Analog quantum simulation of chemical dynamics

Ultrafast chemical reactions are difficult to simulate because they involve entangled, many-body wavefunctions whose computational complexity grows rapidly with molecular size. In photochemistry, the breakdown of the Born–Oppenheimer approximation further complicates the problem by entangling nuclear and electronic degrees of freedom. Here, we show that analog quantum simulators can efficiently simulate molecular dynamics using commonly available bosonic modes to represent molecular vibrations. Our approach can be implemented in any device with a qudit controllably coupled to bosonic oscillators and with quantum hardware resources that scale linearly with molecular size, and offers significant resource savings compared to digital quantum simulation algorithms. Advantages of our approach include a time resolution orders of magnitude better than ultrafast spectroscopy, the ability to simulate large molecules with limited hardware using a Suzuki–Trotter expansion, and the ability to implement realistic system-bath interactions with only one additional interaction per mode. Our approach can be implemented with current technology; e.g., the conical intersection in pyrazine can be simulated using a single trapped ion. Therefore, we expect our method will enable classically intractable chemical dynamics simulations in the near term.

Dynamics governing ultrafast chemical reactions can be efficiently simulated using analog quantum simulators composed of a coupled system of qudits and bosonic modes.     

A heterometallic [LnLn′Ln] lanthanide complex as a qubit with embedded quantum error correction

We show that a [Er–Ce–Er] molecular trinuclear coordination compound is a promising platform to implement the three-qubit quantum error correction code protecting against pure dephasing, the most important error in magnetic molecules. We characterize it by preparing the [Lu–Ce–Lu] and [Er–La–Er] analogues, which contain only one of the two types of qubit, and by combining magnetometry, low-temperature specific heat and electron paramagnetic resonance measurements on both the elementary constituents and the trimer. Using the resulting parameters, we demonstrate by numerical simulations that the proposed molecular device can efficiently suppress pure dephasing of the spin qubits.

We show that a [Er–Ce–Er] molecular trinuclear coordination compound is a promising platform to implement the three-qubit quantum error correction code protecting against pure dephasing, the most important error in magnetic molecules.     

Broad-band spectroscopy of a vanadyl porphyrin: a model electronuclear spin qudit

We explore how to encode more than a qubit in vanadyl porphyrin molecules hosting a S = 1/2 electronic spin coupled to a I = 7/2 nuclear spin. The spin Hamiltonian and its parameters, as well as the spin dynamics, have been determined via a combination of electron paramagnetic resonance, heat capacity, magnetization and on-chip magnetic spectroscopy experiments performed on single crystals. We find low temperature spin coherence times of micro-seconds and spin relaxation times longer than a second. For sufficiently strong magnetic fields (B > 0.1 T, corresponding to resonance frequencies of 9–10 GHz) these properties make vanadyl porphyrin molecules suitable qubit realizations. The presence of multiple equispaced nuclear spin levels then merely provides 8 alternatives to define the ‘1’ and ‘0’ basis states. For lower magnetic fields (B < 0.1 T), and lower frequencies (<2 GHz), we find spectroscopic signatures of a sizeable electronuclear entanglement. This effect generates a larger set of allowed transitions between different electronuclear spin states and removes their degeneracies. Under these conditions, we show that each molecule fulfills the conditions to act as a universal 4-qubit processor or, equivalently, as a d = 16 qudit. These findings widen the catalogue of chemically designed systems able to implement non-trivial quantum functionalities, such as quantum simulations and, especially, quantum error correction at the molecular level.

We show that a sizeable electronuclear entanglement of the S = 1/2 and I = 7/2 spins of a vanadyl porphyrin provides the conditions to act as a universal 4-qubit processor, and thus implement quantum error correction at the molecular level.     

Towards multistate multimode landscapes in singlet fission of pentacene: the dual role of charge-transfer states

Singlet fission duplicates triplet excitons for improving light harvesting efficiency. The presence of the interaction between electronic and nuclear degrees of freedom complicates the interpretation of correlated triplet pairs. We report a quantum chemistry study on the significance and subtleties of multistate and multimode pathways in forming triplet pair states of the pentacene dimer through a six-state vibronic-coupling Hamiltonian derived from many-electron adiabatic wavefunctions of an ab initio density matrix renormalization group. The resulting spin values of the singlet manifolds on each pentacene center are computed, and the varying spin nature can be distinguished clearly with respect to dimer stacking and vibronic progression. Our monomer spin assignments reveal the coexistence of both lower-lying weak and higher-lying strong charge transfer states which interact vibronically with the triplet pair state, providing important implications for its generation and separation occurring in vibronic regions. This work conveys the importance of the many-electron process requiring close low-lying singlet manifolds to determine the subtle fission details, and represents an important step for understanding vibronically resolved spin states and conversions underlying efficient singlet fission.

