materials.

Dimensionality Mediated Highly Repeatable and Fast Transformation of Coordination Polymer Single Crystals for All-Optical Data Processing.

A family of coordination polymers (CPs) based on dynamic structural elements are of great fundamental and commercial interest addressing modern problems in controlled molecular separation, catalysis, and even data processing. Herein, the endurance and fast structural dynamics of such materials at ambient conditions are still a fundamental challenge. Here, we report on the design of a series of Cu-based CPs [Cu(bImB)Cl2] and [Cu(bImB)2Cl2] with flexible ligand bImB (1,4-bis(imidazol-1-yl)butane) packed into one- and two-dimensional (1D, 2D) structures demonstrating dimensionality mediated flexibility and reversible structural transformations. Using the laser pulses as a fast source of activation energy, we initiate CP heating followed by anisotropic thermal expansion and 0.2-0.8% volume changes with the record transformation rates from 2220 to 1640 s-1 for 1D and 2D CPs, respectively. The endurance over 103 cycles of structural transformations, achieved for the CPs at ambient conditions, allows demonstrating optical fiber integrated all-optical data processing.

Theoretical Study of Charge Mobility in Crystal Porphine and a Computer Design of a Porphine-Based Semiconductive Discotic Liquid Mesophase.

Organic semiconductors are the focus of numerous studies; they are used in electronic devices. Modern research involves the production of neuromorphic organic materials, including those based on liquid crystal materials. The purpose of this work involves the theoretical modeling of molecules (the "core with branches" type) to construct a discotic mesophase capable of performing the functions of a neuromorphic material. For this purpose, the conductivity of crystal porphine, which can act as the nucleus of a molecule of the "core with branches" type, was investigated. The Marcus theory charge mobility values for the hole and electron were 0.148 and 0.088 cm2/V·s, respectively (the MOO method for calculating transfer integrals), and 0.561 and 0.160 cm2/V·s (DIPRO method). Based on TD-HF (HF-3c level of theory) calculations, possible structures of molecules for the formation of a discotic mesophase are proposed.

Dual PTP1B/TC-PTP Inhibitors: Biological Evaluation of 3-(Hydroxymethyl)cinnoline-4(1H)-Ones.

Dual inhibitors of protein phosphotyrosine phosphatase 1B (PTP1B)/T-cell protein phosphotyrosine phosphatase (TC-PTP) based on the 3-(hydroxymethyl)-4-oxo-1,4-dihydrocinnoline scaffold have been identified. Their dual affinity to both enzymes has been thoroughly corroborated by in silico modeling experiments. The compounds have been profiled in vivo for their effects on body weight and food intake in obese rats. Likewise, the effects of the compounds on glucose tolerance, insulin resistance, as well as insulin and leptin levels, have been evaluated. In addition, the effects on PTP1B, TC-PTP, and Src homology region 2 domain-containing phosphatase-1 (SHP1), as well as the insulin and leptin receptors gene expressions, have been assessed. In obese male Wistar rats, a five-day administration of all studied compounds led to a decrease in body weight and food intake, improved glucose tolerance, attenuated hyperinsulinemia, hyperleptinemia and insulin resistance, and also compensatory increased expression of the PTP1B and TC-PTP genes in the liver. The highest activity was demonstrated by 6-Chloro-3-(hydroxymethyl)cinnolin-4(1H)-one (compound 3) and 6-Bromo-3-(hydroxymethyl)cinnolin-4(1H)-one (compound 4) with mixed PTP1B/TC-PTP inhibitory activity. Taken together, these data shed light on the pharmacological implications of PTP1B/TC-PTP dual inhibition, and on the promise of using mixed PTP1B/TC-PTP inhibitors to correct metabolic disorders.

Polyaromatic Hydrocarbon (PAH)-Based Aza-POPOPs: Synthesis, Photophysical Studies, and Nitroanalyte Sensing Abilities.

1,4-Bis(5-phenyl-2-oxazolyl)benzene (POPOP) is a common scintillation fluorescent laser dye. In this manuscript, the synthesis of 2-Ar-5-(4-(4-Ar'-1H-1,2,3-triazol-1-yl)phenyl)-1,3,4-oxadiazoles (Ar, Ar' = Ph, naphtalenyl-2, pyrenyl-1, triphenilenyl-2), as PAH-based aza-analogues of POPOP, by means of Cu-catalyzed click reaction between 2-(4-azidophenyl)-5-Ar-1,3,4-oxadiazole and terminal ethynyl-substituted PAHs is reported. An investigation of the photophysical properties of the obtained products was carried out, and their sensory response to nitroanalytes was evaluated. In the case of pyrenyl-1-substituted aza-POPOP, dramatic fluorescence quenching by nitroanalytes was observed.

Iridium Complexes with BIAN-Type Ligands: Synthesis, Structure and Redox Chemistry.

A series of iridium complexes with bis(diisopropylphenyl)iminoacenaphtene (dpp-bian) ligands, [Ir(cod)(dpp-bian)Cl] (1), [Ir(cod)(NO)(dpp-bian)](BF4)2 (2) and [Ir(cod)(dpp-bian)](BF4) (3), were prepared and characterized by spectroscopic techniques, elemental analysis, X-ray diffraction analysis and cyclic voltammetry (CV). The structures of 1-3 feature a square planar backbone consisting of two C = C π-bonds of 1,5-cyclooctadiene (cod) and two nitrogen atoms of dpp-bian supplemented with a chloride ion (for 1) or a NO group (for 2) to complete a square-pyramidal geometry. In the nitrosyl complex 2, the Ir-N-O group has a bent geometry (the angle is 125°). The CV data for 1 and 3 show two reversible waves between 0 and -1.6 V (vs. Ag/AgCl). Reversible oxidation was also found at E1/2 = 0.60 V for 1. Magnetochemical measurements for 2 in a range from 1.77 to 300 K revealed an increase in the magnetic moment with increasing temperature up to 1.2 µB (at 300 K). Nitrosyl complex 2 is unstable in solution and loses its NO group to yield [Ir(cod)(dpp-bian)](BF4) (3). A paramagnetic complex, [Ir(cod)(dpp-bian)](BF4)2 (4), was also detected in the solution of 2 as a result of its decomposition. The EPR spectrum of 4 in CH2Cl2 is described by the spin Hamiltonian H = gßHS with S = 1/2 and gxx = gyy = 2.393 and gzz = 1.88, which are characteristic of the low-spin 5d7-Ir(II) state. DFT calculations were carried out in order to rationalize the experimental results.

Approach to Pyrido[2,1-b][1,3]benzothiazol-1-ones via In Situ Generation of Acyl(1,3-benzothiazol-2-yl)ketenes by Thermolysis of Pyrrolo[2,1-c][1,4]benzothiazine-1,2,4-triones.

Acyl(imidoyl)ketenes are highly reactive heterocumulenes that enable diversity-oriented synthesis of various drug-like heterocycles. Such ketenes, bearing heterocyclic substituents, afford angularly fused pyridin-2(1H)-ones in their [4+2]-cyclodimerization reactions. We have utilized this property for the development of a new synthetic approach to pharmaceutically interesting pyrido[2,1-b][1,3]benzothiazol-1-ones via the [4+2]-cyclodimerization of acyl(1,3-benzothiazol-2-yl)ketenes generated in situ. The thermal behaviors of 3-aroylpyrrolo[2,1-c][1,4]benzothiazine-1,2,4-triones and 3-benzoylpyrrolo[2,1-b][1,3]benzothiazole-1,2-dione (two new types of [e]-fused 1H-pyrrole-2,3-diones reported by us recently) have been studied by thermal analysis and HPLC to elucidate their capability to be a source of acyl(1,3-benzothiazol-2-yl)ketenes. As a result, we have found that only 3-aroylpyrrolo[2,1-c][1,4]benzothiazine-1,2,4-triones are suitable for this. The experimental results are supplemented with computational studies that demonstrate that thermolysis of 3-aroylpyrrolo[2,1-c][1,4]benzothiazine-1,2,4-triones proceeds through an unprecedented cascade of two thermal decarbonylations. Based on these studies, we discovered a novel mode of thermal transformation of [e]-fused 1H-pyrrole-2,3-diones and developed a new pot, atom, and step economic synthetic approach to pyrido[2,1-b][1,3]benzothiazol-1-ones. The synthesized drug-like pyrido[2,1-b][1,3]benzothiazol-1-ones are of interest to pharmaceutics, since their close analogs show significant antiviral activity.