Singlet fission in pentacene necessitates the vibronic progression of weak and strong charge-transfer states with correlated triplet pairs.     

Targeting molecular quantum memory with embedded error correction

The implementation of a quantum computer requires both to protect information from environmental noise and to implement quantum operations efficiently. Achieving this by a fully fault-tolerant platform, in which quantum gates are implemented within quantum-error corrected units, poses stringent requirements on the coherence and control of such hardware. A more feasible architecture could consist of connected memories, that support error-correction by enhancing coherence, and processing units, that ensure fast manipulations. We present here a supramolecular {Cr₇Ni}–Cu system which could form the elementary unit of this platform, where the electronic spin 1/2 of {Cr₇Ni} provides the processor and the naturally isolated nuclear spin 3/2 of the Cu ion is used to encode a logical unit with embedded quantum error-correction. We demonstrate by realistic simulations that microwave pulses allow us to rapidly implement gates on the processor and to swap information between the processor and the quantum memory. By combining the storage into the Cu nuclear spin with quantum error correction, information can be protected for times much longer than the processor coherence.

The implementation of a quantum computer requires protecting of information from noise and the ability to perform quantum gates. We present a molecular architecture providing both these ingredients, via an electronic spin 1/2 processor and a nuclear spin 3/2 memory.     

Chemical tuning of spin clock transitions in molecular monomers based on nuclear spin-free Ni(ii)

We report the existence of a sizeable quantum tunnelling splitting between the two lowest electronic spin levels of mononuclear Ni complexes. The level anti-crossing, or magnetic “clock transition”, associated with this gap has been directly monitored by heat capacity experiments. The comparison of these results with those obtained for a Co derivative, for which tunnelling is forbidden by symmetry, shows that the clock transition leads to an effective suppression of intermolecular spin–spin interactions. In addition, we show that the quantum tunnelling splitting admits a chemical tuning via the modification of the ligand shell that determines the crystal field and the magnetic anisotropy. These properties are crucial to realize model spin qubits that combine the necessary resilience against decoherence, a proper interfacing with other qubits and with the control circuitry and the ability to initialize them by cooling.

We have directly monitored spin level anti-crossings, or “clock transitions”, in Ni(ii) molecular monomers and shown that the quantum tunnelling gap admits a chemical tuning.     

Broadband measurement of true transverse relaxation rates in systems with coupled protons: application to the study of conformational exchange

Accurate measurement of transverse relaxation rates in coupled spin systems is important in the study of molecular dynamics, but is severely complicated by the signal modulations caused by scalar couplings in spin echo experiments. The most widely used experiments for measuring transverse relaxation in coupled systems, CPMG and PROJECT, can suppress such modulations, but they also both suppress some relaxation contributions, and average relaxation rates between coupled spins. Here we introduce a new experiment which for the first time allows accurate broadband measurement of transverse relaxation rates of coupled protons, and hence the determination of exchange rate constants in slow exchange from relaxation measurements. The problems encountered with existing methods are illustrated, and the use of the new method is demonstrated for the classic case of hindered amide rotation and for the more challenging problem of exchange between helical enantiomers of a gold(i) complex.

Existing methods for measuring transverse relaxation give incorrect results in coupled spin systems. Measuring true relaxation rates extends their utility.     

A rare earth metallocene containing a 2,2′-azopyridyl radical anion

Introducing spin onto organic ligands that are coordinated to rare earth metal ions allows direct exchange with metal spin centres. This is particularly relevant for the deeply buried 4f-orbitals of the lanthanide ions that can give rise to unparalleled magnetic properties. For efficacy of exchange coupling, the donor atoms of the radical ligand require high-spin density. Such molecules are extremely rare owing to their reactive nature that renders isolation and purification difficult. Here, we demonstrate that a 2,2′-azopyridyl (abpy) radical (S = 1/2) bound to the rare earth metal yttrium can be realized. This molecule represents the first rare earth metal complex containing an abpy radical and is unambigously characterized by X-ray crystallography, NMR, UV-Vis-NIR, and IR spectroscopy. In addition, the most stable isotope ⁸⁹Y with a natural abundance of 100% and a nuclear spin of ½ allows an in-depth analysis of the yttrium–radical complex via EPR and HYSCORE spectroscopy. Further insight into the electronic ground state of the radical azobispyridine-coordinated metal complex was realized through unrestricted DFT calculations, which suggests that the unpaired spin density of the SOMO is heavily localized on the azo and pyridyl nitrogen atoms. The experimental results are supported by NBO calculations and give a comprehensive picture of the spin density of the azopyridyl ancillary ligand. This unexplored azopyridyl radical anion in heavy element chemistry bears crucial implications for the design of molecule-based magnets particularly comprising anisotropic lanthanide ions.

Unambiguous characterization of the first 2,2′-azobispyridine radical-containing rare earth metal complex through X-ray crystallography, DFT computations, EPR and HYSCORE spectroscopy.     

Charge transport through extended molecular wires with strongly correlated electrons

Electron–electron interactions are at the heart of chemistry and understanding how to control them is crucial for the development of molecular-scale electronic devices. Here, we investigate single-electron tunneling through a redox-active edge-fused porphyrin trimer and demonstrate that its transport behavior is well described by the Hubbard dimer model, providing insights into the role of electron–electron interactions in charge transport. In particular, we empirically determine the molecule''s on-site and inter-site electron–electron repulsion energies, which are in good agreement with density functional calculations, and establish the molecular electronic structure within various oxidation states. The gate-dependent rectification behavior confirms the selection rules and state degeneracies deduced from the Hubbard model. We demonstrate that current flow through the molecule is governed by a non-trivial set of vibrationally coupled electronic transitions between various many-body ground and excited states, and experimentally confirm the importance of electron–electron interactions in single-molecule devices.

Experimental studies of electron transport through an edge-fused porphyrin oligomer in a graphene junction are interpreted within a Hubbard dimer framework.     

Unveiling the complex pattern of intermolecular interactions responsible for the stability of the DNA duplex

Herein, we provide new insights into the intermolecular interactions responsible for the intrinsic stability of the duplex structure of a large portion of human B-DNA by using advanced quantum mechanical methods. Our results indicate that (i) the effect of non-neighboring bases on the inter-strand interaction is negligibly small, (ii) London dispersion effects are essential for the stability of the duplex structure, (iii) the largest contribution to the stability of the duplex structure is the Watson–Crick base pairing – consistent with previous computational investigations, (iv) the effect of stacking between adjacent bases is relatively small but still essential for the duplex structure stability and (v) there are no cooperativity effects between intra-strand stacking and inter-strand base pairing interactions. These results are consistent with atomic force microscope measurements and provide the first theoretical validation of nearest neighbor approaches for predicting thermodynamic data of arbitrary DNA sequences.

Advanced electronic structure methods provide a new insight into the intermolecular interactions responsible for the intrinsic stability of the duplex structure of human DNA.     

Unraveling differences in aluminyl and carbene coordination chemistry: bonding in gold complexes and reactivity with carbon dioxide

The electronic properties of aluminyl anions have been reported to be strictly related to those of carbenes, which are well-known to be easily tunable via selected structural modifications imposed on their backbone. Since peculiar reactivity of gold-aluminyl complexes towards carbon dioxide has been reported, leading to insertion of CO₂ into the Au–Al bond, in this work the electronic structure and reactivity of Au–Al complexes with different aluminyl scaffolds have been systematically studied and compared to carbene analogues. The analyses reveal that, instead, aluminyls and carbenes display a very different behavior when bound to gold, with the aluminyls forming an electron-sharing and weakly polarized Au–Al bond, which turns out to be poorly modulated by structural modifications of the ligand. The reactivity of gold–aluminyl complexes towards CO₂ shows, both qualitatively and quantitatively, similar reaction mechanisms, reflecting the scarce tunability of their electronic structure and bond nature. This work provides further insights and perspectives on the properties of the aluminyl anions and their behavior as coordination ligands.

Aluminyls and carbenes as coordination ligands, although sharing similar electronic properties, reveal fundamental differences in their tunability, bonding to gold and reactivity of their complexes with carbon dioxide.     