Synthesis of Disubstituted Carboxonium Derivatives of Closo-Decaborate Anion [2,6-B10H8O2CC6H5]-: Theoretical and Experimental Study.

A comprehensive study focused on the preparation of disubstituted carboxonium derivatives of closo-decaborate anion [2,6-B10H8O2CC6H5]- was carried out. The proposed synthesis of the target product was based on the interaction between the anion [B10H11]- and benzoic acid C6H5COOH. It was shown that the formation of this product proceeds stepwise through the formation of a mono-substituted product [B10H9OC(OH)C6H5]-. In addition, an alternative one-step approach for obtaining the target derivative is postulated. The structure of tetrabutylammonium salts of carboxonium derivative ((C4H9)4N)[2,6-B10H8O2CC6H5] was established with the help of X-ray structure analysis. The reaction pathway for the formation of [2,6-B10H8O2CC6H5]- was investigated with the help of density functional theory (DFT) calculations. This process has an electrophile induced nucleophilic substitution (EINS) mechanism, and intermediate anionic species play a key role. Such intermediates have a structure in which one boron atom coordinates two hydrogen atoms. The regioselectivity for the process of formation for the 2,6-isomer was also proved by theoretical calculations. Generally, in the experimental part, the simple and available approach for producing disubstituted carboxonium derivative was introduced, and the mechanism of this process was investigated with the help of theoretical calculations. The proposed approach can be applicable for the preparation of a wide range of disubstituted derivatives of closo-borate anions.

Novel Route to Cationic Palladium(II)-Cyclopentadienyl Complexes Containing Phosphine Ligands and Their Catalytic Activities.

The Pd(II) complexes [Pd(Cp)(L)n]m[BF4]m were synthesized via the reaction of cationic acetylacetonate complexes with cyclopentadiene in the presence of BF3∙OEt2 (n = 2, m = 1: L = PPh3 (1), P(p-Tol)3, tris(ortho-methoxyphenyl)phosphine (TOMPP), tri-2-furylphosphine, tri-2-thienylphosphine; n = 1, m = 1: L = dppf, dppp (2), dppb (3), 1,5-bis(diphenylphosphino)pentane; n = 1, m = 2 or 3: 1,6-bis(diphenylphosphino)hexane). Complexes 1-3 were characterized using X-ray diffractometry. The inspection of the crystal structures of the complexes enabled the recognition of (Cp-)⋯(Ph-group) and (Cp-)⋯(CH2-group) interactions, which are of C-H…π nature. The presence of these interactions was confirmed theoretically via DFT calculations using QTAIM analysis. The intermolecular interactions in the X-ray structures are non-covalent in origin with an estimated energy of 0.3-1.6 kcal/mol. The cationic palladium catalyst precursors with monophosphines were found to be active catalysts for the telomerization of 1,3-butadiene with methanol (TON up to 2.4∙104 mol 1,3-butadiene per mol Pd with chemoselectivity of 82%). Complex [Pd(Cp)(TOMPP)2]BF4 was found to be an efficient catalyst for the polymerization of phenylacetylene (PA) (catalyst activities up to 8.9 × 103 gPA·(molPd·h)-1 were observed).