Oxa-spirocycles: synthesis,properties and applications

A general approach to a new generation of spirocyclic molecules – oxa-spirocycles – was developed. The key synthetic step was iodocyclization. More than 150 oxa-spirocyclic compounds were prepared. Incorporation of an oxygen atom into the spirocyclic unit dramatically improved water solubility (by up to 40 times) and lowered lipophilicity. More potent oxa-spirocyclic analogues of antihypertensive drug terazosin were synthesized and studied in vivo.

A general practical approach to a new generation of spirocyclic molecules – oxa-spirocycles – is developed.     

Correction: Cu-catalyzed C–C bond formation of vinylidene cyclopropanes with carbon nucleophiles

Correction for ‘Cu-catalyzed C–C bond formation of vinylidene cyclopropanes with carbon nucleophiles’ by Jichao Chen et al., Chem. Sci., 2019, 10, 10601–10606.

We regret that in the original article the structure of compound 1 in Tables 1–3 was incorrect. The correct structure is given below.The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers.     

Palladium-catalyzed chemoselective direct α-arylation of carbonyl compounds with chloroaryl triflates at the C–Cl site

This study described palladium-catalyzed chemoselective direct α-arylation of carbonyl compounds with chloroaryl triflates in the Ar–Cl bond. The Pd/SelectPhos system showed excellent chemoselectivity toward the Ar–Cl bond in the presence of the Ar–OTf bond with a broad substrate scope and excellent product yields. The electronic and steric hindrance offered by the –PR₂ group of the ligand with the C2-alkyl group was found to be the key factor affecting the reactivity and chemoselectivity of the α-arylation reaction. The chemodivergent approach was also successfully employed in the synthesis of flurbiprofen and its derivatives (e.g., –OMe and –F).

Palladium-catalyzed chemoselective direct α-arylation of carbonyl compounds with chloroaryl triflates in the Ar–Cl bond is reported. The effects of –PR₂ and C2-alkyl groups of the ligands are investigated using experimental and computational methods.     

Accelerated AI development for autonomous materials synthesis in flow

Autonomous robotic experimentation strategies are rapidly rising in use because, without the need for user intervention, they can efficiently and precisely converge onto optimal intrinsic and extrinsic synthesis conditions for a wide range of emerging materials. However, as the material syntheses become more complex, the meta-decisions of artificial intelligence (AI)-guided decision-making algorithms used in autonomous platforms become more important. In this work, a surrogate model is developed using data from over 1000 in-house conducted syntheses of metal halide perovskite quantum dots in a self-driven modular microfluidic material synthesizer. The model is designed to represent the global failure rate, unfeasible regions of the synthesis space, synthesis ground truth, and sampling noise of a real robotic material synthesis system with multiple output parameters (peak emission, emission linewidth, and quantum yield). With this model, over 150 AI-guided decision-making strategies within a single-period horizon reinforcement learning framework are automatically explored across more than 600 000 simulated experiments – the equivalent of 7.5 years of continuous robotic operation and 400 L of reagents – to identify the most effective methods for accelerated materials development with multiple objectives. Specifically, the structure and meta-decisions of an ensemble neural network-based material development strategy are investigated, which offers a favorable technique for intelligently and efficiently navigating a complex material synthesis space with multiple targets. The developed ensemble neural network-based decision-making algorithm enables more efficient material formulation optimization in a no prior information environment than well-established algorithms.

A surrogate model is designed to represent a microfluidic material synthesis system using 1000 automatically conducted experiments. With this model, over 600 000 experiments are simulated to optimize an AI-guided material synthesis algorithm.     

Ultrafast and long-time excited state kinetics of an NIR-emissive vanadium(iii) complex II. Elucidating triplet-to-singlet excited-state dynamics

We report the non-adiabatic dynamics of V^IIICl₃(ddpd), a complex based on the Earth-abundant first-row transition metal vanadium with a d² electronic configuration which is able to emit phosphorescence in solution in the near-infrared spectral region. Trajectory surface-hopping dynamics based on linear vibronic coupling potentials obtained with CASSCF provide molecular-level insights into the intersystem crossing from triplet to singlet metal-centered states. While the majority of the singlet population undergoes back-intersystem crossing to the triplet manifold, 1–2% remains stable during the 10 ps simulation time, enabling the phosphorescence described in Dorn et al. Chem. Sci., 2021, DOI: 10.1039/D1SC02137K. Competing with intersystem crossing, two different relaxation channels via internal conversion through the triplet manifold occur. The nuclear motion that drives the dynamics through the different electronic states corresponds mainly to the increase of all metal–ligand bond distances as well as the decrease of the angles of trans-coordinated ligand atoms. Both motions lead to a decrease in the ligand-field splitting, which stabilizes the interconfigurational excited states populated during the dynamics. Analysis of the electronic character of the states reveals that increasing and stabilizing the singlet population, which in turn can result in enhanced phosphorescence, could be accomplished by further increasing the ligand-field strength.

The ultrafast triplet-to-singlet mechanism, responsible for the photoluminescence of the open-shell V^IIICl₃(ddpd) complex – based on Earth-abundant vanadium – is unraveled using non-adiabatic dynamics in full dimensionality.     

Thioether-enabled palladium-catalyzed atroposelective C–H olefination for N–C and C–C axial chirality

Thioethers allowed for highly atroposelective C–H olefinations by a palladium/chiral phosphoric acid catalytic system under ambient air. Both N–C and C–C axial chiral (hetero)biaryls were successfully constructed, leading to a broad range of axially chiral N-aryl indoles and biaryls with excellent enantioselectivities up to 99% ee. Experimental and computational studies were conducted to unravel the walking mode for the atroposelective C–H olefination. A plausible chiral induction model for the enantioselectivity-determining step was established by detailed DFT calculations.

Thioethers allowed for highly atroposelective C–H olefinations by a palladium/chiral phosphoric acid catalytic system under ambient air.     

Fluorescence detected circular dichroism (FDCD) for supramolecular host–guest complexes

Fluorescence-detected circular dichroism (FDCD) spectroscopy is applied for the first time to supramolecular host–guest and host–protein systems and compared to the more known electronic circular dichroism (ECD). We find that FDCD can be an excellent choice for common supramolecular applications, e.g. for the detection and chirality sensing of chiral organic analytes, as well as for reaction monitoring. Our comprehensive investigations demonstrate that FDCD can be conducted in favorable circumstances at much lower concentrations than ECD measurements, even in chromophoric and auto-emissive biofluids such as blood serum, overcoming the sensitivity limitation of absorbance-based chiroptical spectroscopy. Besides, the combined use of FDCD and ECD can provide additional valuable information about the system, e.g. the chemical identity of an analyte or hidden aggregation phenomena. We believe that simultaneous FDCD- and ECD-based chiroptical characterization of emissive supramolecular systems will be of general benefit for characterizing fluorescent, chiral supramolecular systems due to the higher information content obtained by their combined use.

Fluorescence-detected circular dichroism (FDCD) spectroscopy is applied for the first time to supramolecular host–guest and host–protein systems and compared to the more known electronic circular dichroism (ECD).     

Enantioselective palladaelectro-catalyzed C–H olefinations and allylations for N–C axial chirality

Enantioselective palladaelectro-catalyzed C–H alkenylations and allylations were achieved with easily-accessible amino acids as transient directing groups. This strategy provided access to highly enantiomerically-enriched N–C axially chiral scaffolds under exceedingly mild conditions. The synthetic utility of our strategy was demonstrated by a variety of alkenes, while the versatility of our approach was reflected by atroposelective C–H allylations. Computational studies provided insights into a facile C–H activation by a seven-membered palladacycle.

Enantioselective palladaelectro-catalyzed C–H alkenylations and allylations were achieved by the means of an easily-accessible amino acid for the synthesis of N–C axially chiral indole biaryls.     

Ruthenaelectro-catalyzed C–H acyloxylation for late-stage tyrosine and oligopeptide diversification

Ruthenaelectro(ii/iv)-catalyzed intermolecular C–H acyloxylations of phenols have been developed by guidance of experimental, CV and computational insights. The use of electricity bypassed the need for stoichiometric chemical oxidants. The sustainable electrocatalysis strategy was characterized by ample scope, and its unique robustness enabled the late-stage C–H diversification of tyrosine-derived peptides.

Ruthenaelectro(ii/iv)-catalyzed intermolecular C–H acyloxylations of oligopeptides have been developed by the guidance of key experimental, CV and computational insights.